BOSL2/drawing.scad
Adrian Mariano 7da26d32cd arc() bugfix
2024-09-28 08:44:14 -04:00

1380 lines
70 KiB
OpenSCAD

//////////////////////////////////////////////////////////////////////
// LibFile: drawing.scad
// This file includes stroke(), which converts a path into a
// geometric object, like drawing with a pen. It even works on
// three-dimensional paths. You can make a dashed line or add arrow
// heads. The turtle() function provides a turtle graphics style
// approach for producing paths. The arc() function produces arc paths,
// and helix() produces helical paths.
// Includes:
// include <BOSL2/std.scad>
// FileGroup: Basic Modeling
// FileSummary: Create and draw 2D and 3D paths: arc, helix, turtle graphics
// FileFootnotes: STD=Included in std.scad
//////////////////////////////////////////////////////////////////////
// Section: Line Drawing
// Module: stroke()
// Synopsis: Draws a line along a path or region boundry.
// SynTags: Geom
// Topics: Paths (2D), Paths (3D), Drawing Tools
// See Also: dashed_stroke(), offset_stroke(), path_sweep()
// Usage:
// stroke(path, [width], [closed], [endcaps], [endcap_width], [endcap_length], [endcap_extent], [trim]);
// stroke(path, [width], [closed], [endcap1], [endcap2], [endcap_width1], [endcap_width2], [endcap_length1], [endcap_length2], [endcap_extent1], [endcap_extent2], [trim1], [trim2]);
// Description:
// Draws a 2D or 3D path with a given line width. Joints and each endcap can be replaced with
// various marker shapes, and can be assigned different colors. If passed a region instead of
// a path, draws each path in the region as a closed polygon by default. If `closed=false` is
// given with a region or list of paths, then each path is drawn without the closing line segment.
// When drawing a closed path or region, there are no endcaps, so you cannot give the endcap parameters.
// To facilitate debugging, stroke() accepts "paths" that have a single point. These are drawn with
// the style of endcap1, but have their own scale parameter, `singleton_scale`, which defaults to 2
// so that singleton dots with endcap "round" are clearly visible.
// .
// In 2d the stroke module works by creating a sequence of rectangles (or trapezoids if line width varies) and
// filling in the gaps with rounded wedges. This is fast and produces a good result. In 3d the modules
// creates a cylinders (or cones) and fills the gaps with rounded wedges made using rotate_extrude. This process will be slow for
// long paths due to the 3d unions, and the faces on sequential cylinders may not line up. In many cases, {{path_sweep()}} will be
// a better choice, both running faster and producing superior output, when working in three dimensions.
// Figure(Med,NoAxes,2D,VPR=[0,0,0],VPD=250): Endcap Types
// cap_pairs = [
// ["butt", "chisel" ],
// ["round", "square" ],
// ["line", "cross" ],
// ["x", "diamond"],
// ["dot", "block" ],
// ["tail", "arrow" ],
// ["tail2", "arrow2" ]
// ];
// for (i = idx(cap_pairs)) {
// fwd((i-len(cap_pairs)/2+0.5)*13) {
// stroke([[-20,0], [20,0]], width=3, endcap1=cap_pairs[i][0], endcap2=cap_pairs[i][1]);
// color("black") {
// stroke([[-20,0], [20,0]], width=0.25, endcaps=false);
// left(28) text(text=cap_pairs[i][0], size=5, halign="right", valign="center");
// right(28) text(text=cap_pairs[i][1], size=5, halign="left", valign="center");
// }
// }
// }
// Arguments:
// path = The path to draw along.
// 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.
// closed = If true, draw an additional line from the end of the path to the start.
// joints = Specifies the joint shape for each joint of the line. If a 2D polygon is given, use that to draw custom joints.
// endcaps = Specifies the endcap type for both ends of the line. If a 2D polygon is given, use that to draw custom endcaps.
// endcap1 = Specifies the endcap type for the start of the line. If a 2D polygon is given, use that to draw a custom endcap.
// endcap2 = Specifies the endcap type for the end of the line. If a 2D polygon is given, use that to draw a custom endcap.
// dots = Specifies both the endcap and joint types with one argument. If given `true`, sets both to "dot". If a 2D polygon is given, uses that to draw custom dots.
// joint_width = Some joint shapes are wider than the line. This specifies the width of the shape, in multiples of the line width.
// endcap_width = Some endcap types are wider than the line. This specifies the size of endcaps, in multiples of the line width.
// endcap_width1 = This specifies the size of starting endcap, in multiples of the line width.
// endcap_width2 = This specifies the size of ending endcap, in multiples of the line width.
// dots_width = This specifies the size of the joints and endcaps, in multiples of the line width.
// joint_length = Length of joint shape, in multiples of the line width.
// endcap_length = Length of endcaps, in multiples of the line width.
// endcap_length1 = Length of starting endcap, in multiples of the line width.
// endcap_length2 = Length of ending endcap, in multiples of the line width.
// dots_length = Length of both joints and endcaps, in multiples of the line width.
// joint_extent = Extents length of joint shape, in multiples of the line width.
// endcap_extent = Extents length of endcaps, in multiples of the line width.
// endcap_extent1 = Extents length of starting endcap, in multiples of the line width.
// endcap_extent2 = Extents length of ending endcap, in multiples of the line width.
// dots_extent = Extents length of both joints and endcaps, in multiples of the line width.
// joint_angle = Extra rotation given to joint shapes, in degrees. If not given, the shapes are fully spun (for 3D lines).
// endcap_angle = Extra rotation given to endcaps, in degrees. If not given, the endcaps are fully spun (for 3D lines).
// endcap_angle1 = Extra rotation given to a starting endcap, in degrees. If not given, the endcap is fully spun (for 3D lines).
// endcap_angle2 = Extra rotation given to a ending endcap, in degrees. If not given, the endcap is fully spun (for 3D lines).
// dots_angle = Extra rotation given to both joints and endcaps, in degrees. If not given, the endcap is fully spun (for 3D lines).
// trim = Trim the the start and end line segments by this much, to keep them from interfering with custom endcaps.
// trim1 = Trim the the starting line segment by this much, to keep it from interfering with a custom endcap.
// trim2 = Trim the the ending line segment by this much, to keep it from interfering with a custom endcap.
// color = If given, sets the color of the line segments, joints and endcap.
// endcap_color = If given, sets the color of both endcaps. Overrides `color=` and `dots_color=`.
// endcap_color1 = If give, sets the color of the starting endcap. Overrides `color=`, `dots_color=`, and `endcap_color=`.
// endcap_color2 = If given, sets the color of the ending endcap. Overrides `color=`, `dots_color=`, and `endcap_color=`.
// joint_color = If given, sets the color of the joints. Overrides `color=` and `dots_color=`.
// dots_color = If given, sets the color of the endcaps and joints. Overrides `color=`.
// singleton_scale = Change the scale of the endcap shape drawn for singleton paths. Default: 2.
// convexity = Max number of times a line could intersect a wall of an endcap.
// Example(2D): Drawing a Path
// path = [[0,100], [100,100], [200,0], [100,-100], [100,0]];
// stroke(path, width=20);
// Example(2D): Closing a Path
// path = [[0,100], [100,100], [200,0], [100,-100], [100,0]];
// stroke(path, width=20, closed=true);
// Example(2D): Fancy Arrow Endcaps
// path = [[0,100], [100,100], [200,0], [100,-100], [100,0]];
// stroke(path, width=10, endcaps="arrow2");
// Example(2D): Modified Fancy Arrow Endcaps
// path = [[0,100], [100,100], [200,0], [100,-100], [100,0]];
// stroke(path, width=10, endcaps="arrow2", endcap_width=6, endcap_length=3, endcap_extent=2);
// Example(2D): Mixed Endcaps
// path = [[0,100], [100,100], [200,0], [100,-100], [100,0]];
// stroke(path, width=10, endcap1="tail2", endcap2="arrow2");
// Example(2D): Plotting Points. Setting endcap_angle to zero results in the weird arrow orientation.
// path = [for (a=[0:30:360]) [a-180, 60*sin(a)]];
// stroke(path, width=3, joints="diamond", endcaps="arrow2", endcap_angle=0, endcap_width=5, joint_angle=0, joint_width=5);
// Example(2D): Default joint gives curves along outside corners of the path:
// stroke([square(40)], width=18);
// Example(2D): Setting `joints="square"` gives flat outside corners
// stroke([square(40)], width=18, joints="square");
// Example(2D): Setting `joints="butt"` does not draw any transitions, just rectangular strokes for each segment, meeting at their centers:
// stroke([square(40)], width=18, joints="butt");
// Example(2D): Joints and Endcaps
// path = [for (a=[0:30:360]) [a-180, 60*sin(a)]];
// stroke(path, width=8, joints="dot", endcaps="arrow2");
// Example(2D): Custom Endcap Shapes
// path = [[0,100], [100,100], [200,0], [100,-100], [100,0]];
// 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]];
// stroke(path, width=10, trim=3.5, endcaps=arrow);
// Example(2D): Variable Line Width
// path = circle(d=50,$fn=18);
// widths = [for (i=idx(path)) 10*i/len(path)+2];
// stroke(path,width=widths,$fa=1,$fs=1);
// Example: 3D Path with Endcaps
// path = rot([15,30,0], p=path3d(pentagon(d=50)));
// stroke(path, width=2, endcaps="arrow2", $fn=18);
// Example: 3D Path with Flat Endcaps
// path = rot([15,30,0], p=path3d(pentagon(d=50)));
// stroke(path, width=2, endcaps="arrow2", endcap_angle=0, $fn=18);
// Example: 3D Path with Mixed Endcaps
// path = rot([15,30,0], p=path3d(pentagon(d=50)));
// stroke(path, width=2, endcap1="arrow2", endcap2="tail", endcap_angle2=0, $fn=18);
// Example: 3D Path with Joints and Endcaps
// path = [for (i=[0:10:360]) [(i-180)/2,20*cos(3*i),20*sin(3*i)]];
// stroke(path, width=2, joints="dot", endcap1="round", endcap2="arrow2", joint_width=2.0, endcap_width2=3, $fn=18);
// Example: Coloring Lines, Joints, and Endcaps
// path = [for (i=[0:15:360]) [(i-180)/3,20*cos(2*i),20*sin(2*i)]];
// stroke(
// path, width=2, joints="dot", endcap1="dot", endcap2="arrow2",
// color="lightgreen", joint_color="red", endcap_color="blue",
// joint_width=2.0, endcap_width2=3, $fn=18
// );
// Example(2D): Simplified Plotting
// path = [for (i=[0:15:360]) [(i-180)/3,20*cos(2*i)]];
// stroke(path, width=2, dots=true, color="lightgreen", dots_color="red", $fn=18);
// Example(2D): Drawing a Region
// rgn = [square(100,center=true), circle(d=60,$fn=18)];
// stroke(rgn, width=2);
// Example(2D): Drawing a List of Lines
// paths = [
// for (y=[-60:60:60]) [
// for (a=[-180:15:180])
// [a, 2*y+60*sin(a+y)]
// ]
// ];
// stroke(paths, closed=false, width=5);
// Example(2D): Paths with a singleton. Note that the singleton is not a single point, but a list containing a single point.
// stroke([
// [[0,0],[1,1]],
// [[1.5,1.5]],
// [[2,2],[3,3]]
// ],width=0.2,closed=false,$fn=16);
function stroke(
path, width=1, closed,
endcaps, endcap1, endcap2, joints, dots,
endcap_width, endcap_width1, endcap_width2, joint_width, dots_width,
endcap_length, endcap_length1, endcap_length2, joint_length, dots_length,
endcap_extent, endcap_extent1, endcap_extent2, joint_extent, dots_extent,
endcap_angle, endcap_angle1, endcap_angle2, joint_angle, dots_angle,
endcap_color, endcap_color1, endcap_color2, joint_color, dots_color, color,
trim, trim1, trim2, singleton_scale=2,
convexity=10
) = no_function("stroke");
module stroke(
path, width=1, closed,
endcaps, endcap1, endcap2, joints, dots,
endcap_width, endcap_width1, endcap_width2, joint_width, dots_width,
endcap_length, endcap_length1, endcap_length2, joint_length, dots_length,
endcap_extent, endcap_extent1, endcap_extent2, joint_extent, dots_extent,
endcap_angle, endcap_angle1, endcap_angle2, joint_angle, dots_angle,
endcap_color, endcap_color1, endcap_color2, joint_color, dots_color, color,
trim, trim1, trim2, singleton_scale=2,
convexity=10
) {
no_children($children);
module setcolor(clr) {
if (clr==undef) {
children();
} else {
color(clr) children();
}
}
function _shape_defaults(cap) =
cap==undef? [1.00, 0.00, 0.00] :
cap==false? [1.00, 0.00, 0.00] :
cap==true? [1.00, 1.00, 0.00] :
cap=="butt"? [1.00, 0.00, 0.00] :
cap=="round"? [1.00, 1.00, 0.00] :
cap=="chisel"? [1.00, 1.00, 0.00] :
cap=="square"? [1.00, 1.00, 0.00] :
cap=="block"? [2.00, 1.00, 0.00] :
cap=="diamond"? [2.50, 1.00, 0.00] :
cap=="dot"? [2.00, 1.00, 0.00] :
cap=="x"? [2.50, 0.40, 0.00] :
cap=="cross"? [3.00, 0.33, 0.00] :
cap=="line"? [3.50, 0.22, 0.00] :
cap=="arrow"? [3.50, 0.40, 0.50] :
cap=="arrow2"? [3.50, 1.00, 0.14] :
cap=="tail"? [3.50, 0.47, 0.50] :
cap=="tail2"? [3.50, 0.28, 0.50] :
is_path(cap)? [0.00, 0.00, 0.00] :
assert(false, str("Invalid cap or joint: ",cap));
function _shape_path(cap,linewidth,w,l,l2) = (
cap=="butt" || cap==false || cap==undef ? [] :
cap=="round" || cap==true ? scale([w,l], p=circle(d=1, $fn=max(8, segs(w/2)))) :
cap=="chisel"? scale([w,l], p=circle(d=1,$fn=4)) :
cap=="diamond"? circle(d=w,$fn=4) :
cap=="square"? scale([w,l], p=square(1,center=true)) :
cap=="block"? scale([w,l], p=square(1,center=true)) :
cap=="dot"? circle(d=w, $fn=max(12, segs(w*3/2))) :
cap=="x"? [for (a=[0:90:270]) each rot(a,p=[[w+l/2,w-l/2]/2, [w-l/2,w+l/2]/2, [0,l/2]]) ] :
cap=="cross"? [for (a=[0:90:270]) each rot(a,p=[[l,w]/2, [-l,w]/2, [-l,l]/2]) ] :
cap=="line"? scale([w,l], p=square(1,center=true)) :
cap=="arrow"? [[0,0], [w/2,-l2], [w/2,-l2-l], [0,-l], [-w/2,-l2-l], [-w/2,-l2]] :
cap=="arrow2"? [[0,0], [w/2,-l2-l], [0,-l], [-w/2,-l2-l]] :
cap=="tail"? [[0,0], [w/2,l2], [w/2,l2-l], [0,-l], [-w/2,l2-l], [-w/2,l2]] :
cap=="tail2"? [[w/2,0], [w/2,-l], [0,-l-l2], [-w/2,-l], [-w/2,0]] :
is_path(cap)? cap :
assert(false, str("Invalid endcap: ",cap))
) * linewidth;
closed = default(closed, is_region(path));
check1 = assert(is_bool(closed))
assert(!closed || num_defined([endcaps,endcap1,endcap2])==0, "Cannot give endcap parameter(s) with closed path or region");
dots = dots==true? "dot" : dots;
endcap1 = first_defined([endcap1, endcaps, dots, "round"]);
endcap2 = first_defined([endcap2, endcaps, if (!closed) dots, "round"]);
joints = first_defined([joints, dots, "round"]);
check2 =
assert(is_bool(endcap1) || is_string(endcap1) || is_path(endcap1))
assert(is_bool(endcap2) || is_string(endcap2) || is_path(endcap2))
assert(is_bool(joints) || is_string(joints) || is_path(joints));
endcap1_dflts = _shape_defaults(endcap1);
endcap2_dflts = _shape_defaults(endcap2);
joint_dflts = _shape_defaults(joints);
endcap_width1 = first_defined([endcap_width1, endcap_width, dots_width, endcap1_dflts[0]]);
endcap_width2 = first_defined([endcap_width2, endcap_width, dots_width, endcap2_dflts[0]]);
joint_width = first_defined([joint_width, dots_width, joint_dflts[0]]);
endcap_length1 = first_defined([endcap_length1, endcap_length, dots_length, endcap1_dflts[1]*endcap_width1]);
endcap_length2 = first_defined([endcap_length2, endcap_length, dots_length, endcap2_dflts[1]*endcap_width2]);
joint_length = first_defined([joint_length, dots_length, joint_dflts[1]*joint_width]);
endcap_extent1 = first_defined([endcap_extent1, endcap_extent, dots_extent, endcap1_dflts[2]*endcap_width1]);
endcap_extent2 = first_defined([endcap_extent2, endcap_extent, dots_extent, endcap2_dflts[2]*endcap_width2]);
joint_extent = first_defined([joint_extent, dots_extent, joint_dflts[2]*joint_width]);
endcap_angle1 = first_defined([endcap_angle1, endcap_angle, dots_angle]);
endcap_angle2 = first_defined([endcap_angle2, endcap_angle, dots_angle]);
joint_angle = first_defined([joint_angle, dots_angle]);
check3 =
assert(all_nonnegative([endcap_length1]))
assert(all_nonnegative([endcap_length2]))
assert(all_nonnegative([joint_length]));
assert(all_nonnegative([endcap_extent1]))
assert(all_nonnegative([endcap_extent2]))
assert(all_nonnegative([joint_extent]));
assert(is_undef(endcap_angle1)||is_finite(endcap_angle1))
assert(is_undef(endcap_angle2)||is_finite(endcap_angle2))
assert(is_undef(joint_angle)||is_finite(joint_angle))
assert(all_positive([singleton_scale]))
assert(all_positive(width));
endcap_color1 = first_defined([endcap_color1, endcap_color, dots_color, color]);
endcap_color2 = first_defined([endcap_color2, endcap_color, dots_color, color]);
joint_color = first_defined([joint_color, dots_color, color]);
// We want to allow "paths" with length 1, so we can't use the normal path/region checks
paths = is_matrix(path) ? [path] : path;
assert(is_list(paths),"The path argument must be a list of 2D or 3D points, or a region.");
attachable(){
for (path = paths) {
pathvalid = is_path(path,[2,3]) || same_shape(path,[[0,0]]) || same_shape(path,[[0,0,0]]);
assert(pathvalid,"The path argument must be a list of 2D or 3D points, or a region.");
check4 = assert(is_num(width) || len(width)==len(path),
"width must be a number or a vector the same length as the path (or all components of a region)");
path = deduplicate( closed? list_wrap(path) : path );
width = is_num(width)? [for (x=path) width]
: closed? list_wrap(width)
: width;
check4a=assert(len(width)==len(path), "path had duplicated points and width was given as a list: this is not allowd");
endcap_shape1 = _shape_path(endcap1, width[0], endcap_width1, endcap_length1, endcap_extent1);
endcap_shape2 = _shape_path(endcap2, last(width), endcap_width2, endcap_length2, endcap_extent2);
trim1 = width[0] * first_defined([
trim1, trim,
(endcap1=="arrow")? endcap_length1-0.01 :
(endcap1=="arrow2")? endcap_length1*3/4 :
0
]);
trim2 = last(width) * first_defined([
trim2, trim,
(endcap2=="arrow")? endcap_length2-0.01 :
(endcap2=="arrow2")? endcap_length2*3/4 :
0
]);
check10 = assert(is_finite(trim1))
assert(is_finite(trim2));
if (len(path) == 1) {
if (len(path[0]) == 2) {
// Endcap1
setcolor(endcap_color1) {
translate(path[0]) {
mat = is_undef(endcap_angle1)? ident(3) : zrot(endcap_angle1);
multmatrix(mat) polygon(scale(singleton_scale,endcap_shape1));
}
}
} else {
// Endcap1
setcolor(endcap_color1) {
translate(path[0]) {
$fn = segs(width[0]/2);
if (is_undef(endcap_angle1)) {
rotate_extrude(convexity=convexity) {
right_half(planar=true) {
polygon(endcap_shape1);
}
}
} else {
rotate([90,0,endcap_angle1]) {
linear_extrude(height=max(widths[0],0.001), center=true, convexity=convexity) {
polygon(endcap_shape1);
}
}
}
}
}
}
} else {
dummy=assert(trim1<path_length(path)-trim2, "Path is too short for endcap(s). Try a smaller width, or set endcap_length to a smaller value.");
// This section shortens the path to allow room for the specified endcaps. Note that if
// the path is closed, there are not endcaps, so we don't shorten the path, but in that case we
// duplicate entry 1 so that the path wraps around a little more and we can correctly create all the joints.
// (Why entry 1? Because entry 0 was already duplicated by a list_wrap() call.)
pathcut = path_cut_points(path, [trim1, path_length(path)-trim2], closed=false);
pathcut_su = _cut_to_seg_u_form(pathcut,path);
path2 = closed ? [each path, path[1]]
: _path_cut_getpaths(path, pathcut, closed=false)[1];
widths = closed ? [each width, width[1]]
: _path_select(width, pathcut_su[0][0], pathcut_su[0][1], pathcut_su[1][0], pathcut_su[1][1]);
start_vec = path[0] - path[1];
end_vec = last(path) - select(path,-2);
if (len(path[0]) == 2) { // Two dimensional case
// Straight segments
setcolor(color) {
for (i = idx(path2,e=-2)) {
seg = select(path2,i,i+1);
delt = seg[1] - seg[0];
translate(seg[0]) {
rot(from=BACK,to=delt) {
trapezoid(w1=widths[i], w2=widths[i+1], h=norm(delt), anchor=FRONT);
}
}
}
}
// Joints
setcolor(joint_color) {
for (i = [1:1:len(path2)-2]) {
$fn = quantup(segs(widths[i]/2),4);
translate(path2[i]) {
if (joints != undef && joints != "round" && joints != "square") {
joint_shape = _shape_path(
joints, widths[i],
joint_width,
joint_length,
joint_extent
);
v1 = unit(path2[i] - path2[i-1]);
v2 = unit(path2[i+1] - path2[i]);
mat = is_undef(joint_angle)
? rot(from=BACK,to=v1)
: zrot(joint_angle);
multmatrix(mat) polygon(joint_shape);
} else {
// These are parallel to the path
v1 = path2[i] - path2[i-1];
v2 = path2[i+1] - path2[i];
ang = modang(v_theta(v2) - v_theta(v1));
// Need 90 deg offset to make wedge perpendicular to path, and the wedge
// position depends on whether we turn left (ang<0) or right (ang>0)
theta = v_theta(v1) - sign(ang)*90;
if (!approx(ang,0)){
// This section creates a rounded wedge to fill in gaps. The wedge needs to be oversized for overlap
// in all directions, including its apex, but not big enough to create artifacts.
// The core of the wedge is the proper arc we need to create. We then add side points based
// on firstang and secondang, where we try 1 degree, but if that appears too big we based it
// on the segment length. We pick the radius based on the smaller of the width at this point
// and the adjacent width, which could be much smaller---meaning that we need a much smaller radius.
// The apex offset we pick to be simply based on the width at this point.
firstang = sign(ang)*min(1,0.5*norm(v1)/PI/widths[i]*360);
secondang = sign(ang)*min(1,0.5*norm(v2)/PI/widths[i]*360);
firstR = 0.5*min(widths[i], lerp(widths[i],widths[i-1], abs(firstang)*PI*widths[i]/360/norm(v1)));
secondR = 0.5*min(widths[i], lerp(widths[i],widths[i+1], abs(secondang)*PI*widths[i]/360/norm(v2)));
apex_offset = widths[i]/10;
arcpath = [
firstR*[cos(theta-firstang), sin(theta-firstang)],
each arc(d=widths[i], angle=[theta, theta+ang],n=joints=="square"?2:undef),
secondR*[cos(theta+ang+secondang), sin(theta+ang+secondang)],
-apex_offset*[cos(theta+ang/2), sin(theta+ang/2)]
];
polygon(arcpath);
}
}
}
}
}
if (!closed){
// Endcap1
setcolor(endcap_color1) {
translate(path[0]) {
mat = is_undef(endcap_angle1)? rot(from=BACK,to=start_vec) :
zrot(endcap_angle1);
multmatrix(mat) polygon(endcap_shape1);
}
}
// Endcap2
setcolor(endcap_color2) {
translate(last(path)) {
mat = is_undef(endcap_angle2)? rot(from=BACK,to=end_vec) :
zrot(endcap_angle2);
multmatrix(mat) polygon(endcap_shape2);
}
}
}
} else { // Three dimensional case
rotmats = cumprod([
for (i = idx(path2,e=-2)) let(
vec1 = i==0? UP : unit(path2[i]-path2[i-1], UP),
vec2 = unit(path2[i+1]-path2[i], UP)
) rot(from=vec1,to=vec2)
]);
sides = [
for (i = idx(path2,e=-2))
quantup(segs(max(widths[i],widths[i+1])/2),4)
];
// Straight segments
setcolor(color) {
for (i = idx(path2,e=-2)) {
dist = norm(path2[i+1] - path2[i]);
w1 = widths[i]/2;
w2 = widths[i+1]/2;
$fn = sides[i];
translate(path2[i]) {
multmatrix(rotmats[i]) {
cylinder(r1=w1, r2=w2, h=dist, center=false);
}
}
}
}
// Joints
setcolor(joint_color) {
for (i = [1:1:len(path2)-2]) {
$fn = sides[i];
translate(path2[i]) {
if (joints != undef && joints != "round") {
joint_shape = _shape_path(
joints, width[i],
joint_width,
joint_length,
joint_extent
);
multmatrix(rotmats[i] * xrot(180)) {
$fn = sides[i];
if (is_undef(joint_angle)) {
rotate_extrude(convexity=convexity) {
right_half(planar=true) {
polygon(joint_shape);
}
}
} else {
rotate([90,0,joint_angle]) {
linear_extrude(height=max(widths[i],0.001), center=true, convexity=convexity) {
polygon(joint_shape);
}
}
}
}
} else {
corner = select(path2,i-1,i+1);
axis = vector_axis(corner);
ang = vector_angle(corner);
if (!approx(ang,0)) {
frame_map(x=path2[i-1]-path2[i], z=-axis) {
zrot(90-0.5) {
rotate_extrude(angle=180-ang+1) {
arc(d=widths[i], start=-90, angle=180);
}
}
}
}
}
}
}
}
if (!closed){
// Endcap1
setcolor(endcap_color1) {
translate(path[0]) {
multmatrix(rotmats[0] * xrot(180)) {
$fn = sides[0];
if (is_undef(endcap_angle1)) {
rotate_extrude(convexity=convexity) {
right_half(planar=true) {
polygon(endcap_shape1);
}
}
} else {
rotate([90,0,endcap_angle1]) {
linear_extrude(height=max(widths[0],0.001), center=true, convexity=convexity) {
polygon(endcap_shape1);
}
}
}
}
}
}
// Endcap2
setcolor(endcap_color2) {
translate(last(path)) {
multmatrix(last(rotmats)) {
$fn = last(sides);
if (is_undef(endcap_angle2)) {
rotate_extrude(convexity=convexity) {
right_half(planar=true) {
polygon(endcap_shape2);
}
}
} else {
rotate([90,0,endcap_angle2]) {
linear_extrude(height=max(last(widths),0.001), center=true, convexity=convexity) {
polygon(endcap_shape2);
}
}
}
}
}
}
}
}
}
}
union();
}
}
// Function&Module: dashed_stroke()
// Synopsis: Draws a dashed line along a path or region boundry.
// SynTags: Geom, PathList
// Topics: Paths, Drawing Tools
// See Also: stroke(), path_cut()
// Usage: As a Module
// dashed_stroke(path, dashpat, [width=], [closed=]);
// Usage: As a Function
// dashes = dashed_stroke(path, dashpat, [closed=]);
// Description:
// Given a path (or region) and a dash pattern, creates a dashed line that follows that
// path or region boundary with the given dash pattern.
// - When called as a function, returns a list of dash sub-paths.
// - When called as a module, draws all those subpaths using `stroke()`.
// .
// When called as a module the dash pattern is multiplied by the line width. When called as
// a function the dash pattern applies as you specify it.
// Arguments:
// path = The path or region to subdivide into dashes.
// dashpat = A list of alternating dash lengths and space lengths for the dash pattern. This will be scaled by the width of the line.
// ---
// width = The width of the dashed line to draw. Module only. Default: 1
// closed = If true, treat path as a closed polygon. Default: false
// fit = If true, shrink or stretch the dash pattern so that the path ends ofter a logical dash. Default: true
// roundcaps = (Module only) If true, draws dashes with rounded caps. This often looks better. Default: true
// mindash = (Function only) Specifies the minimal dash length to return at the end of a path when fit is false. Default: 0.5
// Example(2D): Open Path
// path = [for (a=[-180:10:180]) [a/3,20*sin(a)]];
// dashed_stroke(path, [3,2], width=1);
// Example(2D): Closed Polygon
// path = circle(d=100,$fn=72);
// dashpat = [10,2, 3,2, 3,2];
// dashed_stroke(path, dashpat, width=1, closed=true);
// Example(FlatSpin,VPD=250): 3D Dashed Path
// path = [for (a=[-180:5:180]) [a/3, 20*cos(3*a), 20*sin(3*a)]];
// dashed_stroke(path, [3,2], width=1);
function dashed_stroke(path, dashpat=[3,3], closed=false, fit=true, mindash=0.5) =
is_region(path) ? [
for (p = path)
each dashed_stroke(p, dashpat, closed=true, fit=fit)
] :
let(
path = closed? list_wrap(path) : path,
dashpat = len(dashpat)%2==0? dashpat : concat(dashpat,[0]),
plen = path_length(path),
dlen = sum(dashpat),
doff = cumsum(dashpat),
freps = plen / dlen,
reps = max(1, fit? round(freps) : floor(freps)),
tlen = !fit? plen :
reps * dlen + (closed? 0 : dashpat[0]),
sc = plen / tlen,
cuts = [
for (i = [0:1:reps], off = doff*sc)
let (x = i*dlen*sc + off)
if (x > 0 && x < plen-EPSILON) x
],
dashes = path_cut(path, cuts, closed=false),
dcnt = len(dashes),
evens = [
for (i = idx(dashes))
if (i % 2 == 0)
let( dash = dashes[i] )
if (i < dcnt-1 || path_length(dash) > mindash)
dashes[i]
]
) evens;
module dashed_stroke(path, dashpat=[3,3], width=1, closed=false, fit=true, roundcaps=false) {
no_children($children);
segs = dashed_stroke(path, dashpat=dashpat*width, closed=closed, fit=fit, mindash=0.5*width);
for (seg = segs)
stroke(seg, width=width, endcaps=roundcaps? "round" : false);
}
// Section: Computing paths
// Function&Module: arc()
// Synopsis: Draws a 2D pie-slice or returns 2D or 3D path forming an arc.
// SynTags: Geom, Path
// Topics: Paths (2D), Paths (3D), Shapes (2D), Path Generators
// See Also: pie_slice(), stroke(), ring()
//
// Usage: 2D arc from 0º to `angle` degrees.
// path=arc(n, r|d=, angle);
// Usage: 2D arc from START to END degrees.
// path=arc(n, r|d=, angle=[START,END]);
// Usage: 2D arc from `start` to `start+angle` degrees.
// path=arc(n, r|d=, start=, angle=);
// Usage: 2D circle segment by `width` and `thickness`, starting and ending on the X axis.
// path=arc(n, width=, thickness=);
// Usage: Shortest 2D or 3D arc around centerpoint `cp`, starting at P0 and ending on the vector pointing from `cp` to `P1`.
// path=arc(n, cp=, points=[P0,P1], [long=], [cw=], [ccw=]);
// Usage: 2D or 3D arc, starting at `P0`, passing through `P1` and ending at `P2`.
// path=arc(n, points=[P0,P1,P2]);
// Usage: 2D or 3D arc, fron tangent point on segment `[P0,P1]` to the tangent point on segment `[P1,P2]`.
// path=arc(n, corner=[P0,P1,P2], r=);
// Usage: Create a wedge using any other arc parameters
// path=arc(wedge=true,...)
// Usage: as module
// arc(...) [ATTACHMENTS];
// Description:
// If called as a function, returns a 2D or 3D path forming an arc. If `wedge` is true, the centerpoint of the arc appears as the first point in the result.
// If called as a module, creates a 2D arc polygon or pie slice shape.
// Arguments:
// n = Number of vertices to form the arc curve from.
// r = Radius of the arc.
// 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.
// ---
// d = Diameter of the arc.
// cp = Centerpoint of arc.
// points = Points on the arc.
// corner = A path of two segments to fit an arc tangent to.
// long = if given with cp and points takes the long arc instead of the default short arc. Default: false
// cw = if given with cp and 2 points takes the arc in the clockwise direction. Default: false
// ccw = if given with cp and 2 points takes the arc in the counter-clockwise direction. Default: false
// width = If given with `thickness`, arc starts and ends on X axis, to make a circle segment.
// thickness = If given with `width`, arc starts and ends on X axis, to make a circle segment.
// start = Start angle of arc. Default: 0
// wedge = If true, include centerpoint `cp` in output to form pie slice shape. Default: false
// endpoint = If false exclude the last point (function only). Default: true
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). (Module only) Default: `CENTER`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#subsection-spin). (Module only) Default: `0`
// Examples(2D):
// arc(n=4, r=30, angle=30, wedge=true);
// arc(r=30, angle=30, wedge=true);
// arc(d=60, angle=30, wedge=true);
// arc(d=60, angle=120);
// 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);
// Example(2D): Fit to three points.
// 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,VPD=175):
// path = arc(points=[[0,30,0],[0,0,30],[30,0,0]]);
// stroke(path, dots=true, dots_color="blue");
// Example(2D): Fit to a corner.
// pts = [[0,40], [-40,-10], [30,0]];
// path = arc(corner=pts, r=20);
// stroke(pts, endcaps="arrow2");
// stroke(path, endcap2="arrow2", color="blue");
function arc(n, r, angle, d, cp, points, corner, 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")
list_head(arc(u_add(n,1),r,angle,d,cp,points,corner,width,thickness,start,wedge,long,cw,ccw,true))
:
assert(is_undef(start) || is_def(angle), "start requires angle")
assert(is_undef(angle) || !any_defined([thickness,width,points,corner]), "Cannot give angle with points, corner, width or thickness")
assert(is_undef(n) || (is_integer(n) && n>=2), "Number of points must be an integer 2 or larger")
assert(is_undef(points) || is_path(points, [2,3]), "Points must be a list of 2d or 3d points")
assert((is_def(points) && len(points)==2) || !any([cw,ccw,long]), "cw, ccw, and long are only allowed when points is a list of length 2")
// First try for 2D arc specified by width and thickness
is_def(width) && is_def(thickness)?
assert(!any_defined([r,cp,points,angle,start]),"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_finite(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(is_def(r) && r>0, "Arc radius invalid")
let(
n = is_def(n) ? n : max(3, ceil(segs(r)*abs(angle)/360)),
arcpoints = [for(i=[0:n-1]) let(theta = start + i*angle/(n-1)) r*[cos(theta),sin(theta)]+cp]
)
[
if (wedge) cp,
each arcpoints
]
: is_def(corner)?
assert(is_path(corner,[2,3]) && len(corner)==3,str("Point list is invalid"))
assert(is_undef(cp) && !any([long,cw,ccw]), "Cannot use cp, long, cw, or ccw with corner")
// Arc is 3D, so transform corner to 2D and make a recursive call, then remap back to 3D
len(corner[0]) == 3? (
let(
plane = [corner[2], corner[0], corner[1]],
points2d = project_plane(plane, corner)
)
lift_plane(plane,arc(n,corner=points2d,wedge=wedge,r=r, d=d))
) :
assert(is_path(corner) && len(corner) == 3)
let(col = is_collinear(corner[0],corner[1],corner[2]))
assert(!col, "Collinear inputs do not define an arc")
let( r = get_radius(r=r, d=d) )
assert(is_finite(r) && r>0, "Must specify r= or d= when corner= is given.")
let(
ci = circle_2tangents(r, corner[0], corner[1], corner[2], tangents=true),
cp = ci[0], nrm = ci[1], tp1 = ci[2], tp2 = ci[3],
dir = det2([corner[1]-corner[0],corner[2]-corner[1]]) > 0,
corner = dir? [tp1,tp2] : [tp2,tp1],
theta_start = atan2(corner[0].y-cp.y, corner[0].x-cp.x),
theta_end = atan2(corner[1].y-cp.y, corner[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 : wedge ? reverse_polygon(arcpts) : reverse(arcpts)
: assert(is_def(points), "Arc not specified: must give points, angle, or width and thickness")
assert(is_path(points,[2,3]),"Point list is invalid")
// If arc is 3D, 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(
plane = [is_def(cp) ? cp : points[2], points[0], points[1]],
center2d = is_def(cp) ? project_plane(plane,cp) : undef,
points2d = project_plane(plane, points)
)
lift_plane(plane,arc(n,cp=center2d,points=points2d,wedge=wedge,long=long))
: len(points)==2?
// 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 is required when points has length 2 and it 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(num_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,
sa = atan2(v1.y,v1.x)
)
arc(n,cp=cp,r=r,start=sa,angle=final_angle,wedge=wedge)
: // Final case is arc passing through three points, starting at point[0] and ending at point[3]
let(col = is_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),
// Specify endpoints exactly; skip those endpoints when producing arc points
// Generating the whole arc and clipping ends is the easiest way to ensure that we
// generate the proper number of points.
arcpts = [ if (wedge) cp,
points[0],
each select(arc(n,cp=cp,r=r,start=theta_start,angle=angle),1,-2),
points[1]
]
)
dir ? arcpts
: wedge ? reverse_polygon(arcpts) // Keep the centerpoint at position 0 in the list
: reverse(arcpts);
module arc(n, r, angle, d, cp, points, corner, width, thickness, start, wedge=false, anchor=CENTER, spin=0)
{
path = arc(n=n, r=r, angle=angle, d=d, cp=cp, points=points, corner=corner, width=width, thickness=thickness, start=start, wedge=wedge);
attachable(anchor,spin, two_d=true, path=path, extent=false) {
polygon(path);
children();
}
}
// Function: catenary()
// Synopsis: Returns a 2D Catenary chain or arch path.
// SynTags: Path
// Topics: Paths
// See Also: circle(), stroke()
// Usage:
// path = catenary(width, droop=|angle=, n=);
// Description:
// Returns a 2D Catenary path, which is the path a chain held at both ends will take.
// The path will have the endpoints at `[±width/2, 0]`, and the middle of the path will droop
// towards Y- if the given droop= or angle= is positive. It will droop towards Y+ if the
// droop= or angle= is negative. You *must* specify one of droop= or angle=.
// Arguments:
// width = The straight-line distance between the endpoints of the path.
// droop = If given, specifies the height difference between the endpoints and the hanging middle of the path. If given a negative value, returns an arch *above* the Y axis.
// n = The number of points to return in the path. Default: 100
// ---
// angle = If given, specifies the angle that the path will droop by at the endpoints. If given a negative value, returns an arch *above* the Y axis.
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). (Module only) Default: `CENTER`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#subsection-spin). (Module only) Default: `0`
// Example(2D): By Droop
// stroke(catenary(100, droop=30));
// Example(2D): By Angle
// stroke(catenary(100, angle=30));
// Example(2D): Upwards Arch by Angle
// stroke(catenary(100, angle=30));
// Example(2D): Upwards Arch by Height Delta
// stroke(catenary(100, droop=-30));
// Example(2D): Specifying Vertex Count
// stroke(catenary(100, angle=-85, n=11), dots="dot");
// Example(3D): Sweeping a Catenary Path
// path = xrot(90, p=path3d(catenary(100, droop=20, n=41)));
// path_sweep(circle(r=1.5, $fn=24), path);
function catenary(width, droop, n=100, angle) =
assert(one_defined([droop, angle],"droop,angle"))
let(
sgn = is_undef(droop)? sign(angle) : sign(droop),
droop = droop==undef? undef : abs(droop),
angle = angle==undef? undef : abs(angle)
)
assert(is_finite(width) && width>0, "Bad width= value.")
assert(is_integer(n) && n>0, "Bad n= value. Must be a positive integer.")
assert(is_undef(droop) || is_finite(droop), "Bad droop= value.")
assert(is_undef(angle) || (is_finite(angle) && angle != 0 && abs(angle) < 90), "Bad angle= value.")
let(
catlup_fn = is_undef(droop)
? function(x) let(
p1 = [x-0.001, cosh(x-0.001)-1],
p2 = [x+0.001, cosh(x+0.001)-1],
delta = p2-p1,
ang = atan2(delta.y, delta.x)
) ang
: function(x) (cosh(x)-1)/x,
binsearch_fn = function(targ,x=0,inc=4)
inc < 1e-9? lookup(targ,[[catlup_fn(x),x],[catlup_fn(x+inc),x+inc]]) :
catlup_fn(x+inc) > targ? binsearch_fn(targ,x,inc/2) :
binsearch_fn(targ,x+inc,inc),
scx = is_undef(droop)? binsearch_fn(angle) :
binsearch_fn(droop / (width/2)),
sc = width/2 / scx,
droop = !is_undef(droop)? droop : (cosh(scx)-1) * sc,
path = [
for (x = lerpn(-scx,scx,n))
let(
xval = x * sc,
yval = approx(abs(x),scx)? 0 :
(cosh(x)-1) * sc - droop
)
[xval, yval]
],
out = sgn>0? path : yflip(p=path)
) out;
module catenary(width, droop, n=100, angle, anchor=CTR, spin=0) {
path = catenary(width=width, droop=droop, n=n, angle=angle);
attachable(anchor,spin, two_d=true, path=path, extent=true) {
polygon(path);
children();
}
}
// Function: helix()
// Synopsis: Creates a 2d spiral or 3d helical path.
// SynTags: Path
// Topics: Path Generators, Paths, Drawing Tools
// See Also: pie_slice(), stroke(), thread_helix(), path_sweep()
//
// Usage:
// path = helix(l|h, [turns=], [angle=], r=|r1=|r2=, d=|d1=|d2=);
// Description:
// Returns a 3D helical path on a cone, including the degerate case of flat spirals.
// You can specify start and end radii. You can give the length, the helix angle, or the number of turns: two
// of these three parameters define the helix. For a flat helix you must give length 0 and a turn count.
// Helix will be right handed if turns is positive and left handed if it is negative.
// The angle is calculateld based on the radius at the base of the helix.
// Arguments:
// h/l = Height/length of helix, zero for a flat spiral
// ---
// turns = Number of turns in helix, positive for right handed
// angle = helix angle
// r = Radius of helix
// r1 = Radius of bottom of helix
// r2 = Radius of top of helix
// d = Diameter of helix
// d1 = Diameter of bottom of helix
// d2 = Diameter of top of helix
// Example(3D):
// stroke(helix(turns=2.5, h=100, r=50), dots=true, dots_color="blue");
// Example(3D): Helix that turns the other way
// stroke(helix(turns=-2.5, h=100, r=50), dots=true, dots_color="blue");
// Example(3D): Flat helix (note points are still 3d)
// stroke(helix(h=0,r1=50,r2=25,l=0, turns=4));
module helix(l,h,turns,angle, r, r1, r2, d, d1, d2) {no_module();}
function helix(l,h,turns,angle, r, r1, r2, d, d1, d2)=
let(
r1=get_radius(r=r,r1=r1,d=d,d1=d1,dflt=1),
r2=get_radius(r=r,r1=r2,d=d,d1=d2,dflt=1),
length = first_defined([l,h])
)
assert(num_defined([length,turns,angle])==2,"Must define exactly two of l/h, turns, and angle")
assert(is_undef(angle) || length!=0, "Cannot give length 0 with an angle")
let(
// length advances dz for each turn
dz = is_def(angle) && length!=0 ? 2*PI*r1*tan(angle) : length/abs(turns),
maxtheta = is_def(turns) ? 360*turns : 360*length/dz,
N = segs(max(r1,r2))
)
[for(theta=lerpn(0,maxtheta, max(3,ceil(abs(maxtheta)*N/360))))
let(R=lerp(r1,r2,theta/maxtheta))
[R*cos(theta), R*sin(theta), abs(theta)/360 * dz]];
function _normal_segment(p1,p2) =
let(center = (p1+p2)/2)
[center, center + norm(p1-p2)/2 * line_normal(p1,p2)];
// Function: turtle()
// Synopsis: Uses [turtle graphics](https://en.wikipedia.org/wiki/Turtle_graphics) to generate a 2D path.
// SynTags: Path
// Topics: Shapes (2D), Path Generators (2D), Mini-Language
// See Also: turtle3d(), stroke(), path_sweep()
// Usage:
// path = turtle(commands, [state], [full_state=], [repeat=])
// Description:
// Use a sequence of [turtle graphics](https://en.wikipedia.org/wiki/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 ytarget 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=.7);
// Example(2DMed): yet another spiral, without using `repeat`
// path = turtle(concat(["angle",71],flatten(repeat(["move","left","addlength",1],50))));
// stroke(path,width=.7);
// 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=.15);
// 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));
module turtle(commands, state=[[[0,0]],[1,0],90,0], full_state=false, repeat=1) {no_module();}
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 = last(state[path])
)
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])) :
command=="right" ? list_set(state, step, rot(-default(parm,state[angle]),p=state[step])) :
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], list_tail(arcpath)),
rot(lrsign * myangle,p=state[step])
]
) :
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], list_tail(arcpath)),
rot(delta_angle,p=state[step])
]
) :
assert(false,str("Unknown turtle command \"",command,"\" at index",index))
[];
// Section: Debugging polygons
// Module: debug_polygon()
// Synopsis: Draws an annotated polygon.
// SynTags: Geom
// Topics: Shapes (2D)
// See Also: debug_region(), debug_vnf(), debug_bezier()
//
// Usage:
// debug_polygon(points, paths, [vertices=], [edges=], [convexity=], [size=]);
// Description:
// A drop-in replacement for `polygon()` that renders and labels the path points and
// edges. The start of each path is marked with a blue circle and the end with a pink diamond.
// You can suppress the display of vertex or edge labeling using the `vertices` and `edges` arguments.
// Arguments:
// points = The array of 2D polygon vertices.
// paths = The path connections between the vertices.
// ---
// vertices = if true display vertex labels and start/end markers. Default: true
// edges = if true display edge labels. Default: true
// convexity = The max number of walls a ray can pass through the given polygon paths.
// size = The base size of the line and labels.
// Example(Big2D):
// debug_polygon(
// points=concat(
// regular_ngon(or=10, n=8),
// regular_ngon(or=8, n=8)
// ),
// paths=[
// [for (i=[0:7]) i],
// [for (i=[15:-1:8]) i]
// ]
// );
module debug_polygon(points, paths, vertices=true, edges=true, convexity=2, size=1)
{
no_children($children);
print_paths=is_def(paths);
echo(points=points);
if (print_paths)
echo(paths=paths);
paths = is_undef(paths)? [count(points)] :
is_num(paths[0])? [paths] :
paths;
linear_extrude(height=0.01, convexity=convexity, center=true) {
polygon(points=points, paths=paths, convexity=convexity);
}
if (vertices)
_debug_poly_verts(points,size);
if (edges)
for (j = [0:1:len(paths)-1]) _debug_poly_edges(j, points, paths[j], vertices, size);
}
module _debug_poly_verts(points, size)
{
labels=is_vector(points[0]) ? [for(i=idx(points)) str(i)]
:[for(j=idx(points), i=idx(points[j])) str(chr(97+j),i)];
points = is_vector(points[0]) ? points : flatten(points);
dups = vector_search(points, EPSILON, points);
color("red") {
for (ind=dups){
numstr = str_join(select(labels,ind),",");
up(0.2) {
translate(points[ind[0]]) {
linear_extrude(height=0.1, convexity=10, center=true) {
text(text=numstr, size=size, halign="center", valign="center");
}
}
}
}
}
}
module _debug_poly_edges(j,points, path,vertices,size)
{
path = default(path, count(len(points)));
if (vertices){
translate(points[path[0]]) {
color("cyan") up(0.1) cylinder(d=size*1.5, h=0.01, center=false, $fn=12);
}
translate(points[path[len(path)-1]]) {
color("pink") up(0.11) cylinder(d=size*1.5, h=0.01, center=false, $fn=4);
}
}
for (i = [0:1:len(path)-1]) {
midpt = (points[path[i]] + points[path[(i+1)%len(path)]])/2;
color("blue") {
up(0.2) {
translate(midpt) {
linear_extrude(height=0.1, convexity=10, center=true) {
text(text=str(chr(65+j),i), size=size/2, halign="center", valign="center");
}
}
}
}
}
}
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap