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