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tmp update

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This commit is contained in:
张壹 2021-09-18 08:56:06 +08:00
parent 081012221e
commit 0ba513f2c7
6 changed files with 631 additions and 158 deletions
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337
delaunay.h
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@ -12,6 +12,8 @@
#include "cmath"
#include "vector"
#include "iostream"
#define ZERO 1e-5
// Start vertex definition
@ -37,55 +39,63 @@ bool operator ==(const vertex2dc &a, const vertex2dc &b) // overload the == oper
}
return false;
}
// End vertex definition
// Start edge definition
struct edge
void circumcircle(vertex2dc *v0, vertex2dc *v1, vertex2dc *v2, double &cx, double &cy, double &cr) // calculate the circumcircle from three points
{
vertex2dc *vert[2]; // vertex of the edge
double s = 0.5 / ((v1->x - v0->x) * (v2->y - v0->y) - (v1->y - v0->y) * (v2->x - v0->x));
double m = v1->x*v1->x - v0->x*v0->x + v1->y*v1->y - v0->y*v0->y;
double u = v2->x*v2->x - v0->x*v0->x + v2->y*v2->y - v0->y*v0->y;
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;
cx = ((v2->y - v0->y)*m + (v0->y - v1->y)*u)*s;
cy = ((v0->x - v2->x)*m + (v1->x - v0->x)*u)*s;
cr = (v0->x - cx)*(v0->x - cx) + (v0->y - cy)*(v0->y - cy); // not need to calculate the squared root here
return;
}
// End edge definition
// End vertex definition
// Start triangle definition
struct triangle
{
int id;
vertex2dc *vert[3]; // vertex of the triangle
triangle *neigh[3]; // neighbors 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() {vert[0] = vert[1] = vert[2] = nullptr; neigh[0] = neigh[1] = neigh[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;
neigh[0] = neigh[1] = neigh[2] = nullptr;
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
circumcircle(vert[0], vert[1], vert[2], cx, cy, cr);
return;
}
void set_neighbor(triangle *n0ptr, triangle *n1ptr, triangle *n2ptr)
{
neigh[0] = n0ptr; neigh[1] = n1ptr; neigh[2] = n2ptr;
return;
}
bool bound_location(double inx, double iny) // Test if the location is inside the triangle
{
double l1x, l1y, l2x, l2y;
for (int i = 0; i < 3; i++)
{
l1x = vert[(i+1)%3]->x - vert[i]->x;
l1y = vert[(i+1)%3]->y - vert[i]->y;
l2x = inx - vert[i]->x;
l2y = iny - vert[i]->y;
if ((l1x*l2y - l1y*l2x) < 0) // This condition includes points on the triangle's edge
{
return false;
}
}
return true;
}
};
// End triangle definition
@ -95,7 +105,7 @@ struct triangle
* @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)
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;
@ -130,107 +140,242 @@ void triangulation(std::vector<vertex2dc> &in_verts, std::vector<triangle> &out_
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;
triangle *old_tri = nullptr, *tmp_tri = nullptr;
triangle *cnst_tri[3], *old_neigh[6];
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);
out_tris.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);
out_tris.push_back(tmp_tri);
out_tris[0]->set_neighbor(nullptr, nullptr, out_tris[1]);
out_tris[1]->set_neighbor(out_tris[0], nullptr, nullptr);
// 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(); )
// determine the triangle that includes the new vertex and remove it from out_tris
for (t_iter = out_tris.begin(); t_iter != out_tris.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
old_tri = *t_iter;
if (old_tri->bound_location(in_verts[i].x, in_verts[i].y))
{
t_iter = exist_tri.erase(t_iter);
cnst_tri.push_back(tmp_tri);
t_iter = out_tris.erase(t_iter);
break;
}
else t_iter++;
}
// loop to remove duplicate edges
cnst_edge.clear();
for (int c = 0; c < cnst_tri.size(); ++c)
// build three new triangles
for (int n = 0; n < 3; ++n)
{
for (int e = 0; e < 3; ++e)
tmp_tri = new triangle(old_tri->vert[n], old_tri->vert[(n+1)%3], &in_verts[i]);
cnst_tri[n] = tmp_tri;
out_tris.push_back(tmp_tri);
}
// sort neighbors
for (int n = 0; n < 3; ++n)
{
if (old_tri->neigh[n] == nullptr)
{
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(); )
cnst_tri[n]->set_neighbor(nullptr, cnst_tri[(n+1)%3], cnst_tri[(n+2)%3]);
}
else
{
cnst_tri[n]->set_neighbor(old_tri->neigh[n], cnst_tri[(n+1)%3], cnst_tri[(n+2)%3]);
for (int k = 0; k < 3; ++k) // replace neighbor for the oppositing triangle
{
if (tmp_edge == *e_iter) // duplicate edge, remove from cnst_edge
if (old_tri->neigh[n]->neigh[k] == old_tri)
{
e_iter = cnst_edge.erase(e_iter);
removed = true;
break; // no need to search more
old_tri->neigh[n]->neigh[k] = cnst_tri[n];
break;
}
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);
}
// delete the old triangle
delete old_tri; old_tri = nullptr;
// destroy memories used by cnst_edge
for (int c = 0; c < cnst_tri.size(); ++c)
// test if the cnst_tri need to be flipped
for (int n = 0; n < 3; ++n)
{
tmp_tri = cnst_tri[c];
delete tmp_tri; tmp_tri = nullptr;
if (cnst_tri[n]->neigh[0] != nullptr) // must has neighbor on this side
{
old_tri = cnst_tri[n]->neigh[0];
for (int v = 0; v < 3; ++v)
{
tmp_vert = old_tri->vert[v];
if (tmp_vert != cnst_tri[n]->vert[0] && tmp_vert != cnst_tri[n]->vert[1]) // find the opposite vertex
{
//dist = (cnst_tri[n]->cx - tmp_vert->x) * (cnst_tri[n]->cx - tmp_vert->x) +
// (cnst_tri[n]->cy - tmp_vert->y) * (cnst_tri[n]->cy - tmp_vert->y);
//if ((dist - cnst_tri[n]->cr) <= ZERO) // need to be flipped
dist = (old_tri->cx - cnst_tri[n]->vert[2]->x) * (old_tri->cx - cnst_tri[n]->vert[2]->x) +
(old_tri->cy - cnst_tri[n]->vert[2]->y) * (old_tri->cy - cnst_tri[n]->vert[2]->y);
if ((dist - old_tri->cr) <= ZERO) // need to be flipped
{
// record the original neighbors
old_neigh[0] = cnst_tri[n]->neigh[0];
old_neigh[1] = cnst_tri[n]->neigh[1];
old_neigh[2] = cnst_tri[n]->neigh[2];
old_neigh[3] = old_tri->neigh[0];
old_neigh[4] = old_tri->neigh[1];
old_neigh[5] = old_tri->neigh[2];
cnst_tri[n]->set(cnst_tri[n]->vert[0], tmp_vert, cnst_tri[n]->vert[2]); // flip
if (v == 0)
{
old_tri->set(old_tri->vert[0], old_tri->vert[1], cnst_tri[n]->vert[2]); //flip
// Sort neighbors
cnst_tri[n]->set_neighbor(old_neigh[5], old_tri, old_neigh[2]);
old_tri->set_neighbor(old_neigh[3], old_neigh[1], cnst_tri[n]);
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[1] != nullptr && old_tri->neigh[1]->neigh[k] == cnst_tri[n])
{
old_tri->neigh[1]->neigh[k] = old_tri;
break;
}
}
}
else if (v == 1)
{
old_tri->set(cnst_tri[n]->vert[2], old_tri->vert[1], old_tri->vert[2]); //flip
// Sort neighbors
cnst_tri[n]->set_neighbor(old_neigh[3], old_tri, old_neigh[2]);
old_tri->set_neighbor(cnst_tri[n], old_neigh[4], old_neigh[1]);
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[2] != nullptr && old_tri->neigh[2]->neigh[k] == cnst_tri[n])
{
old_tri->neigh[2]->neigh[k] = old_tri;
break;
}
}
}
else
{
old_tri->set(old_tri->vert[0], cnst_tri[n]->vert[2], old_tri->vert[2]); //flip
// Sort neighbors
cnst_tri[n]->set_neighbor(old_neigh[4], old_tri, old_neigh[2]);
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 exist_tri
for (t_iter = exist_tri.begin(); t_iter != exist_tri.end(); )
// 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;
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])
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])
{
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
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;
}
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)
// assign triangles index
for (int i = 0; i < out_tris.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;
out_tris[i]->id = i;
}
// destroy memories located for assit_vert
for (int i = 0; i < 4; ++i)
{
@ -271,9 +416,9 @@ bool duplicated_vertex(const std::vector<vertex2dc> &in_verts)
*
* @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;
double dist;
@ -282,10 +427,10 @@ bool fully_delaunay(const std::vector<triangle> &in_tris, const std::vector<vert
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);
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)
if ((dist - in_tris[i]->cr) <= ZERO)
{
count++;
}

303
delaunay_tmp.h Normal file
View 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
View File

@ -1,8 +1,11 @@
#include "delaunay.h"
#include "iostream"
#include "fstream"
#include "iomanip"
int main(int argc, char const *argv[])
{
/*
std::vector<vertex2dc> points(21);
points[0].set(-0.8, -0.8, 0);
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[19].set(3.5, 1.8, 19);
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))
{
@ -32,7 +45,7 @@ int main(int argc, char const *argv[])
return 0;
}
std::vector<triangle> elements;
std::vector<triangle*> elements;
triangulation(points, elements);
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";
std::cout << "OFF\n";
std::cout << points.size() << " " << elements.size() << " 0\n";
for (int i = 0; i < points.size(); ++i)
// Write a Gmsh's .msh file
std::ofstream outfile("demo.msh");
outfile << "$MeshFormat" << std::endl << "2.2 0 8" << std::endl << "$EndMeshFormat "<<std::endl;
outfile << "$Nodes" << std::endl << points.size() << std::endl;
for (int i = 0; i < points.size(); i++)
{
std::cout << points[i].x << " " << points[i].y << " 0\n";
outfile << points[i].id + 1 << " " << std::setprecision(16)
<< points[i].x << " " << points[i].y << " 0.0" << std::endl;
}
for (int i = 0; i < elements.size(); ++i)
outfile<<"$EndNodes"<<std::endl;
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;
}

23
demo.msh Normal file
View 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
View 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
View File

@ -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