Serrated blade demo

[nt3d] / nt3d.js

diff --git a/nt3d.js b/nt3d.js
index d0d716125a3b9357c1820f6e23868bf5e1b57920..7e0fa2540e04b9d57787802d36f2ae404efd5b30 100644 (file)
--- a/nt3d.js
+++ b/nt3d.js
@@ -46,73 +46,163 @@ 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);
+       circle: function(r, n) {
+               var points = [];
+               for (var i = 0; i < n; i++) {
+                       points.push([r*Math.cos(2*Math.PI*i/n),
+                                    r*Math.sin(2*Math.PI*i/n),
+                                    0]);
+               }
+               return points;
+       },
+       cone: function(base_center, apex, radius, steps) {
+               var base = this.circle(radius, steps);
+               base = this.rotate_onto(base, [0,0,1], this.sub(apex, base_center));
+               base = this.translate(base, base_center);
+               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;
+                       var next = (i == path.length-1) ? 0 : i+1;
+                       return nt3d.sub(path[next], path[prev]);
+               };
+       },
+       shapenormals_from_path_and_extra_points: function(path, first_point, last_point) {
+               return function(i) {
+                       var prev = (i == 0) ? first_point : path[i-1];
+                       var next = (i == path.length-1) ? last_point : path[i+1];
+                       return nt3d.sub(next, prev);
+               };
+       },
+       shapenormals_from_path_and_first_and_last_normals: function(path, first_normal, last_normal) {
+               return function(i) {
+                       if (i == 0) { return first_normal; }
+                       if (i == path.length-1) { return last_normal; }
+                       return nt3d.sub(path[i+1], path[i-1]);
+               };
+       },
+       pathnormals_from_point: function(path, p) {
+               // Use this with any point that is not on any path tangent line
+               var pathnormals = [];
+               for (var i = 0; i < path.length; i++) {
+                       pathnormals.push(this.sub(path[i], p));
+               }
+               return pathnormals;
+       },
+       to_function: function(thing, make_indexer) {
+               // If thing is a point, just yield thing every time.
+               // If thing is a list of points && make_indexer, index into thing.
+               // If thing is already a function, just return it.
+               if (({}).toString.call(thing) === "[object Function]") {
+                       return thing;  // Already a function
+               }
+               if (make_indexer && Array.isArray(thing[0])) {
+                       // Looks like a list of points.
+                       return function(i) { return thing[i]; }
+               }
+               return function() { return thing; }
+       },
+       extrude: function(path, shape, shapenormals, pathnormals) {
+
+               var guts_result = this._extrude_guts(path, shape, shapenormals, pathnormals);

                // Add the end-caps
                // XXX: This doesn't work if shape is not convex
                return guts_result.points.concat(
                // 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));
+                       this.trianglefan(guts_result.first_loop.reverse()),
+                       this.trianglefan(guts_result.last_loop));

 
        },
 
        },

-       closed_extrude: function(shape, path, shapenormals, pathnormals) {
-               var guts_result = nt3d._extrude_guts(shape, path, shapenormals, pathnormals);
+       closed_extrude: function(path, shape, shapenormals, pathnormals) {
+               var guts_result = this._extrude_guts(path, shape, shapenormals, pathnormals);

                // Stitch the ends together
                return guts_result.points.concat(
                // 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;
+                       this.closed_quadstrip(this.zip(guts_result.first_loop, guts_result.last_loop)));

        },
        },

-       _extrude_guts: function(shape, path, shapenormals, pathnormals) {
-               var fixedpathnormals = this._fix_pathnormals(shapenormals, pathnormals);
+       _extrude_guts: function(path, shape, shapenormals, pathnormals) {
+               var shape_fun = this.to_function(shape, false);
+               var shapenormal_fun = this.to_function(shapenormals, true);
+               var pathnormal_fun = this.to_function(pathnormals, true);

                var result = { points: [] };
                var prev_loop;
                for (var i = 0; i < path.length; i++) {
                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 = [];
+                       var shapenormali = shapenormal_fun(i, path[i]);
+                       var pathnormali = pathnormal_fun(i, path[i], shapenormali);
+
+                       // Fix pathnormali to be perfectly perpendicular to
+                       // shapenormali.  pathnormali must be perpendicular to
+                       // shapenormali or the second rotation will take loop
+                       // back out of the shapenormali plane that the first
+                       // rotation so carefully placed it in.  But, letting
+                       // callers be sloppy with the pathnormals can greatly
+                       // simplify generating them -- so much so that you can
+                       // often just pass a constant to use the same value
+                       // along the whole path.
+                       pathnormali = this.project_to_orthogonal(shapenormali, pathnormali);
+
+                       var shapei = shape_fun(i, path[i], shapenormali, pathnormali);
+
+                       // loop is shapei in 3d with (0,0) at path[i], shape's
+                       // z axis in the direction of shapenormali, and shape's
+                       // x axis in the direction of pathnormali.  We tack
+                       // [1,0,0] onto the end as a hack to see where it ends
+                       // up after the first rotation.  This is removed later.
+                       var loop = shapei.concat([[1,0,0]]);
+

                        // This is done in three steps:
                        // 1. Rotate shape out of the xy plane so that [0,0,1]
                        // 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]));
-                       // 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]));
-                       // 3. Translate to path[i].
-                       // This would probably be faster and more numerically stable
-                       // if the two rotations were applied as one combined operation
-                       // rather than separate steps.
-                       for (var j = 0; j < shape.length; j++) {
-                               var p = [shape[j][0], shape[j][1], 0];
-                               if (rot1angle > 1e-7) {
-                                       p = this.rotate(p, rot1axis, rot1angle);
-                               }
-                               if (rot2angle > 1e-7) {
-                                       p = this.rotate(p, rot2axis, rot2angle);
-                               }
-                               p = this.translate(p, path[i]);
-                               loop[j] = p;
+                       //    becomes shapenormali.  This puts the shape in
+                       //    the correct plane, but does not constrain its
+                       //    rotation about shapenormali.
+                       loop = this.rotate_onto(loop, [0,0,1], shapenormali);
+                       var shapex = loop.pop();
+
+                       // 2. Rotate around shapenormali so that [1,0,0]
+                       //    becomes 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
+                       // rather than separate steps.)
+
+                       // 3. Translate to path[i].
+                       loop = this.translate(loop, path[i]);
+

                        if (i == 0) {
                                result.first_loop = loop;
                        } else {
                        if (i == 0) {
                                result.first_loop = loop;
                        } else {

-                               result.points = result.points.concat(nt3d.closed_quadstrip(nt3d.zip(loop, prev_loop)));
+                               result.points = result.points.concat(this.closed_quadstrip(this.zip(loop, prev_loop)));

                        }
                        prev_loop = loop;
                }
                        }
                        prev_loop = loop;
                }


@@ -140,6 +230,9 @@ nt3d = {
                        a[1] - b[1],
                        a[2] - b[2]];
        },
                        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];
        },
        dot: function(a, b) {
                return a[0]*b[0] + a[1]*b[1] + a[2]*b[2];
        },


@@ -156,40 +249,170 @@ nt3d = {
        },
        project: function(a, b) { // Project b onto a
                var a_magnitude = this.magnitude(a);
        },
        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);
+               return this.scale(a, this.dot(a, b) / (a_magnitude * a_magnitude));

        },
        },

-       translate: function(a, b) {
-               return [a[0] + b[0], a[1] + b[1], a[2] + b[2]];
+       project_to_orthogonal: function(a, b) {
+               // The nearest thing to b that is orthogonal to a
+               return this.sub(b, this.project(a, b));
+       },
+       translate: function(points, offset) {
+               var translated = [];
+               for (var i = 0; i < points.length; i++) {
+                       translated[i] = this.translate_point(points[i], offset);
+               }
+               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: function(point, axis, angle) { // axis must be a unit vector
+       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);
                // From http://inside.mines.edu/~gmurray/ArbitraryAxisRotation/
                var cosangle = Math.cos(angle);
                var sinangle = Math.sin(angle);

-               var tmp = this.dot(point, axis) * (1 - cosangle);
-               return [axis[0]*tmp + point[0]*cosangle + (-axis[2]*point[1] + axis[1]*point[2])*sinangle,
-                       axis[1]*tmp + point[1]*cosangle + ( axis[2]*point[0] - axis[0]*point[2])*sinangle,
-                       axis[2]*tmp + point[2]*cosangle + (-axis[1]*point[0] + axis[0]*point[1])*sinangle];
+               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;
+       },
+       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));
+               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;
+               }
+               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.translate(
+                       this.rotate_about_origin(
+                               this.translate(points, this.neg(center)),
+                               axis,
+                               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);

        },
        go: function() {
        },
        go: function() {

+               // Remove any previous download links
+               var old_download_link = document.getElementById("nt3d_download");
+               if (old_download_link) {
+                       old_download_link.parentNode.removeChild(old_download_link);
+               }
+
+               // Continue in a callback, so that there's not a stale download
+               // link hanging around while we process.
+               setTimeout(function(the_this) { (function() {
+

                // Get params from form
                var params = [];
                for (var i = 0; i < this.user_params.length; i++) {
                // Get params from form
                var params = [];
                for (var i = 0; i < this.user_params.length; i++) {

-                       params[i] = this.form.elements["param"+i].value;
+                       var as_string = this.form.elements["param"+i].value;
+                       var as_num = +as_string;
+                       params[i] = isNaN(as_num) ? as_string : as_num;

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

+
+               // Do a little validation

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

-               var n = this.points.length / 3;
+               var nan_count = 0;
+               var nan_point_count = 0;
+               var nan_face_count = 0;
+               for (var i = 0; i < this.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(this.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 / (this.points.length/3)) + "% of faces).");
+               }
+
+               // Remove degenerate faces
+               var degenerate_face_count = 0;
+               for (var i = 0; i < this.points.length/3; i++) {
+                       if (this.is_degenerate(this.points[i*3+0], 
+                                              this.points[i*3+1], 
+                                              this.points[i*3+2])) {
+                               this.points.splice(i*3, 3);
+                               i--;
+                               degenerate_face_count ++;
+                       }
+               }
+               if (degenerate_face_count != 0) {
+                       console.log("Removed " + degenerate_face_count + " degenerate faces");
+               }

 
                // Make STL
                this.stl = "solid " + this.user_function.name + "\n";
 
                // Make STL
                this.stl = "solid " + this.user_function.name + "\n";

-               for (var i = 0; i < n; i++) {
+               for (var i = 0; i < this.points.length/3; i++) {

                        var a = this.points[i*3+0];
                        var b = this.points[i*3+1];
                        var c = this.points[i*3+2];
                        var a = this.points[i*3+0];
                        var b = this.points[i*3+1];
                        var c = this.points[i*3+2];


@@ -204,11 +427,6 @@ nt3d = {
                }
                this.stl += "endsolid " + this.user_function.name + "\n";
 
                }
                this.stl += "endsolid " + this.user_function.name + "\n";
 

-               // Remove any previous download links
-               var old_download_link = document.getElementById("nt3d_download");
-               if (old_download_link) {
-                       old_download_link.parentNode.removeChild(old_download_link);
-               }

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


@@ -219,6 +437,8 @@ nt3d = {
                download_link.setAttribute("href", "data:application/sla," + encodeURIComponent(this.stl));
                this.ui.appendChild(download_link);
                setTimeout(function() { download_link.setAttribute("style", "-webkit-transition: background-color 0.4s; -moz-transition: background-color 0.4s; -o-transition: background-color 0.4s; -ms-transition: background-color 0.4s; transition: background-color 0.4s; background-color: inherit"); }, 0);
                download_link.setAttribute("href", "data:application/sla," + encodeURIComponent(this.stl));
                this.ui.appendChild(download_link);
                setTimeout(function() { download_link.setAttribute("style", "-webkit-transition: background-color 0.4s; -moz-transition: background-color 0.4s; -o-transition: background-color 0.4s; -ms-transition: background-color 0.4s; transition: background-color 0.4s; background-color: inherit"); }, 0);

+
+               }).call(the_this); }, 0, this); // (We were in a callback this whole time, remember?)

        },
        framework: function (f, params) {
                this.user_function = f;
        },
        framework: function (f, params) {
                this.user_function = f;