Factor out rotate_onto()

[nt3d] / nt3d.js

diff --git a/nt3d.js b/nt3d.js
index d0d716125a3b9357c1820f6e23868bf5e1b57920..bae29f2fa351aa5a9e90cd5bdc29f4a3806baad0 100644 (file)
--- a/nt3d.js
+++ b/nt3d.js
@@ -80,35 +80,29 @@ nt3d = {
                        // 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].
                        // 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 = [];
+                       // We tack [1,0,0] onto the end as a hack to see where
+                       // it ends up after rotation.  This is removed later.
+                       var loop = shape.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]));
+                       //    becomes shapenormals[i].  This puts the shape in
+                       //    the correct plane, but does not constrain its
+                       //    rotation about shapenormals[i].
+                       loop = this.rotate_onto(loop, [0,0,1], shapenormals[i]);
+                       var shapex = loop.pop();
+

                        // 2. Rotate around shapenormals[i] so that [1,0,0]
                        //    becomes fixedpathnormals[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
+                       loop = this.rotate_onto(loop, shapex, fixedpathnormals[i]);
+
+                       // (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.
-                       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;
-                       }
+                       // 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 {


@@ -140,6 +134,9 @@ 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];
        },


@@ -158,26 +155,71 @@ 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);
        },

-       translate: function(a, b) {
-               return [a[0] + b[0], a[1] + b[1], a[2] + b[2]];
+       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));
        },
        },
        angle_between: function(a, b) { // a and b must be unit vectors
                return Math.acos(this.dot(a, b));
        },

-       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;
+       },
+       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(
+                               this.translate(points, this.neg(center)),
+                               axis,
+                               angle),
+                       center);

        },
        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
                }
 
                // Run user_function


@@ -204,11 +246,6 @@ 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 +256,8 @@ 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;