Optimization in quaternion::rotationFromTo from Robert Eisele

Turns out we can avoid a square root and a division.
Patch comes even with proof: https://raw.org/proof/quaternion-from-two-vectors
(I also tested it a while and indeed got same results)


git-svn-id: svn://svn.code.sf.net/p/irrlicht/code/trunk@6511 dfc29bdd-3216-0410-991c-e03cc46cb475

changes.txt

@@ -1,6 +1,7 @@
 --------------------------
 Changes in 1.9 (not yet released)
 
+- Optimize quaternion::rotationFromTo. Thanks @Robert Eisele for patch and proof (https://raw.org/proof/quaternion-from-two-vectors)
 - Shader materials shows now how to pass material values.
   In 1.8 we could still use gl_FrontMaterial, but that is no longer supported in shaders
 - Get IMeshBuffer::append functions working for a few more cases and adapt interface so one can prevent the BoundingBox update.

include/quaternion.h

@@ -721,6 +721,8 @@ inline core::quaternion& quaternion::makeIdentity()
 inline core::quaternion& quaternion::rotationFromTo(const vector3df& from, const vector3df& to)
 {
 	// Based on Stan Melax's article in Game Programming Gems
+	// Optimized by Robert Eisele: https://raw.org/proof/quaternion-from-two-vectors
+
 	// Copy, since cannot modify local
 	vector3df v0 = from;
 	vector3df v1 = to;
@@ -745,10 +747,8 @@ inline core::quaternion& quaternion::rotationFromTo(const vector3df& from, const
 		return set(axis.X, axis.Y, axis.Z, 0).normalize();
 	}
 
-	const f32 s = sqrtf( (1+d)*2 ); // optimize inv_sqrt
-	const f32 invs = 1.f / s;
-	const vector3df c = v0.crossProduct(v1)*invs;
-	return set(c.X, c.Y, c.Z, s * 0.5f).normalize();
+	const vector3df c = v0.crossProduct(v1);
+	return set(c.X, c.Y, c.Z, 1 + d).normalize();
 }