Handle opposite vectors in rotate_onto

[nt3d] / nt3d.js

diff --git a/nt3d.js b/nt3d.js
index 9eee5045617c0a612bd1eed527f98845e7e89845..7e0fa2540e04b9d57787802d36f2ae404efd5b30 100644 (file)
--- a/nt3d.js
+++ b/nt3d.js
@@ -181,7 +181,16 @@ nt3d = {
 
                        // 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
@@ -259,7 +268,14 @@ nt3d = {
                        point[2] + offset[2]];
        },
        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/
@@ -276,17 +292,40 @@ nt3d = {
                }
                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));
-               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;
                }
-               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