Factor out rotate_onto()

[nt3d] / nt3d.js

diff --git a/nt3d.js b/nt3d.js
index 5f7fad750de86a8064f433ab44d049e86f278a9b..bae29f2fa351aa5a9e90cd5bdc29f4a3806baad0 100644 (file)
--- a/nt3d.js
+++ b/nt3d.js
@@ -80,31 +80,25 @@ 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].
-                       var loop = shape;
+                       // 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]
-                       //    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 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].
-                       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
+                       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
-                       // rather than separate steps.
+                       // rather than separate steps.)
 
                        // 3. Translate to path[i].
                        loop = this.translate(loop, path[i]);
@@ -188,6 +182,19 @@ nt3d = {
                }
                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(