Twirl the fingers

[nt3d] / nt3d.js

diff --git a/nt3d.js b/nt3d.js
index 62d898e6ae7a64d03a9a5a29464b12328aa1b121..bc11c71520157e9b708ace929d7c7ce71d5bcc6d 100644 (file)
--- a/nt3d.js
+++ b/nt3d.js
@@ -62,6 +62,27 @@ nt3d = {
                return this.closed_trianglefan([apex].concat(base)).concat(
                       this.trianglefan(base.reverse()));
        },
                return this.closed_trianglefan([apex].concat(base)).concat(
                       this.trianglefan(base.reverse()));
        },

+       sphere: function(center, radius, latitude_steps, longitude_steps) {
+               return this.oriented_sphere(center, radius, [0,0,1], [1,0,0], latitude_steps, longitude_steps);
+       },
+       oriented_sphere: function(center, radius, north, greenwich, latitude_steps, longitude_steps) {
+               var unit_north = this.unit(north);
+               var north_pole = this.translate_point(this.scale(unit_north,  radius), center);
+               var south_pole = this.translate_point(this.scale(unit_north, -radius), center);
+               return this.spheroid(north_pole, south_pole, radius, greenwich, latitude_steps, longitude_steps);
+       },
+       spheroid: function(north_pole, south_pole, radius, greenwich, latitude_steps, longitude_steps) {
+               var delta = this.sub(north_pole, south_pole);
+               var path = [];
+               for (var i = 0; i < latitude_steps-1; i++) {
+                       path.push(this.translate_point(south_pole, this.scale(delta, (1-Math.cos(Math.PI*i/(latitude_steps-1)))/2)));
+               }
+               path.push(north_pole);
+               function shape(i) {
+                       return nt3d.circle(radius*Math.sin(Math.PI*i/(latitude_steps-1)), longitude_steps);
+               }
+               return this.extrude(path, shape, delta, greenwich);
+       },

        shapenormals_from_closed_path: function(path) {
                return function(i) {
                        var prev = (i == 0) ? path.length-1 : i-1;
        shapenormals_from_closed_path: function(path) {
                return function(i) {
                        var prev = (i == 0) ? path.length-1 : i-1;


@@ -160,7 +181,16 @@ nt3d = {
 
                        // 2. Rotate around shapenormali so that [1,0,0]
                        //    becomes pathnormali.
 
                        // 2. Rotate around shapenormali so that [1,0,0]
                        //    becomes pathnormali.

-                       loop = this.rotate_onto(loop, shapex, pathnormali);
+                       if (!this.opposite(shapex, pathnormali)) {
+                               loop = this.rotate_onto(loop, shapex, pathnormali);
+                       } else {
+                               // Rare edge case: When shapex and pathnormali are
+                               // opposite, rotate_onto cannot cross them to get
+                               // an axis of rotation.  In this case, we (extrude)
+                               // already know what to do -- just rotate PI around
+                               // shapenormali!
+                               loop = this.rotate_about_origin(loop, shapenormali, Math.PI);
+                       }

 
                        // (This would probably be faster and more numerically stable
                        // if the two rotations were applied as one combined operation
 
                        // (This would probably be faster and more numerically stable
                        // if the two rotations were applied as one combined operation


@@ -228,14 +258,24 @@ nt3d = {
        translate: function(points, offset) {
                var translated = [];
                for (var i = 0; i < points.length; i++) {
        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]];
+                       translated[i] = this.translate_point(points[i], offset);

                }
                return translated;
        },
                }
                return translated;
        },

+       translate_point: function(point, offset) {
+               return [point[0] + offset[0],
+                       point[1] + offset[1],
+                       point[2] + offset[2]];
+       },

        angle_between: function(a, b) { // a and b must be unit vectors
        angle_between: function(a, b) { // a and b must be unit vectors

-               return Math.acos(this.dot(a, b));
+               var the_dot = this.dot(a, b);
+               if (the_dot <= -1) {
+                       return Math.PI;
+               }
+               if (the_dot >= 1) {
+                       return 0;
+               }
+               return Math.acos(the_dot);

        },
        rotate_about_origin: function(points, axis, angle) { // axis must be a unit vector
                // From http://inside.mines.edu/~gmurray/ArbitraryAxisRotation/
        },
        rotate_about_origin: function(points, axis, angle) { // axis must be a unit vector
                // From http://inside.mines.edu/~gmurray/ArbitraryAxisRotation/


@@ -252,17 +292,40 @@ nt3d = {
                }
                return rotated;
        },
                }
                return rotated;
        },

+       angle_epsilon: 1e-7,
+       opposite: function(a, b) {
+               // Do a and b point in exactly opposite directions?
+               return Math.abs(this.angle_between(this.unit(a), this.unit(b)) - Math.PI) < this.angle_epsilon;
+       },

        rotate_onto: function(points, a, b) {
                // Rotate points such that a (in points-space) maps onto b
                // by crossing a and b to get a rotation axis and using
                // angle_between to get a rotation angle.
                var angle = this.angle_between(this.unit(a), this.unit(b));
        rotate_onto: function(points, a, b) {
                // Rotate points such that a (in points-space) maps onto b
                // by crossing a and b to get a rotation axis and using
                // angle_between to get a rotation angle.
                var angle = this.angle_between(this.unit(a), this.unit(b));

-               if (Math.abs(angle) < 1e-15) {
-                       // No siginificant rotation to perform.  Bail to avoid
+               var abs_angle = Math.abs(angle);
+               if (Math.abs(angle) < this.angle_epsilon) {
+                       // No significant rotation to perform.  Bail to avoid

                        // NaNs and numerical error
                        return points;
                }
                        // NaNs and numerical error
                        return points;
                }

-               var axis = this.unit(this.cross(a, b));
+               var axis;
+               if (Math.abs(abs_angle - Math.PI) < this.angle_epsilon) {
+                       // a and b point in opposite directions, so
+                       // we cannot cross them.  So just pick something.
+                       // If the caller wishes to avoid this behaviour,
+                       // they should check with this.opposite() first.
+                       axis = this.project_to_orthogonal(a, [1,0,0]);
+                       console.log("rotate_onto: a and b are opposite!  If you carefully chose them to meet some other constraint, you will be sad!  Arbitrarily using axis [1,0,0] ->", axis);
+                       if (this.magnitude(axis) < this.angle_epsilon) {
+                               // Oh, double bad luck!  Our arbitrary choice
+                               // lines up too!  A second, orthogonal arbitrary
+                               // choice is now guaranteed to succeed.
+                               axis = this.project_to_orthogonal(a, [0,1,0]);
+                               console.log("rotate_onto: Double bad luck!  Arbitrarily using axis [0,1,0] ->", axis);
+                       }
+               } else {
+                       axis = this.unit(this.cross(a, b));
+               }

                return this.rotate_about_origin(points, axis, angle);
        },
        rotate: function(points, center, axis, angle) { // axis must be a unit vector
                return this.rotate_about_origin(points, axis, angle);
        },
        rotate: function(points, center, axis, angle) { // axis must be a unit vector


@@ -273,6 +336,79 @@ nt3d = {
                                angle),
                        center);
        },
                                angle),
                        center);
        },

+       point_equal: function(a, b, epsilon) {
+               return Math.abs(a[0] - b[0]) < epsilon &&
+                      Math.abs(a[1] - b[1]) < epsilon &&
+                      Math.abs(a[2] - b[2]) < epsilon;
+       },
+       degenerate_face_epsilon: 1e-10,
+       is_degenerate: function(a, b, c) {
+               return this.point_equal(a, b, this.degenerate_face_epsilon) ||
+                      this.point_equal(b, c, this.degenerate_face_epsilon) ||
+                      this.point_equal(c, a, this.degenerate_face_epsilon);
+       },
+       validate: function(points) {
+               // Do a little validation
+               if (points.length % 3 != 0) {
+                       alert("Points list length not divisble by 3!");
+               }
+               var nan_count = 0;
+               var nan_point_count = 0;
+               var nan_face_count = 0;
+               for (var i = 0; i < points.length/3; i++) {
+                       var nan_in_face = false;
+                       for (var j = 0; j < 3; j++) {
+                               var nan_in_point = false;
+                               for (var k = 0; k < 3; k++) {
+                                       if (isNaN(points[i*3+j][k])) {
+                                               nan_count++;
+                                               nan_in_point = true;
+                                               nan_in_face = true;
+                                       }
+                               }
+                               if (nan_in_point) nan_point_count ++;
+                       }
+                       if (nan_in_face) nan_face_count ++;
+               }
+               if (nan_count != 0) {
+                       alert(nan_count + " NaNs in " + nan_point_count + " points in " + nan_face_count + " faces (" + (100 * nan_face_count / (points.length/3)) + "% of faces).");
+               }
+       },
+       remove_degenerate_faces: function(points) {
+               // Note: This modifies points
+               var degenerate_face_count = 0;
+               for (var i = 0; i < points.length/3; i++) {
+                       if (this.is_degenerate(points[i*3+0], 
+                                              points[i*3+1], 
+                                              points[i*3+2])) {
+                               points.splice(i*3, 3);
+                               i--;
+                               degenerate_face_count ++;
+                       }
+               }
+               if (degenerate_face_count != 0) {
+                       console.log("Removed " + degenerate_face_count + " degenerate faces");
+               }
+               return points;
+       },
+       to_stl: function(points, name) {
+               var stl = "solid " + name + "\n";
+               for (var i = 0; i < points.length/3; i++) {
+                       var a = points[i*3+0];
+                       var b = points[i*3+1];
+                       var c = points[i*3+2];
+                       var normal = this.normal(a, b, c);
+                       stl += "facet normal " + normal[0] + " " + normal[1] + " " + normal[2] + "\n" +
+                               "outer loop\n" +
+                               "vertex " + a[0] + " " + a[1] + " " + a[2] + "\n"+
+                               "vertex " + b[0] + " " + b[1] + " " + b[2] + "\n"+
+                               "vertex " + c[0] + " " + c[1] + " " + c[2] + "\n"+
+                               "endloop\n" +
+                               "endfacet\n";
+               }
+               stl += "endsolid " + name + "\n";
+               return stl;
+       },

        go: function() {
                // Remove any previous download links
                var old_download_link = document.getElementById("nt3d_download");
        go: function() {
                // Remove any previous download links
                var old_download_link = document.getElementById("nt3d_download");


@@ -292,30 +428,13 @@ nt3d = {
                        params[i] = isNaN(as_num) ? as_string : as_num;
                }
 
                        params[i] = isNaN(as_num) ? as_string : as_num;
                }
 

-               // Run user_function

                this.points = this.user_function.apply(null, params);
                this.points = this.user_function.apply(null, params);

-               if (this.points.length % 3 != 0) {
-                       alert("Points list length not divisble by 3!");
-               }
-               var n = this.points.length / 3;

 
 

-               // Make STL
-               this.stl = "solid " + this.user_function.name + "\n";
-               for (var i = 0; i < n; i++) {
-                       var a = this.points[i*3+0];
-                       var b = this.points[i*3+1];
-                       var c = this.points[i*3+2];
-                       var normal = this.normal(a, b, c);
-                       this.stl += "facet normal " + normal[0] + " " + normal[1] + " " + normal[2] + "\n" +
-                               "outer loop\n" +
-                               "vertex " + a[0] + " " + a[1] + " " + a[2] + "\n"+
-                               "vertex " + b[0] + " " + b[1] + " " + b[2] + "\n"+
-                               "vertex " + c[0] + " " + c[1] + " " + c[2] + "\n"+
-                               "endloop\n" +
-                               "endfacet\n";
-               }
-               this.stl += "endsolid " + this.user_function.name + "\n";
+               this.validate(this.points);
+
+               this.remove_degenerate_faces(this.points);

 
 

+               this.stl = this.to_stl(this.points, this.user_function.name);

 
                // Offer result as download
                var download_link = document.createElement("a");
 
                // Offer result as download
                var download_link = document.createElement("a");