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fixed quaternion slerp to always use the 'short way', updated documentation

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Wenzel Jakob 2013-02-17 18:28:53 -05:00
parent bedef4a672
commit 3d93215e81
2 changed files with 20 additions and 9 deletions
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4
doc/python.tex
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@ -362,8 +362,8 @@ sensor.setShutterOpenTime(1)
stepSize = 5 stepSize = 5
for i in range(0,360 / stepSize): for i in range(0,360 / stepSize):
rotationCur = Transform.rotate(Vector(0, 0, 1), i); rotationCur = Transform.rotate(Vector(0, 0, 1), i*stepSize);
rotationNext = Transform.rotate(Vector(0, 0, 1), i+stepSize); rotationNext = Transform.rotate(Vector(0, 0, 1), (i+1)*stepSize);
trafoCur = Transform.lookAt(rotationCur * Point(0,-6,4), trafoCur = Transform.lookAt(rotationCur * Point(0,-6,4),
Point(0, 0, .5), rotationCur * Vector(0, 1, 0)) Point(0, 0, .5), rotationCur * Vector(0, 1, 0))

25
include/mitsuba/core/quat.h
View File

@ -84,6 +84,11 @@ template <typename T> struct TQuaternion {
return *this; return *this;
} }
/// Unary negation operator
TQuaternion operator-() const {
return TQuaternion(-v, -w);
}
/// Multiply the quaternion by the given scalar and return the result /// Multiply the quaternion by the given scalar and return the result
TQuaternion operator*(T f) const { TQuaternion operator*(T f) const {
return TQuaternion(v*f, w*f); return TQuaternion(v*f, w*f);
@ -230,20 +235,19 @@ template <typename T> struct TQuaternion {
* rotation matrix. * rotation matrix.
*/ */
static TQuaternion fromMatrix(const Matrix4x4 &m) { static TQuaternion fromMatrix(const Matrix4x4 &m) {
/// Implementation from PBRT // Implementation from PBRT, originally based on the matrix
// and quaternion FAQ (http://www.j3d.org/matrix_faq/matrfaq_latest.html)
T trace = m(0, 0) + m(1, 1) + m(2, 2); T trace = m(0, 0) + m(1, 1) + m(2, 2);
TVector3<T> v; T w; TVector3<T> v; T w;
if (trace > 0.f) {
// Compute w from matrix trace, then xyz if (trace > Epsilon) {
// 4w^2 = m[0, 0] + m[1, 1] + m[2, 2] + m[3, 3] (but m[3, 3] == 1)
T s = std::sqrt(trace + 1.0f); T s = std::sqrt(trace + 1.0f);
w = s / 2.0f; w = s * 0.5f;
s = 0.5f / s; s = 0.5f / s;
v.x = (m(2, 1) - m(1, 2)) * s; v.x = (m(2, 1) - m(1, 2)) * s;
v.y = (m(0, 2) - m(2, 0)) * s; v.y = (m(0, 2) - m(2, 0)) * s;
v.z = (m(1, 0) - m(0, 1)) * s; v.z = (m(1, 0) - m(0, 1)) * s;
} else { } else {
// Compute largest of $x$, $y$, or $z$, then remaining components
const int nxt[3] = {1, 2, 0}; const int nxt[3] = {1, 2, 0};
T q[3]; T q[3];
int i = 0; int i = 0;
@ -350,8 +354,15 @@ template <typename T> inline TQuaternion<T> normalize(const TQuaternion<T> &q) {
} }
template <typename T> inline TQuaternion<T> slerp(const TQuaternion<T> &q1, template <typename T> inline TQuaternion<T> slerp(const TQuaternion<T> &q1,
const TQuaternion<T> &q2, Float t) { const TQuaternion<T> &_q2, Float t) {
TQuaternion<T> q2(_q2);
T cosTheta = dot(q1, q2); T cosTheta = dot(q1, q2);
if (cosTheta < 0) {
/* Take the short way! */
q2 = -q2;
cosTheta = -cosTheta;
}
if (cosTheta > .9995f) { if (cosTheta > .9995f) {
// Revert to plain linear interpolation // Revert to plain linear interpolation
return normalize(q1 * (1.0f - t) + q2 * t); return normalize(q1 * (1.0f - t) + q2 * t);