Resolve the opposite vector ambiguity in Damped Track constraint.

Damped Track by specification attempts to arrive at the desired
direction via the shortest rotation. However with opposite vectors
there are infinitely many valid 180 degree rotations. Currently
it gives up and does nothing.

I think that it would be more reasonable to resolve the ambiguity
arbitrarily, so that Damped Track won't have a weird dead zone.
To make it more predictable I use a local axis.

In addition, the singularity area vicinity has some floating
point precision problems that result in significant jitter.
This applies workarounds for two causes of instability.

Differential Revision: https://developer.blender.org/D3530

1 files changed, 10 insertions, 0 deletions

diff --git a/source/blender/blenlib/intern/math_vector_inline.c b/source/blender/blenlib/intern/math_vector_inline.c
index 08687a1ab47..715e2e65c96 100644
--- a/source/blender/blenlib/intern/math_vector_inline.c
+++ b/source/blender/blenlib/intern/math_vector_inline.c
@@ -753,6 +753,16 @@ MINLINE void cross_v3_v3v3(float r[3], const float a[3], const float b[3])
 	r[2] = a[0] * b[1] - a[1] * b[0];
 }
 
+/* cross product suffers from severe precision loss when vectors are
+ * nearly parallel or opposite; doing the computation in double helps a lot */
+MINLINE void cross_v3_v3v3_hi_prec(float r[3], const float a[3], const float b[3])
+{
+	BLI_assert(r != a && r != b);
+	r[0] = (float)((double)a[1] * (double)b[2] - (double)a[2] * (double)b[1]);
+	r[1] = (float)((double)a[2] * (double)b[0] - (double)a[0] * (double)b[2]);
+	r[2] = (float)((double)a[0] * (double)b[1] - (double)a[1] * (double)b[0]);
+}
+
 /* Newell's Method */
 /* excuse this fairly specific function,
  * its used for polygon normals all over the place