void RowEchelon<T>::getAllSolutions(VectorT& x0,MatrixT& N) const
{
getNullspace(N);
VectorT* N0 = new VectorT[N.n];
for(int i=0;i<N.n;i++) N.getColRef(i,N0[i]);
backSub(x0);
Orthogonalize(x0,N0,N.n);
delete [] N0;
}
void CameraBase::ComputeModelView( bool forceIdentity /*= false*/ )
{
m_camInvDirty = true;
m_frustumPlanesDirty = true;
if (forceIdentity)
{
hkgMat4Identity(m_viewMat);
return;
}
Orthogonalize();
noVec3 eye;
eye = m_from;
noVec3 f;
// right hand
f = m_to - eye;
// left hand
//f = eye - m_to;
f.Normalize();
m_up.Normalize();
noVec3 s,u;
s = f.Cross(m_up);
u = s.Cross(f);
m_viewMat[0] = s[0]; m_viewMat[4] = s[1]; m_viewMat[8] = s[2];
m_viewMat[1] = u[0]; m_viewMat[5] = u[1]; m_viewMat[9] = u[2];
m_viewMat[2] = -f[0]; m_viewMat[6] = -f[1]; m_viewMat[10] = -f[2];
m_viewMat[3] = 0.0f; m_viewMat[7] = 0.0f; m_viewMat[11] = 0.0f;
eye = -eye;
m_viewMat[12] = (m_viewMat[0]*eye[0]) + (m_viewMat[4]*eye[1]) + (m_viewMat[8] *eye[2]);
m_viewMat[13] = (m_viewMat[1]*eye[0]) + (m_viewMat[5]*eye[1]) + (m_viewMat[9] *eye[2]);
m_viewMat[14] = (m_viewMat[2]*eye[0]) + (m_viewMat[6]*eye[1]) + (m_viewMat[10]*eye[2]);
m_viewMat[15] = 1.0f;
}
/**
* @brief Calculates normals and tangents for all frames and does vertex merging based on smoothness
* @param mesh The mesh to calculate normals for
* @param nFrames How many frames the mesh has
* @param smoothness How aggressively should normals be smoothed; value is compared with dotproduct of vectors to decide if they should be merged
* @sa R_ModCalcNormalsAndTangents
*/
void R_ModCalcUniqueNormalsAndTangents (mAliasMesh_t *mesh, int nFrames, float smoothness)
{
int i, j;
vec3_t triangleNormals[MAX_ALIAS_TRIS];
vec3_t triangleTangents[MAX_ALIAS_TRIS];
vec3_t triangleBitangents[MAX_ALIAS_TRIS];
const mAliasVertex_t *vertexes = mesh->vertexes;
mAliasCoord_t *stcoords = mesh->stcoords;
mAliasVertex_t *newVertexes;
mAliasComplexVertex_t tmpVertexes[MAX_ALIAS_VERTS];
vec3_t tmpBitangents[MAX_ALIAS_VERTS];
mAliasCoord_t *newStcoords;
const int numIndexes = mesh->num_tris * 3;
const int32_t *indexArray = mesh->indexes;
int32_t *newIndexArray;
int indRemap[MAX_ALIAS_VERTS];
int sharedTris[MAX_ALIAS_VERTS];
int numVerts = 0;
newIndexArray = (int32_t *)Mem_PoolAlloc(sizeof(int32_t) * numIndexes, vid_modelPool, 0);
/* calculate per-triangle surface normals */
for (i = 0, j = 0; i < numIndexes; i += 3, j++) {
vec3_t dir1, dir2;
vec2_t dir1uv, dir2uv;
/* calculate two mostly perpendicular edge directions */
VectorSubtract(vertexes[indexArray[i + 0]].point, vertexes[indexArray[i + 1]].point, dir1);
VectorSubtract(vertexes[indexArray[i + 2]].point, vertexes[indexArray[i + 1]].point, dir2);
Vector2Subtract(stcoords[indexArray[i + 0]], stcoords[indexArray[i + 1]], dir1uv);
Vector2Subtract(stcoords[indexArray[i + 2]], stcoords[indexArray[i + 1]], dir2uv);
/* we have two edge directions, we can calculate a third vector from
* them, which is the direction of the surface normal */
CrossProduct(dir1, dir2, triangleNormals[j]);
/* then we use the texture coordinates to calculate a tangent space */
if ((dir1uv[1] * dir2uv[0] - dir1uv[0] * dir2uv[1]) != 0.0) {
const float frac = 1.0 / (dir1uv[1] * dir2uv[0] - dir1uv[0] * dir2uv[1]);
vec3_t tmp1, tmp2;
/* calculate tangent */
VectorMul(-1.0 * dir2uv[1] * frac, dir1, tmp1);
VectorMul(dir1uv[1] * frac, dir2, tmp2);
VectorAdd(tmp1, tmp2, triangleTangents[j]);
/* calculate bitangent */
VectorMul(-1.0 * dir2uv[0] * frac, dir1, tmp1);
VectorMul(dir1uv[0] * frac, dir2, tmp2);
VectorAdd(tmp1, tmp2, triangleBitangents[j]);
} else {
const float frac = 1.0 / (0.00001);
vec3_t tmp1, tmp2;
/* calculate tangent */
VectorMul(-1.0 * dir2uv[1] * frac, dir1, tmp1);
VectorMul(dir1uv[1] * frac, dir2, tmp2);
VectorAdd(tmp1, tmp2, triangleTangents[j]);
/* calculate bitangent */
VectorMul(-1.0 * dir2uv[0] * frac, dir1, tmp1);
VectorMul(dir1uv[0] * frac, dir2, tmp2);
VectorAdd(tmp1, tmp2, triangleBitangents[j]);
}
/* normalize */
VectorNormalizeFast(triangleNormals[j]);
VectorNormalizeFast(triangleTangents[j]);
VectorNormalizeFast(triangleBitangents[j]);
Orthogonalize(triangleTangents[j], triangleBitangents[j]);
}
/* do smoothing */
for (i = 0; i < numIndexes; i++) {
const int idx = (i - i % 3) / 3;
VectorCopy(triangleNormals[idx], tmpVertexes[i].normal);
VectorCopy(triangleTangents[idx], tmpVertexes[i].tangent);
VectorCopy(triangleBitangents[idx], tmpBitangents[i]);
for (j = 0; j < numIndexes; j++) {
const int idx2 = (j - j % 3) / 3;
/* don't add a vertex with itself */
if (j == i)
continue;
/* only average normals if vertices have the same position
* and the normals aren't too far apart to start with */
if (VectorEqual(vertexes[indexArray[i]].point, vertexes[indexArray[j]].point)
&& DotProduct(triangleNormals[idx], triangleNormals[idx2]) > smoothness) {
/* average the normals */
VectorAdd(tmpVertexes[i].normal, triangleNormals[idx2], tmpVertexes[i].normal);
/* if the tangents match as well, average them too.
* Note that having matching normals without matching tangents happens
* when the order of vertices in two triangles sharing the vertex
* in question is different. This happens quite frequently if the
* modeler does not go out of their way to avoid it. */
if (Vector2Equal(stcoords[indexArray[i]], stcoords[indexArray[j]])
&& DotProduct(triangleTangents[idx], triangleTangents[idx2]) > smoothness
&& DotProduct(triangleBitangents[idx], triangleBitangents[idx2]) > smoothness) {
/* average the tangents */
VectorAdd(tmpVertexes[i].tangent, triangleTangents[idx2], tmpVertexes[i].tangent);
VectorAdd(tmpBitangents[i], triangleBitangents[idx2], tmpBitangents[i]);
}
}
}
VectorNormalizeFast(tmpVertexes[i].normal);
VectorNormalizeFast(tmpVertexes[i].tangent);
VectorNormalizeFast(tmpBitangents[i]);
}
/* assume all vertices are unique until proven otherwise */
for (i = 0; i < numIndexes; i++)
indRemap[i] = -1;
/* merge vertices that have become identical */
for (i = 0; i < numIndexes; i++) {
vec3_t n, b, t, v;
if (indRemap[i] != -1)
continue;
for (j = i + 1; j < numIndexes; j++) {
if (Vector2Equal(stcoords[indexArray[i]], stcoords[indexArray[j]])
&& VectorEqual(vertexes[indexArray[i]].point, vertexes[indexArray[j]].point)
&& (DotProduct(tmpVertexes[i].normal, tmpVertexes[j].normal) > smoothness)
&& (DotProduct(tmpVertexes[i].tangent, tmpVertexes[j].tangent) > smoothness)) {
indRemap[j] = i;
newIndexArray[j] = numVerts;
}
}
VectorCopy(tmpVertexes[i].normal, n);
VectorCopy(tmpVertexes[i].tangent, t);
VectorCopy(tmpBitangents[i], b);
/* normalization here does shared-vertex smoothing */
VectorNormalizeFast(n);
VectorNormalizeFast(t);
VectorNormalizeFast(b);
/* Grahm-Schmidt orthogonalization */
VectorMul(DotProduct(t, n), n, v);
VectorSubtract(t, v, t);
VectorNormalizeFast(t);
/* calculate handedness */
CrossProduct(n, t, v);
tmpVertexes[i].tangent[3] = (DotProduct(v, b) < 0.0) ? -1.0 : 1.0;
VectorCopy(n, tmpVertexes[i].normal);
VectorCopy(t, tmpVertexes[i].tangent);
newIndexArray[i] = numVerts++;
indRemap[i] = i;
}
for (i = 0; i < numVerts; i++)
sharedTris[i] = 0;
for (i = 0; i < numIndexes; i++)
sharedTris[newIndexArray[i]]++;
/* set up reverse-index that maps Vertex objects to a list of triangle verts */
mesh->revIndexes = (mIndexList_t *)Mem_PoolAlloc(sizeof(mIndexList_t) * numVerts, vid_modelPool, 0);
for (i = 0; i < numVerts; i++) {
mesh->revIndexes[i].length = 0;
mesh->revIndexes[i].list = (int32_t *)Mem_PoolAlloc(sizeof(int32_t) * sharedTris[i], vid_modelPool, 0);
}
/* merge identical vertexes, storing only unique ones */
newVertexes = (mAliasVertex_t *)Mem_PoolAlloc(sizeof(mAliasVertex_t) * numVerts * nFrames, vid_modelPool, 0);
newStcoords = (mAliasCoord_t *)Mem_PoolAlloc(sizeof(mAliasCoord_t) * numVerts, vid_modelPool, 0);
for (i = 0; i < numIndexes; i++) {
const int idx = indexArray[indRemap[i]];
const int idx2 = newIndexArray[i];
/* add vertex to new vertex array */
VectorCopy(vertexes[idx].point, newVertexes[idx2].point);
Vector2Copy(stcoords[idx], newStcoords[idx2]);
mesh->revIndexes[idx2].list[mesh->revIndexes[idx2].length++] = i;
}
/* copy over the points from successive frames */
for (i = 1; i < nFrames; i++) {
for (j = 0; j < numIndexes; j++) {
const int idx = indexArray[indRemap[j]] + (mesh->num_verts * i);
const int idx2 = newIndexArray[j] + (numVerts * i);
VectorCopy(vertexes[idx].point, newVertexes[idx2].point);
}
}
/* copy new arrays back into original mesh */
Mem_Free(mesh->stcoords);
Mem_Free(mesh->indexes);
Mem_Free(mesh->vertexes);
mesh->num_verts = numVerts;
mesh->vertexes = newVertexes;
mesh->stcoords = newStcoords;
mesh->indexes = newIndexArray;
}
/**
* @brief Calculates a per-vertex tangentspace basis and stores it in GL arrays attached to the mesh
* @param mesh The mesh to calculate normals for
* @param framenum The animation frame to calculate normals for
* @param translate The frame translation for the given animation frame
* @param backlerp Whether to store the results in the GL arrays for the previous keyframe or the next keyframe
* @sa R_ModCalcUniqueNormalsAndTangents
*/
static void R_ModCalcNormalsAndTangents (mAliasMesh_t *mesh, int framenum, const vec3_t translate, qboolean backlerp)
{
int i, j;
mAliasVertex_t *vertexes = &mesh->vertexes[framenum * mesh->num_verts];
mAliasCoord_t *stcoords = mesh->stcoords;
const int numIndexes = mesh->num_tris * 3;
const int32_t *indexArray = mesh->indexes;
vec3_t triangleNormals[MAX_ALIAS_TRIS];
vec3_t triangleTangents[MAX_ALIAS_TRIS];
vec3_t triangleBitangents[MAX_ALIAS_TRIS];
float *texcoords, *verts, *normals, *tangents;
/* set up array pointers for either the previous keyframe or the next keyframe */
texcoords = mesh->texcoords;
if (backlerp) {
verts = mesh->verts;
normals = mesh->normals;
tangents = mesh->tangents;
} else {
verts = mesh->next_verts;
normals = mesh->next_normals;
tangents = mesh->next_tangents;
}
/* calculate per-triangle surface normals and tangents*/
for (i = 0, j = 0; i < numIndexes; i += 3, j++) {
vec3_t dir1, dir2;
vec2_t dir1uv, dir2uv;
/* calculate two mostly perpendicular edge directions */
VectorSubtract(vertexes[indexArray[i + 0]].point, vertexes[indexArray[i + 1]].point, dir1);
VectorSubtract(vertexes[indexArray[i + 2]].point, vertexes[indexArray[i + 1]].point, dir2);
Vector2Subtract(stcoords[indexArray[i + 0]], stcoords[indexArray[i + 1]], dir1uv);
Vector2Subtract(stcoords[indexArray[i + 2]], stcoords[indexArray[i + 1]], dir2uv);
/* we have two edge directions, we can calculate a third vector from
* them, which is the direction of the surface normal */
CrossProduct(dir1, dir2, triangleNormals[j]);
/* normalize */
VectorNormalizeFast(triangleNormals[j]);
/* then we use the texture coordinates to calculate a tangent space */
if ((dir1uv[1] * dir2uv[0] - dir1uv[0] * dir2uv[1]) != 0.0) {
const float frac = 1.0 / (dir1uv[1] * dir2uv[0] - dir1uv[0] * dir2uv[1]);
vec3_t tmp1, tmp2;
/* calculate tangent */
VectorMul(-1.0 * dir2uv[1] * frac, dir1, tmp1);
VectorMul(dir1uv[1] * frac, dir2, tmp2);
VectorAdd(tmp1, tmp2, triangleTangents[j]);
/* calculate bitangent */
VectorMul(-1.0 * dir2uv[0] * frac, dir1, tmp1);
VectorMul(dir1uv[0] * frac, dir2, tmp2);
VectorAdd(tmp1, tmp2, triangleBitangents[j]);
/* normalize */
VectorNormalizeFast(triangleTangents[j]);
VectorNormalizeFast(triangleBitangents[j]);
} else {
VectorClear(triangleTangents[j]);
VectorClear(triangleBitangents[j]);
}
}
/* for each vertex */
for (i = 0; i < mesh->num_verts; i++) {
vec3_t n, b, v;
vec4_t t;
const int len = mesh->revIndexes[i].length;
const int32_t *list = mesh->revIndexes[i].list;
VectorClear(n);
VectorClear(t);
VectorClear(b);
/* for each vertex that got mapped to this one (ie. for each triangle this vertex is a part of) */
for (j = 0; j < len; j++) {
const int32_t idx = list[j] / 3;
VectorAdd(n, triangleNormals[idx], n);
VectorAdd(t, triangleTangents[idx], t);
VectorAdd(b, triangleBitangents[idx], b);
}
/* normalization here does shared-vertex smoothing */
VectorNormalizeFast(n);
VectorNormalizeFast(t);
VectorNormalizeFast(b);
/* Grahm-Schmidt orthogonalization */
Orthogonalize(t, n);
/* calculate handedness */
CrossProduct(n, t, v);
t[3] = (DotProduct(v, b) < 0.0) ? -1.0 : 1.0;
/* copy this vertex's info to all the right places in the arrays */
for (j = 0; j < len; j++) {
const int32_t idx = list[j];
const int meshIndex = mesh->indexes[list[j]];
Vector2Copy(stcoords[meshIndex], (texcoords + (2 * idx)));
VectorAdd(vertexes[meshIndex].point, translate, (verts + (3 * idx)));
VectorCopy(n, (normals + (3 * idx)));
Vector4Copy(t, (tangents + (4 * idx)));
}
}
}
