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Optimize Quat_FromMtx()

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This commit is contained in:
fincs 2017-12-29 22:32:44 +01:00
parent 8f3fda7986
commit c2226e2182
2 changed files with 54 additions and 45 deletions
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93
source/maths/quat_frommtx.c
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@ -2,54 +2,61 @@
C3D_FQuat Quat_FromMtx(const C3D_Mtx* m)
{
//Taken from Gamasutra:
//http://www.gamasutra.com/view/feature/131686/rotating_objects_using_quaternions.php
//Expanded upon from:
//http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/
//Variables we need.
float trace, sqrtTrace;
// Original algorithm taken from here (with some optimizations):
// https://d3cw3dd2w32x2b.cloudfront.net/wp-content/uploads/2015/01/matrix-to-quat.pdf
// Layout of the algorithm:
// First, we select a large (non-zero!) component "P" in the output quaternion (q)
// (we can test this just by looking at the diagonal of the matrix)
// Second, we calculate q' which is our desired output quaternion (q) scaled by 4P
// (this can be done with simple additions; the 4P factor is large and non-zero thanks to above)
// Third, we normalize q' to finally obtain q
// (this will work because normalize(kq) = q for any k scalar and q unit quaternion)
C3D_FQuat q;
//Check the main diagonal of the passed-in matrix for positive/negative signs.
trace = m->r[0].x + m->r[1].y + m->r[2].z;
if (trace > 0.0f)
C3D_FVec diagonal = FVec4_New(m->r[0].x, m->r[1].y, m->r[2].z, 1.0f);
// Check if x^2 + y^2 >= z^2 + w^2
if (diagonal.z <= 0.0f)
{
//Diagonal is positive.
sqrtTrace = sqrtf(trace + 1.0f);
q.w = sqrtTrace / 2.0f;
sqrtTrace = 0.5 / sqrtTrace;
q.x = (m->r[1].z - m->r[2].y) * sqrtTrace;
q.y = (m->r[2].x - m->r[0].z) * sqrtTrace;
q.z = (m->r[0].y - m->r[1].x) * sqrtTrace;
}
else
{
//Diagonal is negative or equals to zero. We need to identify which major diagonal element has the greatest value.
if (m->r[0].x > m->r[1].y && m->r[0].x > m->r[2].z)
// Check if |x| >= |y|
if (diagonal.x >= diagonal.y)
{
sqrtTrace = 2.0f * sqrtf(1.0f + m->r[0].x - m->r[1].y - m->r[2].z);
q.w = (m->r[2].y - m->r[1].z) / sqrtTrace;
q.x = 0.25f * sqrtTrace;
q.y = (m->r[0].y - m->r[1].x) / sqrtTrace;
q.z = (m->r[0].z - m->r[2].x) / sqrtTrace;
// X case
q.x = diagonal.w + diagonal.x - diagonal.y - diagonal.z;
q.y = m->r[1].x + m->r[0].y;
q.z = m->r[2].x + m->r[0].z;
q.w = m->r[2].y - m->r[1].z;
}
else if (m->r[1].y > m->r[2].z)
else
{
sqrtTrace = 2.0f * sqrtf(1.0f + m->r[1].y - m->r[0].x - m->r[2].z);
q.w = (m->r[0].z - m->r[2].x) / sqrtTrace;
q.x = (m->r[0].y - m->r[1].x) / sqrtTrace;
q.y = 0.25f * sqrtTrace;
q.z = (m->r[1].z - m->r[2].y) / sqrtTrace;
}
else
{
sqrtTrace = 2.0f * sqrtf(1.0f + m->r[2].z - m->r[0].x - m->r[1].y);
q.w = (m->r[1].x - m->r[0].y) / sqrtTrace;
q.x = (m->r[0].z - m->r[2].x) / sqrtTrace;
q.y = (m->r[1].z - m->r[2].y) / sqrtTrace;
q.z = 0.25f * sqrtTrace;
// Y case
q.x = m->r[1].x + m->r[0].y;
q.y = diagonal.w - diagonal.x + diagonal.y - diagonal.z;
q.z = m->r[2].y + m->r[1].z;
q.w = m->r[0].z - m->r[2].x;
}
}
return q;
else
{
// Check if |z| >= |w|
if (-diagonal.x >= diagonal.y)
{
// Z case
q.x = m->r[2].x + m->r[0].z;
q.y = m->r[2].y + m->r[1].z;
q.z = diagonal.w - diagonal.x - diagonal.y + diagonal.z;
q.w = m->r[1].x - m->r[0].y;
}
else
{
// W case
q.x = m->r[2].y - m->r[1].z;
q.y = m->r[0].z - m->r[2].x;
q.z = m->r[1].x - m->r[0].y;
q.w = diagonal.w + diagonal.x + diagonal.y + diagonal.z;
}
}
// Normalize the quaternion
return Quat_Normalize(q);
}

6
test/pc/main.cpp
View File

@ -953,13 +953,15 @@ check_quaternion(generator_t &gen, distribution_t &dist)
// check conversion to matrix
{
C3D_FQuat q = randomQuat(gen, dist);
C3D_FQuat q = Quat_Normalize(randomQuat(gen, dist));
glm::quat g = loadQuat(q);
C3D_Mtx m;
Mtx_FromQuat(&m, q);
assert(m == glm::mat4_cast(g));
C3D_FQuat q2 = Quat_FromMtx(&m);
assert(q2 == q || q2 == FVec4_Negate(q));
}
}
}