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Updated bezier code to support N-point beziers.
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Revar Desmera
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3 changed files with 62 additions and 48 deletions
104
beziers.scad
104
beziers.scad
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@ -12,11 +12,11 @@ Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are met:
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* Redistributions of source code must retain the above copyright notice, this
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list of conditions and the following disclaimer.
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list of conditions and the following disclaimer.
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* Redistributions in binary form must reproduce the above copyright notice,
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this list of conditions and the following disclaimer in the documentation
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and/or other materials provided with the distribution.
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this list of conditions and the following disclaimer in the documentation
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and/or other materials provided with the distribution.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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@ -33,40 +33,46 @@ OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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include <math.scad>
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include <paths.scad>
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include <transforms.scad>
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// Formulae to calculate points on a cubic bezier curve.
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function bez_B0(curve,u) = curve[0]*pow((1-u),3);
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function bez_B1(curve,u) = curve[1]*(3*u*pow((1-u),2));
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function bez_B2(curve,u) = curve[2]*(3*pow(u,2)*(1-u));
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function bez_B3(curve,u) = curve[3]*pow(u,3);
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function bez_point(curve,u) = bez_B0(curve,u) + bez_B1(curve,u) + bez_B2(curve,u) + bez_B3(curve,u);
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// Formulae to calculate points on an N-point bezier curve.
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function bez_point(curve,u)=
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(len(curve) <= 1) ?
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curve[0] :
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bez_point(
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[for(i=[0:len(curve)-2]) curve[i]*(1-u)+curve[i+1]*u],
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u
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);
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// Takes an array of bezier points and converts it into a 3D polyline.
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function bezier_polyline(bezier, splinesteps=16) = concat(
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function bezier_polyline(bezier, splinesteps=16, N=3) = concat(
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[
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for (
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b = [0 : 3 : len(bezier)-4],
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b = [0 : N : len(bezier)-N-1],
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l = [0 : splinesteps-1]
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) let (
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crv = [bezier[b+0], bezier[b+1], bezier[b+2], bezier[b+3]],
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crv = [for (i=[0 : N]) bezier[b+i]],
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u = l / splinesteps
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) bez_point(crv, u)
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],
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[bez_point([bezier[len(bezier)-4], bezier[len(bezier)-3], bezier[len(bezier)-2], bezier[len(bezier)-1]], 1.0)]
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[bez_point([for (i=[-(N+1) : -1]) bezier[len(bezier)+i]], 1.0)]
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);
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// Takes a closed 2D bezier path, and creates a 2D polygon from it.
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module bezier_polygon(bezier, splinesteps=16) {
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polypoints=bezier_polyline(bezier, splinesteps);
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// bezier = array of 2D bezier path points
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// splinesteps = number of straight lines to split each bezier segment into
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// N = number of points in each bezier segment. Cubic = 3
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module bezier_polygon(bezier, splinesteps=16, N=3) {
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polypoints=bezier_polyline(bezier, splinesteps, N);
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polygon(points=slice(polypoints, 0, -1));
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}
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// Generate bezier curve to fillet 2 line segments between 3 points.
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// Returns two path points with surrounding cubic bezier control points.
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// Returns two path points with surrounding cubic (N=3) bezier control points.
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function fillet3pts(p0, p1, p2, r) = let(
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v0 = normalize(p0-p1),
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v1 = normalize(p2-p1),
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@ -82,7 +88,7 @@ function fillet3pts(p0, p1, p2, r) = let(
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) [tp0, tp0, cp0, cp1, tp1, tp1];
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// Takes a 3D polyline path and fillets it into a 3d cubic bezier path.
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// Takes a 3D polyline path and fillets it into a 3d cubic (N=3) bezier path.
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function fillet_path(pts, fillet) = concat(
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[pts[0], pts[0]],
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(len(pts) < 3)? [] : [
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@ -98,6 +104,7 @@ function fillet_path(pts, fillet) = concat(
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// Takes a closed 2D bezier and rotates it around the X axis, forming a solid.
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// bezier = array of points for the bezier path to rotate.
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// splinesteps = number of segments to divide each bezier segment into.
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// N = number of points in each bezier segment. Cubic = 3
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// Example:
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// path = [
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// [ 0, 10], [ 50, 0], [ 50, 40],
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@ -107,36 +114,37 @@ function fillet_path(pts, fillet) = concat(
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// [ 0, 10]
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// ];
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// revolve_bezier(path, splinesteps=32, $fn=180);
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module revolve_bezier(bezier, splinesteps=16) {
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module revolve_bezier(bezier, splinesteps=16, N=3) {
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yrot(90) rotate_extrude(convexity=10) {
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xrot(180) zrot(-90) bezier_polygon(bezier, splinesteps);
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xrot(180) zrot(-90) bezier_polygon(bezier, splinesteps, N);
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}
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}
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// Takes a bezier path and closes it to the X axis.
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function bezier_close_to_axis(bezier) =
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let(bezend = len(bezier)-1)
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concat(
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[ [bezier[0][0], 0], [bezier[0][0], 0], bezier[0] ],
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bezier,
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[ bezier[bezend], [bezier[bezend][0], 0], [bezier[bezend][0], 0] ]
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);
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// Takes a 2D bezier path and closes it to the X axis.
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function bezier_close_to_axis(bezier, N=3) =
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let(
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bezend = len(bezier)-1
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) concat(
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[for (i=[0:N-1]) lerp([bezier[0][0], 0], bezier[0], i/N)],
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bezier,
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[for (i=[1:N]) lerp(bezier[bezend], [bezier[bezend][0], 0], i/N)],
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[for (i=[1:N]) lerp([bezier[bezend][0], 0], [bezier[0][0], 0], i/N)]
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);
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// Takes a bezier curve and closes it with a matching path that is
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// lowered by a given amount towards the X axis.
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function bezier_offset(inset, bezier) =
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let(backbez = reverse([ for (pt = bezier) [pt[0], pt[1]-inset] ]))
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concat(
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bezier,
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[bezier[len(bezier)-1]],
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[backbez[0]],
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backbez,
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[backbez[len(backbez)-1]],
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[bezier[0]],
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[bezier[0]]
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);
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function bezier_offset(inset, bezier, N=3) =
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let(
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backbez = reverse([ for (pt = bezier) [pt[0], pt[1]-inset] ]),
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bezend = len(bezier)-1
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) concat(
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bezier,
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[for (i=[1:N-1]) lerp(bezier[bezend], backbez[0], i/N)],
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backbez,
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[for (i=[1:N]) lerp(backbez[bezend], bezier[0], i/N)]
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);
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// Takes a 2D bezier and rotates it around the X axis, forming a solid.
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@ -145,8 +153,8 @@ function bezier_offset(inset, bezier) =
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// Example:
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// path = [ [0, 10], [33, 10], [66, 40], [100, 40] ];
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// revolve_bezier_solid_to_axis(path, splinesteps=32, $fn=72);
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module revolve_bezier_solid_to_axis(bezier, splinesteps=16) {
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revolve_bezier(bezier=bezier_close_to_axis(bezier), splinesteps=splinesteps);
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module revolve_bezier_solid_to_axis(bezier, splinesteps=16, N=3) {
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revolve_bezier(bezier=bezier_close_to_axis(bezier), splinesteps=splinesteps, N=N);
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}
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@ -157,8 +165,8 @@ module revolve_bezier_solid_to_axis(bezier, splinesteps=16) {
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// Example:
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// path = [ [0, 10], [33, 10], [66, 40], [100, 40] ];
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// revolve_bezier_offset_shell(path, offset=1, splinesteps=32, $fn=72);
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module revolve_bezier_offset_shell(bezier, offset=1, splinesteps=16) {
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revolve_bezier(bezier=bezier_offset(offset, bezier), splinesteps=splinesteps);
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module revolve_bezier_offset_shell(bezier, offset=1, splinesteps=16, N=3) {
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revolve_bezier(bezier=bezier_offset(offset, bezier), splinesteps=splinesteps, N=N);
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}
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@ -169,8 +177,8 @@ module revolve_bezier_offset_shell(bezier, offset=1, splinesteps=16) {
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// path = [ [0, 0, 0], [33, 33, 33], [66, -33, -33], [100, 0, 0] ];
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// extrude_2d_shapes_along_bezier(path, splinesteps=32)
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// circle(r=10, center=true);
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module extrude_2d_shapes_along_bezier(bezier, splinesteps=16) {
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pointslist = slice(bezier_polyline(bezier, splinesteps), 0, -1);
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module extrude_2d_shapes_along_bezier(bezier, splinesteps=16, N=3) {
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pointslist = slice(bezier_polyline(bezier, splinesteps, N), 0, -1);
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ptcount = len(pointslist);
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for (i = [0 : ptcount-2]) {
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pt1 = pointslist[i];
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@ -218,13 +226,15 @@ module extrude_2d_shapes_along_bezier(bezier, splinesteps=16) {
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// path = Array of points of a bezier path, to extrude along.
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// pathsteps = number of steps to divide each path segment into.
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// bezsteps = number of steps to divide each bezier segment into.
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// bezN = number of points in each extruded bezier segment. Cubic = 3
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// pathN = number of points in each path bezier segment. Cubic = 3
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// Example:
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// bez = [ [-15, 0], [25, -15], [-5, 10], [0, 10], [5, 10], [10, 5], [15, 0], [10, -5], [5, -10], [0, -10], [-5, -10], [-10, -5], [-15, 0] ];
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// path = [ [0, 0, 0], [33, 33, 33], [66, -33, -33], [100, 0, 0] ];
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// extrude_bezier_along_bezier(bez, path, pathsteps=64, bezsteps=32);
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module extrude_bezier_along_bezier(bezier, path, pathsteps=16, bezsteps=16) {
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bez_points = simplify2d_path(bezier_polyline(bezier, bezsteps));
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path_points = simplify3d_path(path3d(bezier_polyline(path, pathsteps)));
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module extrude_bezier_along_bezier(bezier, path, pathsteps=16, bezsteps=16, bezN=3, pathN=3) {
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bez_points = simplify2d_path(bezier_polyline(bezier, bezsteps, bezN));
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path_points = simplify3d_path(path3d(bezier_polyline(path, pathsteps, pathN)));
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extrude_2dpath_along_3dpath(bez_points, path_points);
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}
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@ -51,6 +51,10 @@ function quantup(x,y) = ceil(x/y)*y;
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function segs(r) = $fn>0?($fn>3?$fn:3):(ceil(max(min(360.0/$fa,abs(r)*2*Cpi()/$fs),5)));
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// Interpolate between two values or vectors. 0.0 <= u <= 1.0
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function lerp(a,b,u) = (b-a)*u + a;
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// Calculate hypotenuse length of 2D triangle.
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function hypot(x,y) = sqrt(x*x+y*y);
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@ -189,7 +189,7 @@ function points_along_path3d(
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// Example:
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// shape = [ [-15, 0], [0, 0], [-5, 10], [0, 10], [5, 10], [10, 5], [15, 0], [10, -5], [5, -10], [0, -10], [-5, -10], [-10, -5], [-15, 0] ];
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// path = [ [0, 0, 0], [100, 33, 33], [200, -33, -33], [300, 0, 0] ];
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// extrude_2dpath_along_3dpath(shape, path, tilt=false);
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// extrude_2dpath_along_3dpath(shape, path);
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module extrude_2dpath_along_3dpath(polyline, path, convexity=10) {
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pline_count = len(polyline);
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path_count = len(path);
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