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Ridiculously complicated minimization code.
This commit is contained in:
Andrzej Kapolka
parent
aa0b3a18ef
commit
8ebb2a7fb4
1 changed files with 134 additions and 15 deletions
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@ -1657,7 +1657,7 @@ int VoxelAugmentVisitor::visit(MetavoxelInfo& info) {
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crossing.color = colorX[0];
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crossing.material = materialBase[0];
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}
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crossing.point = glm::vec3(qAlpha(hermite), 0.0f, 0.0f);
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crossing.point = glm::vec3(qAlpha(hermite) * EIGHT_BIT_MAXIMUM_RECIPROCAL, 0.0f, 0.0f);
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}
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if (middleY) {
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if (alpha1 != alpha3) {
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@ -1671,7 +1671,7 @@ int VoxelAugmentVisitor::visit(MetavoxelInfo& info) {
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crossing.color = colorX[1];
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crossing.material = materialBase[1];
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}
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crossing.point = glm::vec3(EIGHT_BIT_MAXIMUM, qAlpha(hermite), 0.0f);
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crossing.point = glm::vec3(1.0f, qAlpha(hermite) * EIGHT_BIT_MAXIMUM_RECIPROCAL, 0.0f);
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}
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if (alpha2 != alpha3) {
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QRgb hermite = hermiteBase[hermiteStride];
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@ -1684,7 +1684,7 @@ int VoxelAugmentVisitor::visit(MetavoxelInfo& info) {
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crossing.color = colorX[size];
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crossing.material = materialBase[size];
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}
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crossing.point = glm::vec3(qAlpha(hermite), EIGHT_BIT_MAXIMUM, 0.0f);
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crossing.point = glm::vec3(qAlpha(hermite) * EIGHT_BIT_MAXIMUM_RECIPROCAL, 1.0f, 0.0f);
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}
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if (middleZ) {
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if (alpha3 != alpha7) {
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@ -1698,7 +1698,7 @@ int VoxelAugmentVisitor::visit(MetavoxelInfo& info) {
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crossing.color = colorX[offset3];
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crossing.material = materialBase[offset3];
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}
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crossing.point = glm::vec3(EIGHT_BIT_MAXIMUM, EIGHT_BIT_MAXIMUM, qAlpha(hermite));
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crossing.point = glm::vec3(1.0f, 1.0f, qAlpha(hermite) * EIGHT_BIT_MAXIMUM_RECIPROCAL);
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}
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if (alpha5 != alpha7) {
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QRgb hermite = hermiteBase[hermiteArea + VoxelHermiteData::EDGE_COUNT + 1];
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@ -1711,7 +1711,7 @@ int VoxelAugmentVisitor::visit(MetavoxelInfo& info) {
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crossing.color = colorX[offset5];
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crossing.material = materialBase[offset5];
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}
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crossing.point = glm::vec3(EIGHT_BIT_MAXIMUM, qAlpha(hermite), EIGHT_BIT_MAXIMUM);
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crossing.point = glm::vec3(1.0f, qAlpha(hermite) * EIGHT_BIT_MAXIMUM_RECIPROCAL, 1.0f);
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}
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if (alpha6 != alpha7) {
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QRgb hermite = hermiteBase[hermiteArea + hermiteStride];
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@ -1724,7 +1724,7 @@ int VoxelAugmentVisitor::visit(MetavoxelInfo& info) {
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crossing.color = colorX[offset6];
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crossing.material = materialBase[offset6];
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}
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crossing.point = glm::vec3(qAlpha(hermite), EIGHT_BIT_MAXIMUM, EIGHT_BIT_MAXIMUM);
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crossing.point = glm::vec3(qAlpha(hermite) * EIGHT_BIT_MAXIMUM_RECIPROCAL, 1.0f, 1.0f);
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}
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}
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}
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@ -1740,7 +1740,7 @@ int VoxelAugmentVisitor::visit(MetavoxelInfo& info) {
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crossing.color = colorX[1];
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crossing.material = materialBase[1];
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}
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crossing.point = glm::vec3(EIGHT_BIT_MAXIMUM, 0.0f, qAlpha(hermite));
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crossing.point = glm::vec3(1.0f, 0.0f, qAlpha(hermite) * EIGHT_BIT_MAXIMUM_RECIPROCAL);
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}
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if (alpha4 != alpha5) {
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QRgb hermite = hermiteBase[hermiteArea];
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@ -1753,7 +1753,7 @@ int VoxelAugmentVisitor::visit(MetavoxelInfo& info) {
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crossing.color = colorX[area];
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crossing.material = materialBase[area];
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}
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crossing.point = glm::vec3(qAlpha(hermite), 0.0f, EIGHT_BIT_MAXIMUM);
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crossing.point = glm::vec3(qAlpha(hermite) * EIGHT_BIT_MAXIMUM_RECIPROCAL, 0.0f, 1.0f);
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}
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}
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}
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@ -1769,7 +1769,7 @@ int VoxelAugmentVisitor::visit(MetavoxelInfo& info) {
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crossing.color = colorX[0];
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crossing.material = materialBase[0];
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}
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crossing.point = glm::vec3(0.0f, qAlpha(hermite), 0.0f);
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crossing.point = glm::vec3(0.0f, qAlpha(hermite) * EIGHT_BIT_MAXIMUM_RECIPROCAL, 0.0f);
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}
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if (middleZ) {
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if (alpha2 != alpha6) {
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@ -1783,7 +1783,7 @@ int VoxelAugmentVisitor::visit(MetavoxelInfo& info) {
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crossing.color = colorX[size];
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crossing.material = materialBase[size];
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}
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crossing.point = glm::vec3(0.0f, EIGHT_BIT_MAXIMUM, qAlpha(hermite));
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crossing.point = glm::vec3(0.0f, 1.0f, qAlpha(hermite) * EIGHT_BIT_MAXIMUM_RECIPROCAL);
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}
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if (alpha4 != alpha6) {
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QRgb hermite = hermiteBase[hermiteArea + 1];
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@ -1796,7 +1796,7 @@ int VoxelAugmentVisitor::visit(MetavoxelInfo& info) {
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crossing.color = colorX[area];
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crossing.material = materialBase[area];
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}
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crossing.point = glm::vec3(0.0f, qAlpha(hermite), EIGHT_BIT_MAXIMUM);
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crossing.point = glm::vec3(0.0f, qAlpha(hermite) * EIGHT_BIT_MAXIMUM_RECIPROCAL, 1.0f);
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}
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}
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}
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@ -1811,7 +1811,7 @@ int VoxelAugmentVisitor::visit(MetavoxelInfo& info) {
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crossing.color = colorX[0];
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crossing.material = materialBase[0];
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}
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crossing.point = glm::vec3(0.0f, 0.0f, qAlpha(hermite));
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crossing.point = glm::vec3(0.0f, 0.0f, qAlpha(hermite) * EIGHT_BIT_MAXIMUM_RECIPROCAL);
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}
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// at present, we simply average the properties of each crossing as opposed to finding the vertex that
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// minimizes the quadratic error function as described in the reference paper
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@ -1857,7 +1857,7 @@ int VoxelAugmentVisitor::visit(MetavoxelInfo& info) {
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glm::vec4 bottom;
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for (int i = 0; i < crossingCount; i++) {
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const EdgeCrossing& crossing = crossings[i];
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bottom = glm::vec4(crossing.normal, glm::dot(crossing.normal, crossing.point));
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bottom = glm::vec4(crossing.normal, glm::dot(crossing.normal, crossing.point - center));
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for (int j = 0; j < 4; j++) {
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float angle = glm::atan(-bottom[j], r[j][j]);
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@ -1872,11 +1872,130 @@ int VoxelAugmentVisitor::visit(MetavoxelInfo& info) {
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}
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}
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// extract the submatrices, form ata
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glm::mat3 a(r);
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glm::vec3 b(r[3]);
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glm::mat3 atrans = glm::transpose(a);
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glm::mat3 ata = atrans * a;
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// compute the SVD of ata; first, find the eigenvalues
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// (see http://en.wikipedia.org/wiki/Eigenvalue_algorithm#3.C3.973_matrices)
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glm::vec3 eigenvalues;
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float p1 = ata[0][1] * ata[0][1] + ata[0][2] * ata[0][2] + ata[1][2] * ata[1][2];
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if (p1 < EPSILON) {
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eigenvalues = glm::vec3(ata[0][0], ata[1][1], ata[2][2]);
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if (eigenvalues[2] < eigenvalues[1]) {
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qSwap(eigenvalues[2], eigenvalues[1]);
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}
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if (eigenvalues[1] < eigenvalues[0]) {
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qSwap(eigenvalues[1], eigenvalues[0]);
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}
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if (eigenvalues[2] < eigenvalues[1]) {
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qSwap(eigenvalues[2], eigenvalues[1]);
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}
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} else {
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float q = (ata[0][0] + ata[1][1] + ata[2][2]) / 3.0f;
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float d1 = ata[0][0] - q, d2 = ata[1][1] - q, d3 = ata[2][2] - q;
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float p2 = d1 * d1 + d2 * d2 + d3 * d3 + 2.0f * p1;
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float p = glm::sqrt(p2 / 6.0f);
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glm::mat3 b = (ata - glm::mat3(q)) / p;
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float r = glm::determinant(b) / 2.0f;
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float phi;
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if (r <= -1.0f) {
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phi = PI / 3.0f;
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} else if (r >= 1.0f) {
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phi = 0.0f;
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} else {
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phi = glm::acos(r) / 3.0f;
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}
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eigenvalues[2] = q + 2.0f * p * glm::cos(phi);
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eigenvalues[0] = q + 2.0f * p * glm::cos(phi + (2.0f * PI / 3.0f));
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eigenvalues[1] = 3.0f * q - eigenvalues[0] - eigenvalues[2];
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}
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// form the singular matrix from the eigenvalues
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glm::mat3 d;
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const float MIN_SINGULAR_THRESHOLD = 0.1f;
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d[0][0] = (eigenvalues[0] < MIN_SINGULAR_THRESHOLD) ? 0.0f : 1.0f / eigenvalues[0];
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d[1][1] = (eigenvalues[1] < MIN_SINGULAR_THRESHOLD) ? 0.0f : 1.0f / eigenvalues[1];
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d[2][2] = (eigenvalues[2] < MIN_SINGULAR_THRESHOLD) ? 0.0f : 1.0f / eigenvalues[2];
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glm::mat3 m[] = { ata - glm::mat3(eigenvalues[0]), ata - glm::mat3(eigenvalues[1]),
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ata - glm::mat3(eigenvalues[2]) };
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// form the orthogonal matrix from the eigenvectors
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// see http://www.geometrictools.com/Documentation/EigenSymmetric3x3.pdf
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bool same01 = glm::abs(eigenvalues[0] - eigenvalues[1]) < EPSILON;
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bool same12 = glm::abs(eigenvalues[1] - eigenvalues[2]) < EPSILON;
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glm::mat3 u;
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if (!(same01 && same12)) {
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if (same01 || same12) {
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int i = same01 ? 2 : 0;
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for (int j = 0; j < 3; j++) {
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glm::vec3 first = glm::vec3(m[i][0][j], m[i][1][j], m[i][2][j]);
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int j2 = (j + 1) % 3;
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glm::vec3 second = glm::vec3(m[i][0][j2], m[i][1][j2], m[i][2][j2]);
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glm::vec3 cross = glm::cross(first, second);
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float length = glm::length(cross);
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if (length > EPSILON) {
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u[0][i] = cross[0] / length;
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u[1][i] = cross[1] / length;
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u[2][i] = cross[2] / length;
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break;
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}
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}
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i = (i + 1) % 3;
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for (int j = 0; j < 3; j++) {
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glm::vec3 first = glm::vec3(m[i][0][j], m[i][1][j], m[i][2][j]);
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float length = glm::length(first);
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if (length > EPSILON) {
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glm::vec3 second = glm::cross(first, glm::vec3(1.0f, 0.0f, 0.0f));
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length = glm::length(second);
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if (length < EPSILON) {
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second = glm::cross(first, glm::vec3(0.0f, 1.0f, 0.0f));
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length = glm::length(second);
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}
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u[0][i] = second[0] / length;
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u[1][i] = second[1] / length;
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u[2][i] = second[2] / length;
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second = glm::normalize(glm::cross(second, first));
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i = (i + 1) % 3;
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u[0][i] = second[0];
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u[1][i] = second[1];
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u[2][i] = second[2];
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break;
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}
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}
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} else {
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for (int i = 0; i < 3; i++) {
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for (int j = 0; j < 3; j++) {
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glm::vec3 first = glm::vec3(m[i][0][j], m[i][1][j], m[i][2][j]);
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int j2 = (j + 1) % 3;
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glm::vec3 second = glm::vec3(m[i][0][j2], m[i][1][j2], m[i][2][j2]);
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glm::vec3 cross = glm::cross(first, second);
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float length = glm::length(cross);
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if (length > EPSILON) {
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u[0][i] = cross[0] / length;
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u[1][i] = cross[1] / length;
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u[2][i] = cross[2] / length;
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break;
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}
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}
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}
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}
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}
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// compute the pseudo-inverse, ataplus
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glm::mat3 ataplus = glm::transpose(u) * d * u;
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glm::vec3 solution = (ataplus * atrans * b) + center;
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center = glm::clamp(solution, 0.0f, 1.0f);
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if (totalWeight > 0.0f) {
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materialWeights *= (EIGHT_BIT_MAXIMUM / totalWeight);
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}
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VoxelPoint point = { info.minimum + (glm::vec3(clampedX, clampedY, clampedZ) +
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center * EIGHT_BIT_MAXIMUM_RECIPROCAL) * scale,
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VoxelPoint point = { info.minimum + (glm::vec3(clampedX, clampedY, clampedZ) + center) * scale,
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{ (quint8)(red / crossingCount), (quint8)(green / crossingCount), (quint8)(blue / crossingCount) },
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{ (char)(normal.x * 127.0f), (char)(normal.y * 127.0f), (char)(normal.z * 127.0f) },
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{ materials[0], materials[1], materials[2], materials[3] },
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