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Updated bezier code to support N-point beziers.

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Revar Desmera 2018-02-16 14:49:32 -08:00
parent 453ebcb83f
commit 2d9fa565b3
3 changed files with 62 additions and 48 deletions
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104
beziers.scad
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@ -12,11 +12,11 @@ Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met: modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this * Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer. list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice, * Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution. and/or other materials provided with the distribution.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
@ -33,40 +33,46 @@ OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
include <math.scad> include <math.scad>
include <paths.scad> include <paths.scad>
include <transforms.scad>
// Formulae to calculate points on a cubic bezier curve. // Formulae to calculate points on an N-point bezier curve.
function bez_B0(curve,u) = curve[0]*pow((1-u),3); function bez_point(curve,u)=
function bez_B1(curve,u) = curve[1]*(3*u*pow((1-u),2)); (len(curve) <= 1) ?
function bez_B2(curve,u) = curve[2]*(3*pow(u,2)*(1-u)); curve[0] :
function bez_B3(curve,u) = curve[3]*pow(u,3); bez_point(
function bez_point(curve,u) = bez_B0(curve,u) + bez_B1(curve,u) + bez_B2(curve,u) + bez_B3(curve,u); [for(i=[0:len(curve)-2]) curve[i]*(1-u)+curve[i+1]*u],
u
);
// Takes an array of bezier points and converts it into a 3D polyline. // Takes an array of bezier points and converts it into a 3D polyline.
function bezier_polyline(bezier, splinesteps=16) = concat( function bezier_polyline(bezier, splinesteps=16, N=3) = concat(
[ [
for ( for (
b = [0 : 3 : len(bezier)-4], b = [0 : N : len(bezier)-N-1],
l = [0 : splinesteps-1] l = [0 : splinesteps-1]
) let ( ) let (
crv = [bezier[b+0], bezier[b+1], bezier[b+2], bezier[b+3]], crv = [for (i=[0 : N]) bezier[b+i]],
u = l / splinesteps u = l / splinesteps
) bez_point(crv, u) ) bez_point(crv, u)
], ],
[bez_point([bezier[len(bezier)-4], bezier[len(bezier)-3], bezier[len(bezier)-2], bezier[len(bezier)-1]], 1.0)] [bez_point([for (i=[-(N+1) : -1]) bezier[len(bezier)+i]], 1.0)]
); );
// Takes a closed 2D bezier path, and creates a 2D polygon from it. // Takes a closed 2D bezier path, and creates a 2D polygon from it.
module bezier_polygon(bezier, splinesteps=16) { // bezier = array of 2D bezier path points
polypoints=bezier_polyline(bezier, splinesteps); // splinesteps = number of straight lines to split each bezier segment into
// N = number of points in each bezier segment. Cubic = 3
module bezier_polygon(bezier, splinesteps=16, N=3) {
polypoints=bezier_polyline(bezier, splinesteps, N);
polygon(points=slice(polypoints, 0, -1)); polygon(points=slice(polypoints, 0, -1));
} }
// Generate bezier curve to fillet 2 line segments between 3 points. // Generate bezier curve to fillet 2 line segments between 3 points.
// Returns two path points with surrounding cubic bezier control points. // Returns two path points with surrounding cubic (N=3) bezier control points.
function fillet3pts(p0, p1, p2, r) = let( function fillet3pts(p0, p1, p2, r) = let(
v0 = normalize(p0-p1), v0 = normalize(p0-p1),
v1 = normalize(p2-p1), v1 = normalize(p2-p1),
@ -82,7 +88,7 @@ function fillet3pts(p0, p1, p2, r) = let(
) [tp0, tp0, cp0, cp1, tp1, tp1]; ) [tp0, tp0, cp0, cp1, tp1, tp1];
// Takes a 3D polyline path and fillets it into a 3d cubic bezier path. // Takes a 3D polyline path and fillets it into a 3d cubic (N=3) bezier path.
function fillet_path(pts, fillet) = concat( function fillet_path(pts, fillet) = concat(
[pts[0], pts[0]], [pts[0], pts[0]],
(len(pts) < 3)? [] : [ (len(pts) < 3)? [] : [
@ -98,6 +104,7 @@ function fillet_path(pts, fillet) = concat(
// Takes a closed 2D bezier and rotates it around the X axis, forming a solid. // Takes a closed 2D bezier and rotates it around the X axis, forming a solid.
// bezier = array of points for the bezier path to rotate. // bezier = array of points for the bezier path to rotate.
// splinesteps = number of segments to divide each bezier segment into. // splinesteps = number of segments to divide each bezier segment into.
// N = number of points in each bezier segment. Cubic = 3
// Example: // Example:
// path = [ // path = [
// [ 0, 10], [ 50, 0], [ 50, 40], // [ 0, 10], [ 50, 0], [ 50, 40],
@ -107,36 +114,37 @@ function fillet_path(pts, fillet) = concat(
// [ 0, 10] // [ 0, 10]
// ]; // ];
// revolve_bezier(path, splinesteps=32, $fn=180); // revolve_bezier(path, splinesteps=32, $fn=180);
module revolve_bezier(bezier, splinesteps=16) { module revolve_bezier(bezier, splinesteps=16, N=3) {
yrot(90) rotate_extrude(convexity=10) { yrot(90) rotate_extrude(convexity=10) {
xrot(180) zrot(-90) bezier_polygon(bezier, splinesteps); xrot(180) zrot(-90) bezier_polygon(bezier, splinesteps, N);
} }
} }
// Takes a bezier path and closes it to the X axis. // Takes a 2D bezier path and closes it to the X axis.
function bezier_close_to_axis(bezier) = function bezier_close_to_axis(bezier, N=3) =
let(bezend = len(bezier)-1) let(
concat( bezend = len(bezier)-1
[ [bezier[0][0], 0], [bezier[0][0], 0], bezier[0] ], ) concat(
bezier, [for (i=[0:N-1]) lerp([bezier[0][0], 0], bezier[0], i/N)],
[ bezier[bezend], [bezier[bezend][0], 0], [bezier[bezend][0], 0] ] bezier,
); [for (i=[1:N]) lerp(bezier[bezend], [bezier[bezend][0], 0], i/N)],
[for (i=[1:N]) lerp([bezier[bezend][0], 0], [bezier[0][0], 0], i/N)]
);
// Takes a bezier curve and closes it with a matching path that is // Takes a bezier curve and closes it with a matching path that is
// lowered by a given amount towards the X axis. // lowered by a given amount towards the X axis.
function bezier_offset(inset, bezier) = function bezier_offset(inset, bezier, N=3) =
let(backbez = reverse([ for (pt = bezier) [pt[0], pt[1]-inset] ])) let(
concat( backbez = reverse([ for (pt = bezier) [pt[0], pt[1]-inset] ]),
bezier, bezend = len(bezier)-1
[bezier[len(bezier)-1]], ) concat(
[backbez[0]], bezier,
backbez, [for (i=[1:N-1]) lerp(bezier[bezend], backbez[0], i/N)],
[backbez[len(backbez)-1]], backbez,
[bezier[0]], [for (i=[1:N]) lerp(backbez[bezend], bezier[0], i/N)]
[bezier[0]] );
);
// Takes a 2D bezier and rotates it around the X axis, forming a solid. // Takes a 2D bezier and rotates it around the X axis, forming a solid.
@ -145,8 +153,8 @@ function bezier_offset(inset, bezier) =
// Example: // Example:
// path = [ [0, 10], [33, 10], [66, 40], [100, 40] ]; // path = [ [0, 10], [33, 10], [66, 40], [100, 40] ];
// revolve_bezier_solid_to_axis(path, splinesteps=32, $fn=72); // revolve_bezier_solid_to_axis(path, splinesteps=32, $fn=72);
module revolve_bezier_solid_to_axis(bezier, splinesteps=16) { module revolve_bezier_solid_to_axis(bezier, splinesteps=16, N=3) {
revolve_bezier(bezier=bezier_close_to_axis(bezier), splinesteps=splinesteps); revolve_bezier(bezier=bezier_close_to_axis(bezier), splinesteps=splinesteps, N=N);
} }
@ -157,8 +165,8 @@ module revolve_bezier_solid_to_axis(bezier, splinesteps=16) {
// Example: // Example:
// path = [ [0, 10], [33, 10], [66, 40], [100, 40] ]; // path = [ [0, 10], [33, 10], [66, 40], [100, 40] ];
// revolve_bezier_offset_shell(path, offset=1, splinesteps=32, $fn=72); // revolve_bezier_offset_shell(path, offset=1, splinesteps=32, $fn=72);
module revolve_bezier_offset_shell(bezier, offset=1, splinesteps=16) { module revolve_bezier_offset_shell(bezier, offset=1, splinesteps=16, N=3) {
revolve_bezier(bezier=bezier_offset(offset, bezier), splinesteps=splinesteps); revolve_bezier(bezier=bezier_offset(offset, bezier), splinesteps=splinesteps, N=N);
} }
@ -169,8 +177,8 @@ module revolve_bezier_offset_shell(bezier, offset=1, splinesteps=16) {
// path = [ [0, 0, 0], [33, 33, 33], [66, -33, -33], [100, 0, 0] ]; // path = [ [0, 0, 0], [33, 33, 33], [66, -33, -33], [100, 0, 0] ];
// extrude_2d_shapes_along_bezier(path, splinesteps=32) // extrude_2d_shapes_along_bezier(path, splinesteps=32)
// circle(r=10, center=true); // circle(r=10, center=true);
module extrude_2d_shapes_along_bezier(bezier, splinesteps=16) { module extrude_2d_shapes_along_bezier(bezier, splinesteps=16, N=3) {
pointslist = slice(bezier_polyline(bezier, splinesteps), 0, -1); pointslist = slice(bezier_polyline(bezier, splinesteps, N), 0, -1);
ptcount = len(pointslist); ptcount = len(pointslist);
for (i = [0 : ptcount-2]) { for (i = [0 : ptcount-2]) {
pt1 = pointslist[i]; pt1 = pointslist[i];
@ -218,13 +226,15 @@ module extrude_2d_shapes_along_bezier(bezier, splinesteps=16) {
// path = Array of points of a bezier path, to extrude along. // path = Array of points of a bezier path, to extrude along.
// pathsteps = number of steps to divide each path segment into. // pathsteps = number of steps to divide each path segment into.
// bezsteps = number of steps to divide each bezier segment into. // bezsteps = number of steps to divide each bezier segment into.
// bezN = number of points in each extruded bezier segment. Cubic = 3
// pathN = number of points in each path bezier segment. Cubic = 3
// Example: // Example:
// 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] ]; // 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] ];
// path = [ [0, 0, 0], [33, 33, 33], [66, -33, -33], [100, 0, 0] ]; // path = [ [0, 0, 0], [33, 33, 33], [66, -33, -33], [100, 0, 0] ];
// extrude_bezier_along_bezier(bez, path, pathsteps=64, bezsteps=32); // extrude_bezier_along_bezier(bez, path, pathsteps=64, bezsteps=32);
module extrude_bezier_along_bezier(bezier, path, pathsteps=16, bezsteps=16) { module extrude_bezier_along_bezier(bezier, path, pathsteps=16, bezsteps=16, bezN=3, pathN=3) {
bez_points = simplify2d_path(bezier_polyline(bezier, bezsteps)); bez_points = simplify2d_path(bezier_polyline(bezier, bezsteps, bezN));
path_points = simplify3d_path(path3d(bezier_polyline(path, pathsteps))); path_points = simplify3d_path(path3d(bezier_polyline(path, pathsteps, pathN)));
extrude_2dpath_along_3dpath(bez_points, path_points); extrude_2dpath_along_3dpath(bez_points, path_points);
} }

4
math.scad
View file

@ -51,6 +51,10 @@ function quantup(x,y) = ceil(x/y)*y;
function segs(r) = $fn>0?($fn>3?$fn:3):(ceil(max(min(360.0/$fa,abs(r)*2*Cpi()/$fs),5))); function segs(r) = $fn>0?($fn>3?$fn:3):(ceil(max(min(360.0/$fa,abs(r)*2*Cpi()/$fs),5)));
// Interpolate between two values or vectors. 0.0 <= u <= 1.0
function lerp(a,b,u) = (b-a)*u + a;
// Calculate hypotenuse length of 2D triangle. // Calculate hypotenuse length of 2D triangle.
function hypot(x,y) = sqrt(x*x+y*y); function hypot(x,y) = sqrt(x*x+y*y);

2
paths.scad
View file

@ -189,7 +189,7 @@ function points_along_path3d(
// Example: // Example:
// 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] ]; // 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] ];
// path = [ [0, 0, 0], [100, 33, 33], [200, -33, -33], [300, 0, 0] ]; // path = [ [0, 0, 0], [100, 33, 33], [200, -33, -33], [300, 0, 0] ];
// extrude_2dpath_along_3dpath(shape, path, tilt=false); // extrude_2dpath_along_3dpath(shape, path);
module extrude_2dpath_along_3dpath(polyline, path, convexity=10) { module extrude_2dpath_along_3dpath(polyline, path, convexity=10) {
pline_count = len(polyline); pline_count = len(polyline);
path_count = len(path); path_count = len(path);