////////////////////////////////////////////////////////////////////// // LibFile: shapes2d.scad // Common useful 2D shapes. // To use, add the following lines to the beginning of your file: // ``` // include <BOSL2/std.scad> // ``` ////////////////////////////////////////////////////////////////////// // Section: 2D Drawing Helpers // Module: stroke() // Usage: // stroke(path, width, [endcap], [closed]); // Description: // Draws a 2D line path with a given line thickness. // Arguments: // path = The 2D path to draw along. // width = The width of the line to draw. // endcaps = If true, draw round endcaps at the ends of the line. // closed = If true, draw an additional line from the end of the path to the start. // Example(2D): // path = [[0,100], [100,100], [200,0], [100,-100], [100,0]]; // stroke(path, width=10, endcaps=false); // Example(2D): // path = [[0,100], [100,100], [200,0], [100,-100], [100,0]]; // stroke(path, width=20, endcaps=true); // Example(2D): // path = [[0,100], [100,100], [200,0], [100,-100], [100,0]]; // stroke(path, width=20, endcaps=true, closed=true); module stroke(path, width=1, endcaps=true, closed=false) { $fn = quantup(segs(width/2),4); path = closed? concat(path,[path[0]]) : path; assert(is_list(path) && is_vector(path[0]) && len(path[0])==2, "path must be a 2D list of points."); segments = pair(path); segpairs = pair(segments); // Line segments for (seg = segments) { delt = seg[1] - seg[0]; translate(seg[0]) rot(from=BACK,to=delt) left(width/2) square([width, norm(delt)], center=false); } // Joints for (segpair = segpairs) { seg1 = segpair[0]; seg2 = segpair[1]; delt1 = seg1[1] - seg1[0]; delt2 = seg2[1] - seg2[0]; hull() { translate(seg1[1]) rot(from=BACK,to=delt1) circle(d=width); translate(seg2[0]) rot(from=BACK,to=delt2) circle(d=width); } } // Endcaps if (endcaps) { seg1 = segments[0]; delt1 = seg1[1] - seg1[0]; translate(seg1[0]) rot(from=BACK, to=delt1) circle(d=width); seg2 = select(segments,-1); delt2 = seg2[1] - seg2[0]; translate(seg2[1]) rot(from=BACK, to=delt2) circle(d=width); } } // Section: 2D Shapes // Function&Module: arc() // Usage: 2D arc from 0ยบ to `angle` degrees. // arc(N, r|d, angle); // Usage: 2D arc from START to END degrees. // arc(N, r|d, angle=[START,END]) // Usage: 2D arc from `start` to `start+angle` degrees. // arc(N, r|d, start, angle) // Usage: 2D circle segment by `width` and `thickness`, starting and ending on the X axis. // 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`. // arc(N, cp, points=[P0,P1]) // Usage: 2D or 3D arc, starting at `P0`, passing through `P1` and ending at `P2`. // arc(N, points=[P0,P1,P2]) // Description: // If called as a function, returns a 2D or 3D path forming an arc. // 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. // d = Diameter of the arc. // angle = If a scalar, specifies the end angle in degrees. If a vector of two scalars, specifies start and end angles. // cp = Centerpoint of arc. // points = Points on the arc. // 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. // wedge = If true, include centerpoint `cp` in output to form pie slice shape. // 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); // 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): // include <BOSL2/paths.scad> // path = arc(points=[[0,30,0],[0,0,30],[30,0,0]]); // trace_polyline(path, showpts=true, color="cyan"); function arc(N, r, angle, d, cp, points, width, thickness, start, wedge=false) = // First try for 2D arc specified by angles is_def(width) && is_def(thickness)? ( arc(N,points=[[width/2,0], [0,thickness], [-width/2,0]],wedge=wedge) ) : is_def(angle)? ( let( parmok = is_undef(points) && is_undef(width) && is_undef(thickness) && ((is_vector(angle) && len(angle)==2 && is_undef(start)) || is_num(angle)) ) assert(parmok,"Invalid parameters in arc") let( cp = is_def(cp) ? 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), 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_list(points),"Invalid parameters") // Arc is 3D, so transform points to 2D and make a recursive call, then remap back to 3D len(points[0])==3? ( 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),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 let( angle = vector_angle(points[0], cp, points[1]), v1 = points[0]-cp, v2 = points[1]-cp, dir = sign(det2([v1,v2])), // z component of cross product r=norm(v1) ) assert(dir!=0,"Collinear inputs don't define a unique arc") arc(N,cp=cp,r=r,start=atan2(v1.y,v1.x),angle=dir*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],1e-3)) 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&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. // 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); // Example(2D): Called as Function // stroke(closed=true, trapezoid(h=30, w1=40, w2=20)); function trapezoid(h, w1, w2, anchor=CENTER, spin=0) = let( s = anchor.y>0? [w2,h] : anchor.y<0? [w1,h] : [(w1+w2)/2,h], path = [[-w1/2,-h/2], [-w2/2,h/2], [w2/2,h/2], [w1/2,-h/2]] ) rot(spin, p=move(-vmul(anchor,s/2), p=path)); module trapezoid(h, w1, w2, anchor=CENTER, spin=0) polygon(trapezoid(h=h, w1=w1, w2=w2, anchor=anchor, spin=spin)); // Function&Module: regular_ngon() // Usage: // regular_ngon(n, 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. // od = Outside diameter, at points. // ir = Inside radius, at center of sides. // id = Inside diameter, at center of sides. // side = Length of each side. // 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 // 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 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): Called as Function // stroke(closed=true, regular_ngon(n=6, or=30)); function regular_ngon(n=6, or=undef, od=undef, ir=undef, id=undef, side=undef, realign=false, anchor=CENTER, spin=0) = let( sc = 1/cos(180/n), r = get_radius(r1=ir*sc, r=or, d1=id*sc, d=od, dflt=side/2/sin(180/n)), offset = 90 + (realign? (180/n) : 0), path = [for (a=[0:360/n:360-EPSILON]) r*[cos(a+offset),sin(a+offset)]] ) rot(spin, p=move(-r*normalize(anchor), p=path)); module regular_ngon(n=6, or=undef, od=undef, ir=undef, id=undef, side=undef, realign=false, anchor=CENTER, spin=0) polygon(regular_ngon(n=n,or=or,od=od,ir=ir,id=id,side=side,realign=realign, anchor=anchor, spin=spin)); // 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. // od = Outside diameter, at points. // ir = Inside radius, at center of sides. // id = Inside diameter, at center of sides. // side = Length of each side. // 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 // 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 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): Called as Function // stroke(closed=true, pentagon(or=30)); function pentagon(or=undef, od=undef, ir=undef, id=undef, side=undef, realign=false, anchor=CENTER, spin=0) = regular_ngon(n=5, or=or, od=od, ir=ir, id=id, side=side, realign=realign, anchor=anchor, spin=spin); module pentagon(or=undef, od=undef, ir=undef, id=undef, side=undef, realign=false, anchor=CENTER, spin=0) polygon(pentagon(or=or, od=od, ir=ir, id=id, side=side, realign=realign, anchor=anchor, spin=spin)); // 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. // od = Outside diameter, at points. // ir = Inside radius, at center of sides. // id = Inside diameter, at center of sides. // side = Length of each side. // 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 // 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 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): Called as Function // stroke(closed=true, hexagon(or=30)); function hexagon(or=undef, od=undef, ir=undef, id=undef, side=undef, realign=false, anchor=CENTER, spin=0) = regular_ngon(n=6, or=or, od=od, ir=ir, id=id, side=side, realign=realign, anchor=anchor, spin=spin); module hexagon(or=undef, od=undef, ir=undef, id=undef, side=undef, realign=false, anchor=CENTER, spin=0) polygon(hexagon(or=or, od=od, ir=ir, id=id, side=side, realign=realign, anchor=anchor, spin=spin)); // 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. // od = Outside diameter, at points. // ir = Inside radius, at center of sides. // id = Inside diameter, at center of sides. // side = Length of each side. // 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 // 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 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): Called as Function // stroke(closed=true, octagon(or=30)); function octagon(or=undef, od=undef, ir=undef, id=undef, side=undef, realign=false, anchor=CENTER, spin=0) = regular_ngon(n=8, or=or, od=od, ir=ir, id=id, side=side, realign=realign, anchor=anchor, spin=spin); module octagon(or=undef, od=undef, ir=undef, id=undef, side=undef, realign=false, anchor=CENTER, spin=0) polygon(octagon(or=or, od=od, ir=ir, id=id, side=side, realign=realign, anchor=anchor, spin=spin)); // 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. // tangent = The angle in degrees of the tangent point for the joining arcs, measured away from the Y axis. // 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=undef, d=undef, 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, s = [spread/2+r, r], 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] ) ) rot(spin, p=move(-vmul(anchor,s), p=path)); module glued_circles(r=undef, d=undef, spread=10, tangent=30, anchor=CENTER, spin=0) polygon(glued_circles(r=r, d=d, spread=spread, tangent=tangent, anchor=anchor, spin=spin)); // Function&Module: star() // Usage: // star(n, r|d, 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. // d = The diameter to the tips of the star. // 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 // 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): // 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): Called as Function // stroke(closed=true, star(n=5, r=50, ir=25)); function star(n, r, d, ir, id, step, realign=false, anchor=CENTER, spin=0) = let( r = get_radius(r=r, d=d), count = num_defined([ir,id,step]), stepOK = is_undef(step) || (step>1 && step<n/2) ) 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( 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 = 90+(realign? 180/n : 0), path = [for(i=[0:1:2*n-1]) let(theta=180*i/n+offset, radius=(i%2)?ir:r) radius*[cos(theta), sin(theta)]] ) rot(spin, p=move(-r*normalize(anchor), p=path)); module star(n, r, d, ir, id, step, realign=false, anchor=CENTER, spin=0) polygon(star(n=n, r=r, d=d, ir=ir, id=id, step=step, realign=realign, anchor=anchor, spin=spin)); 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); 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-1]) 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 = [0:steps-1]) let(a=angs[i]) scale*rads[i]*[cos(a), sin(a)]] ) rot(spin, p=move(-scale*max(rads)*normalize(anchor), 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) polygon(supershape(step=step,m1=m1,m2=m2,n1=n1,n2=n2,n3=n3,a=a,b=b, r=r,d=d, anchor=anchor, spin=spin)); // Function: turtle() // Usage: // turtle(commands, [state], [return_state]) // 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. // // For the list below, `dist` is the current movement distance. // // Turtle commands: // - "move", [scale]: Move turtle scale*dist units in the turtle direction. Default scale=1. // - "xmove", [scale]: Move turtle scale*dist units in the x direction. Default scale=1. // - "ymove", [scale]: Move turtle scale*dist units in the y direction. Default scale=1. // - "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, comands: Repeats a list of commands `count` times. // // Arguments: // commands = list of turtle commands // state = starting turtle state (from previous call) or starting point. Default: start at the origin // 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=10); // stroke(path,width=.05); // 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(replist(["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], full_state=false, repeat=1) = let( state = is_vector(state) ? [[state],[1,0],90] : 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) = commands[index] == "repeat" ? 3 : // Repeat command requires 2 args 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] function _turtle_command(command, parm, parm2, state, index) = command == "repeat" ? assert(is_num(parm),str("\"repeat\" command requires a numeric parameter 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, parm = !is_string(parm) ? parm : undef, needvec = ["jump"], neednum = ["untilx","untily","xjump","yjump","angle","length","scale","addlength"], needeither = ["setdir"], chvec = !in_list(command,needvec) || is_vector(parm), chnum = !in_list(command,neednum) || is_num(parm), vec_or_num = !in_list(command,needeither) || (is_num(parm) || is_vector(parm)), 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]]), ffd=echo(int=int), 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=="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]) * normalize(parm)) : list_set(state, step, norm(state[step]) * [cos(parm),sin(parm)]) ) : command=="length" ? list_set(state, step, parm*normalize(state[step])) : command=="scale" ? list_set(state, step, parm*state[step]) : command=="addlength" ? list_set(state, step, state[step]+normalize(state[step])*parm) : assert(false,str("Unknown turtle command \"",command,"\" at index",index)) []; // vim: noexpandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap