tmp update
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335
delaunay.h
335
delaunay.h
@ -12,6 +12,8 @@
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#include "cmath"
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#include "cmath"
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#include "vector"
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#include "vector"
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#include "iostream"
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#define ZERO 1e-5
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#define ZERO 1e-5
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// Start vertex definition
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// Start vertex definition
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@ -37,55 +39,63 @@ bool operator ==(const vertex2dc &a, const vertex2dc &b) // overload the == oper
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}
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}
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return false;
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return false;
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}
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}
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// End vertex definition
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// Start edge definition
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void circumcircle(vertex2dc *v0, vertex2dc *v1, vertex2dc *v2, double &cx, double &cy, double &cr) // calculate the circumcircle from three points
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struct edge
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{
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{
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vertex2dc *vert[2]; // vertex of the edge
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double s = 0.5 / ((v1->x - v0->x) * (v2->y - v0->y) - (v1->y - v0->y) * (v2->x - v0->x));
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double m = v1->x*v1->x - v0->x*v0->x + v1->y*v1->y - v0->y*v0->y;
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double u = v2->x*v2->x - v0->x*v0->x + v2->y*v2->y - v0->y*v0->y;
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edge() {vert[0] = vert[1] = nullptr;}
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cx = ((v2->y - v0->y)*m + (v0->y - v1->y)*u)*s;
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edge(vertex2dc *v0ptr, vertex2dc *v1ptr) {set(v0ptr, v1ptr);}
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cy = ((v0->x - v2->x)*m + (v1->x - v0->x)*u)*s;
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void set(vertex2dc *v0ptr, vertex2dc *v1ptr)
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cr = (v0->x - cx)*(v0->x - cx) + (v0->y - cy)*(v0->y - cy); // not need to calculate the squared root here
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{
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vert[0] = v0ptr; vert[1] = v1ptr;
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return;
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return;
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}
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};
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bool operator ==(const edge &a, const edge &b) // overload the == operator for edge type
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{
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if((a.vert[0] == b.vert[0] && a.vert[1] == b.vert[1]) ||
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(a.vert[0] == b.vert[1] && a.vert[1] == b.vert[0]))
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{
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return true;
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}
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return false;
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}
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}
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// End edge definition
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// End vertex definition
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// Start triangle definition
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// Start triangle definition
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struct triangle
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struct triangle
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{
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{
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int id;
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vertex2dc *vert[3]; // vertex of the triangle
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vertex2dc *vert[3]; // vertex of the triangle
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triangle *neigh[3]; // neighbors of the triangle
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double cx, cy; // center of the triangle's circumcircle
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double cx, cy; // center of the triangle's circumcircle
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double cr; // radius of the circumcircle
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double cr; // radius of the circumcircle
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triangle() {vert[0] = vert[1] = vert[2] = nullptr;}
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triangle() {vert[0] = vert[1] = vert[2] = nullptr; neigh[0] = neigh[1] = neigh[2] = nullptr;}
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triangle(vertex2dc *v0ptr, vertex2dc *v1ptr, vertex2dc *v2ptr) {set(v0ptr, v1ptr, v2ptr);}
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triangle(vertex2dc *v0ptr, vertex2dc *v1ptr, vertex2dc *v2ptr) {set(v0ptr, v1ptr, v2ptr);}
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void set(vertex2dc *v0ptr, vertex2dc *v1ptr, vertex2dc *v2ptr)
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void set(vertex2dc *v0ptr, vertex2dc *v1ptr, vertex2dc *v2ptr)
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{
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{
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vert[0] = v0ptr; vert[1] = v1ptr; vert[2] = v2ptr;
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vert[0] = v0ptr; vert[1] = v1ptr; vert[2] = v2ptr;
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neigh[0] = neigh[1] = neigh[2] = nullptr;
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double s = 0.5 / ((vert[1]->x - vert[0]->x) * (vert[2]->y - vert[0]->y) - (vert[1]->y - vert[0]->y) * (vert[2]->x - vert[0]->x));
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circumcircle(vert[0], vert[1], vert[2], cx, cy, cr);
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double m = vert[1]->x * vert[1]->x - vert[0]->x * vert[0]->x + vert[1]->y * vert[1]->y - vert[0]->y * vert[0]->y;
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double u = vert[2]->x * vert[2]->x - vert[0]->x * vert[0]->x + vert[2]->y * vert[2]->y - vert[0]->y * vert[0]->y;
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cx = ((vert[2]->y - vert[0]->y) * m + (vert[0]->y - vert[1]->y) * u) * s;
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cy = ((vert[0]->x - vert[2]->x) * m + (vert[1]->x - vert[0]->x) * u) * s;
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cr = (vert[0]->x - cx) * (vert[0]->x - cx) + (vert[0]->y - cy) * (vert[0]->y - cy); // not need to sqrt() here
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return;
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return;
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}
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}
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void set_neighbor(triangle *n0ptr, triangle *n1ptr, triangle *n2ptr)
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{
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neigh[0] = n0ptr; neigh[1] = n1ptr; neigh[2] = n2ptr;
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return;
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}
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bool bound_location(double inx, double iny) // Test if the location is inside the triangle
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{
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double l1x, l1y, l2x, l2y;
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for (int i = 0; i < 3; i++)
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{
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l1x = vert[(i+1)%3]->x - vert[i]->x;
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l1y = vert[(i+1)%3]->y - vert[i]->y;
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l2x = inx - vert[i]->x;
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l2y = iny - vert[i]->y;
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if ((l1x*l2y - l1y*l2x) < 0) // This condition includes points on the triangle's edge
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{
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return false;
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}
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}
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return true;
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}
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};
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};
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// End triangle definition
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// End triangle definition
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@ -95,7 +105,7 @@ struct triangle
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* @param in_verts Input vertexes. Defined by the user.
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* @param in_verts Input vertexes. Defined by the user.
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* @param out_tris Output triangles. Compute by the function.
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* @param out_tris Output triangles. Compute by the function.
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*/
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*/
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void triangulation(std::vector<vertex2dc> &in_verts, std::vector<triangle> &out_tris)
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void triangulation(std::vector<vertex2dc> &in_verts, std::vector<triangle*> &out_tris)
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{
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{
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if (!out_tris.empty()) out_tris.clear();
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if (!out_tris.empty()) out_tris.clear();
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if (in_verts.size() < 3) return;
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if (in_verts.size() < 3) return;
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@ -130,105 +140,240 @@ void triangulation(std::vector<vertex2dc> &in_verts, std::vector<triangle> &out_
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tmp_vert = new vertex2dc(midx - maxi_s, midy + maxi_s); // upper left corner
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tmp_vert = new vertex2dc(midx - maxi_s, midy + maxi_s); // upper left corner
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assit_vert.push_back(tmp_vert);
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assit_vert.push_back(tmp_vert);
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triangle *tmp_tri = nullptr;
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triangle *old_tri = nullptr, *tmp_tri = nullptr;
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std::vector<triangle*> exist_tri, cnst_tri;
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triangle *cnst_tri[3], *old_neigh[6];
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std::vector<triangle*>::iterator t_iter;
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std::vector<triangle*>::iterator t_iter;
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tmp_tri = new triangle(assit_vert[0], assit_vert[1], assit_vert[2]); // order the vertex anti-clock wise
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tmp_tri = new triangle(assit_vert[0], assit_vert[1], assit_vert[2]); // order the vertex anti-clock wise
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exist_tri.push_back(tmp_tri);
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out_tris.push_back(tmp_tri);
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tmp_tri = new triangle(assit_vert[0], assit_vert[2], assit_vert[3]); // order the vertex anti-clock wise
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tmp_tri = new triangle(assit_vert[0], assit_vert[2], assit_vert[3]); // order the vertex anti-clock wise
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exist_tri.push_back(tmp_tri);
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out_tris.push_back(tmp_tri);
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out_tris[0]->set_neighbor(nullptr, nullptr, out_tris[1]);
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out_tris[1]->set_neighbor(out_tris[0], nullptr, nullptr);
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// loop all input vertice
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// loop all input vertice
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bool removed;
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double dist;
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double dist;
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edge tmp_edge;
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std::vector<edge> cnst_edge;
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std::vector<edge>::iterator e_iter;
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for (int i = 0; i < in_verts.size(); ++i)
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for (int i = 0; i < in_verts.size(); ++i)
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{
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{
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// determine triangles that include the point and add the triangle to the cnst_tri and remove the triangle from exist_tri
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// determine the triangle that includes the new vertex and remove it from out_tris
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// this is the part that could take a lot of time if we are working with a large amount of points. We will fix this later
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for (t_iter = out_tris.begin(); t_iter != out_tris.end(); )
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cnst_tri.clear();
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for (t_iter = exist_tri.begin(); t_iter != exist_tri.end(); )
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{
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{
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tmp_tri = *t_iter;
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old_tri = *t_iter;
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if (old_tri->bound_location(in_verts[i].x, in_verts[i].y))
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dist = (tmp_tri->cx - in_verts[i].x) * (tmp_tri->cx - in_verts[i].x) +
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(tmp_tri->cy - in_verts[i].y) * (tmp_tri->cy - in_verts[i].y);
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if ((dist - tmp_tri->cr) <= ZERO) // Points on the circumcircle are also included
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{
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{
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t_iter = exist_tri.erase(t_iter);
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t_iter = out_tris.erase(t_iter);
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cnst_tri.push_back(tmp_tri);
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break;
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}
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}
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else t_iter++;
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else t_iter++;
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}
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}
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// loop to remove duplicate edges
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// build three new triangles
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cnst_edge.clear();
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for (int n = 0; n < 3; ++n)
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for (int c = 0; c < cnst_tri.size(); ++c)
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{
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{
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for (int e = 0; e < 3; ++e)
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tmp_tri = new triangle(old_tri->vert[n], old_tri->vert[(n+1)%3], &in_verts[i]);
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{
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cnst_tri[n] = tmp_tri;
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tmp_edge.set(cnst_tri[c]->vert[e], cnst_tri[c]->vert[(e+1)%3]);
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out_tris.push_back(tmp_tri);
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removed = false;
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for (e_iter = cnst_edge.begin(); e_iter != cnst_edge.end(); )
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{
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if (tmp_edge == *e_iter) // duplicate edge, remove from cnst_edge
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{
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e_iter = cnst_edge.erase(e_iter);
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removed = true;
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break; // no need to search more
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}
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else e_iter++;
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}
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}
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if (!removed) // not a duplicate edge, add to the cnst_edge
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// sort neighbors
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for (int n = 0; n < 3; ++n)
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{
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{
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cnst_edge.push_back(tmp_edge);
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if (old_tri->neigh[n] == nullptr)
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{
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cnst_tri[n]->set_neighbor(nullptr, cnst_tri[(n+1)%3], cnst_tri[(n+2)%3]);
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}
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else
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{
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cnst_tri[n]->set_neighbor(old_tri->neigh[n], cnst_tri[(n+1)%3], cnst_tri[(n+2)%3]);
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for (int k = 0; k < 3; ++k) // replace neighbor for the oppositing triangle
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{
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if (old_tri->neigh[n]->neigh[k] == old_tri)
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{
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old_tri->neigh[n]->neigh[k] = cnst_tri[n];
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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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}
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}
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// construct new triangles and add to exist_tri
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// delete the old triangle
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for (int c = 0; c < cnst_edge.size(); ++c)
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delete old_tri; old_tri = nullptr;
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{
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tmp_tri = new triangle(cnst_edge[c].vert[0], cnst_edge[c].vert[1], &in_verts[i]); // order the vertex anti-clock wise
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exist_tri.push_back(tmp_tri);
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}
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// destroy memories used by cnst_edge
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// test if the cnst_tri need to be flipped
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for (int c = 0; c < cnst_tri.size(); ++c)
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for (int n = 0; n < 3; ++n)
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{
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{
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tmp_tri = cnst_tri[c];
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if (cnst_tri[n]->neigh[0] != nullptr) // must has neighbor on this side
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delete tmp_tri; tmp_tri = nullptr;
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{
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old_tri = cnst_tri[n]->neigh[0];
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for (int v = 0; v < 3; ++v)
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{
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tmp_vert = old_tri->vert[v];
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if (tmp_vert != cnst_tri[n]->vert[0] && tmp_vert != cnst_tri[n]->vert[1]) // find the opposite vertex
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{
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//dist = (cnst_tri[n]->cx - tmp_vert->x) * (cnst_tri[n]->cx - tmp_vert->x) +
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// (cnst_tri[n]->cy - tmp_vert->y) * (cnst_tri[n]->cy - tmp_vert->y);
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//if ((dist - cnst_tri[n]->cr) <= ZERO) // need to be flipped
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dist = (old_tri->cx - cnst_tri[n]->vert[2]->x) * (old_tri->cx - cnst_tri[n]->vert[2]->x) +
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(old_tri->cy - cnst_tri[n]->vert[2]->y) * (old_tri->cy - cnst_tri[n]->vert[2]->y);
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if ((dist - old_tri->cr) <= ZERO) // need to be flipped
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{
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// record the original neighbors
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old_neigh[0] = cnst_tri[n]->neigh[0];
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old_neigh[1] = cnst_tri[n]->neigh[1];
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old_neigh[2] = cnst_tri[n]->neigh[2];
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old_neigh[3] = old_tri->neigh[0];
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old_neigh[4] = old_tri->neigh[1];
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old_neigh[5] = old_tri->neigh[2];
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cnst_tri[n]->set(cnst_tri[n]->vert[0], tmp_vert, cnst_tri[n]->vert[2]); // flip
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if (v == 0)
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{
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old_tri->set(old_tri->vert[0], old_tri->vert[1], cnst_tri[n]->vert[2]); //flip
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// Sort neighbors
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cnst_tri[n]->set_neighbor(old_neigh[5], old_tri, old_neigh[2]);
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old_tri->set_neighbor(old_neigh[3], old_neigh[1], cnst_tri[n]);
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for (int k = 0; k < 3; ++k)
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{
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if (cnst_tri[n]->neigh[0] != nullptr && cnst_tri[n]->neigh[0]->neigh[k] == old_tri)
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{
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cnst_tri[n]->neigh[0]->neigh[k] = cnst_tri[n];
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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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// remove any triangles has an assistant vertex from exist_tri
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for (int k = 0; k < 3; ++k)
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for (t_iter = exist_tri.begin(); t_iter != exist_tri.end(); )
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{
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if (old_tri->neigh[1] != nullptr && old_tri->neigh[1]->neigh[k] == cnst_tri[n])
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{
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old_tri->neigh[1]->neigh[k] = old_tri;
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break;
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}
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}
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}
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else if (v == 1)
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{
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old_tri->set(cnst_tri[n]->vert[2], old_tri->vert[1], old_tri->vert[2]); //flip
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// Sort neighbors
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cnst_tri[n]->set_neighbor(old_neigh[3], old_tri, old_neigh[2]);
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old_tri->set_neighbor(cnst_tri[n], old_neigh[4], old_neigh[1]);
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for (int k = 0; k < 3; ++k)
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{
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if (cnst_tri[n]->neigh[0] != nullptr && cnst_tri[n]->neigh[0]->neigh[k] == old_tri)
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{
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cnst_tri[n]->neigh[0]->neigh[k] = cnst_tri[n];
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break;
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}
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}
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for (int k = 0; k < 3; ++k)
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{
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if (old_tri->neigh[2] != nullptr && old_tri->neigh[2]->neigh[k] == cnst_tri[n])
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{
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old_tri->neigh[2]->neigh[k] = old_tri;
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break;
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}
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}
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}
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else
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{
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old_tri->set(old_tri->vert[0], cnst_tri[n]->vert[2], old_tri->vert[2]); //flip
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// Sort neighbors
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cnst_tri[n]->set_neighbor(old_neigh[4], old_tri, old_neigh[2]);
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||||||
|
old_tri->set_neighbor(old_neigh[1], cnst_tri[n], old_neigh[5]);
|
||||||
|
|
||||||
|
for (int k = 0; k < 3; ++k)
|
||||||
|
{
|
||||||
|
if (cnst_tri[n]->neigh[0] != nullptr && cnst_tri[n]->neigh[0]->neigh[k] == old_tri)
|
||||||
|
{
|
||||||
|
cnst_tri[n]->neigh[0]->neigh[k] = cnst_tri[n];
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
for (int k = 0; k < 3; ++k)
|
||||||
|
{
|
||||||
|
if (old_tri->neigh[0] != nullptr && old_tri->neigh[0]->neigh[k] == cnst_tri[n])
|
||||||
|
{
|
||||||
|
old_tri->neigh[0]->neigh[k] = old_tri;
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// remove any triangles has an assistant vertex from out_tris
|
||||||
|
for (t_iter = out_tris.begin(); t_iter != out_tris.end(); )
|
||||||
{
|
{
|
||||||
tmp_tri = *t_iter;
|
tmp_tri = *t_iter;
|
||||||
if (tmp_tri->vert[0] == assit_vert[0] || tmp_tri->vert[0] == assit_vert[1] || tmp_tri->vert[0] == assit_vert[2] || tmp_tri->vert[0] == assit_vert[3] ||
|
if (tmp_tri->vert[0] == assit_vert[0] || tmp_tri->vert[0] == assit_vert[1] || tmp_tri->vert[0] == assit_vert[2] || tmp_tri->vert[0] == assit_vert[3])
|
||||||
tmp_tri->vert[1] == assit_vert[0] || tmp_tri->vert[1] == assit_vert[1] || tmp_tri->vert[1] == assit_vert[2] || tmp_tri->vert[1] == assit_vert[3] ||
|
|
||||||
tmp_tri->vert[2] == assit_vert[0] || tmp_tri->vert[2] == assit_vert[1] || tmp_tri->vert[2] == assit_vert[2] || tmp_tri->vert[2] == assit_vert[3])
|
|
||||||
{
|
{
|
||||||
|
for (int k = 0; k < 3; ++k)
|
||||||
|
{
|
||||||
|
if (tmp_tri->neigh[1] != nullptr && tmp_tri->neigh[1]->neigh[k] == tmp_tri)
|
||||||
|
{
|
||||||
|
tmp_tri->neigh[1]->neigh[k] = nullptr;
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
// destroy the memories located and remove from the vector
|
// destroy the memories located and remove from the vector
|
||||||
t_iter = exist_tri.erase(t_iter);
|
t_iter = out_tris.erase(t_iter);
|
||||||
|
delete tmp_tri; tmp_tri = nullptr;
|
||||||
|
}
|
||||||
|
else if (tmp_tri->vert[1] == assit_vert[0] || tmp_tri->vert[1] == assit_vert[1] || tmp_tri->vert[1] == assit_vert[2] || tmp_tri->vert[1] == assit_vert[3])
|
||||||
|
{
|
||||||
|
for (int k = 0; k < 3; ++k)
|
||||||
|
{
|
||||||
|
if (tmp_tri->neigh[2] != nullptr && tmp_tri->neigh[2]->neigh[k] == tmp_tri)
|
||||||
|
{
|
||||||
|
tmp_tri->neigh[2]->neigh[k] = nullptr;
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// destroy the memories located and remove from the vector
|
||||||
|
t_iter = out_tris.erase(t_iter);
|
||||||
|
delete tmp_tri; tmp_tri = nullptr;
|
||||||
|
}
|
||||||
|
else if (tmp_tri->vert[2] == assit_vert[0] || tmp_tri->vert[2] == assit_vert[1] || tmp_tri->vert[2] == assit_vert[2] || tmp_tri->vert[2] == assit_vert[3])
|
||||||
|
{
|
||||||
|
for (int k = 0; k < 3; ++k)
|
||||||
|
{
|
||||||
|
if (tmp_tri->neigh[0] != nullptr && tmp_tri->neigh[0]->neigh[k] == tmp_tri)
|
||||||
|
{
|
||||||
|
tmp_tri->neigh[0]->neigh[k] = nullptr;
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// destroy the memories located and remove from the vector
|
||||||
|
t_iter = out_tris.erase(t_iter);
|
||||||
delete tmp_tri; tmp_tri = nullptr;
|
delete tmp_tri; tmp_tri = nullptr;
|
||||||
}
|
}
|
||||||
else t_iter++;
|
else t_iter++;
|
||||||
}
|
}
|
||||||
|
|
||||||
// copy exist_tri to out_tris and destroy memories located
|
// assign triangles index
|
||||||
out_tris.resize(exist_tri.size());
|
for (int i = 0; i < out_tris.size(); i++)
|
||||||
for (int i = 0; i < exist_tri.size(); ++i)
|
|
||||||
{
|
{
|
||||||
out_tris[i].set(exist_tri[i]->vert[0], exist_tri[i]->vert[1], exist_tri[i]->vert[2]);
|
out_tris[i]->id = i;
|
||||||
delete exist_tri[i]; exist_tri[i] = nullptr;
|
|
||||||
}
|
}
|
||||||
|
|
||||||
// destroy memories located for assit_vert
|
// destroy memories located for assit_vert
|
||||||
@ -271,9 +416,9 @@ bool duplicated_vertex(const std::vector<vertex2dc> &in_verts)
|
|||||||
*
|
*
|
||||||
* @return If the triangulation is fully delaunay
|
* @return If the triangulation is fully delaunay
|
||||||
*/
|
*/
|
||||||
bool fully_delaunay(const std::vector<triangle> &in_tris, const std::vector<vertex2dc> &in_verts)
|
bool fully_delaunay(const std::vector<triangle*> &in_tris, const std::vector<vertex2dc> &in_verts)
|
||||||
{
|
{
|
||||||
if (in_tris.empty()) return true;
|
if (in_tris.empty()) return false;
|
||||||
|
|
||||||
int count;
|
int count;
|
||||||
double dist;
|
double dist;
|
||||||
@ -282,10 +427,10 @@ bool fully_delaunay(const std::vector<triangle> &in_tris, const std::vector<vert
|
|||||||
count = 0;
|
count = 0;
|
||||||
for (int j = 0; j < in_verts.size(); ++j)
|
for (int j = 0; j < in_verts.size(); ++j)
|
||||||
{
|
{
|
||||||
dist = (in_tris[i].cx - in_verts[j].x) * (in_tris[i].cx - in_verts[j].x) +
|
dist = (in_tris[i]->cx - in_verts[j].x) * (in_tris[i]->cx - in_verts[j].x) +
|
||||||
(in_tris[i].cy - in_verts[j].y) * (in_tris[i].cy - in_verts[j].y);
|
(in_tris[i]->cy - in_verts[j].y) * (in_tris[i]->cy - in_verts[j].y);
|
||||||
|
|
||||||
if ((dist - in_tris[i].cr) <= ZERO)
|
if ((dist - in_tris[i]->cr) <= ZERO)
|
||||||
{
|
{
|
||||||
count++;
|
count++;
|
||||||
}
|
}
|
||||||
|
|||||||
303
delaunay_tmp.h
Normal file
303
delaunay_tmp.h
Normal file
@ -0,0 +1,303 @@
|
|||||||
|
/**
|
||||||
|
* @defgroup DELAUNAY
|
||||||
|
*
|
||||||
|
* @brief An implementation of the 2D Delaunay triangulation using the Bowyer-Watson algorithm.
|
||||||
|
*
|
||||||
|
* @author Yi Zhang
|
||||||
|
* @date 2021-09-12
|
||||||
|
*/
|
||||||
|
|
||||||
|
#ifndef _BW_2D_DELAUNAY_H
|
||||||
|
#define _BW_2D_DELAUNAY_H
|
||||||
|
#include "cmath"
|
||||||
|
#include "vector"
|
||||||
|
|
||||||
|
#define ZERO 1e-5
|
||||||
|
|
||||||
|
// Start vertex definition
|
||||||
|
struct vertex2dc
|
||||||
|
{
|
||||||
|
unsigned int id; // index of the vertex
|
||||||
|
double x, y; // position of the vertex
|
||||||
|
|
||||||
|
vertex2dc() : x(NAN), y(NAN), id(0) {}
|
||||||
|
vertex2dc(double inx, double iny, unsigned int inid = 0) {set(inx, iny, inid);}
|
||||||
|
void set(double inx, double iny, unsigned int inid = 0)
|
||||||
|
{
|
||||||
|
x = inx; y = iny; id = inid;
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
bool operator ==(const vertex2dc &a, const vertex2dc &b) // overload the == operator for vertex2dc type
|
||||||
|
{
|
||||||
|
if(fabs(a.x - b.x) <= ZERO && fabs(a.y - b.y) <= ZERO)
|
||||||
|
{
|
||||||
|
return true;
|
||||||
|
}
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
// End vertex definition
|
||||||
|
|
||||||
|
// Start edge definition
|
||||||
|
struct edge
|
||||||
|
{
|
||||||
|
vertex2dc *vert[2]; // vertex of the edge
|
||||||
|
|
||||||
|
edge() {vert[0] = vert[1] = nullptr;}
|
||||||
|
edge(vertex2dc *v0ptr, vertex2dc *v1ptr) {set(v0ptr, v1ptr);}
|
||||||
|
void set(vertex2dc *v0ptr, vertex2dc *v1ptr)
|
||||||
|
{
|
||||||
|
vert[0] = v0ptr; vert[1] = v1ptr;
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
bool operator ==(const edge &a, const edge &b) // overload the == operator for edge type
|
||||||
|
{
|
||||||
|
if((a.vert[0] == b.vert[0] && a.vert[1] == b.vert[1]) ||
|
||||||
|
(a.vert[0] == b.vert[1] && a.vert[1] == b.vert[0]))
|
||||||
|
{
|
||||||
|
return true;
|
||||||
|
}
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
// End edge definition
|
||||||
|
|
||||||
|
// Start triangle definition
|
||||||
|
struct triangle
|
||||||
|
{
|
||||||
|
vertex2dc *vert[3]; // vertex of the triangle
|
||||||
|
double cx, cy; // center of the triangle's circumcircle
|
||||||
|
double cr; // radius of the circumcircle
|
||||||
|
|
||||||
|
triangle() {vert[0] = vert[1] = vert[2] = nullptr;}
|
||||||
|
triangle(vertex2dc *v0ptr, vertex2dc *v1ptr, vertex2dc *v2ptr) {set(v0ptr, v1ptr, v2ptr);}
|
||||||
|
void set(vertex2dc *v0ptr, vertex2dc *v1ptr, vertex2dc *v2ptr)
|
||||||
|
{
|
||||||
|
vert[0] = v0ptr; vert[1] = v1ptr; vert[2] = v2ptr;
|
||||||
|
|
||||||
|
double s = 0.5 / ((vert[1]->x - vert[0]->x) * (vert[2]->y - vert[0]->y) - (vert[1]->y - vert[0]->y) * (vert[2]->x - vert[0]->x));
|
||||||
|
double m = vert[1]->x * vert[1]->x - vert[0]->x * vert[0]->x + vert[1]->y * vert[1]->y - vert[0]->y * vert[0]->y;
|
||||||
|
double u = vert[2]->x * vert[2]->x - vert[0]->x * vert[0]->x + vert[2]->y * vert[2]->y - vert[0]->y * vert[0]->y;
|
||||||
|
|
||||||
|
cx = ((vert[2]->y - vert[0]->y) * m + (vert[0]->y - vert[1]->y) * u) * s;
|
||||||
|
cy = ((vert[0]->x - vert[2]->x) * m + (vert[1]->x - vert[0]->x) * u) * s;
|
||||||
|
cr = (vert[0]->x - cx) * (vert[0]->x - cx) + (vert[0]->y - cy) * (vert[0]->y - cy); // not need to sqrt() here
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
};
|
||||||
|
// End triangle definition
|
||||||
|
|
||||||
|
/**
|
||||||
|
* @brief 2D Delaunay triangulation of some given points using the Bowyer-Watson algorithm.
|
||||||
|
*
|
||||||
|
* @param in_verts Input vertexes. Defined by the user.
|
||||||
|
* @param out_tris Output triangles. Compute by the function.
|
||||||
|
*/
|
||||||
|
void triangulation(std::vector<vertex2dc> &in_verts, std::vector<triangle> &out_tris)
|
||||||
|
{
|
||||||
|
if (!out_tris.empty()) out_tris.clear();
|
||||||
|
if (in_verts.size() < 3) return;
|
||||||
|
|
||||||
|
// locate the surrounding box and initiate the staring two triangles
|
||||||
|
double xmin = in_verts[0].x, xmax = in_verts[0].x;
|
||||||
|
double ymin = in_verts[0].y, ymax = in_verts[0].y;
|
||||||
|
for (int i = 0; i < in_verts.size(); ++i)
|
||||||
|
{
|
||||||
|
xmin = std::min(xmin, in_verts[i].x);
|
||||||
|
xmax = std::max(xmax, in_verts[i].x);
|
||||||
|
ymin = std::min(ymin, in_verts[i].y);
|
||||||
|
ymax = std::max(ymax, in_verts[i].y);
|
||||||
|
}
|
||||||
|
|
||||||
|
double midx = 0.5*(xmin + xmax);
|
||||||
|
double midy = 0.5*(ymin + ymax);
|
||||||
|
double maxi_s = std::max(xmax - xmin, ymax - ymin); // use an four times bigger rectangle to include all points
|
||||||
|
|
||||||
|
vertex2dc *tmp_vert = nullptr;
|
||||||
|
std::vector<vertex2dc*> assit_vert;
|
||||||
|
|
||||||
|
tmp_vert = new vertex2dc(midx - maxi_s, midy - maxi_s); // lower left corner
|
||||||
|
assit_vert.push_back(tmp_vert);
|
||||||
|
|
||||||
|
tmp_vert = new vertex2dc(midx + maxi_s, midy - maxi_s); // lower right corner
|
||||||
|
assit_vert.push_back(tmp_vert);
|
||||||
|
|
||||||
|
tmp_vert = new vertex2dc(midx + maxi_s, midy + maxi_s); // upper right corner
|
||||||
|
assit_vert.push_back(tmp_vert);
|
||||||
|
|
||||||
|
tmp_vert = new vertex2dc(midx - maxi_s, midy + maxi_s); // upper left corner
|
||||||
|
assit_vert.push_back(tmp_vert);
|
||||||
|
|
||||||
|
triangle *tmp_tri = nullptr;
|
||||||
|
std::vector<triangle*> exist_tri, cnst_tri;
|
||||||
|
std::vector<triangle*>::iterator t_iter;
|
||||||
|
|
||||||
|
tmp_tri = new triangle(assit_vert[0], assit_vert[1], assit_vert[2]); // order the vertex anti-clock wise
|
||||||
|
exist_tri.push_back(tmp_tri);
|
||||||
|
|
||||||
|
tmp_tri = new triangle(assit_vert[0], assit_vert[2], assit_vert[3]); // order the vertex anti-clock wise
|
||||||
|
exist_tri.push_back(tmp_tri);
|
||||||
|
|
||||||
|
// loop all input vertice
|
||||||
|
bool removed;
|
||||||
|
double dist;
|
||||||
|
edge tmp_edge;
|
||||||
|
std::vector<edge> cnst_edge;
|
||||||
|
std::vector<edge>::iterator e_iter;
|
||||||
|
for (int i = 0; i < in_verts.size(); ++i)
|
||||||
|
{
|
||||||
|
// determine triangles that include the point and add the triangle to the cnst_tri and remove the triangle from exist_tri
|
||||||
|
// this is the part that could take a lot of time if we are working with a large amount of points. We will fix this later
|
||||||
|
cnst_tri.clear();
|
||||||
|
for (t_iter = exist_tri.begin(); t_iter != exist_tri.end(); )
|
||||||
|
{
|
||||||
|
tmp_tri = *t_iter;
|
||||||
|
|
||||||
|
dist = (tmp_tri->cx - in_verts[i].x) * (tmp_tri->cx - in_verts[i].x) +
|
||||||
|
(tmp_tri->cy - in_verts[i].y) * (tmp_tri->cy - in_verts[i].y);
|
||||||
|
|
||||||
|
if ((dist - tmp_tri->cr) <= ZERO) // Points on the circumcircle are also included
|
||||||
|
{
|
||||||
|
t_iter = exist_tri.erase(t_iter);
|
||||||
|
cnst_tri.push_back(tmp_tri);
|
||||||
|
}
|
||||||
|
else t_iter++;
|
||||||
|
}
|
||||||
|
|
||||||
|
// loop to remove duplicate edges
|
||||||
|
cnst_edge.clear();
|
||||||
|
for (int c = 0; c < cnst_tri.size(); ++c)
|
||||||
|
{
|
||||||
|
for (int e = 0; e < 3; ++e)
|
||||||
|
{
|
||||||
|
tmp_edge.set(cnst_tri[c]->vert[e], cnst_tri[c]->vert[(e+1)%3]);
|
||||||
|
|
||||||
|
removed = false;
|
||||||
|
for (e_iter = cnst_edge.begin(); e_iter != cnst_edge.end(); )
|
||||||
|
{
|
||||||
|
if (tmp_edge == *e_iter) // duplicate edge, remove from cnst_edge
|
||||||
|
{
|
||||||
|
e_iter = cnst_edge.erase(e_iter);
|
||||||
|
removed = true;
|
||||||
|
break; // no need to search more
|
||||||
|
}
|
||||||
|
else e_iter++;
|
||||||
|
}
|
||||||
|
|
||||||
|
if (!removed) // not a duplicate edge, add to the cnst_edge
|
||||||
|
{
|
||||||
|
cnst_edge.push_back(tmp_edge);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// construct new triangles and add to exist_tri
|
||||||
|
for (int c = 0; c < cnst_edge.size(); ++c)
|
||||||
|
{
|
||||||
|
tmp_tri = new triangle(cnst_edge[c].vert[0], cnst_edge[c].vert[1], &in_verts[i]); // order the vertex anti-clock wise
|
||||||
|
exist_tri.push_back(tmp_tri);
|
||||||
|
}
|
||||||
|
|
||||||
|
// destroy memories used by cnst_edge
|
||||||
|
for (int c = 0; c < cnst_tri.size(); ++c)
|
||||||
|
{
|
||||||
|
tmp_tri = cnst_tri[c];
|
||||||
|
delete tmp_tri; tmp_tri = nullptr;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// remove any triangles has an assistant vertex from exist_tri
|
||||||
|
for (t_iter = exist_tri.begin(); t_iter != exist_tri.end(); )
|
||||||
|
{
|
||||||
|
tmp_tri = *t_iter;
|
||||||
|
if (tmp_tri->vert[0] == assit_vert[0] || tmp_tri->vert[0] == assit_vert[1] || tmp_tri->vert[0] == assit_vert[2] || tmp_tri->vert[0] == assit_vert[3] ||
|
||||||
|
tmp_tri->vert[1] == assit_vert[0] || tmp_tri->vert[1] == assit_vert[1] || tmp_tri->vert[1] == assit_vert[2] || tmp_tri->vert[1] == assit_vert[3] ||
|
||||||
|
tmp_tri->vert[2] == assit_vert[0] || tmp_tri->vert[2] == assit_vert[1] || tmp_tri->vert[2] == assit_vert[2] || tmp_tri->vert[2] == assit_vert[3])
|
||||||
|
{
|
||||||
|
// destroy the memories located and remove from the vector
|
||||||
|
t_iter = exist_tri.erase(t_iter);
|
||||||
|
delete tmp_tri; tmp_tri = nullptr;
|
||||||
|
}
|
||||||
|
else t_iter++;
|
||||||
|
}
|
||||||
|
|
||||||
|
// copy exist_tri to out_tris and destroy memories located
|
||||||
|
out_tris.resize(exist_tri.size());
|
||||||
|
for (int i = 0; i < exist_tri.size(); ++i)
|
||||||
|
{
|
||||||
|
out_tris[i].set(exist_tri[i]->vert[0], exist_tri[i]->vert[1], exist_tri[i]->vert[2]);
|
||||||
|
delete exist_tri[i]; exist_tri[i] = nullptr;
|
||||||
|
}
|
||||||
|
|
||||||
|
// destroy memories located for assit_vert
|
||||||
|
for (int i = 0; i < 4; ++i)
|
||||||
|
{
|
||||||
|
delete assit_vert[i]; assit_vert[i] = nullptr;
|
||||||
|
}
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* @brief Check for duplicated vertex
|
||||||
|
*
|
||||||
|
* @param[in] in_verts Input vertexes
|
||||||
|
*
|
||||||
|
* @return If there is duplicated vertex
|
||||||
|
*/
|
||||||
|
bool duplicated_vertex(const std::vector<vertex2dc> &in_verts)
|
||||||
|
{
|
||||||
|
if (in_verts.empty()) return false;
|
||||||
|
|
||||||
|
for (int i = 0; i < in_verts.size()-1; ++i)
|
||||||
|
{
|
||||||
|
for (int j = i+1; j < in_verts.size(); ++j)
|
||||||
|
{
|
||||||
|
if (in_verts[i] == in_verts[j])
|
||||||
|
{
|
||||||
|
return true;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* @brief Check to see if the triangulation is fully delaunay
|
||||||
|
*
|
||||||
|
* @param[in] in_tris Input triangles
|
||||||
|
* @param[in] in_verts Input vertexes
|
||||||
|
*
|
||||||
|
* @return If the triangulation is fully delaunay
|
||||||
|
*/
|
||||||
|
bool fully_delaunay(const std::vector<triangle> &in_tris, const std::vector<vertex2dc> &in_verts)
|
||||||
|
{
|
||||||
|
if (in_tris.empty()) return true;
|
||||||
|
|
||||||
|
int count;
|
||||||
|
double dist;
|
||||||
|
for (int i = 0; i < in_tris.size(); ++i)
|
||||||
|
{
|
||||||
|
count = 0;
|
||||||
|
for (int j = 0; j < in_verts.size(); ++j)
|
||||||
|
{
|
||||||
|
dist = (in_tris[i].cx - in_verts[j].x) * (in_tris[i].cx - in_verts[j].x) +
|
||||||
|
(in_tris[i].cy - in_verts[j].y) * (in_tris[i].cy - in_verts[j].y);
|
||||||
|
|
||||||
|
if ((dist - in_tris[i].cr) <= ZERO)
|
||||||
|
{
|
||||||
|
count++;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
if (count > 3)
|
||||||
|
{
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
return true;
|
||||||
|
}
|
||||||
|
|
||||||
|
#endif // _BW_2D_DELAUNAY_H
|
||||||
65
demo.cpp
65
demo.cpp
@ -1,8 +1,11 @@
|
|||||||
#include "delaunay.h"
|
#include "delaunay.h"
|
||||||
#include "iostream"
|
#include "iostream"
|
||||||
|
#include "fstream"
|
||||||
|
#include "iomanip"
|
||||||
|
|
||||||
int main(int argc, char const *argv[])
|
int main(int argc, char const *argv[])
|
||||||
{
|
{
|
||||||
|
/*
|
||||||
std::vector<vertex2dc> points(21);
|
std::vector<vertex2dc> points(21);
|
||||||
points[0].set(-0.8, -0.8, 0);
|
points[0].set(-0.8, -0.8, 0);
|
||||||
points[1].set(0.4, -1.2, 1);
|
points[1].set(0.4, -1.2, 1);
|
||||||
@ -25,6 +28,16 @@ int main(int argc, char const *argv[])
|
|||||||
points[18].set(2.4, 2.8, 18);
|
points[18].set(2.4, 2.8, 18);
|
||||||
points[19].set(3.5, 1.8, 19);
|
points[19].set(3.5, 1.8, 19);
|
||||||
points[20].set(3.6, 3.1, 20);
|
points[20].set(3.6, 3.1, 20);
|
||||||
|
*/
|
||||||
|
|
||||||
|
std::vector<vertex2dc> points(7);
|
||||||
|
points[0].set(-0.8, -0.8, 0);
|
||||||
|
points[1].set(0.4, -1.2, 1);
|
||||||
|
points[2].set(1.2, 0.9, 2);
|
||||||
|
points[3].set(-0.4, 0.5, 3);
|
||||||
|
points[4].set(0.2, -0.15, 4);
|
||||||
|
points[5].set(0.5, 0.375, 5);
|
||||||
|
points[6].set(0.7, -0.15, 6);
|
||||||
|
|
||||||
if (duplicated_vertex(points))
|
if (duplicated_vertex(points))
|
||||||
{
|
{
|
||||||
@ -32,7 +45,7 @@ int main(int argc, char const *argv[])
|
|||||||
return 0;
|
return 0;
|
||||||
}
|
}
|
||||||
|
|
||||||
std::vector<triangle> elements;
|
std::vector<triangle*> elements;
|
||||||
triangulation(points, elements);
|
triangulation(points, elements);
|
||||||
|
|
||||||
if (fully_delaunay(elements, points))
|
if (fully_delaunay(elements, points))
|
||||||
@ -41,17 +54,51 @@ int main(int argc, char const *argv[])
|
|||||||
}
|
}
|
||||||
else std::clog << "The triangulation is not fully delaunay\n";
|
else std::clog << "The triangulation is not fully delaunay\n";
|
||||||
|
|
||||||
std::cout << "OFF\n";
|
// Write a Gmsh's .msh file
|
||||||
std::cout << points.size() << " " << elements.size() << " 0\n";
|
std::ofstream outfile("demo.msh");
|
||||||
|
outfile << "$MeshFormat" << std::endl << "2.2 0 8" << std::endl << "$EndMeshFormat "<<std::endl;
|
||||||
for (int i = 0; i < points.size(); ++i)
|
outfile << "$Nodes" << std::endl << points.size() << std::endl;
|
||||||
|
for (int i = 0; i < points.size(); i++)
|
||||||
{
|
{
|
||||||
std::cout << points[i].x << " " << points[i].y << " 0\n";
|
outfile << points[i].id + 1 << " " << std::setprecision(16)
|
||||||
|
<< points[i].x << " " << points[i].y << " 0.0" << std::endl;
|
||||||
}
|
}
|
||||||
|
outfile<<"$EndNodes"<<std::endl;
|
||||||
for (int i = 0; i < elements.size(); ++i)
|
outfile << "$Elements" << std::endl << elements.size() <<std::endl;
|
||||||
|
for (int i = 0; i < elements.size(); i++)
|
||||||
{
|
{
|
||||||
std::cout << "3 " << elements[i].vert[0]->id << " " << elements[i].vert[1]->id << " " << elements[i].vert[2]->id << std::endl;
|
outfile << i + 1 << " 2 0";
|
||||||
|
for (int j = 0; j < 3; j++)
|
||||||
|
{
|
||||||
|
outfile << " " << elements[i]->vert[j]->id + 1;
|
||||||
|
}
|
||||||
|
outfile << std::endl;
|
||||||
|
}
|
||||||
|
outfile << "$EndElements"<< std::endl;
|
||||||
|
outfile.close();
|
||||||
|
|
||||||
|
// write a neighbor file
|
||||||
|
outfile.open("demo.neigh");
|
||||||
|
outfile << elements.size() << std::endl;
|
||||||
|
for (int i = 0; i < elements.size(); i++)
|
||||||
|
{
|
||||||
|
outfile << i + 1;
|
||||||
|
for (int j = 0; j < 3; j++)
|
||||||
|
{
|
||||||
|
if (elements[i]->neigh[j] != nullptr)
|
||||||
|
{
|
||||||
|
outfile << " " << elements[i]->neigh[j]->id + 1;
|
||||||
|
}
|
||||||
|
else outfile << " -1";
|
||||||
|
}
|
||||||
|
outfile << std::endl;
|
||||||
|
}
|
||||||
|
outfile.close();
|
||||||
|
|
||||||
|
// destroy allocated memories
|
||||||
|
for (int i = 0; i < elements.size(); i++)
|
||||||
|
{
|
||||||
|
delete elements[i];
|
||||||
}
|
}
|
||||||
return 0;
|
return 0;
|
||||||
}
|
}
|
||||||
|
|||||||
23
demo.msh
Normal file
23
demo.msh
Normal file
@ -0,0 +1,23 @@
|
|||||||
|
$MeshFormat
|
||||||
|
2.2 0 8
|
||||||
|
$EndMeshFormat
|
||||||
|
$Nodes
|
||||||
|
7
|
||||||
|
1 -0.8 -0.8 0.0
|
||||||
|
2 0.4 -1.2 0.0
|
||||||
|
3 1.2 0.9 0.0
|
||||||
|
4 -0.4 0.5 0.0
|
||||||
|
5 0.2 -0.15 0.0
|
||||||
|
6 0.5 0.375 0.0
|
||||||
|
7 0.7 -0.15 0.0
|
||||||
|
$EndNodes
|
||||||
|
$Elements
|
||||||
|
7
|
||||||
|
1 2 0 1 2 5
|
||||||
|
2 2 0 4 1 5
|
||||||
|
3 2 0 3 4 6
|
||||||
|
4 2 0 4 5 6
|
||||||
|
5 2 0 5 2 7
|
||||||
|
6 2 0 3 6 7
|
||||||
|
7 2 0 6 5 7
|
||||||
|
$EndElements
|
||||||
8
demo.neigh
Normal file
8
demo.neigh
Normal file
@ -0,0 +1,8 @@
|
|||||||
|
7
|
||||||
|
1 -1 5 2
|
||||||
|
2 -1 1 4
|
||||||
|
3 -1 4 6
|
||||||
|
4 2 7 3
|
||||||
|
5 1 -1 7
|
||||||
|
6 3 7 -1
|
||||||
|
7 4 5 6
|
||||||
53
demo.off
53
demo.off
@ -1,53 +0,0 @@
|
|||||||
OFF
|
|
||||||
21 30 0
|
|
||||||
-0.8 -0.8 0
|
|
||||||
0.4 -1.2 0
|
|
||||||
1.2 -0.9 0
|
|
||||||
1.6 0.1 0
|
|
||||||
2.5 0.5 0
|
|
||||||
4.1 0.7 0
|
|
||||||
5.7 1.8 0
|
|
||||||
5.1 3.4 0
|
|
||||||
2.5 4.4 0
|
|
||||||
1.2 3.7 0
|
|
||||||
-1.2 3.9 0
|
|
||||||
-3.2 5.1 0
|
|
||||||
-4.3 2.9 0
|
|
||||||
-3.1 0.7 0
|
|
||||||
-1.3 0.6 0
|
|
||||||
-2.1 2.9 0
|
|
||||||
0.6 1.2 0
|
|
||||||
0.1 2.4 0
|
|
||||||
2.4 2.8 0
|
|
||||||
3.5 1.8 0
|
|
||||||
3.6 3.1 0
|
|
||||||
3 1 2 3
|
|
||||||
3 3 2 4
|
|
||||||
3 4 2 5
|
|
||||||
3 9 8 10
|
|
||||||
3 10 8 11
|
|
||||||
3 13 0 14
|
|
||||||
3 10 11 15
|
|
||||||
3 11 12 15
|
|
||||||
3 12 13 15
|
|
||||||
3 13 14 15
|
|
||||||
3 0 1 16
|
|
||||||
3 1 3 16
|
|
||||||
3 3 4 16
|
|
||||||
3 14 0 16
|
|
||||||
3 9 10 17
|
|
||||||
3 10 15 17
|
|
||||||
3 15 14 17
|
|
||||||
3 14 16 17
|
|
||||||
3 8 9 18
|
|
||||||
3 16 4 18
|
|
||||||
3 9 17 18
|
|
||||||
3 17 16 18
|
|
||||||
3 5 6 19
|
|
||||||
3 6 7 19
|
|
||||||
3 4 5 19
|
|
||||||
3 18 4 19
|
|
||||||
3 7 8 20
|
|
||||||
3 8 18 20
|
|
||||||
3 18 19 20
|
|
||||||
3 19 7 20
|
|
||||||
Loading…
Reference in New Issue
Block a user