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/*
* Copyright 2011-2013 Blender Foundation
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/*
* Adapted from code with license:
*
* Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
* Digital Ltd. LLC. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are
* met:
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
* * Neither the name of Industrial Light & Magic nor the names of its
* contributors may be used to endorse or promote products derived
* from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include "util/util_transform.h"
#include "util/util_boundbox.h"
#include "util/util_math.h"
CCL_NAMESPACE_BEGIN
/* Transform Inverse */
static bool transform_matrix4_gj_inverse(float R[][4], float M[][4])
{
/* forward elimination */
for(int i = 0; i < 4; i++) {
int pivot = i;
float pivotsize = M[i][i];
if(pivotsize < 0)
pivotsize = -pivotsize;
for(int j = i + 1; j < 4; j++) {
float tmp = M[j][i];
if(tmp < 0)
tmp = -tmp;
if(tmp > pivotsize) {
pivot = j;
pivotsize = tmp;
}
}
if(UNLIKELY(pivotsize == 0.0f))
return false;
if(pivot != i) {
for(int j = 0; j < 4; j++) {
float tmp;
tmp = M[i][j];
M[i][j] = M[pivot][j];
M[pivot][j] = tmp;
tmp = R[i][j];
R[i][j] = R[pivot][j];
R[pivot][j] = tmp;
}
}
for(int j = i + 1; j < 4; j++) {
float f = M[j][i] / M[i][i];
for(int k = 0; k < 4; k++) {
M[j][k] -= f*M[i][k];
R[j][k] -= f*R[i][k];
}
}
}
/* backward substitution */
for(int i = 3; i >= 0; --i) {
float f;
if(UNLIKELY((f = M[i][i]) == 0.0f))
return false;
for(int j = 0; j < 4; j++) {
M[i][j] /= f;
R[i][j] /= f;
}
for(int j = 0; j < i; j++) {
f = M[j][i];
for(int k = 0; k < 4; k++) {
M[j][k] -= f*M[i][k];
R[j][k] -= f*R[i][k];
}
}
}
return true;
}
Transform transform_inverse(const Transform& tfm)
{
Transform tfmR = transform_identity();
float M[4][4], R[4][4];
memcpy(R, &tfmR, sizeof(R));
memcpy(M, &tfm, sizeof(M));
if(UNLIKELY(!transform_matrix4_gj_inverse(R, M))) {
/* matrix is degenerate (e.g. 0 scale on some axis), ideally we should
* never be in this situation, but try to invert it anyway with tweak */
M[0][0] += 1e-8f;
M[1][1] += 1e-8f;
M[2][2] += 1e-8f;
if(UNLIKELY(!transform_matrix4_gj_inverse(R, M))) {
return transform_identity();
}
}
memcpy(&tfmR, R, sizeof(R));
return tfmR;
}
/* Motion Transform */
float4 transform_to_quat(const Transform& tfm)
{
double trace = (double)(tfm[0][0] + tfm[1][1] + tfm[2][2]);
float4 qt;
if(trace > 0.0) {
double s = sqrt(trace + 1.0);
qt.w = (float)(s/2.0);
s = 0.5/s;
qt.x = (float)((double)(tfm[2][1] - tfm[1][2]) * s);
qt.y = (float)((double)(tfm[0][2] - tfm[2][0]) * s);
qt.z = (float)((double)(tfm[1][0] - tfm[0][1]) * s);
}
else {
int i = 0;
if(tfm[1][1] > tfm[i][i])
i = 1;
if(tfm[2][2] > tfm[i][i])
i = 2;
int j = (i + 1)%3;
int k = (j + 1)%3;
double s = sqrt((double)(tfm[i][i] - (tfm[j][j] + tfm[k][k])) + 1.0);
double q[3];
q[i] = s * 0.5;
if(s != 0.0)
s = 0.5/s;
double w = (double)(tfm[k][j] - tfm[j][k]) * s;
q[j] = (double)(tfm[j][i] + tfm[i][j]) * s;
q[k] = (double)(tfm[k][i] + tfm[i][k]) * s;
qt.x = (float)q[0];
qt.y = (float)q[1];
qt.z = (float)q[2];
qt.w = (float)w;
}
return qt;
}
static void transform_decompose(Transform *decomp, const Transform *tfm)
{
/* extract translation */
decomp->y = make_float4(tfm->x.w, tfm->y.w, tfm->z.w, 0.0f);
/* extract rotation */
Transform M = *tfm;
M.x.w = 0.0f; M.y.w = 0.0f; M.z.w = 0.0f; M.w.w = 1.0f;
Transform R = M;
float norm;
int iteration = 0;
do {
Transform Rnext;
Transform Rit = transform_inverse(transform_transpose(R));
for(int i = 0; i < 4; i++)
for(int j = 0; j < 4; j++)
Rnext[i][j] = 0.5f * (R[i][j] + Rit[i][j]);
norm = 0.0f;
for(int i = 0; i < 3; i++) {
norm = max(norm,
fabsf(R[i][0] - Rnext[i][0]) +
fabsf(R[i][1] - Rnext[i][1]) +
fabsf(R[i][2] - Rnext[i][2]));
}
R = Rnext;
iteration++;
} while(iteration < 100 && norm > 1e-4f);
if(transform_negative_scale(R))
R = R * transform_scale(-1.0f, -1.0f, -1.0f);
decomp->x = transform_to_quat(R);
/* extract scale and pack it */
Transform scale = transform_inverse(R) * M;
decomp->y.w = scale.x.x;
decomp->z = make_float4(scale.x.y, scale.x.z, scale.y.x, scale.y.y);
decomp->w = make_float4(scale.y.z, scale.z.x, scale.z.y, scale.z.z);
}
void transform_motion_decompose(MotionTransform *decomp, const MotionTransform *motion, const Transform *mid)
{
transform_decompose(&decomp->pre, &motion->pre);
transform_decompose(&decomp->mid, mid);
transform_decompose(&decomp->post, &motion->post);
/* ensure rotation around shortest angle, negated quaternions are the same
* but this means we don't have to do the check in quat_interpolate */
if(dot(decomp->pre.x, decomp->mid.x) < 0.0f)
decomp->pre.x = -decomp->pre.x;
if(dot(decomp->mid.x, decomp->post.x) < 0.0f)
decomp->mid.x = -decomp->mid.x;
}
Transform transform_from_viewplane(BoundBox2D& viewplane)
{
return
transform_scale(1.0f / (viewplane.right - viewplane.left),
1.0f / (viewplane.top - viewplane.bottom),
1.0f) *
transform_translate(-viewplane.left,
-viewplane.bottom,
0.0f);
}
CCL_NAMESPACE_END
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