void Delaunay::computeDelaunay(Mesh &mesh)
{
int size = (int)mesh.getVerticesSize();
if (size == 0)
{
return;
}
mesh.computeVerticesNormals();
m_preSize = mesh.m_curIndex;
TriangleSet triSet;
// 依次遍历每个点，寻找最近邻，进行三角化
for (; mesh.m_curIndex < size; mesh.m_curIndex++)
{
Vertex v = mesh.getVertex(mesh.m_curIndex);
if (v.m_isInner)
{
mesh.pushTriBeginIndex((int)triSet.size());
continue;
}
Vec3d normal = v.m_normal;
int id = 2;
// 判断法向量哪个不为0，z->y->x
if (normal[2] != 0) // z
{
id = 2;
}
else if (normal[1] != 0)// y
{
id = 1;
}
else if (normal[0] != 0)// x
{
id = 0;
}
else // 法向量为(0, 0, 0)，
{
mesh.pushTriBeginIndex((int)triSet.size());
continue;
}
double minDistance = -1;
int cnt = v.m_neighbors[0]; // 最近邻数目
double dists[k];
for (int j = 1; j < cnt + 1; j++)
{
Vec3d dv = mesh.getVertex(v.m_neighbors[j]).m_xyz - v.m_xyz;
dists[j] = dv.ddot(dv);
}
minDistance = dists[1];
VertexVector vVector, tmpvVector;
// 将最近邻点投射到该点的切平面上
for (int j = 1; j < cnt + 1; j++)
{
Vertex tmpv = mesh.getVertex(v.m_neighbors[j]);
if (dists[j] < u * minDistance || // 去除非常接近的点
(tmpv.m_index < v.m_index && tmpv.m_index >= m_preSize) || // 去除已遍历过的点
tmpv.m_isInner) // 去除内点
{
continue;
}
Vec3d vv = tmpv.m_xyz - v.m_xyz;
double dist2 = dists[j] * 0.75f; // sqrt
double alpha = vv.dot(normal);
alpha = alpha * alpha;
if (alpha > dist2) // 去除与法向量夹角小于30度或大于150度的点
{
continue;
}
Vec3d proj = tmpv.m_xyz - alpha * normal; // 投射到切平面
tmpvVector.push_back(Vertex(proj, v.m_neighbors[j]));
}
if (tmpvVector.size() < 3) // 少于3个不能构成三角形
{
mesh.pushTriBeginIndex((int)triSet.size());
continue;
}
// 将切平面转换为x-y平面进行三角形计算
vVector.push_back(Vertex(Vec3d(0, 0, 0), mesh.m_curIndex)); // 原点
Vec3d vx = tmpvVector[0].m_xyz - v.m_xyz; // x轴
vx = normalize(vx);
for (int j = 0; j < tmpvVector.size(); j++)
{
Vec3d vv = tmpvVector[j].m_xyz - v.m_xyz;
double x = vv.dot(vx);
double y = vx.cross(vv)[id] / normal[id];
Vec3d proj(x, y, 0);
vVector.push_back(Vertex(proj, tmpvVector[j].m_index));
}
TriangleVector tVector;
computeDelaunay(vVector, tVector);
// cout << vVector.size() << " " << tVector.size() << endl;
// drawTrianglesOnPlane(tVector);
for (int j = 0; j < tVector.size(); j++)
{
Triangle t = tVector[j];
t.m_vertices[0] = mesh.getVertex(t.m_vertices[0].m_index);
t.m_vertices[1] = mesh.getVertex(t.m_vertices[1].m_index);
t.m_vertices[2] = mesh.getVertex(t.m_vertices[2].m_index);
triSet.insert(t);
}
mesh.pushTriBeginIndex((int)triSet.size());
}
for (TriangleSet::iterator iter = triSet.begin();
iter != triSet.end(); iter++)
{
mesh.m_triangles.push_back(*iter);
}
}
void Delaunay::Triangulate(const VertexSet& vertices, TriangleSet& output)
{
if (vertices.size() < 3)
{
return;
}
cVertexIterator iterVertex = vertices.begin();
double xMin = iterVertex->GetX();
double yMin = iterVertex->GetY();
double xMax = xMin;
double yMax = yMin;
++iterVertex;
for (; iterVertex != vertices.end(); ++iterVertex)
{
xMax = iterVertex->GetX();
double y = iterVertex->GetY();
if (y < yMin)
{
yMin = y;
}
if (y > yMax)
{
yMax = y;
}
}
double dx = xMax - xMin;
double dy = yMax - yMin;
double ddx = dx * 0.01;
double ddy = dy * 0.01;
xMin -= ddx;
xMax += ddx;
dx += 2 * ddx;
yMin -= ddy;
yMax += ddy;
dy += 2 * ddy;
Vertex vSuper[3];
vSuper[0] = Vertex(xMin - dy * sqrt3 / 3.0, yMin);
vSuper[1] = Vertex(xMax + dy * sqrt3 / 3.0, yMin);
vSuper[2] = Vertex((xMin + xMax) * 0.5, yMax + dx * sqrt3 * 0.5);
TriangleSet workset;
workset.insert(Triangle(vSuper));
for (iterVertex = vertices.begin(); iterVertex != vertices.end(); ++iterVertex)
{
TriangleIsCompleted pred1(iterVertex, output, vSuper);
TriangleSet::iterator iter = workset.begin();
while (iter != workset.end())
{
if (pred1(*iter))
{
iter = workset.erase(iter);
}
else
{
++iter;
}
}
EdgeSet edges;
VertexIsInCircumstanceCircle pred2(iterVertex, edges);
iter = workset.begin();
while (iter != workset.end())
{
if (pred2(*iter))
{
iter = workset.erase(iter);
}
else
{
++iter;
}
}
for (EdgeIterator edgeIter = edges.begin(); edgeIter != edges.end(); ++edgeIter)
{
workset.insert(Triangle(edgeIter->m_pv0, edgeIter->m_pv1, &(*iterVertex)));
}
}
TriangleIterator where = output.begin();
TriangleHasVertex pred(vSuper);
for (auto t : workset)
{
if (!pred(t))
{
output.insert(output.begin(), t);
}
}
}