////  Transform.cpp//  shared/src/gpu////  Created by Sam Gateau on 11/4/2014.//  Copyright 2014 High Fidelity, Inc.////  Distributed under the Apache License, Version 2.0.//  See the accompanying file LICENSE or http://www.apache.org/licenses/LICENSE-2.0.html// #include "Transform.h"  void Transform::evalRotationScale(Quat& rotation, Vec3& scale, const Mat3& rotationScaleMatrix) {    const float ACCURACY_THREASHOLD = 0.00001f;     // Following technique taken from:    // http://callumhay.blogspot.com/2010/10/decomposing-affine-transforms.html    // Extract the rotation component - this is done using polar decompostion, where    // we successively average the matrix with its inverse transpose until there is    // no/a very small difference between successive averages    float norm;    int count = 0;    Mat3 rotationMat = rotationScaleMatrix;    do {        Mat3 currInvTranspose = glm::inverse(glm::transpose(rotationMat));                Mat3 nextRotation = 0.5f * (rotationMat + currInvTranspose);         norm = 0.0;        for (int i = 0; i < 3; i++) {            float n = static_cast<float>(                         fabs(rotationMat[0][i] - nextRotation[0][i]) +                         fabs(rotationMat[1][i] - nextRotation[1][i]) +                         fabs(rotationMat[2][i] - nextRotation[2][i]));            norm = (norm > n ? norm : n);        }        rotationMat = nextRotation;    } while (count < 100 && norm > ACCURACY_THREASHOLD);      // extract scale of the matrix as the length of each axis    Mat3 scaleMat = glm::inverse(rotationMat) * rotationScaleMatrix;     scale = glm::max(Vec3(ACCURACY_THREASHOLD), Vec3(scaleMat[0][0], scaleMat[1][1], scaleMat[2][2]));     // Let's work on a local matrix containing rotation only    Mat3 matRot(        rotationScaleMatrix[0] / scale.x,        rotationScaleMatrix[1] / scale.y,        rotationScaleMatrix[2] / scale.z);     // Beware!!! needs to detect for the case there is a negative scale    // Based on the determinant sign we just can flip the scale sign of one component: we choose X axis    float determinant = glm::determinant(matRot);    if (determinant < 0.0f) {        scale.x = -scale.x;        matRot[0] *= -1.0f;    }     // Beware: even though the matRot is supposed to be normalized at that point,    // glm::quat_cast doesn't always return a normalized quaternion...   // rotation = glm::normalize(glm::quat_cast(matRot));    rotation = (glm::quat_cast(matRot));}