linmath: make raising quaternion to power more meaningful

Fixes #160

panda/src/linmath/lquaternion_src.cxx

@@ -26,6 +26,29 @@ pure_imaginary(const FLOATNAME(LVector3) &v) {
   return FLOATNAME(LQuaternion)(0, v[0], v[1], v[2]);
 }
 
+/**
+ * Returns a new quaternion that represents this quaternion raised to the
+ * given power.
+ */
+FLOATNAME(LQuaternion) FLOATNAME(LQuaternion)::
+__pow__(FLOATTYPE power) const {
+  if (IS_NEARLY_ZERO(power)) {
+    return FLOATNAME(LQuaternion)(1, 0, 0, 0);
+  }
+
+  FLOATTYPE l = length();
+  FLOATTYPE norm = _v(0) / l;
+  if (IS_NEARLY_EQUAL(cabs(norm), (FLOATTYPE)1)) {
+    return FLOATNAME(LQuaternion)(cpow(_v(0), power), 0, 0, 0);
+  }
+
+  FLOATTYPE angle = acos(norm);
+  FLOATTYPE angle2 = angle * power;
+  FLOATTYPE mag = cpow(l, power - 1);
+  FLOATTYPE mult = mag * (sin(angle2) / sin(angle));
+  return FLOATNAME(LQuaternion)(cos(angle2) * mag * l, _v(1) * mult, _v(2) * mult, _v(3) * mult);
+}
+
 /**
  * Based on the quat lib from VRPN.
  */

panda/src/linmath/lquaternion_src.h

@@ -57,6 +57,8 @@ PUBLISHED:
   INLINE_LINMATH FLOATNAME(LMatrix3) operator *(const FLOATNAME(LMatrix3) &);
   INLINE_LINMATH FLOATNAME(LMatrix4) operator *(const FLOATNAME(LMatrix4) &);
 
+  FLOATNAME(LQuaternion) __pow__(FLOATTYPE) const;
+
   INLINE_LINMATH bool almost_equal(
       const FLOATNAME(LQuaternion) &other) const;
   INLINE_LINMATH bool almost_equal(