Helper functions for shapenormals

[nt3d] / nt3d.js

diff --git a/nt3d.js b/nt3d.js
index 4cec096683d971b7c95b0b390c3e88725bad6a0e..9c4aeb18693000a43267508722918b30c6cdfe80 100644 (file)
--- a/nt3d.js
+++ b/nt3d.js
@@ -46,8 +46,59 @@ 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()));
+       },
+       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]);
+               };
+       },
+       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 = nt3d._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(


@@ -55,56 +106,57 @@ nt3d = {
                        nt3d.trianglefan(guts_result.last_loop));
 
        },
                        nt3d.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 = nt3d._extrude_guts(path, shape, shapenormals, pathnormals);

                // Stitch the ends together
                return guts_result.points.concat(
                        nt3d.closed_quadstrip(nt3d.zip(guts_result.first_loop, guts_result.last_loop)));
        },
                // 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);
+       _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 = shape;
+                       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]));
-                       if (rot1angle > 1e-7) {
-                               loop = this.rotate_about_origin(loop, rot1axis, rot1angle);
-                       }
+                       //    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 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
+                       // 2. Rotate around shapenormali so that [1,0,0]
+                       //    becomes pathnormali.
+                       loop = this.rotate_onto(loop, shapex, pathnormali);
+
+                       // (This would probably be faster and more numerically stable

                        // if the two rotations were applied as one combined operation
                        // if the two rotations were applied as one combined operation

-                       // rather than separate steps.
+                       // rather than separate steps.)

 
                        // 3. Translate to path[i].
                        loop = this.translate(loop, path[i]);
 
                        // 3. Translate to path[i].
                        loop = this.translate(loop, path[i]);


@@ -161,6 +213,10 @@ nt3d = {
                var a_magnitude = this.magnitude(a);
                return this.scale(a, this.dot(a, b) / a_magnitude * a_magnitude);
        },
                var a_magnitude = this.magnitude(a);
                return this.scale(a, this.dot(a, b) / a_magnitude * a_magnitude);
        },

+       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++) {
        translate: function(points, offset) {
                var translated = [];
                for (var i = 0; i < points.length; i++) {


@@ -188,6 +244,19 @@ nt3d = {
                }
                return rotated;
        },
                }
                return rotated;
        },

+       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
+                       // NaNs and numerical error
+                       return points;
+               }
+               var 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(
        rotate: function(points, center, axis, angle) { // axis must be a unit vector
                return this.translate(
                        this.rotate_about_origin(


@@ -197,6 +266,16 @@ nt3d = {
                        center);
        },
        go: function() {
                        center);
        },
        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++) {


@@ -229,11 +308,6 @@ 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");


@@ -244,6 +318,8 @@ 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;