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2017 lines
92 KiB
OpenSCAD
2017 lines
92 KiB
OpenSCAD
//////////////////////////////////////////////////////////////////////
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// LibFile: shapes2d.scad
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// Common useful 2D shapes.
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// To use, add the following lines to the beginning of your file:
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// ```
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// include <BOSL2/std.scad>
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// ```
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//////////////////////////////////////////////////////////////////////
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// Section: 2D Drawing Helpers
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// Module: stroke()
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// Usage:
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// stroke(path, [width], [closed], [endcaps], [endcap_width], [endcap_length], [endcap_extent], [trim]);
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// stroke(path, [width], [closed], [endcap1], [endcap2], [endcap_width1], [endcap_width2], [endcap_length1], [endcap_length2], [endcap_extent1], [endcap_extent2], [trim1], [trim2]);
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// Description:
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// Draws a 2D or 3D path with a given line width. Endcaps can be specified for each end individually.
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// Figure(2D,Big): Endcap Types
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// endcaps = [
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// ["butt", "square", "round", "chisel", "tail", "tail2"],
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// ["line", "cross", "dot", "diamond", "x", "arrow", "arrow2"]
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// ];
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// for (x=idx(endcaps), y=idx(endcaps[x])) {
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// cap = endcaps[x][y];
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// right(x*60-60+5) fwd(y*10+15) {
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// right(28) color("black") text(text=cap, size=5, halign="left", valign="center");
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// stroke([[0,0], [20,0]], width=3, endcap_width=3, endcap1=false, endcap2=cap);
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// color("black") stroke([[0,0], [20,0]], width=0.25, endcaps=false);
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// }
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// }
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// Arguments:
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// path = The 2D path to draw along.
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// width = The width of the line to draw. If given as a list of widths, (one for each path point), draws the line with varying thickness to each point.
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// closed = If true, draw an additional line from the end of the path to the start.
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// endcaps = Specifies the endcap type for both ends of the line. If a 2D path is given, use that to draw custom endcaps.
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// endcap1 = Specifies the endcap type for the start of the line. If a 2D path is given, use that to draw a custom endcap.
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// endcap2 = Specifies the endcap type for the end of the line. If a 2D path is given, use that to draw a custom endcap.
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// endcap_width = Some endcap types are wider than the line. This specifies the size of endcaps, in multiples of the line width. Default: 3.5
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// endcap_width1 = This specifies the size of starting endcap, in multiples of the line width. Default: 3.5
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// endcap_width2 = This specifies the size of ending endcap, in multiples of the line width. Default: 3.5
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// endcap_length = Length of endcaps, in multiples of the line width. Default: `endcap_width*0.5`
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// endcap_length1 = Length of starting endcap, in multiples of the line width. Default: `endcap_width1*0.5`
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// endcap_length2 = Length of ending endcap, in multiples of the line width. Default: `endcap_width2*0.5`
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// endcap_extent = Extents length of endcaps, in multiples of the line width. Default: `endcap_width*0.5`
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// endcap_extent1 = Extents length of starting endcap, in multiples of the line width. Default: `endcap_width1*0.5`
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// endcap_extent2 = Extents length of ending endcap, in multiples of the line width. Default: `endcap_width2*0.5`
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// endcap_angle = Extra axial rotation given to flat endcaps for 3D paths, in degrees. If not given, the endcaps are fully spun. Default: `undef` (Fully spun cap)
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// endcap_angle1 = Extra axial rotation given to a flat starting endcap for 3D paths, in degrees. If not given, the endcap is fully spun. Default: `undef` (Fully spun cap)
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// endcap_angle2 = Extra axial rotation given to a flat ending endcap for 3D paths, in degrees. If not given, the endcap is fully spun. Default: `undef` (Fully spun cap)
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// trim = Trim the the start and end line segments by this much, to keep them from interfering with custom endcaps.
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// trim1 = Trim the the starting line segment by this much, to keep it from interfering with a custom endcap.
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// trim2 = Trim the the ending line segment by this much, to keep it from interfering with a custom endcap.
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// convexity = Max number of times a line could intersect a wall of an endcap.
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// hull = If true, use `hull()` to make higher quality joints between segments, at the cost of being much slower. Default: true
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// Example(2D): Drawing a Path
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// path = [[0,100], [100,100], [200,0], [100,-100], [100,0]];
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// stroke(path, width=20);
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// Example(2D): Closing a Path
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// path = [[0,100], [100,100], [200,0], [100,-100], [100,0]];
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// stroke(path, width=20, endcaps=true, closed=true);
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// Example(2D): Fancy Arrow Endcaps
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// path = [[0,100], [100,100], [200,0], [100,-100], [100,0]];
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// stroke(path, width=10, endcaps="arrow2");
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// Example(2D): Modified Fancy Arrow Endcaps
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// path = [[0,100], [100,100], [200,0], [100,-100], [100,0]];
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// stroke(path, width=10, endcaps="arrow2", endcap_width=6, endcap_length=3, endcap_extent=2);
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// Example(2D): Mixed Endcaps
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// path = [[0,100], [100,100], [200,0], [100,-100], [100,0]];
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// stroke(path, width=10, endcap1="tail2", endcap2="arrow2");
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// Example(2D): Custom Endcap Shapes
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// path = [[0,100], [100,100], [200,0], [100,-100], [100,0]];
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// arrow = [[0,0], [2,-3], [0.5,-2.3], [2,-4], [0.5,-3.5], [-0.5,-3.5], [-2,-4], [-0.5,-2.3], [-2,-3]];
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// stroke(path, width=10, trim=3.5, endcaps=arrow);
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// Example(2D): Variable Line Width
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// path = circle(d=50,$fn=18);
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// widths = [for (i=idx(path)) 10*i/len(path)+2];
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// stroke(path,width=widths,$fa=1,$fs=1);
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// Example: 3D Path with Endcaps
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// path = rot([15,30,0], p=path3d(pentagon(d=50)));
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// stroke(path, width=2, endcaps="arrow2", $fn=18);
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// Example: 3D Path with Flat Endcaps
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// path = rot([15,30,0], p=path3d(pentagon(d=50)));
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// stroke(path, width=2, endcaps="arrow2", endcap_angle=0, $fn=18);
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// Example: 3D Path with Mixed Endcaps
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// path = rot([15,30,0], p=path3d(pentagon(d=50)));
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// stroke(path, width=2, endcap1="arrow2", endcap2="tail", endcap_angle2=0, $fn=18);
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module stroke(
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path, width=1, closed=false,
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endcaps, endcap1, endcap2,
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trim, trim1, trim2,
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endcap_width, endcap_width1, endcap_width2,
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endcap_length, endcap_length1, endcap_length2,
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endcap_extent, endcap_extent1, endcap_extent2,
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endcap_angle, endcap_angle1, endcap_angle2,
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convexity=10, hull=true
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) {
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function _endcap_shape(cap,linewidth,w,l,l2) = (
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let(sq2=sqrt(2), l3=l-l2)
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(cap=="round" || cap==true)? circle(d=1, $fn=max(8, segs(w/2))) :
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cap=="chisel"? [[-0.5,0], [0,0.5], [0.5,0], [0,-0.5]] :
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cap=="square"? [[-0.5,-0.5], [-0.5,0.5], [0.5,0.5], [0.5,-0.5]] :
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cap=="diamond"? [[0,w/2], [w/2,0], [0,-w/2], [-w/2,0]] :
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cap=="dot"? circle(d=3, $fn=max(12, segs(w*3/2))) :
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cap=="x"? [for (a=[0:90:270]) each rot(a,p=[[w+sq2/2,w-sq2/2]/2, [w-sq2/2,w+sq2/2]/2, [0,sq2/2]]) ] :
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cap=="cross"? [for (a=[0:90:270]) each rot(a,p=[[1,w]/2, [-1,w]/2, [-1,1]/2]) ] :
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cap=="line"? [[w/2,0.5], [w/2,-0.5], [-w/2,-0.5], [-w/2,0.5]] :
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cap=="arrow"? [[0,0], [w/2,-l2], [w/2,-l2-l], [0,-l], [-w/2,-l2-l], [-w/2,-l2]] :
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cap=="arrow2"? [[0,0], [w/2,-l2-l], [0,-l], [-w/2,-l2-l]] :
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cap=="tail"? [[0,0], [w/2,l2], [w/2,l2-l], [0,-l], [-w/2,l2-l], [-w/2,l2]] :
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cap=="tail2"? [[w/2,0], [w/2,-l], [0,-l-l2], [-w/2,-l], [-w/2,0]] :
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is_path(cap)? cap :
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[]
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) * linewidth;
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assert(is_bool(closed));
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assert(is_list(path));
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if (len(path) > 1) {
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assert(is_path(path,[2,3]), "The path argument must be a list of 2D or 3D points.");
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}
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path = deduplicate( closed? close_path(path) : path );
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assert(is_num(width) || (is_vector(width) && len(width)==len(path)));
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width = is_num(width)? [for (x=path) width] : width;
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endcap1 = first_defined([endcap1, endcaps, "round"]);
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endcap2 = first_defined([endcap2, endcaps, "round"]);
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assert(is_bool(endcap1) || is_string(endcap1) || is_path(endcap1));
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assert(is_bool(endcap2) || is_string(endcap2) || is_path(endcap2));
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endcap_width1 = first_defined([endcap_width1, endcap_width, 3.5]);
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endcap_width2 = first_defined([endcap_width2, endcap_width, 3.5]);
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assert(is_num(endcap_width1));
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assert(is_num(endcap_width2));
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endcap_length1 = first_defined([endcap_length1, endcap_length, endcap_width1*0.5]);
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endcap_length2 = first_defined([endcap_length2, endcap_length, endcap_width2*0.5]);
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assert(is_num(endcap_length1));
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assert(is_num(endcap_length2));
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endcap_extent1 = first_defined([endcap_extent1, endcap_extent, endcap_width1*0.5]);
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endcap_extent2 = first_defined([endcap_extent2, endcap_extent, endcap_width2*0.5]);
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assert(is_num(endcap_extent1));
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assert(is_num(endcap_extent2));
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endcap_angle1 = first_defined([endcap_angle1, endcap_angle]);
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endcap_angle2 = first_defined([endcap_angle2, endcap_angle]);
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assert(is_undef(endcap_angle1)||is_num(endcap_angle1));
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assert(is_undef(endcap_angle2)||is_num(endcap_angle2));
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endcap_shape1 = _endcap_shape(endcap1, select(width,0), endcap_width1, endcap_length1, endcap_extent1);
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endcap_shape2 = _endcap_shape(endcap2, select(width,-1), endcap_width2, endcap_length2, endcap_extent2);
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trim1 = select(width,0) * first_defined([
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trim1, trim,
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(endcap1=="arrow")? endcap_length1-0.01 :
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(endcap1=="arrow2")? endcap_length1*3/4 :
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0
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]);
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assert(is_num(trim1));
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trim2 = select(width,-1) * first_defined([
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trim2, trim,
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(endcap2=="arrow")? endcap_length2-0.01 :
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(endcap2=="arrow2")? endcap_length2*3/4 :
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0
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]);
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assert(is_num(trim2));
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if (len(path) == 1) {
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if (len(path[0]) == 2) {
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translate(path[0]) circle(d=width[0]);
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} else {
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translate(path[0]) sphere(d=width[0]);
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}
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} else {
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spos = path_pos_from_start(path,trim1,closed=false);
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epos = path_pos_from_end(path,trim2,closed=false);
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path2 = path_subselect(path, spos[0], spos[1], epos[0], epos[1]);
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widths = concat(
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[lerp(width[spos[0]], width[(spos[0]+1)%len(width)], spos[1])],
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[for (i = [spos[0]+1:1:epos[0]]) width[i]],
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[lerp(width[epos[0]], width[(epos[0]+1)%len(width)], epos[1])]
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);
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start_vec = select(path,0) - select(path,1);
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end_vec = select(path,-1) - select(path,-2);
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if (len(path[0]) == 2) {
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// Straight segments
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for (i = idx(path2,end=-2)) {
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seg = select(path2,i,i+1);
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delt = seg[1] - seg[0];
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translate(seg[0]) {
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rot(from=BACK,to=delt) {
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trapezoid(w1=widths[i], w2=widths[i+1], h=norm(delt), anchor=FRONT);
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}
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}
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}
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// Joints
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for (i = [1:1:len(path2)-2]) {
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$fn = quantup(segs(widths[i]/2),4);
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if (hull) {
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hull() {
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translate(path2[i]) {
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rot(from=BACK, to=path2[i]-path2[i-1])
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circle(d=widths[i]);
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rot(from=BACK, to=path2[i+1]-path2[i])
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circle(d=widths[i]);
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}
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}
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} else {
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translate(path2[i]) {
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rot(from=BACK, to=path2[i]-path2[i-1])
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circle(d=widths[i]);
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rot(from=BACK, to=path2[i+1]-path2[i])
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circle(d=widths[i]);
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}
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}
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}
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// Endcap1
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translate(path[0]) {
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start_vec = select(path,0) - select(path,1);
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rot(from=BACK, to=start_vec) {
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polygon(endcap_shape1);
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}
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}
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// Endcap2
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translate(select(path,-1)) {
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rot(from=BACK, to=end_vec) {
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polygon(endcap_shape2);
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}
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}
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} else {
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quatsums = Q_Cumulative([
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for (i = idx(path2,end=-2)) let(
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vec1 = i==0? UP : unit(path2[i]-path2[i-1], UP),
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vec2 = unit(path2[i+1]-path2[i], UP),
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axis = vector_axis(vec1,vec2),
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ang = vector_angle(vec1,vec2)
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) Quat(axis,ang)
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]);
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rotmats = [for (q=quatsums) Q_Matrix4(q)];
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sides = [
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for (i = idx(path2,end=-2))
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quantup(segs(max(widths[i],widths[i+1])/2),4)
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];
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// Straight segments
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for (i = idx(path2,end=-2)) {
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dist = norm(path2[i+1] - path2[i]);
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w1 = widths[i]/2;
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w2 = widths[i+1]/2;
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$fn = sides[i];
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translate(path2[i]) {
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multmatrix(rotmats[i]) {
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cylinder(r1=w1, r2=w2, h=dist, center=false);
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}
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}
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}
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// Joints
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for (i = [1:1:len(path2)-2]) {
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$fn = sides[i];
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translate(path2[i]) {
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if (hull) {
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hull(){
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multmatrix(rotmats[i]) {
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sphere(d=widths[i],style="aligned");
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}
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multmatrix(rotmats[i-1]) {
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sphere(d=widths[i],style="aligned");
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}
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}
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} else {
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multmatrix(rotmats[i]) {
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sphere(d=widths[i],style="aligned");
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}
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multmatrix(rotmats[i-1]) {
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sphere(d=widths[i],style="aligned");
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}
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}
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}
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}
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// Endcap1
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translate(path[0]) {
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multmatrix(rotmats[0] * xrot(180)) {
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$fn = sides[0];
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if (is_undef(endcap_angle1)) {
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rotate_extrude(convexity=convexity) {
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right_half(planar=true) {
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polygon(endcap_shape1);
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}
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}
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} else {
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rotate([90,0,endcap_angle1]) {
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linear_extrude(height=max(widths[0],0.001), center=true, convexity=convexity) {
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polygon(endcap_shape1);
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}
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}
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}
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}
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}
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// Endcap2
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translate(select(path,-1)) {
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multmatrix(select(rotmats,-1)) {
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$fn = select(sides,-1);
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if (is_undef(endcap_angle2)) {
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rotate_extrude(convexity=convexity) {
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right_half(planar=true) {
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polygon(endcap_shape2);
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}
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}
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} else {
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rotate([90,0,endcap_angle2]) {
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linear_extrude(height=max(select(widths,-1),0.001), center=true, convexity=convexity) {
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polygon(endcap_shape2);
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}
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}
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}
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}
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}
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}
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}
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}
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// Function&Module: arc()
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// Usage: 2D arc from 0º to `angle` degrees.
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// arc(N, r|d, angle);
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// Usage: 2D arc from START to END degrees.
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// arc(N, r|d, angle=[START,END])
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// Usage: 2D arc from `start` to `start+angle` degrees.
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// arc(N, r|d, start, angle)
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// Usage: 2D circle segment by `width` and `thickness`, starting and ending on the X axis.
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// arc(N, width, thickness)
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// Usage: Shortest 2D or 3D arc around centerpoint `cp`, starting at P0 and ending on the vector pointing from `cp` to `P1`.
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// arc(N, cp, points=[P0,P1],[long],[cw],[ccw])
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// Usage: 2D or 3D arc, starting at `P0`, passing through `P1` and ending at `P2`.
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// arc(N, points=[P0,P1,P2])
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// Description:
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// If called as a function, returns a 2D or 3D path forming an arc.
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// If called as a module, creates a 2D arc polygon or pie slice shape.
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// Arguments:
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// N = Number of vertices to form the arc curve from.
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// r = Radius of the arc.
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// d = Diameter of the arc.
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// angle = If a scalar, specifies the end angle in degrees (relative to start parameter). If a vector of two scalars, specifies start and end angles.
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// cp = Centerpoint of arc.
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// points = Points on the arc.
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// long = if given with cp and points takes the long arc instead of the default short arc. Default: false
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// cw = if given with cp and 2 points takes the arc in the clockwise direction. Default: false
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// ccw = if given with cp and 2 points takes the arc in the counter-clockwise direction. Default: false
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// width = If given with `thickness`, arc starts and ends on X axis, to make a circle segment.
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// thickness = If given with `width`, arc starts and ends on X axis, to make a circle segment.
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// start = Start angle of arc.
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// wedge = If true, include centerpoint `cp` in output to form pie slice shape.
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// endpoint = If false exclude the last point (function only). Default: true
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// Examples(2D):
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// arc(N=4, r=30, angle=30, wedge=true);
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// arc(r=30, angle=30, wedge=true);
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// arc(d=60, angle=30, wedge=true);
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// arc(d=60, angle=120);
|
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// arc(d=60, angle=120, wedge=true);
|
|
// arc(r=30, angle=[75,135], wedge=true);
|
|
// arc(r=30, start=45, angle=75, wedge=true);
|
|
// arc(width=60, thickness=20);
|
|
// arc(cp=[-10,5], points=[[20,10],[0,35]], wedge=true);
|
|
// arc(points=[[30,-5],[20,10],[-10,20]], wedge=true);
|
|
// arc(points=[[5,30],[-10,-10],[30,5]], wedge=true);
|
|
// Example(2D):
|
|
// path = arc(points=[[5,30],[-10,-10],[30,5]], wedge=true);
|
|
// stroke(closed=true, path);
|
|
// Example(FlatSpin):
|
|
// path = arc(points=[[0,30,0],[0,0,30],[30,0,0]]);
|
|
// trace_path(path, showpts=true, color="cyan");
|
|
function arc(N, r, angle, d, cp, points, width, thickness, start, wedge=false, long=false, cw=false, ccw=false, endpoint=true) =
|
|
assert(is_bool(endpoint))
|
|
!endpoint ? assert(!wedge, "endpoint cannot be false if wedge is true")
|
|
slice(arc(N,r,angle,d,cp,points,width,thickness,start,wedge,long,cw,ccw,true),0,-2) :
|
|
// First try for 2D arc specified by width and thickness
|
|
is_def(width) && is_def(thickness)? (
|
|
assert(!any_defined([r,cp,points]) && !any([cw,ccw,long]),"Conflicting or invalid parameters to arc")
|
|
assert(width>0, "Width must be postive")
|
|
assert(thickness>0, "Thickness must be positive")
|
|
arc(N,points=[[width/2,0], [0,thickness], [-width/2,0]],wedge=wedge)
|
|
) : is_def(angle)? (
|
|
let(
|
|
parmok = !any_defined([points,width,thickness]) &&
|
|
((is_vector(angle,2) && is_undef(start)) || is_num(angle))
|
|
)
|
|
assert(parmok,"Invalid parameters in arc")
|
|
let(
|
|
cp = first_defined([cp,[0,0]]),
|
|
start = is_def(start)? start : is_vector(angle) ? angle[0] : 0,
|
|
angle = is_vector(angle)? angle[1]-angle[0] : angle,
|
|
r = get_radius(r=r, d=d)
|
|
)
|
|
assert(is_vector(cp,2),"Centerpoint must be a 2d vector")
|
|
assert(angle!=0, "Arc has zero length")
|
|
assert(r>0, "Arc radius invalid")
|
|
let(
|
|
N = max(3, is_undef(N)? ceil(segs(r)*abs(angle)/360) : N),
|
|
arcpoints = [for(i=[0:N-1]) let(theta = start + i*angle/(N-1)) r*[cos(theta),sin(theta)]+cp],
|
|
extra = wedge? [cp] : []
|
|
)
|
|
concat(extra,arcpoints)
|
|
) :
|
|
assert(is_path(points,[2,3]),"Point list is invalid")
|
|
// Arc is 3D, so transform points to 2D and make a recursive call, then remap back to 3D
|
|
len(points[0])==3? (
|
|
assert(!(cw || ccw), "(Counter)clockwise isn't meaningful in 3d, so `cw` and `ccw` must be false")
|
|
assert(is_undef(cp) || is_vector(cp,3),"points are 3d so cp must be 3d")
|
|
let(
|
|
thirdpoint = is_def(cp) ? cp : points[2],
|
|
center2d = is_def(cp) ? project_plane(cp,thirdpoint,points[0],points[1]) : undef,
|
|
points2d = project_plane(points,thirdpoint,points[0],points[1])
|
|
)
|
|
lift_plane(arc(N,cp=center2d,points=points2d,wedge=wedge,long=long),thirdpoint,points[0],points[1])
|
|
) : is_def(cp)? (
|
|
// Arc defined by center plus two points, will have radius defined by center and points[0]
|
|
// and extent defined by direction of point[1] from the center
|
|
assert(is_vector(cp,2), "Centerpoint must be a 2d vector")
|
|
assert(len(points)==2, "When pointlist has length 3 centerpoint is not allowed")
|
|
assert(points[0]!=points[1], "Arc endpoints are equal")
|
|
assert(cp!=points[0]&&cp!=points[1], "Centerpoint equals an arc endpoint")
|
|
assert(count_true([long,cw,ccw])<=1, str("Only one of `long`, `cw` and `ccw` can be true",cw,ccw,long))
|
|
let(
|
|
angle = vector_angle(points[0], cp, points[1]),
|
|
v1 = points[0]-cp,
|
|
v2 = points[1]-cp,
|
|
prelim_dir = sign(det2([v1,v2])), // z component of cross product
|
|
dir = prelim_dir != 0
|
|
? prelim_dir
|
|
: assert(cw || ccw, "Collinear inputs don't define a unique arc")
|
|
1,
|
|
r=norm(v1),
|
|
final_angle = long || (ccw && dir<0) || (cw && dir>0) ? -dir*(360-angle) : dir*angle
|
|
)
|
|
arc(N,cp=cp,r=r,start=atan2(v1.y,v1.x),angle=final_angle,wedge=wedge)
|
|
) : (
|
|
// Final case is arc passing through three points, starting at point[0] and ending at point[3]
|
|
let(col = collinear(points[0],points[1],points[2]))
|
|
assert(!col, "Collinear inputs do not define an arc")
|
|
let(
|
|
cp = line_intersection(_normal_segment(points[0],points[1]),_normal_segment(points[1],points[2])),
|
|
// select order to be counterclockwise
|
|
dir = det2([points[1]-points[0],points[2]-points[1]]) > 0,
|
|
points = dir? select(points,[0,2]) : select(points,[2,0]),
|
|
r = norm(points[0]-cp),
|
|
theta_start = atan2(points[0].y-cp.y, points[0].x-cp.x),
|
|
theta_end = atan2(points[1].y-cp.y, points[1].x-cp.x),
|
|
angle = posmod(theta_end-theta_start, 360),
|
|
arcpts = arc(N,cp=cp,r=r,start=theta_start,angle=angle,wedge=wedge)
|
|
)
|
|
dir ? arcpts : reverse(arcpts)
|
|
);
|
|
|
|
|
|
module arc(N, r, angle, d, cp, points, width, thickness, start, wedge=false)
|
|
{
|
|
path = arc(N=N, r=r, angle=angle, d=d, cp=cp, points=points, width=width, thickness=thickness, start=start, wedge=wedge);
|
|
polygon(path);
|
|
}
|
|
|
|
|
|
function _normal_segment(p1,p2) =
|
|
let(center = (p1+p2)/2)
|
|
[center, center + norm(p1-p2)/2 * line_normal(p1,p2)];
|
|
|
|
|
|
// Function: turtle()
|
|
// Usage:
|
|
// turtle(commands, [state], [full_state], [repeat], [endpoint])
|
|
// Description:
|
|
// Use a sequence of turtle graphics commands to generate a path. The parameter `commands` is a list of
|
|
// turtle commands and optional parameters for each command. The turtle state has a position, movement direction,
|
|
// movement distance, and default turn angle. If you do not give `state` as input then the turtle starts at the
|
|
// origin, pointed along the positive x axis with a movement distance of 1. By default, `turtle` returns just
|
|
// the computed turtle path. If you set `full_state` to true then it instead returns the full turtle state.
|
|
// You can invoke `turtle` again with this full state to continue the turtle path where you left off.
|
|
// .
|
|
// The turtle state is a list with three entries: the path constructed so far, the current step as a 2-vector, the current default angle,
|
|
// and the current arcsteps setting.
|
|
// .
|
|
// Commands | Arguments | What it does
|
|
// ------------ | ------------------ | -------------------------------
|
|
// "move" | [dist] | Move turtle scale*dist units in the turtle direction. Default dist=1.
|
|
// "xmove" | [dist] | Move turtle scale*dist units in the x direction. Default dist=1. Does not change turtle direction.
|
|
// "ymove" | [dist] | Move turtle scale*dist units in the y direction. Default dist=1. Does not change turtle direction.
|
|
// "xymove" | vector | Move turtle by the specified vector. Does not change turtle direction.
|
|
// "untilx" | xtarget | Move turtle in turtle direction until x==xtarget. Produces an error if xtarget is not reachable.
|
|
// "untily" | ytarget | Move turtle in turtle direction until y==ytarget. Produces an error if xtarget is not reachable.
|
|
// "jump" | point | Move the turtle to the specified point
|
|
// "xjump" | x | Move the turtle's x position to the specified value
|
|
// "yjump | y | Move the turtle's y position to the specified value
|
|
// "turn" | [angle] | Turn turtle direction by specified angle, or the turtle's default turn angle. The default angle starts at 90.
|
|
// "left" | [angle] | Same as "turn"
|
|
// "right" | [angle] | Same as "turn", -angle
|
|
// "angle" | angle | Set the default turn angle.
|
|
// "setdir" | dir | Set turtle direction. The parameter `dir` can be an angle or a vector.
|
|
// "length" | length | Change the turtle move distance to `length`
|
|
// "scale" | factor | Multiply turtle move distance by `factor`
|
|
// "addlength" | length | Add `length` to the turtle move distance
|
|
// "repeat" | count, commands | Repeats a list of commands `count` times.
|
|
// "arcleft" | radius, [angle] | Draw an arc from the current position toward the left at the specified radius and angle. The turtle turns by `angle`. A negative angle draws the arc to the right instead of the left, and leaves the turtle facing right. A negative radius draws the arc to the right but leaves the turtle facing left.
|
|
// "arcright" | radius, [angle] | Draw an arc from the current position toward the right at the specified radius and angle
|
|
// "arcleftto" | radius, angle | Draw an arc at the given radius turning toward the left until reaching the specified absolute angle.
|
|
// "arcrightto" | radius, angle | Draw an arc at the given radius turning toward the right until reaching the specified absolute angle.
|
|
// "arcsteps" | count | Specifies the number of segments to use for drawing arcs. If you set it to zero then the standard `$fn`, `$fa` and `$fs` variables define the number of segments.
|
|
//
|
|
// Arguments:
|
|
// commands = List of turtle commands
|
|
// state = Starting turtle state (from previous call) or starting point. Default: start at the origin, pointing right.
|
|
// full_state = If true return the full turtle state for continuing the path in subsequent turtle calls. Default: false
|
|
// repeat = Number of times to repeat the command list. Default: 1
|
|
//
|
|
// Example(2D): Simple rectangle
|
|
// path = turtle(["xmove",3, "ymove", "xmove",-3, "ymove",-1]);
|
|
// stroke(path,width=.1);
|
|
// Example(2D): Pentagon
|
|
// path=turtle(["angle",360/5,"move","turn","move","turn","move","turn","move"]);
|
|
// stroke(path,width=.1,closed=true);
|
|
// Example(2D): Pentagon using the repeat argument
|
|
// path=turtle(["move","turn",360/5],repeat=5);
|
|
// stroke(path,width=.1,closed=true);
|
|
// Example(2D): Pentagon using the repeat turtle command, setting the turn angle
|
|
// path=turtle(["angle",360/5,"repeat",5,["move","turn"]]);
|
|
// stroke(path,width=.1,closed=true);
|
|
// Example(2D): Pentagram
|
|
// path = turtle(["move","left",144], repeat=4);
|
|
// stroke(path,width=.05,closed=true);
|
|
// Example(2D): Sawtooth path
|
|
// path = turtle([
|
|
// "turn", 55,
|
|
// "untily", 2,
|
|
// "turn", -55-90,
|
|
// "untily", 0,
|
|
// "turn", 55+90,
|
|
// "untily", 2.5,
|
|
// "turn", -55-90,
|
|
// "untily", 0,
|
|
// "turn", 55+90,
|
|
// "untily", 3,
|
|
// "turn", -55-90,
|
|
// "untily", 0
|
|
// ]);
|
|
// stroke(path, width=.1);
|
|
// Example(2D): Simpler way to draw the sawtooth. The direction of the turtle is preserved when executing "yjump".
|
|
// path = turtle([
|
|
// "turn", 55,
|
|
// "untily", 2,
|
|
// "yjump", 0,
|
|
// "untily", 2.5,
|
|
// "yjump", 0,
|
|
// "untily", 3,
|
|
// "yjump", 0,
|
|
// ]);
|
|
// stroke(path, width=.1);
|
|
// Example(2DMed): square spiral
|
|
// path = turtle(["move","left","addlength",1],repeat=50);
|
|
// stroke(path,width=.2);
|
|
// Example(2DMed): pentagonal spiral
|
|
// path = turtle(["move","left",360/5,"addlength",1],repeat=50);
|
|
// stroke(path,width=.2);
|
|
// Example(2DMed): yet another spiral, without using `repeat`
|
|
// path = turtle(concat(["angle",71],flatten(repeat(["move","left","addlength",1],50))));
|
|
// stroke(path,width=.2);
|
|
// Example(2DMed): The previous spiral grows linearly and eventually intersects itself. This one grows geometrically and does not.
|
|
// path = turtle(["move","left",71,"scale",1.05],repeat=50);
|
|
// stroke(path,width=.05);
|
|
// Example(2D): Koch Snowflake
|
|
// function koch_unit(depth) =
|
|
// depth==0 ? ["move"] :
|
|
// concat(
|
|
// koch_unit(depth-1),
|
|
// ["right"],
|
|
// koch_unit(depth-1),
|
|
// ["left","left"],
|
|
// koch_unit(depth-1),
|
|
// ["right"],
|
|
// koch_unit(depth-1)
|
|
// );
|
|
// koch=concat(["angle",60,"repeat",3],[concat(koch_unit(3),["left","left"])]);
|
|
// polygon(turtle(koch));
|
|
function turtle(commands, state=[[[0,0]],[1,0],90,0], full_state=false, repeat=1) =
|
|
let( state = is_vector(state) ? [[state],[1,0],90,0] : state )
|
|
repeat == 1?
|
|
_turtle(commands,state,full_state) :
|
|
_turtle_repeat(commands, state, full_state, repeat);
|
|
|
|
function _turtle_repeat(commands, state, full_state, repeat) =
|
|
repeat==1?
|
|
_turtle(commands,state,full_state) :
|
|
_turtle_repeat(commands, _turtle(commands, state, true), full_state, repeat-1);
|
|
|
|
function _turtle_command_len(commands, index) =
|
|
let( one_or_two_arg = ["arcleft","arcright", "arcleftto", "arcrightto"] )
|
|
commands[index] == "repeat"? 3 : // Repeat command requires 2 args
|
|
// For these, the first arg is required, second arg is present if it is not a string
|
|
in_list(commands[index], one_or_two_arg) && len(commands)>index+2 && !is_string(commands[index+2]) ? 3 :
|
|
is_string(commands[index+1])? 1 : // If 2nd item is a string it's must be a new command
|
|
2; // Otherwise we have command and arg
|
|
|
|
function _turtle(commands, state, full_state, index=0) =
|
|
index < len(commands) ?
|
|
_turtle(commands,
|
|
_turtle_command(commands[index],commands[index+1],commands[index+2],state,index),
|
|
full_state,
|
|
index+_turtle_command_len(commands,index)
|
|
) :
|
|
( full_state ? state : state[0] );
|
|
|
|
// Turtle state: state = [path, step_vector, default angle, default arcsteps]
|
|
|
|
function _turtle_command(command, parm, parm2, state, index) =
|
|
command == "repeat"?
|
|
assert(is_num(parm),str("\"repeat\" command requires a numeric repeat count at index ",index))
|
|
assert(is_list(parm2),str("\"repeat\" command requires a command list parameter at index ",index))
|
|
_turtle_repeat(parm2, state, true, parm) :
|
|
let(
|
|
path = 0,
|
|
step=1,
|
|
angle=2,
|
|
arcsteps=3,
|
|
parm = !is_string(parm) ? parm : undef,
|
|
parm2 = !is_string(parm2) ? parm2 : undef,
|
|
needvec = ["jump", "xymove"],
|
|
neednum = ["untilx","untily","xjump","yjump","angle","length","scale","addlength"],
|
|
needeither = ["setdir"],
|
|
chvec = !in_list(command,needvec) || is_vector(parm,2),
|
|
chnum = !in_list(command,neednum) || is_num(parm),
|
|
vec_or_num = !in_list(command,needeither) || (is_num(parm) || is_vector(parm,2)),
|
|
lastpt = select(state[path],-1)
|
|
)
|
|
assert(chvec,str("\"",command,"\" requires a vector parameter at index ",index))
|
|
assert(chnum,str("\"",command,"\" requires a numeric parameter at index ",index))
|
|
assert(vec_or_num,str("\"",command,"\" requires a vector or numeric parameter at index ",index))
|
|
|
|
command=="move" ? list_set(state, path, concat(state[path],[default(parm,1)*state[step]+lastpt])) :
|
|
command=="untilx" ? (
|
|
let(
|
|
int = line_intersection([lastpt,lastpt+state[step]], [[parm,0],[parm,1]]),
|
|
xgood = sign(state[step].x) == sign(int.x-lastpt.x)
|
|
)
|
|
assert(xgood,str("\"untilx\" never reaches desired goal at index ",index))
|
|
list_set(state,path,concat(state[path],[int]))
|
|
) :
|
|
command=="untily" ? (
|
|
let(
|
|
int = line_intersection([lastpt,lastpt+state[step]], [[0,parm],[1,parm]]),
|
|
ygood = is_def(int) && sign(state[step].y) == sign(int.y-lastpt.y)
|
|
)
|
|
assert(ygood,str("\"untily\" never reaches desired goal at index ",index))
|
|
list_set(state,path,concat(state[path],[int]))
|
|
) :
|
|
command=="xmove" ? list_set(state, path, concat(state[path],[default(parm,1)*norm(state[step])*[1,0]+lastpt])):
|
|
command=="ymove" ? list_set(state, path, concat(state[path],[default(parm,1)*norm(state[step])*[0,1]+lastpt])):
|
|
command=="xymove" ? list_set(state, path, concat(state[path], [lastpt+parm])):
|
|
command=="jump" ? list_set(state, path, concat(state[path],[parm])):
|
|
command=="xjump" ? list_set(state, path, concat(state[path],[[parm,lastpt.y]])):
|
|
command=="yjump" ? list_set(state, path, concat(state[path],[[lastpt.x,parm]])):
|
|
command=="turn" || command=="left" ? list_set(state, step, rot(default(parm,state[angle]),p=state[step],planar=true)) :
|
|
command=="right" ? list_set(state, step, rot(-default(parm,state[angle]),p=state[step],planar=true)) :
|
|
command=="angle" ? list_set(state, angle, parm) :
|
|
command=="setdir" ? (
|
|
is_vector(parm) ?
|
|
list_set(state, step, norm(state[step]) * unit(parm)) :
|
|
list_set(state, step, norm(state[step]) * [cos(parm),sin(parm)])
|
|
) :
|
|
command=="length" ? list_set(state, step, parm*unit(state[step])) :
|
|
command=="scale" ? list_set(state, step, parm*state[step]) :
|
|
command=="addlength" ? list_set(state, step, state[step]+unit(state[step])*parm) :
|
|
command=="arcsteps" ? list_set(state, arcsteps, parm) :
|
|
command=="arcleft" || command=="arcright" ?
|
|
assert(is_num(parm),str("\"",command,"\" command requires a numeric radius value at index ",index))
|
|
let(
|
|
myangle = default(parm2,state[angle]),
|
|
lrsign = command=="arcleft" ? 1 : -1,
|
|
radius = parm*sign(myangle),
|
|
center = lastpt + lrsign*radius*line_normal([0,0],state[step]),
|
|
steps = state[arcsteps]==0 ? segs(abs(radius)) : state[arcsteps],
|
|
arcpath = myangle == 0 || radius == 0 ? [] : arc(
|
|
steps,
|
|
points = [
|
|
lastpt,
|
|
rot(cp=center, p=lastpt, a=sign(parm)*lrsign*myangle/2),
|
|
rot(cp=center, p=lastpt, a=sign(parm)*lrsign*myangle)
|
|
]
|
|
)
|
|
)
|
|
list_set(
|
|
state, [path,step], [
|
|
concat(state[path], slice(arcpath,1,-1)),
|
|
rot(lrsign * myangle,p=state[step],planar=true)
|
|
]
|
|
) :
|
|
command=="arcleftto" || command=="arcrightto" ?
|
|
assert(is_num(parm),str("\"",command,"\" command requires a numeric radius value at index ",index))
|
|
assert(is_num(parm2),str("\"",command,"\" command requires a numeric angle value at index ",index))
|
|
let(
|
|
radius = parm,
|
|
lrsign = command=="arcleftto" ? 1 : -1,
|
|
center = lastpt + lrsign*radius*line_normal([0,0],state[step]),
|
|
steps = state[arcsteps]==0 ? segs(abs(radius)) : state[arcsteps],
|
|
start_angle = posmod(atan2(state[step].y, state[step].x),360),
|
|
end_angle = posmod(parm2,360),
|
|
delta_angle = -start_angle + (lrsign * end_angle < lrsign*start_angle ? end_angle+lrsign*360 : end_angle),
|
|
arcpath = delta_angle == 0 || radius==0 ? [] : arc(
|
|
steps,
|
|
points = [
|
|
lastpt,
|
|
rot(cp=center, p=lastpt, a=sign(radius)*delta_angle/2),
|
|
rot(cp=center, p=lastpt, a=sign(radius)*delta_angle)
|
|
]
|
|
)
|
|
)
|
|
list_set(
|
|
state, [path,step], [
|
|
concat(state[path], slice(arcpath,1,-1)),
|
|
rot(delta_angle,p=state[step],planar=true)
|
|
]
|
|
) :
|
|
assert(false,str("Unknown turtle command \"",command,"\" at index",index))
|
|
[];
|
|
|
|
|
|
|
|
// Section: 2D Primitives
|
|
|
|
// Function&Module: rect()
|
|
// Usage:
|
|
// rect(size, [center], [rounding], [chamfer], [anchor], [spin])
|
|
// Description:
|
|
// When called as a module, creates a 2D rectangle of the given size, with optional rounding or chamfering.
|
|
// When called as a function, returns a 2D path/list of points for a square/rectangle of the given size.
|
|
// Arguments:
|
|
// size = The size of the rectangle to create. If given as a scalar, both X and Y will be the same size.
|
|
// rounding = The rounding radius for the corners. If given as a list of four numbers, gives individual radii for each corner, in the order [X+Y+,X-Y+,X-Y-,X+Y-]. Default: 0 (no rounding)
|
|
// chamfer = The chamfer size for the corners. If given as a list of four numbers, gives individual chamfers for each corner, in the order [X+Y+,X-Y+,X-Y-,X+Y-]. Default: 0 (no chamfer)
|
|
// center = If given and true, overrides `anchor` to be `CENTER`. If given and false, overrides `anchor` to be `FRONT+LEFT`.
|
|
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
|
|
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
|
|
// Example(2D):
|
|
// rect(40);
|
|
// Example(2D): Centered
|
|
// rect([40,30], center=true);
|
|
// Example(2D): Anchored
|
|
// rect([40,30], anchor=FRONT);
|
|
// Example(2D): Spun
|
|
// rect([40,30], anchor=FRONT, spin=30);
|
|
// Example(2D): Chamferred Rect
|
|
// rect([40,30], chamfer=5, center=true);
|
|
// Example(2D): Rounded Rect
|
|
// rect([40,30], rounding=5, center=true);
|
|
// Example(2D): Mixed Chamferring and Rounding
|
|
// rect([40,30],center=true,rounding=[5,0,10,0],chamfer=[0,8,0,15],$fa=1,$fs=1);
|
|
// Example(2D): Called as Function
|
|
// path = rect([40,30], chamfer=5, anchor=FRONT, spin=30);
|
|
// stroke(path, closed=true);
|
|
// move_copies(path) color("blue") circle(d=2,$fn=8);
|
|
module rect(size=1, center, rounding=0, chamfer=0, anchor, spin=0) {
|
|
size = is_num(size)? [size,size] : point2d(size);
|
|
anchor = get_anchor(anchor, center, FRONT+LEFT, FRONT+LEFT);
|
|
if (rounding==0 && chamfer==0) {
|
|
attachable(anchor,spin, two_d=true, size=size) {
|
|
square(size, center=true);
|
|
children();
|
|
}
|
|
} else {
|
|
pts = rect(size=size, rounding=rounding, chamfer=chamfer, center=true);
|
|
attachable(anchor,spin, two_d=true, path=pts) {
|
|
polygon(pts);
|
|
children();
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
function rect(size=1, center, rounding=0, chamfer=0, anchor, spin=0) =
|
|
assert(is_num(size) || is_vector(size))
|
|
assert(is_num(chamfer) || len(chamfer)==4)
|
|
assert(is_num(rounding) || len(rounding)==4)
|
|
let(
|
|
size = is_num(size)? [size,size] : point2d(size),
|
|
anchor = point2d(get_anchor(anchor, center, FRONT+LEFT, FRONT+LEFT)),
|
|
complex = rounding!=0 || chamfer!=0
|
|
)
|
|
(rounding==0 && chamfer==0)? let(
|
|
path = [
|
|
[ size.x/2, -size.y/2],
|
|
[-size.x/2, -size.y/2],
|
|
[-size.x/2, size.y/2],
|
|
[ size.x/2, size.y/2]
|
|
]
|
|
) rot(spin, p=move(-vmul(anchor,size/2), p=path)) :
|
|
let(
|
|
chamfer = is_list(chamfer)? chamfer : [for (i=[0:3]) chamfer],
|
|
rounding = is_list(rounding)? rounding : [for (i=[0:3]) rounding],
|
|
quadorder = [3,2,1,0],
|
|
quadpos = [[1,1],[-1,1],[-1,-1],[1,-1]],
|
|
insets = [for (i=[0:3]) chamfer[i]>0? chamfer[i] : rounding[i]>0? rounding[i] : 0],
|
|
insets_x = max(insets[0]+insets[1],insets[2]+insets[3]),
|
|
insets_y = max(insets[0]+insets[3],insets[1]+insets[2])
|
|
)
|
|
assert(insets_x <= size.x, "Requested roundings and/or chamfers exceed the rect width.")
|
|
assert(insets_y <= size.y, "Requested roundings and/or chamfers exceed the rect height.")
|
|
let(
|
|
path = [
|
|
for(i = [0:3])
|
|
let(
|
|
quad = quadorder[i],
|
|
inset = insets[quad],
|
|
cverts = quant(segs(inset),4)/4,
|
|
cp = vmul(size/2-[inset,inset], quadpos[quad]),
|
|
step = 90/cverts,
|
|
angs =
|
|
chamfer[quad] > 0? [0,-90]-90*[i,i] :
|
|
rounding[quad] > 0? [for (j=[0:1:cverts]) 360-j*step-i*90] :
|
|
[0]
|
|
)
|
|
each [for (a = angs) cp + inset*[cos(a),sin(a)]]
|
|
]
|
|
) complex?
|
|
reorient(anchor,spin, two_d=true, path=path, p=path) :
|
|
reorient(anchor,spin, two_d=true, size=size, p=path);
|
|
|
|
|
|
// Function&Module: oval()
|
|
// Usage:
|
|
// oval(r|d, [realign], [circum])
|
|
// Description:
|
|
// When called as a module, creates a 2D polygon that approximates a circle of the given size.
|
|
// When called as a function, returns a 2D list of points (path) for a polygon that approximates a circle of the given size.
|
|
// Arguments:
|
|
// r = Radius of the circle/oval to create. Can be a scalar, or a list of sizes per axis.
|
|
// d = Diameter of the circle/oval to create. Can be a scalar, or a list of sizes per axis.
|
|
// realign = If true, rotates the polygon that approximates the circle/oval by half of one size.
|
|
// circum = If true, the polygon that approximates the circle will be upsized slightly to circumscribe the theoretical circle. If false, it inscribes the theoretical circle. Default: false
|
|
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
|
|
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
|
|
// Example(2D): By Radius
|
|
// oval(r=25);
|
|
// Example(2D): By Diameter
|
|
// oval(d=50);
|
|
// Example(2D): Anchoring
|
|
// oval(d=50, anchor=FRONT);
|
|
// Example(2D): Spin
|
|
// oval(d=50, anchor=FRONT, spin=45);
|
|
// Example(NORENDER): Called as Function
|
|
// path = oval(d=50, anchor=FRONT, spin=45);
|
|
module oval(r, d, realign=false, circum=false, anchor=CENTER, spin=0) {
|
|
r = get_radius(r=r, d=d, dflt=1);
|
|
sides = segs(max(r));
|
|
sc = circum? (1 / cos(180/sides)) : 1;
|
|
rx = default(r[0],r) * sc;
|
|
ry = default(r[1],r) * sc;
|
|
attachable(anchor,spin, two_d=true, r=[rx,ry]) {
|
|
if (rx < ry) {
|
|
xscale(rx/ry) {
|
|
zrot(realign? 180/sides : 0) {
|
|
circle(r=ry, $fn=sides);
|
|
}
|
|
}
|
|
} else {
|
|
yscale(ry/rx) {
|
|
zrot(realign? 180/sides : 0) {
|
|
circle(r=rx, $fn=sides);
|
|
}
|
|
}
|
|
}
|
|
children();
|
|
}
|
|
}
|
|
|
|
|
|
function oval(r, d, realign=false, circum=false, anchor=CENTER, spin=0) =
|
|
let(
|
|
r = get_radius(r=r, d=d, dflt=1),
|
|
sides = segs(max(r)),
|
|
offset = realign? 180/sides : 0,
|
|
sc = circum? (1 / cos(180/sides)) : 1,
|
|
rx = default(r[0],r) * sc,
|
|
ry = default(r[1],r) * sc,
|
|
pts = [for (i=[0:1:sides-1]) let(a=360-offset-i*360/sides) [rx*cos(a), ry*sin(a)]]
|
|
) reorient(anchor,spin, two_d=true, r=[rx,ry], p=pts);
|
|
|
|
|
|
|
|
// Section: 2D N-Gons
|
|
|
|
// Function&Module: regular_ngon()
|
|
// Usage:
|
|
// regular_ngon(n, r|d|or|od, [realign]);
|
|
// regular_ngon(n, ir|id, [realign]);
|
|
// regular_ngon(n, side, [realign]);
|
|
// Description:
|
|
// When called as a function, returns a 2D path for a regular N-sided polygon.
|
|
// When called as a module, creates a 2D regular N-sided polygon.
|
|
// Arguments:
|
|
// n = The number of sides.
|
|
// or = Outside radius, at points.
|
|
// r = Same as or
|
|
// od = Outside diameter, at points.
|
|
// d = Same as od
|
|
// ir = Inside radius, at center of sides.
|
|
// id = Inside diameter, at center of sides.
|
|
// side = Length of each side.
|
|
// rounding = Radius of rounding for the tips of the polygon. Default: 0 (no rounding)
|
|
// realign = If false, a tip is aligned with the Y+ axis. If true, the midpoint of a side is aligned with the Y+ axis. Default: false
|
|
// align_tip = If given as a 2D vector, rotates the whole shape so that the first vertex points in that direction. This occurs before spin.
|
|
// align_side = If given as a 2D vector, rotates the whole shape so that the normal of side0 points in that direction. This occurs before spin.
|
|
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
|
|
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
|
|
// Extra Anchors:
|
|
// "tip0", "tip1", etc. = Each tip has an anchor, pointing outwards.
|
|
// "side0", "side1", etc. = The center of each side has an anchor, pointing outwards.
|
|
// Example(2D): by Outer Size
|
|
// regular_ngon(n=5, or=30);
|
|
// regular_ngon(n=5, od=60);
|
|
// Example(2D): by Inner Size
|
|
// regular_ngon(n=5, ir=30);
|
|
// regular_ngon(n=5, id=60);
|
|
// Example(2D): by Side Length
|
|
// regular_ngon(n=8, side=20);
|
|
// Example(2D): Realigned
|
|
// regular_ngon(n=8, side=20, realign=true);
|
|
// Example(2D): Alignment by Tip
|
|
// regular_ngon(n=5, r=30, align_tip=BACK+RIGHT)
|
|
// attach("tip0", FWD) color("blue")
|
|
// stroke([[0,0],[0,7]], endcap2="arrow2");
|
|
// Example(2D): Alignment by Side
|
|
// regular_ngon(n=5, r=30, align_side=BACK+RIGHT)
|
|
// attach("side0", FWD) color("blue")
|
|
// stroke([[0,0],[0,7]], endcap2="arrow2");
|
|
// Example(2D): Rounded
|
|
// regular_ngon(n=5, od=100, rounding=20, $fn=20);
|
|
// Example(2D): Called as Function
|
|
// stroke(closed=true, regular_ngon(n=6, or=30));
|
|
function regular_ngon(n=6, r, d, or, od, ir, id, side, rounding=0, realign=false, align_tip, align_side, anchor=CENTER, spin=0, _mat, _anchs) =
|
|
assert(is_undef(align_tip) || is_vector(align_tip))
|
|
assert(is_undef(align_side) || is_vector(align_side))
|
|
assert(is_undef(align_tip) || is_undef(align_side), "Can only specify one of align_tip and align-side")
|
|
let(
|
|
sc = 1/cos(180/n),
|
|
ir = is_finite(ir)? ir*sc : undef,
|
|
id = is_finite(id)? id*sc : undef,
|
|
side = is_finite(side)? side/2/sin(180/n) : undef,
|
|
r = get_radius(r1=ir, r2=or, r=r, d1=id, d2=od, d=d, dflt=side)
|
|
)
|
|
assert(!is_undef(r), "regular_ngon(): need to specify one of r, d, or, od, ir, id, side.")
|
|
let(
|
|
inset = opp_ang_to_hyp(rounding, (180-360/n)/2),
|
|
mat = !is_undef(_mat) ? _mat :
|
|
( realign? rot(-180/n, planar=true) : affine2d_identity() ) * (
|
|
!is_undef(align_tip)? rot(from=RIGHT, to=point2d(align_tip), planar=true) :
|
|
!is_undef(align_side)? rot(from=RIGHT, to=point2d(align_side), planar=true) * rot(180/n, planar=true) :
|
|
affine2d_identity()
|
|
),
|
|
path4 = rounding==0? oval(r=r, $fn=n) : (
|
|
let(
|
|
steps = floor(segs(r)/n),
|
|
step = 360/n/steps,
|
|
path2 = [
|
|
for (i = [0:1:n-1]) let(
|
|
a = 360 - i*360/n,
|
|
p = polar_to_xy(r-inset, a)
|
|
)
|
|
each arc(N=steps, cp=p, r=rounding, start=a+180/n, angle=-360/n)
|
|
],
|
|
maxx_idx = max_index(subindex(path2,0)),
|
|
path3 = polygon_shift(path2,maxx_idx)
|
|
) path3
|
|
),
|
|
path = apply(mat, path4),
|
|
anchors = !is_undef(_anchs) ? _anchs :
|
|
!is_string(anchor)? [] : [
|
|
for (i = [0:1:n-1]) let(
|
|
a1 = 360 - i*360/n,
|
|
a2 = a1 - 360/n,
|
|
p1 = apply(mat, polar_to_xy(r,a1)),
|
|
p2 = apply(mat, polar_to_xy(r,a2)),
|
|
tipp = apply(mat, polar_to_xy(r-inset+rounding,a1)),
|
|
pos = (p1+p2)/2
|
|
) each [
|
|
anchorpt(str("tip",i), tipp, unit(tipp,BACK), 0),
|
|
anchorpt(str("side",i), pos, unit(pos,BACK), 0),
|
|
]
|
|
]
|
|
) reorient(anchor,spin, two_d=true, path=path, extent=false, p=path, anchors=anchors);
|
|
|
|
|
|
module regular_ngon(n=6, r, d, or, od, ir, id, side, rounding=0, realign=false, align_tip, align_side, anchor=CENTER, spin=0) {
|
|
sc = 1/cos(180/n);
|
|
ir = is_finite(ir)? ir*sc : undef;
|
|
id = is_finite(id)? id*sc : undef;
|
|
side = is_finite(side)? side/2/sin(180/n) : undef;
|
|
r = get_radius(r1=ir, r2=or, r=r, d1=id, d2=od, d=d, dflt=side);
|
|
assert(!is_undef(r), "regular_ngon(): need to specify one of r, d, or, od, ir, id, side.");
|
|
mat = ( realign? rot(-180/n, planar=true) : affine2d_identity() ) * (
|
|
!is_undef(align_tip)? rot(from=RIGHT, to=point2d(align_tip), planar=true) :
|
|
!is_undef(align_side)? rot(from=RIGHT, to=point2d(align_side), planar=true) * rot(180/n, planar=true) :
|
|
affine2d_identity()
|
|
);
|
|
inset = opp_ang_to_hyp(rounding, (180-360/n)/2);
|
|
anchors = [
|
|
for (i = [0:1:n-1]) let(
|
|
a1 = 360 - i*360/n,
|
|
a2 = a1 - 360/n,
|
|
p1 = apply(mat, polar_to_xy(r,a1)),
|
|
p2 = apply(mat, polar_to_xy(r,a2)),
|
|
tipp = apply(mat, polar_to_xy(r-inset+rounding,a1)),
|
|
pos = (p1+p2)/2
|
|
) each [
|
|
anchorpt(str("tip",i), tipp, unit(tipp,BACK), 0),
|
|
anchorpt(str("side",i), pos, unit(pos,BACK), 0),
|
|
]
|
|
];
|
|
path = regular_ngon(n=n, r=r, rounding=rounding, _mat=mat, _anchs=anchors);
|
|
attachable(anchor,spin, two_d=true, path=path, extent=false, anchors=anchors) {
|
|
polygon(path);
|
|
children();
|
|
}
|
|
}
|
|
|
|
|
|
// Function&Module: pentagon()
|
|
// Usage:
|
|
// pentagon(or|od, [realign]);
|
|
// pentagon(ir|id, [realign]);
|
|
// pentagon(side, [realign]);
|
|
// Description:
|
|
// When called as a function, returns a 2D path for a regular pentagon.
|
|
// When called as a module, creates a 2D regular pentagon.
|
|
// Arguments:
|
|
// or = Outside radius, at points.
|
|
// r = Same as or.
|
|
// od = Outside diameter, at points.
|
|
// d = Same as od.
|
|
// ir = Inside radius, at center of sides.
|
|
// id = Inside diameter, at center of sides.
|
|
// side = Length of each side.
|
|
// rounding = Radius of rounding for the tips of the polygon. Default: 0 (no rounding)
|
|
// realign = If false, a tip is aligned with the Y+ axis. If true, the midpoint of a side is aligned with the Y+ axis. Default: false
|
|
// align_tip = If given as a 2D vector, rotates the whole shape so that the first vertex points in that direction. This occurs before spin.
|
|
// align_side = If given as a 2D vector, rotates the whole shape so that the normal of side0 points in that direction. This occurs before spin.
|
|
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
|
|
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
|
|
// Extra Anchors:
|
|
// "tip0" ... "tip4" = Each tip has an anchor, pointing outwards.
|
|
// "side0" ... "side4" = The center of each side has an anchor, pointing outwards.
|
|
// Example(2D): by Outer Size
|
|
// pentagon(or=30);
|
|
// pentagon(od=60);
|
|
// Example(2D): by Inner Size
|
|
// pentagon(ir=30);
|
|
// pentagon(id=60);
|
|
// Example(2D): by Side Length
|
|
// pentagon(side=20);
|
|
// Example(2D): Realigned
|
|
// pentagon(side=20, realign=true);
|
|
// Example(2D): Alignment by Tip
|
|
// pentagon(r=30, align_tip=BACK+RIGHT)
|
|
// attach("tip0", FWD) color("blue")
|
|
// stroke([[0,0],[0,7]], endcap2="arrow2");
|
|
// Example(2D): Alignment by Side
|
|
// pentagon(r=30, align_side=BACK+RIGHT)
|
|
// attach("side0", FWD) color("blue")
|
|
// stroke([[0,0],[0,7]], endcap2="arrow2");
|
|
// Example(2D): Rounded
|
|
// pentagon(od=100, rounding=20, $fn=20);
|
|
// Example(2D): Called as Function
|
|
// stroke(closed=true, pentagon(or=30));
|
|
function pentagon(r, d, or, od, ir, id, side, rounding=0, realign=false, align_tip, align_side, anchor=CENTER, spin=0) =
|
|
regular_ngon(n=5, r=r, d=d, or=or, od=od, ir=ir, id=id, side=side, rounding=rounding, realign=realign, align_tip=align_tip, align_side=align_side, anchor=anchor, spin=spin);
|
|
|
|
|
|
module pentagon(r, d, or, od, ir, id, side, rounding=0, realign=false, align_tip, align_side, anchor=CENTER, spin=0)
|
|
regular_ngon(n=5, r=r, d=d, or=or, od=od, ir=ir, id=id, side=side, rounding=rounding, realign=realign, align_tip=align_tip, align_side=align_side, anchor=anchor, spin=spin) children();
|
|
|
|
|
|
// Function&Module: hexagon()
|
|
// Usage:
|
|
// hexagon(or, od, ir, id, side);
|
|
// Description:
|
|
// When called as a function, returns a 2D path for a regular hexagon.
|
|
// When called as a module, creates a 2D regular hexagon.
|
|
// Arguments:
|
|
// or = Outside radius, at points.
|
|
// r = Same as or
|
|
// od = Outside diameter, at points.
|
|
// d = Same as od
|
|
// ir = Inside radius, at center of sides.
|
|
// id = Inside diameter, at center of sides.
|
|
// side = Length of each side.
|
|
// rounding = Radius of rounding for the tips of the polygon. Default: 0 (no rounding)
|
|
// realign = If false, a tip is aligned with the Y+ axis. If true, the midpoint of a side is aligned with the Y+ axis. Default: false
|
|
// align_tip = If given as a 2D vector, rotates the whole shape so that the first vertex points in that direction. This occurs before spin.
|
|
// align_side = If given as a 2D vector, rotates the whole shape so that the normal of side0 points in that direction. This occurs before spin.
|
|
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
|
|
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
|
|
// Extra Anchors:
|
|
// "tip0" ... "tip5" = Each tip has an anchor, pointing outwards.
|
|
// "side0" ... "side5" = The center of each side has an anchor, pointing outwards.
|
|
// Example(2D): by Outer Size
|
|
// hexagon(or=30);
|
|
// hexagon(od=60);
|
|
// Example(2D): by Inner Size
|
|
// hexagon(ir=30);
|
|
// hexagon(id=60);
|
|
// Example(2D): by Side Length
|
|
// hexagon(side=20);
|
|
// Example(2D): Realigned
|
|
// hexagon(side=20, realign=true);
|
|
// Example(2D): Alignment by Tip
|
|
// hexagon(r=30, align_tip=BACK+RIGHT)
|
|
// attach("tip0", FWD) color("blue")
|
|
// stroke([[0,0],[0,7]], endcap2="arrow2");
|
|
// Example(2D): Alignment by Side
|
|
// hexagon(r=30, align_side=BACK+RIGHT)
|
|
// attach("side0", FWD) color("blue")
|
|
// stroke([[0,0],[0,7]], endcap2="arrow2");
|
|
// Example(2D): Rounded
|
|
// hexagon(od=100, rounding=20, $fn=20);
|
|
// Example(2D): Called as Function
|
|
// stroke(closed=true, hexagon(or=30));
|
|
function hexagon(r, d, or, od, ir, id, side, rounding=0, realign=false, align_tip, align_side, anchor=CENTER, spin=0) =
|
|
regular_ngon(n=6, r=r, d=d, or=or, od=od, ir=ir, id=id, side=side, rounding=rounding, realign=realign, align_tip=align_tip, align_side=align_side, anchor=anchor, spin=spin);
|
|
|
|
|
|
module hexagon(r, d, or, od, ir, id, side, rounding=0, realign=false, align_tip, align_side, anchor=CENTER, spin=0)
|
|
regular_ngon(n=6, r=r, d=d, or=or, od=od, ir=ir, id=id, side=side, rounding=rounding, realign=realign, align_tip=align_tip, align_side=align_side, anchor=anchor, spin=spin) children();
|
|
|
|
|
|
// Function&Module: octagon()
|
|
// Usage:
|
|
// octagon(or, od, ir, id, side);
|
|
// Description:
|
|
// When called as a function, returns a 2D path for a regular octagon.
|
|
// When called as a module, creates a 2D regular octagon.
|
|
// Arguments:
|
|
// or = Outside radius, at points.
|
|
// r = Same as or
|
|
// od = Outside diameter, at points.
|
|
// d = Same as od
|
|
// ir = Inside radius, at center of sides.
|
|
// id = Inside diameter, at center of sides.
|
|
// side = Length of each side.
|
|
// rounding = Radius of rounding for the tips of the polygon. Default: 0 (no rounding)
|
|
// realign = If false, a tip is aligned with the Y+ axis. If true, the midpoint of a side is aligned with the Y+ axis. Default: false
|
|
// align_tip = If given as a 2D vector, rotates the whole shape so that the first vertex points in that direction. This occurs before spin.
|
|
// align_side = If given as a 2D vector, rotates the whole shape so that the normal of side0 points in that direction. This occurs before spin.
|
|
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
|
|
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
|
|
// Extra Anchors:
|
|
// "tip0" ... "tip7" = Each tip has an anchor, pointing outwards.
|
|
// "side0" ... "side7" = The center of each side has an anchor, pointing outwards.
|
|
// Example(2D): by Outer Size
|
|
// octagon(or=30);
|
|
// octagon(od=60);
|
|
// Example(2D): by Inner Size
|
|
// octagon(ir=30);
|
|
// octagon(id=60);
|
|
// Example(2D): by Side Length
|
|
// octagon(side=20);
|
|
// Example(2D): Realigned
|
|
// octagon(side=20, realign=true);
|
|
// Example(2D): Alignment by Tip
|
|
// octagon(r=30, align_tip=BACK+RIGHT)
|
|
// attach("tip0", FWD) color("blue")
|
|
// stroke([[0,0],[0,7]], endcap2="arrow2");
|
|
// Example(2D): Alignment by Side
|
|
// octagon(r=30, align_side=BACK+RIGHT)
|
|
// attach("side0", FWD) color("blue")
|
|
// stroke([[0,0],[0,7]], endcap2="arrow2");
|
|
// Example(2D): Rounded
|
|
// octagon(od=100, rounding=20, $fn=20);
|
|
// Example(2D): Called as Function
|
|
// stroke(closed=true, octagon(or=30));
|
|
function octagon(r, d, or, od, ir, id, side, rounding=0, realign=false, align_tip, align_side, anchor=CENTER, spin=0) =
|
|
regular_ngon(n=8, r=r, d=d, or=or, od=od, ir=ir, id=id, side=side, rounding=rounding, realign=realign, align_tip=align_tip, align_side=align_side, anchor=anchor, spin=spin);
|
|
|
|
|
|
module octagon(r, d, or, od, ir, id, side, rounding=0, realign=false, align_tip, align_side, anchor=CENTER, spin=0)
|
|
regular_ngon(n=8, r=r, d=d, or=or, od=od, ir=ir, id=id, side=side, rounding=rounding, realign=realign, align_tip=align_tip, align_side=align_side, anchor=anchor, spin=spin) children();
|
|
|
|
|
|
|
|
// Section: Other 2D Shapes
|
|
|
|
|
|
// Function&Module: trapezoid()
|
|
// Usage:
|
|
// trapezoid(h, w1, w2);
|
|
// Description:
|
|
// When called as a function, returns a 2D path for a trapezoid with parallel front and back sides.
|
|
// When called as a module, creates a 2D trapezoid with parallel front and back sides.
|
|
// Arguments:
|
|
// h = The Y axis height of the trapezoid.
|
|
// w1 = The X axis width of the front end of the trapezoid.
|
|
// w2 = The X axis width of the back end of the trapezoid.
|
|
// angle = If given in place of `h`, `w1`, or `w2`, then the missing value is calculated such that the right side has that angle away from the Y axis.
|
|
// shift = Scalar value to shift the back of the trapezoid along the X axis by. Default: 0
|
|
// rounding = The rounding radius for the corners. If given as a list of four numbers, gives individual radii for each corner, in the order [X+Y+,X-Y+,X-Y-,X+Y-]. Default: 0 (no rounding)
|
|
// chamfer = The Length of the chamfer faces at the corners. If given as a list of four numbers, gives individual chamfers for each corner, in the order [X+Y+,X-Y+,X-Y-,X+Y-]. Default: 0 (no chamfer)
|
|
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
|
|
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
|
|
// Examples(2D):
|
|
// trapezoid(h=30, w1=40, w2=20);
|
|
// trapezoid(h=25, w1=20, w2=35);
|
|
// trapezoid(h=20, w1=40, w2=0);
|
|
// trapezoid(h=20, w1=30, angle=30);
|
|
// trapezoid(h=20, w1=20, angle=-30);
|
|
// trapezoid(h=20, w2=10, angle=30);
|
|
// trapezoid(h=20, w2=30, angle=-30);
|
|
// trapezoid(w1=30, w2=10, angle=30);
|
|
// Example(2D): Chamferred Trapezoid
|
|
// trapezoid(h=30, w1=60, w2=40, chamfer=5);
|
|
// Example(2D): Rounded Trapezoid
|
|
// trapezoid(h=30, w1=60, w2=40, rounding=5);
|
|
// Example(2D): Mixed Chamfering and Rounding
|
|
// trapezoid(h=30, w1=60, w2=40, rounding=[5,0,10,0],chamfer=[0,8,0,15],$fa=1,$fs=1);
|
|
// Example(2D): Called as Function
|
|
// stroke(closed=true, trapezoid(h=30, w1=40, w2=20));
|
|
function trapezoid(h, w1, w2, angle, shift=0, chamfer=0, rounding=0, anchor=CENTER, spin=0) =
|
|
assert(is_undef(h) || is_finite(h))
|
|
assert(is_undef(w1) || is_finite(w1))
|
|
assert(is_undef(w2) || is_finite(w2))
|
|
assert(is_undef(angle) || is_finite(angle))
|
|
assert(num_defined([h, w1, w2, angle]) == 3, "Must give exactly 3 of the arguments h, w1, w2, and angle.")
|
|
assert(is_finite(shift))
|
|
assert(is_finite(chamfer) || is_vector(chamfer,4))
|
|
assert(is_finite(rounding) || is_vector(rounding,4))
|
|
let(
|
|
simple = chamfer==0 && rounding==0,
|
|
h = !is_undef(h)? h : opp_ang_to_adj(abs(w2-w1)/2, abs(angle)),
|
|
w1 = !is_undef(w1)? w1 : w2 + 2*(adj_ang_to_opp(h, angle) + shift),
|
|
w2 = !is_undef(w2)? w2 : w1 - 2*(adj_ang_to_opp(h, angle) + shift)
|
|
)
|
|
assert(w1>=0 && w2>=0 && h>0, "Degenerate trapezoid geometry.")
|
|
assert(w1+w2>0, "Degenerate trapezoid geometry.")
|
|
let(
|
|
base_path = [
|
|
[w2/2+shift,h/2],
|
|
[-w2/2+shift,h/2],
|
|
[-w1/2,-h/2],
|
|
[w1/2,-h/2],
|
|
],
|
|
cpath = simple? base_path :
|
|
path_chamfer_and_rounding(
|
|
base_path, closed=true,
|
|
chamfer=chamfer,
|
|
rounding=rounding
|
|
),
|
|
path = reverse(cpath)
|
|
) simple?
|
|
reorient(anchor,spin, two_d=true, size=[w1,h], size2=w2, shift=shift, p=path) :
|
|
reorient(anchor,spin, two_d=true, path=path, p=path);
|
|
|
|
|
|
|
|
module trapezoid(h, w1, w2, angle, shift=0, chamfer=0, rounding=0, anchor=CENTER, spin=0) {
|
|
path = trapezoid(h=h, w1=w1, w2=w2, angle=angle, shift=shift, chamfer=chamfer, rounding=rounding);
|
|
union() {
|
|
simple = chamfer==0 && rounding==0;
|
|
h = !is_undef(h)? h : opp_ang_to_adj(abs(w2-w1)/2, abs(angle));
|
|
w1 = !is_undef(w1)? w1 : w2 + 2*(adj_ang_to_opp(h, angle) + shift);
|
|
w2 = !is_undef(w2)? w2 : w1 - 2*(adj_ang_to_opp(h, angle) + shift);
|
|
if (simple) {
|
|
attachable(anchor,spin, two_d=true, size=[w1,h], size2=w2, shift=shift) {
|
|
polygon(path);
|
|
children();
|
|
}
|
|
} else {
|
|
attachable(anchor,spin, two_d=true, path=path) {
|
|
polygon(path);
|
|
children();
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
// Function&Module: teardrop2d()
|
|
//
|
|
// Description:
|
|
// Makes a 2D teardrop shape. Useful for extruding into 3D printable holes.
|
|
//
|
|
// Usage:
|
|
// teardrop2d(r|d, [ang], [cap_h]);
|
|
//
|
|
// Arguments:
|
|
// r = radius of circular part of teardrop. (Default: 1)
|
|
// d = diameter of spherical portion of bottom. (Use instead of r)
|
|
// ang = angle of hat walls from the Y axis. (Default: 45 degrees)
|
|
// cap_h = if given, height above center where the shape will be truncated.
|
|
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
|
|
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
|
|
//
|
|
// Example(2D): Typical Shape
|
|
// teardrop2d(r=30, ang=30);
|
|
// Example(2D): Crop Cap
|
|
// teardrop2d(r=30, ang=30, cap_h=40);
|
|
// Example(2D): Close Crop
|
|
// teardrop2d(r=30, ang=30, cap_h=20);
|
|
module teardrop2d(r, d, ang=45, cap_h, anchor=CENTER, spin=0)
|
|
{
|
|
path = teardrop2d(r=r, d=d, ang=ang, cap_h=cap_h);
|
|
attachable(anchor,spin, two_d=true, path=path) {
|
|
polygon(path);
|
|
children();
|
|
}
|
|
}
|
|
|
|
|
|
function teardrop2d(r, d, ang=45, cap_h, anchor=CENTER, spin=0) =
|
|
let(
|
|
r = get_radius(r=r, d=d, dflt=1),
|
|
cord = 2 * r * cos(ang),
|
|
cord_h = r * sin(ang),
|
|
tip_y = (cord/2)/tan(ang),
|
|
cap_h = min((!is_undef(cap_h)? cap_h : tip_y+cord_h), tip_y+cord_h),
|
|
cap_w = cord * (1 - (cap_h - cord_h)/tip_y),
|
|
ang = min(ang,asin(cap_h/r)),
|
|
sa = 180 - ang,
|
|
ea = 360 + ang,
|
|
steps = segs(r)*(ea-sa)/360,
|
|
step = (ea-sa)/steps,
|
|
path = deduplicate(
|
|
[
|
|
[ cap_w/2,cap_h],
|
|
for (i=[0:1:steps]) let(a=ea-i*step) r*[cos(a),sin(a)],
|
|
[-cap_w/2,cap_h]
|
|
], closed=true
|
|
),
|
|
maxx_idx = max_index(subindex(path,0)),
|
|
path2 = polygon_shift(path,maxx_idx)
|
|
) reorient(anchor,spin, two_d=true, path=path2, p=path2);
|
|
|
|
|
|
|
|
// Function&Module: glued_circles()
|
|
// Usage:
|
|
// glued_circles(r|d, spread, tangent);
|
|
// Description:
|
|
// When called as a function, returns a 2D path forming a shape of two circles joined by curved waist.
|
|
// When called as a module, creates a 2D shape of two circles joined by curved waist.
|
|
// Arguments:
|
|
// r = The radius of the end circles.
|
|
// d = The diameter of the end circles.
|
|
// spread = The distance between the centers of the end circles. Default: 10
|
|
// tangent = The angle in degrees of the tangent point for the joining arcs, measured away from the Y axis. Default: 30
|
|
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
|
|
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
|
|
// Examples(2D):
|
|
// glued_circles(r=15, spread=40, tangent=45);
|
|
// glued_circles(d=30, spread=30, tangent=30);
|
|
// glued_circles(d=30, spread=30, tangent=15);
|
|
// glued_circles(d=30, spread=30, tangent=-30);
|
|
// Example(2D): Called as Function
|
|
// stroke(closed=true, glued_circles(r=15, spread=40, tangent=45));
|
|
function glued_circles(r, d, spread=10, tangent=30, anchor=CENTER, spin=0) =
|
|
let(
|
|
r = get_radius(r=r, d=d, dflt=10),
|
|
r2 = (spread/2 / sin(tangent)) - r,
|
|
cp1 = [spread/2, 0],
|
|
cp2 = [0, (r+r2)*cos(tangent)],
|
|
sa1 = 90-tangent,
|
|
ea1 = 270+tangent,
|
|
lobearc = ea1-sa1,
|
|
lobesegs = floor(segs(r)*lobearc/360),
|
|
lobestep = lobearc / lobesegs,
|
|
sa2 = 270-tangent,
|
|
ea2 = 270+tangent,
|
|
subarc = ea2-sa2,
|
|
arcsegs = ceil(segs(r2)*abs(subarc)/360),
|
|
arcstep = subarc / arcsegs,
|
|
path = concat(
|
|
[for (i=[0:1:lobesegs]) let(a=sa1+i*lobestep) r * [cos(a),sin(a)] - cp1],
|
|
tangent==0? [] : [for (i=[0:1:arcsegs]) let(a=ea2-i*arcstep+180) r2 * [cos(a),sin(a)] - cp2],
|
|
[for (i=[0:1:lobesegs]) let(a=sa1+i*lobestep+180) r * [cos(a),sin(a)] + cp1],
|
|
tangent==0? [] : [for (i=[0:1:arcsegs]) let(a=ea2-i*arcstep) r2 * [cos(a),sin(a)] + cp2]
|
|
),
|
|
maxx_idx = max_index(subindex(path,0)),
|
|
path2 = reverse_polygon(polygon_shift(path,maxx_idx))
|
|
) reorient(anchor,spin, two_d=true, path=path2, extent=true, p=path2);
|
|
|
|
|
|
module glued_circles(r, d, spread=10, tangent=30, anchor=CENTER, spin=0) {
|
|
path = glued_circles(r=r, d=d, spread=spread, tangent=tangent);
|
|
attachable(anchor,spin, two_d=true, path=path, extent=true) {
|
|
polygon(path);
|
|
children();
|
|
}
|
|
}
|
|
|
|
|
|
// Function&Module: star()
|
|
// Usage:
|
|
// star(n, r|d|or|od, ir|id|step, [realign]);
|
|
// Description:
|
|
// When called as a function, returns the path needed to create a star polygon with N points.
|
|
// When called as a module, creates a star polygon with N points.
|
|
// Arguments:
|
|
// n = The number of stellate tips on the star.
|
|
// r = The radius to the tips of the star.
|
|
// or = Same as r
|
|
// d = The diameter to the tips of the star.
|
|
// od = Same as d
|
|
// ir = The radius to the inner corners of the star.
|
|
// id = The diameter to the inner corners of the star.
|
|
// step = Calculates the radius of the inner star corners by virtually drawing a straight line `step` tips around the star. 2 <= step < n/2
|
|
// realign = If false, a tip is aligned with the Y+ axis. If true, an inner corner is aligned with the Y+ axis. Default: false
|
|
// align_tip = If given as a 2D vector, rotates the whole shape so that the first star tip points in that direction. This occurs before spin.
|
|
// align_pit = If given as a 2D vector, rotates the whole shape so that the first inner corner is pointed towards that direction. This occurs before spin.
|
|
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
|
|
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
|
|
// Extra Anchors:
|
|
// "tip0" ... "tip4" = Each tip has an anchor, pointing outwards.
|
|
// "pit0" ... "pit4" = The inside corner between each tip has an anchor, pointing outwards.
|
|
// "midpt0" ... "midpt4" = The center-point between each pair of tips has an anchor, pointing outwards.
|
|
// Examples(2D):
|
|
// star(n=5, r=50, ir=25);
|
|
// star(n=5, r=50, step=2);
|
|
// star(n=7, r=50, step=2);
|
|
// star(n=7, r=50, step=3);
|
|
// Example(2D): Realigned
|
|
// star(n=7, r=50, step=3, realign=true);
|
|
// Example(2D): Alignment by Tip
|
|
// star(n=5, ir=15, or=30, align_tip=BACK+RIGHT)
|
|
// attach("tip0", FWD) color("blue")
|
|
// stroke([[0,0],[0,7]], endcap2="arrow2");
|
|
// Example(2D): Alignment by Pit
|
|
// star(n=5, ir=15, or=30, align_pit=BACK+RIGHT)
|
|
// attach("pit0", FWD) color("blue")
|
|
// stroke([[0,0],[0,7]], endcap2="arrow2");
|
|
// Example(2D): Called as Function
|
|
// stroke(closed=true, star(n=5, r=50, ir=25));
|
|
function star(n, r, d, or, od, ir, id, step, realign=false, align_tip, align_pit, anchor=CENTER, spin=0, _mat, _anchs) =
|
|
assert(is_undef(align_tip) || is_vector(align_tip))
|
|
assert(is_undef(align_pit) || is_vector(align_pit))
|
|
assert(is_undef(align_tip) || is_undef(align_pit), "Can only specify one of align_tip and align_pit")
|
|
let(
|
|
r = get_radius(r1=or, d1=od, r=r, d=d),
|
|
count = num_defined([ir,id,step]),
|
|
stepOK = is_undef(step) || (step>1 && step<n/2)
|
|
)
|
|
assert(is_def(n), "Must specify number of points, n")
|
|
assert(count==1, "Must specify exactly one of ir, id, step")
|
|
assert(stepOK, str("Parameter 'step' must be between 2 and ",floor(n/2)," for ",n," point star"))
|
|
let(
|
|
mat = !is_undef(_mat) ? _mat :
|
|
( realign? rot(-180/n, planar=true) : affine2d_identity() ) * (
|
|
!is_undef(align_tip)? rot(from=RIGHT, to=point2d(align_tip), planar=true) :
|
|
!is_undef(align_pit)? rot(from=RIGHT, to=point2d(align_pit), planar=true) * rot(180/n, planar=true) :
|
|
affine2d_identity()
|
|
),
|
|
stepr = is_undef(step)? r : r*cos(180*step/n)/cos(180*(step-1)/n),
|
|
ir = get_radius(r=ir, d=id, dflt=stepr),
|
|
offset = realign? 180/n : 0,
|
|
path1 = [for(i=[2*n:-1:1]) let(theta=180*i/n, radius=(i%2)?ir:r) radius*[cos(theta), sin(theta)]],
|
|
path = apply(mat, path1),
|
|
anchors = !is_undef(_anchs) ? _anchs :
|
|
!is_string(anchor)? [] : [
|
|
for (i = [0:1:n-1]) let(
|
|
a1 = 360 - i*360/n,
|
|
a2 = a1 - 180/n,
|
|
a3 = a1 - 360/n,
|
|
p1 = apply(mat, polar_to_xy(r,a1)),
|
|
p2 = apply(mat, polar_to_xy(ir,a2)),
|
|
p3 = apply(mat, polar_to_xy(r,a3)),
|
|
pos = (p1+p3)/2
|
|
) each [
|
|
anchorpt(str("tip",i), p1, unit(p1,BACK), 0),
|
|
anchorpt(str("pit",i), p2, unit(p2,BACK), 0),
|
|
anchorpt(str("midpt",i), pos, unit(pos,BACK), 0),
|
|
]
|
|
]
|
|
) reorient(anchor,spin, two_d=true, path=path, p=path, anchors=anchors);
|
|
|
|
|
|
module star(n, r, d, or, od, ir, id, step, realign=false, align_tip, align_pit, anchor=CENTER, spin=0) {
|
|
assert(is_undef(align_tip) || is_vector(align_tip));
|
|
assert(is_undef(align_pit) || is_vector(align_pit));
|
|
assert(is_undef(align_tip) || is_undef(align_pit), "Can only specify one of align_tip and align_pit");
|
|
r = get_radius(r1=or, d1=od, r=r, d=d, dflt=undef);
|
|
stepr = is_undef(step)? r : r*cos(180*step/n)/cos(180*(step-1)/n);
|
|
ir = get_radius(r=ir, d=id, dflt=stepr);
|
|
mat = ( realign? rot(-180/n, planar=true) : affine2d_identity() ) * (
|
|
!is_undef(align_tip)? rot(from=RIGHT, to=point2d(align_tip), planar=true) :
|
|
!is_undef(align_pit)? rot(from=RIGHT, to=point2d(align_pit), planar=true) * rot(180/n, planar=true) :
|
|
affine2d_identity()
|
|
);
|
|
anchors = [
|
|
for (i = [0:1:n-1]) let(
|
|
a1 = 360 - i*360/n - (realign? 180/n : 0),
|
|
a2 = a1 - 180/n,
|
|
a3 = a1 - 360/n,
|
|
p1 = apply(mat, polar_to_xy(r,a1)),
|
|
p2 = apply(mat, polar_to_xy(ir,a2)),
|
|
p3 = apply(mat, polar_to_xy(r,a3)),
|
|
pos = (p1+p3)/2
|
|
) each [
|
|
anchorpt(str("tip",i), p1, unit(p1,BACK), 0),
|
|
anchorpt(str("pit",i), p2, unit(p2,BACK), 0),
|
|
anchorpt(str("midpt",i), pos, unit(pos,BACK), 0),
|
|
]
|
|
];
|
|
path = star(n=n, r=r, ir=ir, realign=realign, _mat=mat, _anchs=anchors);
|
|
attachable(anchor,spin, two_d=true, path=path, anchors=anchors) {
|
|
polygon(path);
|
|
children();
|
|
}
|
|
}
|
|
|
|
|
|
function _superformula(theta,m1,m2,n1,n2=1,n3=1,a=1,b=1) =
|
|
pow(pow(abs(cos(m1*theta/4)/a),n2)+pow(abs(sin(m2*theta/4)/b),n3),-1/n1);
|
|
|
|
// Function&Module: supershape()
|
|
// Usage:
|
|
// supershape(step,[m1],[m2],[n1],[n2],[n3],[a],[b],[r|d]);
|
|
// Description:
|
|
// When called as a function, returns a 2D path for the outline of the [Superformula](https://en.wikipedia.org/wiki/Superformula) shape.
|
|
// When called as a module, creates a 2D [Superformula](https://en.wikipedia.org/wiki/Superformula) shape.
|
|
// Arguments:
|
|
// step = The angle step size for sampling the superformula shape. Smaller steps are slower but more accurate.
|
|
// m1 = The m1 argument for the superformula. Default: 4.
|
|
// m2 = The m2 argument for the superformula. Default: m1.
|
|
// n1 = The n1 argument for the superformula. Default: 1.
|
|
// n2 = The n2 argument for the superformula. Default: n1.
|
|
// n3 = The n3 argument for the superformula. Default: n2.
|
|
// a = The a argument for the superformula. Default: 1.
|
|
// b = The b argument for the superformula. Default: a.
|
|
// r = Radius of the shape. Scale shape to fit in a circle of radius r.
|
|
// d = Diameter of the shape. Scale shape to fit in a circle of diameter d.
|
|
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
|
|
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
|
|
// Example(2D):
|
|
// supershape(step=0.5,m1=16,m2=16,n1=0.5,n2=0.5,n3=16,r=50);
|
|
// Example(2D): Called as Function
|
|
// stroke(closed=true, supershape(step=0.5,m1=16,m2=16,n1=0.5,n2=0.5,n3=16,d=100));
|
|
// Examples(2D,Med):
|
|
// for(n=[2:5]) right(2.5*(n-2)) supershape(m1=4,m2=4,n1=n,a=1,b=2); // Superellipses
|
|
// m=[2,3,5,7]; for(i=[0:3]) right(2.5*i) supershape(.5,m1=m[i],n1=1);
|
|
// m=[6,8,10,12]; for(i=[0:3]) right(2.7*i) supershape(.5,m1=m[i],n1=1,b=1.5); // m should be even
|
|
// m=[1,2,3,5]; for(i=[0:3]) fwd(1.5*i) supershape(m1=m[i],n1=0.4);
|
|
// supershape(m1=5, n1=4, n2=1); right(2.5) supershape(m1=5, n1=40, n2=10);
|
|
// m=[2,3,5,7]; for(i=[0:3]) right(2.5*i) supershape(m1=m[i], n1=60, n2=55, n3=30);
|
|
// n=[0.5,0.2,0.1,0.02]; for(i=[0:3]) right(2.5*i) supershape(m1=5,n1=n[i], n2=1.7);
|
|
// supershape(m1=2, n1=1, n2=4, n3=8);
|
|
// supershape(m1=7, n1=2, n2=8, n3=4);
|
|
// supershape(m1=7, n1=3, n2=4, n3=17);
|
|
// supershape(m1=4, n1=1/2, n2=1/2, n3=4);
|
|
// supershape(m1=4, n1=4.0,n2=16, n3=1.5, a=0.9, b=9);
|
|
// for(i=[1:4]) right(3*i) supershape(m1=i, m2=3*i, n1=2);
|
|
// m=[4,6,10]; for(i=[0:2]) right(i*5) supershape(m1=m[i], n1=12, n2=8, n3=5, a=2.7);
|
|
// for(i=[-1.5:3:1.5]) right(i*1.5) supershape(m1=2,m2=10,n1=i,n2=1);
|
|
// for(i=[1:3],j=[-1,1]) translate([3.5*i,1.5*j])supershape(m1=4,m2=6,n1=i*j,n2=1);
|
|
// for(i=[1:3]) right(2.5*i)supershape(step=.5,m1=88, m2=64, n1=-i*i,n2=1,r=1);
|
|
// Examples:
|
|
// linear_extrude(height=0.3, scale=0) supershape(step=1, m1=6, n1=0.4, n2=0, n3=6);
|
|
// linear_extrude(height=5, scale=0) supershape(step=1, b=3, m1=6, n1=3.8, n2=16, n3=10);
|
|
function supershape(step=0.5,m1=4,m2=undef,n1=1,n2=undef,n3=undef,a=1,b=undef,r=undef,d=undef,anchor=CENTER, spin=0) =
|
|
let(
|
|
r = get_radius(r=r, d=d, dflt=undef),
|
|
m2 = is_def(m2) ? m2 : m1,
|
|
n2 = is_def(n2) ? n2 : n1,
|
|
n3 = is_def(n3) ? n3 : n2,
|
|
b = is_def(b) ? b : a,
|
|
steps = ceil(360/step),
|
|
step = 360/steps,
|
|
angs = [for (i = [0:steps]) step*i],
|
|
rads = [for (theta = angs) _superformula(theta=theta,m1=m1,m2=m2,n1=n1,n2=n2,n3=n3,a=a,b=b)],
|
|
scale = is_def(r) ? r/max(rads) : 1,
|
|
path = [for (i = [steps:-1:1]) let(a=angs[i]) scale*rads[i]*[cos(a), sin(a)]]
|
|
) reorient(anchor,spin, two_d=true, path=path, p=path);
|
|
|
|
module supershape(step=0.5,m1=4,m2=undef,n1,n2=undef,n3=undef,a=1,b=undef, r=undef, d=undef, anchor=CENTER, spin=0) {
|
|
path = supershape(step=step,m1=m1,m2=m2,n1=n1,n2=n2,n3=n3,a=a,b=b,r=r,d=d);
|
|
attachable(anchor,spin, two_d=true, path=path) {
|
|
polygon(path);
|
|
children();
|
|
}
|
|
}
|
|
|
|
|
|
// Section: 2D Masking Shapes
|
|
|
|
// Function&Module: mask2d_roundover()
|
|
// Usage:
|
|
// mask2d_roundover(r|d, [inset], [excess]);
|
|
// Description:
|
|
// Creates a 2D roundover/bead mask shape that is useful for extruding into a 3D mask for a 90º edge.
|
|
// This 2D mask is designed to be differenced away from the edge of a shape that is in the first (X+Y+) quadrant.
|
|
// If called as a function, this just returns a 2D path of the outline of the mask shape.
|
|
// Arguments:
|
|
// r = Radius of the roundover.
|
|
// d = Diameter of the roundover.
|
|
// inset = Optional bead inset size. Default: 0
|
|
// excess = Extra amount of mask shape to creates on the X- and Y- sides of the shape.
|
|
// Example(2D): 2D Roundover Mask
|
|
// mask2d_roundover(r=10);
|
|
// Example(2D): 2D Bead Mask
|
|
// mask2d_roundover(r=10,inset=2);
|
|
// Example: Masking by Edge Attachment
|
|
// diff("mask")
|
|
// cube([50,60,70],center=true)
|
|
// edge_profile([TOP,"Z"],except=[BACK,TOP+LEFT])
|
|
// mask2d_roundover(r=10, inset=2);
|
|
module mask2d_roundover(r, d, excess, inset=0, anchor=CENTER,spin=0) {
|
|
path = mask2d_roundover(r=r,d=d,excess=excess,inset=inset);
|
|
attachable(anchor,spin, two_d=true, path=path) {
|
|
polygon(path);
|
|
children();
|
|
}
|
|
}
|
|
|
|
function mask2d_roundover(r, d, excess, inset=0, anchor=CENTER,spin=0) =
|
|
assert(is_num(r)||is_num(d))
|
|
assert(is_undef(excess)||is_num(excess))
|
|
assert(is_num(inset)||(is_vector(inset)&&len(inset)==2))
|
|
let(
|
|
inset = is_list(inset)? inset : [inset,inset],
|
|
excess = default(excess,$overlap),
|
|
r = get_radius(r=r,d=d,dflt=1),
|
|
steps = quantup(segs(r),4)/4,
|
|
step = 90/steps,
|
|
path = [
|
|
[r+inset.x,-excess],
|
|
[-excess,-excess],
|
|
[-excess, r+inset.y],
|
|
for (i=[0:1:steps]) [r,r] + inset + polar_to_xy(r,180+i*step)
|
|
]
|
|
) reorient(anchor,spin, two_d=true, path=path, extent=false, p=path);
|
|
|
|
|
|
// Function&Module: mask2d_cove()
|
|
// Usage:
|
|
// mask2d_cove(r|d, [inset], [excess]);
|
|
// Description:
|
|
// Creates a 2D cove mask shape that is useful for extruding into a 3D mask for a 90º edge.
|
|
// This 2D mask is designed to be differenced away from the edge of a shape that is in the first (X+Y+) quadrant.
|
|
// If called as a function, this just returns a 2D path of the outline of the mask shape.
|
|
// Arguments:
|
|
// r = Radius of the cove.
|
|
// d = Diameter of the cove.
|
|
// inset = Optional amount to inset code from corner. Default: 0
|
|
// excess = Extra amount of mask shape to creates on the X- and Y- sides of the shape.
|
|
// Example(2D): 2D Cove Mask
|
|
// mask2d_cove(r=10);
|
|
// Example(2D): 2D Inset Cove Mask
|
|
// mask2d_cove(r=10,inset=3);
|
|
// Example: Masking by Edge Attachment
|
|
// diff("mask")
|
|
// cube([50,60,70],center=true)
|
|
// edge_profile([TOP,"Z"],except=[BACK,TOP+LEFT])
|
|
// mask2d_cove(r=10, inset=2);
|
|
module mask2d_cove(r, d, inset=0, excess, anchor=CENTER,spin=0) {
|
|
path = mask2d_cove(r=r,d=d,excess=excess,inset=inset);
|
|
attachable(anchor,spin, two_d=true, path=path) {
|
|
polygon(path);
|
|
children();
|
|
}
|
|
}
|
|
|
|
function mask2d_cove(r, d, inset=0, excess, anchor=CENTER,spin=0) =
|
|
assert(is_num(r)||is_num(d))
|
|
assert(is_undef(excess)||is_num(excess))
|
|
assert(is_num(inset)||(is_vector(inset)&&len(inset)==2))
|
|
let(
|
|
inset = is_list(inset)? inset : [inset,inset],
|
|
excess = default(excess,$overlap),
|
|
r = get_radius(r=r,d=d,dflt=1),
|
|
steps = quantup(segs(r),4)/4,
|
|
step = 90/steps,
|
|
path = [
|
|
[r+inset.x,-excess],
|
|
[-excess,-excess],
|
|
[-excess, r+inset.y],
|
|
for (i=[0:1:steps]) inset + polar_to_xy(r,90-i*step)
|
|
]
|
|
) reorient(anchor,spin, two_d=true, path=path, p=path);
|
|
|
|
|
|
// Function&Module: mask2d_chamfer()
|
|
// Usage:
|
|
// mask2d_chamfer(x|y|edge, [angle], [inset], [excess]);
|
|
// Description:
|
|
// Creates a 2D chamfer mask shape that is useful for extruding into a 3D mask for a 90º edge.
|
|
// This 2D mask is designed to be differenced away from the edge of a shape that is in the first (X+Y+) quadrant.
|
|
// If called as a function, this just returns a 2D path of the outline of the mask shape.
|
|
// Arguments:
|
|
// x = The width of the chamfer.
|
|
// y = The height of the chamfer.
|
|
// edge = The length of the edge of the chamfer.
|
|
// angle = The angle of the chamfer edge, away from vertical. Default: 45.
|
|
// inset = Optional amount to inset code from corner. Default: 0
|
|
// excess = Extra amount of mask shape to creates on the X- and Y- sides of the shape.
|
|
// Example(2D): 2D Chamfer Mask
|
|
// mask2d_chamfer(x=10);
|
|
// Example(2D): 2D Chamfer Mask by Width.
|
|
// mask2d_chamfer(x=10, angle=30);
|
|
// Example(2D): 2D Chamfer Mask by Height.
|
|
// mask2d_chamfer(y=10, angle=30);
|
|
// Example(2D): 2D Inset Chamfer Mask
|
|
// mask2d_chamfer(x=10, inset=2);
|
|
// Example: Masking by Edge Attachment
|
|
// diff("mask")
|
|
// cube([50,60,70],center=true)
|
|
// edge_profile([TOP,"Z"],except=[BACK,TOP+LEFT])
|
|
// mask2d_chamfer(x=10, inset=2);
|
|
module mask2d_chamfer(x, y, edge, angle=45, excess, inset=0, anchor=CENTER,spin=0) {
|
|
path = mask2d_chamfer(x=x, y=y, edge=edge, angle=angle, excess=excess, inset=inset);
|
|
attachable(anchor,spin, two_d=true, path=path, extent=true) {
|
|
polygon(path);
|
|
children();
|
|
}
|
|
}
|
|
|
|
function mask2d_chamfer(x, y, edge, angle=45, excess, inset=0, anchor=CENTER,spin=0) =
|
|
assert(num_defined([x,y,edge])==1)
|
|
assert(is_num(first_defined([x,y,edge])))
|
|
assert(is_num(angle))
|
|
assert(is_undef(excess)||is_num(excess))
|
|
assert(is_num(inset)||(is_vector(inset)&&len(inset)==2))
|
|
let(
|
|
inset = is_list(inset)? inset : [inset,inset],
|
|
excess = default(excess,$overlap),
|
|
x = !is_undef(x)? x :
|
|
!is_undef(y)? adj_ang_to_opp(adj=y,ang=angle) :
|
|
hyp_ang_to_opp(hyp=edge,ang=angle),
|
|
y = opp_ang_to_adj(opp=x,ang=angle),
|
|
path = [
|
|
[x+inset.x, -excess],
|
|
[-excess, -excess],
|
|
[-excess, y+inset.y],
|
|
[inset.x, y+inset.y],
|
|
[x+inset.x, inset.y]
|
|
]
|
|
) reorient(anchor,spin, two_d=true, path=path, extent=true, p=path);
|
|
|
|
|
|
// Function&Module: mask2d_rabbet()
|
|
// Usage:
|
|
// mask2d_rabbet(size, [excess]);
|
|
// Description:
|
|
// Creates a 2D rabbet mask shape that is useful for extruding into a 3D mask for a 90º edge.
|
|
// This 2D mask is designed to be differenced away from the edge of a shape that is in the first (X+Y+) quadrant.
|
|
// If called as a function, this just returns a 2D path of the outline of the mask shape.
|
|
// Arguments:
|
|
// size = The size of the rabbet, either as a scalar or an [X,Y] list.
|
|
// inset = Optional amount to inset code from corner. Default: 0
|
|
// excess = Extra amount of mask shape to creates on the X- and Y- sides of the shape.
|
|
// Example(2D): 2D Rabbet Mask
|
|
// mask2d_rabbet(size=10);
|
|
// Example(2D): 2D Asymmetrical Rabbet Mask
|
|
// mask2d_rabbet(size=[5,10]);
|
|
// Example: Masking by Edge Attachment
|
|
// diff("mask")
|
|
// cube([50,60,70],center=true)
|
|
// edge_profile([TOP,"Z"],except=[BACK,TOP+LEFT])
|
|
// mask2d_rabbet(size=10);
|
|
module mask2d_rabbet(size, excess, anchor=CENTER,spin=0) {
|
|
path = mask2d_rabbet(size=size, excess=excess);
|
|
attachable(anchor,spin, two_d=true, path=path, extent=false) {
|
|
polygon(path);
|
|
children();
|
|
}
|
|
}
|
|
|
|
function mask2d_rabbet(size, excess, anchor=CENTER,spin=0) =
|
|
assert(is_num(size)||(is_vector(size)&&len(size)==2))
|
|
assert(is_undef(excess)||is_num(excess))
|
|
let(
|
|
excess = default(excess,$overlap),
|
|
size = is_list(size)? size : [size,size],
|
|
path = [
|
|
[size.x, -excess],
|
|
[-excess, -excess],
|
|
[-excess, size.y],
|
|
size
|
|
]
|
|
) reorient(anchor,spin, two_d=true, path=path, extent=false, p=path);
|
|
|
|
|
|
// Function&Module: mask2d_dovetail()
|
|
// Usage:
|
|
// mask2d_dovetail(x|y|edge, [angle], [inset], [shelf], [excess]);
|
|
// Description:
|
|
// Creates a 2D dovetail mask shape that is useful for extruding into a 3D mask for a 90º edge.
|
|
// This 2D mask is designed to be differenced away from the edge of a shape that is in the first (X+Y+) quadrant.
|
|
// If called as a function, this just returns a 2D path of the outline of the mask shape.
|
|
// Arguments:
|
|
// x = The width of the dovetail.
|
|
// y = The height of the dovetail.
|
|
// edge = The length of the edge of the dovetail.
|
|
// angle = The angle of the chamfer edge, away from vertical. Default: 30.
|
|
// inset = Optional amount to inset code from corner. Default: 0
|
|
// shelf = The extra height to add to the inside corner of the dovetail. Default: 0
|
|
// excess = Extra amount of mask shape to creates on the X- and Y- sides of the shape.
|
|
// Example(2D): 2D Dovetail Mask
|
|
// mask2d_dovetail(x=10);
|
|
// Example(2D): 2D Dovetail Mask by Width.
|
|
// mask2d_dovetail(x=10, angle=30);
|
|
// Example(2D): 2D Dovetail Mask by Height.
|
|
// mask2d_dovetail(y=10, angle=30);
|
|
// Example(2D): 2D Inset Dovetail Mask
|
|
// mask2d_dovetail(x=10, inset=2);
|
|
// Example: Masking by Edge Attachment
|
|
// diff("mask")
|
|
// cube([50,60,70],center=true)
|
|
// edge_profile([TOP,"Z"],except=[BACK,TOP+LEFT])
|
|
// mask2d_dovetail(x=10, inset=2);
|
|
module mask2d_dovetail(x, y, edge, angle=30, inset=0, shelf=0, excess, anchor=CENTER, spin=0) {
|
|
path = mask2d_dovetail(x=x, y=y, edge=edge, angle=angle, inset=inset, shelf=shelf, excess=excess);
|
|
attachable(anchor,spin, two_d=true, path=path) {
|
|
polygon(path);
|
|
children();
|
|
}
|
|
}
|
|
|
|
function mask2d_dovetail(x, y, edge, angle=30, inset=0, shelf=0, excess, anchor=CENTER, spin=0) =
|
|
assert(num_defined([x,y,edge])==1)
|
|
assert(is_num(first_defined([x,y,edge])))
|
|
assert(is_num(angle))
|
|
assert(is_undef(excess)||is_num(excess))
|
|
assert(is_num(inset)||(is_vector(inset)&&len(inset)==2))
|
|
let(
|
|
inset = is_list(inset)? inset : [inset,inset],
|
|
excess = default(excess,$overlap),
|
|
x = !is_undef(x)? x :
|
|
!is_undef(y)? adj_ang_to_opp(adj=y,ang=angle) :
|
|
hyp_ang_to_opp(hyp=edge,ang=angle),
|
|
y = opp_ang_to_adj(opp=x,ang=angle),
|
|
path = [
|
|
[inset.x,0],
|
|
[-excess, 0],
|
|
[-excess, y+inset.y+shelf],
|
|
inset+[x,y+shelf],
|
|
inset+[x,y],
|
|
inset
|
|
]
|
|
) reorient(anchor,spin, two_d=true, path=path, p=path);
|
|
|
|
|
|
// Function&Module: mask2d_teardrop()
|
|
// Usage:
|
|
// mask2d_teardrop(r|d, [angle], [excess]);
|
|
// Description:
|
|
// Creates a 2D teardrop mask shape that is useful for extruding into a 3D mask for a 90º edge.
|
|
// This 2D mask is designed to be differenced away from the edge of a shape that is in the first (X+Y+) quadrant.
|
|
// If called as a function, this just returns a 2D path of the outline of the mask shape.
|
|
// This is particularly useful to make partially rounded bottoms, that don't need support to print.
|
|
// Arguments:
|
|
// r = Radius of the rounding.
|
|
// d = Diameter of the rounding.
|
|
// angle = The maximum angle from vertical.
|
|
// excess = Extra amount of mask shape to creates on the X- and Y- sides of the shape.
|
|
// Example(2D): 2D Teardrop Mask
|
|
// mask2d_teardrop(r=10);
|
|
// Example(2D): Using a Custom Angle
|
|
// mask2d_teardrop(r=10,angle=30);
|
|
// Example: Masking by Edge Attachment
|
|
// diff("mask")
|
|
// cube([50,60,70],center=true)
|
|
// edge_profile(BOT)
|
|
// mask2d_teardrop(r=10, angle=40);
|
|
function mask2d_teardrop(r,d,angle=45,excess=0.1,anchor=CENTER,spin=0) =
|
|
assert(is_num(angle))
|
|
assert(angle>0 && angle<90)
|
|
assert(is_num(excess))
|
|
let(
|
|
r = get_radius(r=r, d=d, dflt=1),
|
|
n = ceil(segs(r) * angle/360),
|
|
cp = [r,r],
|
|
tp = cp + polar_to_xy(r,180+angle),
|
|
bp = [tp.x+adj_ang_to_opp(tp.y,angle), 0],
|
|
step = angle/n,
|
|
path = [
|
|
bp, bp-[0,excess], [-excess,-excess], [-excess,r],
|
|
for (i=[0:1:n]) cp+polar_to_xy(r,180+i*step)
|
|
]
|
|
) reorient(anchor,spin, two_d=true, path=path, p=path);
|
|
|
|
module mask2d_teardrop(r,d,angle=45,excess=0.1,anchor=CENTER,spin=0) {
|
|
path = mask2d_teardrop(r=r, d=d, angle=angle, excess=excess);
|
|
attachable(anchor,spin, two_d=true, path=path) {
|
|
polygon(path);
|
|
children();
|
|
}
|
|
}
|
|
|
|
// Function&Module: mask2d_ogee()
|
|
// Usage:
|
|
// mask2d_ogee(pattern, [excess]);
|
|
//
|
|
// Description:
|
|
// Creates a 2D Ogee mask shape that is useful for extruding into a 3D mask for a 90º edge.
|
|
// This 2D mask is designed to be `difference()`d away from the edge of a shape that is in the first (X+Y+) quadrant.
|
|
// Since there are a number of shapes that fall under the name ogee, the shape of this mask is given as a pattern.
|
|
// Patterns are given as TYPE, VALUE pairs. ie: `["fillet",10, "xstep",2, "step",[5,5], ...]`. See Patterns below.
|
|
// If called as a function, this just returns a 2D path of the outline of the mask shape.
|
|
// .
|
|
// ### Patterns
|
|
// .
|
|
// Type | Argument | Description
|
|
// -------- | --------- | ----------------
|
|
// "step" | [x,y] | Makes a line to a point `x` right and `y` down.
|
|
// "xstep" | dist | Makes a `dist` length line towards X+.
|
|
// "ystep" | dist | Makes a `dist` length line towards Y-.
|
|
// "round" | radius | Makes an arc that will mask a roundover.
|
|
// "fillet" | radius | Makes an arc that will mask a fillet.
|
|
//
|
|
// Arguments:
|
|
// pattern = A list of pattern pieces to describe the Ogee.
|
|
// excess = Extra amount of mask shape to creates on the X- and Y- sides of the shape.
|
|
//
|
|
// Example(2D): 2D Ogee Mask
|
|
// mask2d_ogee([
|
|
// "xstep",1, "ystep",1, // Starting shoulder.
|
|
// "fillet",5, "round",5, // S-curve.
|
|
// "ystep",1, "xstep",1 // Ending shoulder.
|
|
// ]);
|
|
// Example: Masking by Edge Attachment
|
|
// diff("mask")
|
|
// cube([50,60,70],center=true)
|
|
// edge_profile(TOP)
|
|
// mask2d_ogee([
|
|
// "xstep",1, "ystep",1, // Starting shoulder.
|
|
// "fillet",5, "round",5, // S-curve.
|
|
// "ystep",1, "xstep",1 // Ending shoulder.
|
|
// ]);
|
|
module mask2d_ogee(pattern, excess, anchor=CENTER,spin=0) {
|
|
path = mask2d_ogee(pattern, excess=excess);
|
|
attachable(anchor,spin, two_d=true, path=path) {
|
|
polygon(path);
|
|
children();
|
|
}
|
|
}
|
|
|
|
function mask2d_ogee(pattern, excess, anchor=CENTER, spin=0) =
|
|
assert(is_list(pattern))
|
|
assert(len(pattern)>0)
|
|
assert(len(pattern)%2==0,"pattern must be a list of TYPE, VAL pairs.")
|
|
assert(all([for (i = idx(pattern,step=2)) in_list(pattern[i],["step","xstep","ystep","round","fillet"])]))
|
|
let(
|
|
excess = default(excess,$overlap),
|
|
x = concat([0], cumsum([
|
|
for (i=idx(pattern,step=2)) let(
|
|
type = pattern[i],
|
|
val = pattern[i+1]
|
|
) (
|
|
type=="step"? val.x :
|
|
type=="xstep"? val :
|
|
type=="round"? val :
|
|
type=="fillet"? val :
|
|
0
|
|
)
|
|
])),
|
|
y = concat([0], cumsum([
|
|
for (i=idx(pattern,step=2)) let(
|
|
type = pattern[i],
|
|
val = pattern[i+1]
|
|
) (
|
|
type=="step"? val.y :
|
|
type=="ystep"? val :
|
|
type=="round"? val :
|
|
type=="fillet"? val :
|
|
0
|
|
)
|
|
])),
|
|
tot_x = select(x,-1),
|
|
tot_y = select(y,-1),
|
|
data = [
|
|
for (i=idx(pattern,step=2)) let(
|
|
type = pattern[i],
|
|
val = pattern[i+1],
|
|
pt = [x[i/2], tot_y-y[i/2]] + (
|
|
type=="step"? [val.x,-val.y] :
|
|
type=="xstep"? [val,0] :
|
|
type=="ystep"? [0,-val] :
|
|
type=="round"? [val,0] :
|
|
type=="fillet"? [0,-val] :
|
|
[0,0]
|
|
)
|
|
) [type, val, pt]
|
|
],
|
|
path = [
|
|
[tot_x,-excess],
|
|
[-excess,-excess],
|
|
[-excess,tot_y],
|
|
for (pat = data) each
|
|
pat[0]=="step"? [pat[2]] :
|
|
pat[0]=="xstep"? [pat[2]] :
|
|
pat[0]=="ystep"? [pat[2]] :
|
|
let(
|
|
r = pat[1],
|
|
steps = segs(abs(r)),
|
|
step = 90/steps
|
|
) [
|
|
for (i=[0:1:steps]) let(
|
|
a = pat[0]=="round"? (180+i*step) : (90-i*step)
|
|
) pat[2] + abs(r)*[cos(a),sin(a)]
|
|
]
|
|
],
|
|
path2 = deduplicate(path)
|
|
) reorient(anchor,spin, two_d=true, path=path2, p=path2);
|
|
|
|
|
|
|
|
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
|