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delaunay.h
40
delaunay.h
@ -12,15 +12,13 @@
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#include "cmath"
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#include "vector"
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#include "iostream"
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#define ZERO 1e-5
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// Start vertex definition
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struct vertex2dc
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{
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unsigned int id;
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double x, y;
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unsigned int id; // index of the vertex
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double x, y; // position of the vertex
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vertex2dc() : x(NAN), y(NAN), id(0) {}
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vertex2dc(double inx, double iny, unsigned int inid = 0) {set(inx, iny, inid);}
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@ -30,12 +28,21 @@ struct vertex2dc
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return;
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}
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};
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bool operator ==(const vertex2dc &a, const vertex2dc &b) // overload the == operator for vertex2dc type
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{
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if(fabs(a.x - b.x) <= ZERO && fabs(a.y - b.y) <= ZERO)
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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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// End vertex definition
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// Start edge definition
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struct edge
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{
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vertex2dc *vert[2];
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vertex2dc *vert[2]; // vertex of the edge
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edge() {vert[0] = vert[1] = nullptr;}
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edge(vertex2dc *v0ptr, vertex2dc *v1ptr) {set(v0ptr, v1ptr);}
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@ -46,7 +53,7 @@ struct edge
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}
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};
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bool operator ==(const edge &a, const edge &b)
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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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@ -60,9 +67,9 @@ bool operator ==(const edge &a, const edge &b)
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// Start triangle definition
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struct triangle
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{
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vertex2dc *vert[3];
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double cx, cy; // triangle's circular center
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double cr; // triangle's circular radius
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vertex2dc *vert[3]; // vertex of the triangle
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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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triangle() {vert[0] = vert[1] = vert[2] = nullptr;}
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triangle(vertex2dc *v0ptr, vertex2dc *v1ptr, vertex2dc *v2ptr) {set(v0ptr, v1ptr, v2ptr);}
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@ -83,10 +90,10 @@ struct triangle
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// End triangle definition
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/**
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* @brief 2D triangulation of given points using the Bowyer-Watson algorithm.
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* @brief 2D Delaunay triangulation of some given points using the Bowyer-Watson algorithm.
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*
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* @param in_verts Input vertexes
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* @param out_tris Output triangles
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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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*/
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void triangulation(std::vector<vertex2dc> &in_verts, std::vector<triangle> &out_tris)
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{
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@ -106,7 +113,7 @@ void triangulation(std::vector<vertex2dc> &in_verts, std::vector<triangle> &out_
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double midx = 0.5*(xmin + xmax);
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double midy = 0.5*(ymin + ymax);
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double maxi_s = std::max(xmax - xmin, ymax - ymin); // use an extra wide rectangle to include all points
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double maxi_s = std::max(xmax - xmin, ymax - ymin); // use an four times bigger rectangle to include all points
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vertex2dc *tmp_vert = nullptr;
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std::vector<vertex2dc*> assit_vert;
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@ -142,6 +149,8 @@ void triangulation(std::vector<vertex2dc> &in_verts, std::vector<triangle> &out_
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{
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// determine triangles that include the point and add the triangle to the cnst_tri
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// Otherwise, add the triangle to the remain_tri
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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
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// We will fix this later
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cnst_tri.clear();
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remain_tri.clear();
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for (int t = 0; t < exist_tri.size(); ++t)
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@ -149,7 +158,7 @@ void triangulation(std::vector<vertex2dc> &in_verts, std::vector<triangle> &out_
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dist = (exist_tri[t]->cx - in_verts[i].x) * (exist_tri[t]->cx - in_verts[i].x) +
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(exist_tri[t]->cy - in_verts[i].y) * (exist_tri[t]->cy - in_verts[i].y);
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if ((dist - exist_tri[t]->cr) <= ZERO) // inside // think more later
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if ((dist - exist_tri[t]->cr) <= ZERO) // Points on the circumcircle are also included
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{
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cnst_tri.push_back(exist_tri[t]);
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}
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@ -168,7 +177,7 @@ void triangulation(std::vector<vertex2dc> &in_verts, std::vector<triangle> &out_
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tmp_edge.set(cnst_tri[c]->vert[e], cnst_tri[c]->vert[(e+1)%3]);
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removed = false;
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for (e_iter = cnst_edge.begin(); e_iter != cnst_edge.end(); ++e_iter)
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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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@ -176,6 +185,7 @@ void triangulation(std::vector<vertex2dc> &in_verts, std::vector<triangle> &out_
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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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if (!removed) // not a duplicate edge, add to the cnst_edge
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33
demo.cpp
33
demo.cpp
@ -3,17 +3,28 @@
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int main(int argc, char const *argv[])
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{
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std::vector<vertex2dc> points(10);
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points[0].set(-0.7, -0.3, 0);
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points[1].set(0.1, -0.4, 1);
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points[2].set(-0.1, -0.1, 2);
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points[3].set(-0.4, 0.0, 3);
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points[4].set(-0.4, -0.3, 4);
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points[5].set(-0.2, -0.1, 5);
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points[6].set(-0.2, -0.6, 6);
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points[7].set(-0.2, -0.4, 7);
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points[8].set(-0.5, -0.5, 8);
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points[9].set(-0.6, -0.2, 9);
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std::vector<vertex2dc> points(21);
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points[0].set(-0.8, -0.8, 0);
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points[1].set(0.4, -1.2, 1);
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points[2].set(1.2, -0.9, 2);
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points[3].set(1.6, 0.1, 3);
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points[4].set(2.5, 0.5, 4);
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points[5].set(4.1, 0.7, 5);
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points[6].set(5.7, 1.8, 6);
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points[7].set(5.1, 3.4, 7);
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points[8].set(2.5, 4.4, 8);
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points[9].set(1.2, 3.7, 9);
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points[10].set(-1.2, 3.9, 10);
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points[11].set(-3.2, 5.1, 11);
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points[12].set(-4.3, 2.9, 12);
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points[13].set(-3.1, 0.7, 13);
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points[14].set(-1.3, 0.6, 14);
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points[15].set(-2.1, 2.9, 15);
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points[16].set(0.6, 1.2, 16);
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points[17].set(0.1, 2.4, 17);
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points[18].set(2.4, 2.8, 18);
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points[19].set(3.5, 1.8, 19);
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points[20].set(3.6, 3.1, 20);
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std::vector<triangle> elements;
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triangulation(points, elements);
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74
demo.off
74
demo.off
@ -1,23 +1,53 @@
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OFF
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10 11 0
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-0.7 -0.3 0
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0.1 -0.4 0
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-0.1 -0.1 0
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-0.4 0 0
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-0.4 -0.3 0
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-0.2 -0.1 0
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-0.2 -0.6 0
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-0.2 -0.4 0
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-0.5 -0.5 0
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-0.6 -0.2 0
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3 2 3 5
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3 3 4 5
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3 1 2 7
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3 6 1 7
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3 2 5 7
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3 5 4 7
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3 6 7 8
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3 7 4 8
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3 4 3 9
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3 0 8 9
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3 8 4 9
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21 30 0
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-0.8 -0.8 0
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0.4 -1.2 0
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1.2 -0.9 0
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1.6 0.1 0
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2.5 0.5 0
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4.1 0.7 0
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5.7 1.8 0
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5.1 3.4 0
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2.5 4.4 0
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1.2 3.7 0
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-1.2 3.9 0
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-3.2 5.1 0
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-4.3 2.9 0
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-3.1 0.7 0
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-1.3 0.6 0
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-2.1 2.9 0
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0.6 1.2 0
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0.1 2.4 0
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2.4 2.8 0
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3.5 1.8 0
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3.6 3.1 0
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3 1 2 3
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3 3 2 4
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3 4 2 5
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3 9 8 10
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3 10 8 11
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3 13 0 14
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3 10 11 15
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3 11 12 15
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3 12 13 15
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3 13 14 15
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3 0 1 16
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3 1 3 16
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3 3 4 16
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3 14 0 16
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3 9 10 17
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3 10 15 17
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3 15 14 17
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3 14 16 17
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3 8 9 18
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3 16 4 18
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3 9 17 18
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3 17 16 18
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3 5 6 19
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3 6 7 19
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3 4 5 19
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3 18 4 19
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3 7 8 20
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3 8 18 20
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3 18 19 20
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3 19 7 20
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