Generalize rotate()

[nt3d] / nt3d.js

diff --git a/nt3d.js b/nt3d.js
index fbd8f50aa34256add50d21c586c0e83a8bd56fea..1cabfb1bf2ffb6fd9394356a7dccb7346f394c74 100644 (file)
--- a/nt3d.js
+++ b/nt3d.js
@@ -46,11 +46,109 @@ nt3d = {
        closed_quadstrip: function(strip) {
                return this.quadstrip(strip.concat([strip[0], strip[1]]));
        },
        closed_quadstrip: function(strip) {
                return this.quadstrip(strip.concat([strip[0], strip[1]]));
        },

+       extrude: function(shape, path, shapenormals, pathnormals) {
+               var guts_result = nt3d._extrude_guts(shape, path, shapenormals, pathnormals);
+               // Add the end-caps
+               // XXX: This doesn't work if shape is not convex
+               return guts_result.points.concat(
+                       nt3d.trianglefan(guts_result.first_loop.reverse()),
+                       nt3d.trianglefan(guts_result.last_loop));
+
+       },
+       closed_extrude: function(shape, path, shapenormals, pathnormals) {
+               var guts_result = nt3d._extrude_guts(shape, path, shapenormals, pathnormals);
+               // Stitch the ends together
+               return guts_result.points.concat(
+                       nt3d.closed_quadstrip(nt3d.zip(guts_result.first_loop, guts_result.last_loop)));
+       },
+       _fix_pathnormals: function(shapenormals, pathnormals) {
+               // Fix pathnormals[i] to be perfectly perpendicular to
+               // shapenormals[i].  This lets extrude callers be sloppy
+               // with pathnormals, which can greatly simplify things.
+               var fixedpathnormals = [];
+               for (var i = 0; i < pathnormals.length; i++) {
+                       var proj = this.project(shapenormals[i], pathnormals[i]);
+                       fixedpathnormals[i] = this.sub(pathnormals[i], proj);
+               }
+               return fixedpathnormals;
+       },
+       _extrude_guts: function(shape, path, shapenormals, pathnormals) {
+               var fixedpathnormals = this._fix_pathnormals(shapenormals, pathnormals);
+               var result = { points: [] };
+               var prev_loop;
+               for (var i = 0; i < path.length; i++) {
+                       // loop is shape in 3d with (0,0) at path[i], shape's
+                       // z axis in the direction of shapenormals[i], and
+                       // shape's x axis in the direction of pathnormals[i].
+                       var loop = shape;
+
+                       // This is done in three steps:
+                       // 1. Rotate shape out of the xy plane so that [0,0,1]
+                       //    becomes shapenormals[i] by crossing [0,0,1] and
+                       //    shapenormals[i] to get a rotation axis and taking
+                       //    their dot product to get a rotation angle.  This
+                       //    puts the shape in the correct plane, but does not
+                       //    constrain its rotation about shapenormals[i].
+                       var rot1axis = this.unit(this.cross([0,0,1], shapenormals[i]));
+                       var rot1angle = this.angle_between([0,0,1], this.unit(shapenormals[i]));
+                       if (rot1angle > 1e-7) {
+                               loop = this.rotate_about_origin(loop, rot1axis, rot1angle);
+                       }
+
+                       // 2. Rotate around shapenormals[i] so that [1,0,0]
+                       //    becomes fixedpathnormals[i].
+                       var rot2axis = this.unit(shapenormals[i]);
+                       var rot2angle = this.angle_between([1,0,0], this.unit(fixedpathnormals[i]));
+                       if (rot2angle > 1e-7) {
+                               loop = this.rotate_about_origin(loop, rot2axis, rot2angle);
+                       }
+                       // This would probably be faster and more numerically stable
+                       // if the two rotations were applied as one combined operation
+                       // rather than separate steps.
+
+                       // 3. Translate to path[i].
+                       loop = this.translate(loop, path[i]);
+
+                       if (i == 0) {
+                               result.first_loop = loop;
+                       } else {
+                               result.points = result.points.concat(nt3d.closed_quadstrip(nt3d.zip(loop, prev_loop)));
+                       }
+                       prev_loop = loop;
+               }
+               result.last_loop = prev_loop;
+               return result;
+       },
+       zip: function(a, b) {
+               var result = [];
+               if (a.length != b.length) {
+                       alert("Zip over different-sized inputs");
+               }
+               for (var i = 0; i < a.length; i++) {
+                       result.push(a[i], b[i]);
+               }
+               return result;
+       },
+       magnitude: function(a) {
+               return Math.sqrt(a[0]*a[0] + a[1]*a[1] + a[2]*a[2]);
+       },
+       unit: function(a) {
+               return this.scale(a, 1 / this.magnitude(a));
+       },

        sub: function(a, b) {
                return [a[0] - b[0],
                        a[1] - b[1],
                        a[2] - b[2]];
        },
        sub: function(a, b) {
                return [a[0] - b[0],
                        a[1] - b[1],
                        a[2] - b[2]];
        },

+       neg: function(a) {
+               return [-a[0], -a[1], -a[2]];
+       },
+       dot: function(a, b) {
+               return a[0]*b[0] + a[1]*b[1] + a[2]*b[2];
+       },
+       scale: function(v, s) { // Scale vector v by scalar s
+               return [s*v[0], s*v[1], s*v[2]];
+       },

        cross: function(a, b) {
                return [a[1]*b[2] - a[2]*b[1],
                        a[2]*b[0] - a[0]*b[2],
        cross: function(a, b) {
                return [a[1]*b[2] - a[2]*b[1],
                        a[2]*b[0] - a[0]*b[2],


@@ -59,6 +157,45 @@ nt3d = {
        normal: function(a, b, c) {
                return this.cross(this.sub(a, b), this.sub(b, c));
        },
        normal: function(a, b, c) {
                return this.cross(this.sub(a, b), this.sub(b, c));
        },

+       project: function(a, b) { // Project b onto a
+               var a_magnitude = this.magnitude(a);
+               return this.scale(a, this.dot(a, b) / a_magnitude * a_magnitude);
+       },
+       translate: function(points, offset) {
+               var translated = [];
+               for (var i = 0; i < points.length; i++) {
+                       translated[i] = [points[i][0] + offset[0],
+                                        points[i][1] + offset[1],
+                                        points[i][2] + offset[2]];
+               }
+               return translated;
+       },
+       angle_between: function(a, b) { // a and b must be unit vectors
+               return Math.acos(this.dot(a, b));
+       },
+       rotate_about_origin: function(points, axis, angle) { // axis must be a unit vector
+               // From http://inside.mines.edu/~gmurray/ArbitraryAxisRotation/
+               var cosangle = Math.cos(angle);
+               var sinangle = Math.sin(angle);
+               var rotated = [];
+               for (var i = 0; i < points.length; i++) {
+                       var p = points[i];
+                       var tmp = this.dot(p, axis) * (1 - cosangle);
+                       rotated[i] = [
+                               axis[0]*tmp + p[0]*cosangle + (-axis[2]*p[1] + axis[1]*p[2])*sinangle,
+                               axis[1]*tmp + p[1]*cosangle + ( axis[2]*p[0] - axis[0]*p[2])*sinangle,
+                               axis[2]*tmp + p[2]*cosangle + (-axis[1]*p[0] + axis[0]*p[1])*sinangle];
+               }
+               return rotated;
+       },
+       rotate: function(points, center, axis, angle) { // axis must be a unit vector
+               return this.translate(
+                       this.rotate_about_origin(
+                               this.translate(points, this.neg(center)),
+                               axis,
+                               angle),
+                       center);
+       },

        go: function() {
                // Get params from form
                var params = [];
        go: function() {
                // Get params from form
                var params = [];