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miketucker/Delauny Triangulation in C Sharp

Created September 27, 2012 17:36
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Formatted version of the code supplied by "SuperProgrammer" at: http://answers.unity3d.com/questions/307544/mesh-from-vertices-polygon-from-spline.html#
Raw
Delauny Triangulation in C Sharp
using UnityEngine;
using System;
using System.Collections;
using System.Collections.Generic;
struct Triangle {
public int p1;
public int p2;
public int p3;
public Triangle(int point1, int point2, int point3) {
p1 = point1;
p2 = point2;
p3 = point3;
}
}
class Edge {
public int p1;
public int p2;
public Edge(int point1, int point2) {
p1 = point1;
p2 = point2;
}
public Edge(): this(0, 0) {}
public bool Equals(Edge other) {
return ((this.p1 == other.p2) && (this.p2 == other.p1)) || ((this.p1 == other.p1) && (this.p2 == other.p2));
}
}
public class Triangulator {
bool TriangulatePolygonSubFunc_InCircle(Vector2 p, Vector2 p1, Vector2 p2, Vector2 p3) {
if (Mathf.Abs(p1.y - p2.y) < float.Epsilon && Mathf.Abs(p2.y - p3.y) < float.Epsilon) {
return false;
}
float m1, m2, mx1, mx2, my1, my2, xc, yc;
if (Mathf.Abs(p2.y - p1.y) < float.Epsilon) {
m2 = -(p3.x - p2.x) / (p3.y - p2.y);
mx2 = (p2.x + p3.x) * 0.5f;
my2 = (p2.y + p3.y) * 0.5f;
xc = (p2.x + p1.x) * 0.5f;
yc = m2 * (xc - mx2) + my2;
} else if (Mathf.Abs(p3.y - p2.y) < float.Epsilon) {
m1 = -(p2.x - p1.x) / (p2.y - p1.y);
mx1 = (p1.x + p2.x) * 0.5f;
my1 = (p1.y + p2.y) * 0.5f;
xc = (p3.x + p2.x) * 0.5f;
yc = m1 * (xc - mx1) + my1;
} else {
m1 = -(p2.x - p1.x) / (p2.y - p1.y);
m2 = -(p3.x - p2.x) / (p3.y - p2.y);
mx1 = (p1.x + p2.x) * 0.5f;
mx2 = (p2.x + p3.x) * 0.5f;
my1 = (p1.y + p2.y) * 0.5f;
my2 = (p2.y + p3.y) * 0.5f;
xc = (m1 * mx1 - m2 * mx2 + my2 - my1) / (m1 - m2);
yc = m1 * (xc - mx1) + my1;
}
float dx = p2.x - xc;
float dy = p2.y - yc;
float rsqr = dx * dx + dy * dy;
dx = p.x - xc;
dy = p.y - yc;
double drsqr = dx * dx + dy * dy;
return (drsqr <= rsqr);
}
GameObject CreateInfluencePolygon(Vector2[] XZofVertices) {
Vector3[] Vertices = new Vector3[XZofVertices.Length];
for (int ii1 = 0; ii1 < XZofVertices.Length; ii1++) {
Vertices[ii1] = new Vector3(XZofVertices[ii1].x, 0, XZofVertices[ii1].y);
}
GameObject OurNewMesh = new GameObject("OurNewMesh1");
Mesh mesh = new Mesh();
mesh.vertices = Vertices;
mesh.uv = XZofVertices;
mesh.triangles = TriangulatePolygon(XZofVertices);
mesh.RecalculateNormals();
MeshFilter mf = OurNewMesh.AddComponent < MeshFilter > ();
OurNewMesh.AddComponent < MeshRenderer > ();
//OurNewMesh.GetComponent().castShadows = false;
//OurNewMesh.GetComponent().receiveShadows = false;
mf.mesh = mesh;
return OurNewMesh;
}
int[] TriangulatePolygon(Vector2[] XZofVertices) {
int VertexCount = XZofVertices.Length;
float xmin = XZofVertices[0].x;
float ymin = XZofVertices[0].y;
float xmax = xmin;
float ymax = ymin;
for (int ii1 = 1; ii1 < VertexCount; ii1++) {
if (XZofVertices[ii1].x < xmin) {
xmin = XZofVertices[ii1].x;
} else if (XZofVertices[ii1].x > xmax) {
xmax = XZofVertices[ii1].x;
}
if (XZofVertices[ii1].y < ymin) {
ymin = XZofVertices[ii1].y;
} else if (XZofVertices[ii1].y > ymax) {
ymax = XZofVertices[ii1].y;
}
}
float dx = xmax - xmin;
float dy = ymax - ymin;
float dmax = (dx > dy) ? dx : dy;
float xmid = (xmax + xmin) * 0.5f;
float ymid = (ymax + ymin) * 0.5f;
Vector2[] ExpandedXZ = new Vector2[3 + VertexCount];
for (int ii1 = 0; ii1 < VertexCount; ii1++) {
ExpandedXZ[ii1] = XZofVertices[ii1];
}
ExpandedXZ[VertexCount] = new Vector2((xmid - 2 * dmax), (ymid - dmax));
ExpandedXZ[VertexCount + 1] = new Vector2(xmid, (ymid + 2 * dmax));
ExpandedXZ[VertexCount + 2] = new Vector2((xmid + 2 * dmax), (ymid - dmax));
List < Triangle > TriangleList = new List < Triangle > ();
TriangleList.Add(new Triangle(VertexCount, VertexCount + 1, VertexCount + 2));
for (int ii1 = 0; ii1 < VertexCount; ii1++) {
List < Edge > Edges = new List < Edge > ();
for (int ii2 = 0; ii2 < TriangleList.Count; ii2++) {
if (TriangulatePolygonSubFunc_InCircle(ExpandedXZ[ii1], ExpandedXZ[TriangleList[ii2].p1], ExpandedXZ[TriangleList[ii2].p2], ExpandedXZ[TriangleList[ii2].p3])) {
Edges.Add(new Edge(TriangleList[ii2].p1, TriangleList[ii2].p2));
Edges.Add(new Edge(TriangleList[ii2].p2, TriangleList[ii2].p3));
Edges.Add(new Edge(TriangleList[ii2].p3, TriangleList[ii2].p1));
TriangleList.RemoveAt(ii2);
ii2--;
}
}
if (ii1 >= VertexCount) {
continue;
}
for (int ii2 = Edges.Count - 2; ii2 >= 0; ii2--) {
for (int ii3 = Edges.Count - 1; ii3 >= ii2 + 1; ii3--) {
if (Edges[ii2].Equals(Edges[ii3])) {
Edges.RemoveAt(ii3);
Edges.RemoveAt(ii2);
ii3--;
continue;
}
}
}
for (int ii2 = 0; ii2 < Edges.Count; ii2++) {
TriangleList.Add(new Triangle(Edges[ii2].p1, Edges[ii2].p2, ii1));
}
Edges.Clear();
Edges = null;
}
for (int ii1 = TriangleList.Count - 1; ii1 >= 0; ii1--) {
if (TriangleList[ii1].p1 >= VertexCount || TriangleList[ii1].p2 >= VertexCount || TriangleList[ii1].p3 >= VertexCount) {
TriangleList.RemoveAt(ii1);
}
}
TriangleList.TrimExcess();
int[] Triangles = new int[3 * TriangleList.Count];
for (int ii1 = 0; ii1 < TriangleList.Count; ii1++) {
Triangles[3 * ii1] = TriangleList[ii1].p1;
Triangles[3 * ii1 + 1] = TriangleList[ii1].p2;
Triangles[3 * ii1 + 2] = TriangleList[ii1].p3;
}
return Triangles;
}
}
Raw
Delauny Triangulation in C#
using UnityEngine;
using System;
using System.Collections;
using System.Collections.Generic;
struct Triangle {
public int p1;
public int p2;
public int p3;
public Triangle(int point1, int point2, int point3) {
p1 = point1;
p2 = point2;
p3 = point3;
}
}
class Edge {
public int p1;
public int p2;
public Edge(int point1, int point2) {
p1 = point1;
p2 = point2;
}
public Edge(): this(0, 0) {}
public bool Equals(Edge other) {
return ((this.p1 == other.p2) && (this.p2 == other.p1)) || ((this.p1 == other.p1) && (this.p2 == other.p2));
}
}
public class Triangulator {
bool TriangulatePolygonSubFunc_InCircle(Vector2 p, Vector2 p1, Vector2 p2, Vector2 p3) {
if (Mathf.Abs(p1.y - p2.y) < float.Epsilon && Mathf.Abs(p2.y - p3.y) < float.Epsilon) {
return false;
}
float m1, m2, mx1, mx2, my1, my2, xc, yc;
if (Mathf.Abs(p2.y - p1.y) < float.Epsilon) {
m2 = -(p3.x - p2.x) / (p3.y - p2.y);
mx2 = (p2.x + p3.x) * 0.5f;
my2 = (p2.y + p3.y) * 0.5f;
xc = (p2.x + p1.x) * 0.5f;
yc = m2 * (xc - mx2) + my2;
} else if (Mathf.Abs(p3.y - p2.y) < float.Epsilon) {
m1 = -(p2.x - p1.x) / (p2.y - p1.y);
mx1 = (p1.x + p2.x) * 0.5f;
my1 = (p1.y + p2.y) * 0.5f;
xc = (p3.x + p2.x) * 0.5f;
yc = m1 * (xc - mx1) + my1;
} else {
m1 = -(p2.x - p1.x) / (p2.y - p1.y);
m2 = -(p3.x - p2.x) / (p3.y - p2.y);
mx1 = (p1.x + p2.x) * 0.5f;
mx2 = (p2.x + p3.x) * 0.5f;
my1 = (p1.y + p2.y) * 0.5f;
my2 = (p2.y + p3.y) * 0.5f;
xc = (m1 * mx1 - m2 * mx2 + my2 - my1) / (m1 - m2);
yc = m1 * (xc - mx1) + my1;
}
float dx = p2.x - xc;
float dy = p2.y - yc;
float rsqr = dx * dx + dy * dy;
dx = p.x - xc;
dy = p.y - yc;
double drsqr = dx * dx + dy * dy;
return (drsqr <= rsqr);
}
GameObject CreateInfluencePolygon(Vector2[] XZofVertices) {
Vector3[] Vertices = new Vector3[XZofVertices.Length];
for (int ii1 = 0; ii1 < XZofVertices.Length; ii1++) {
Vertices[ii1] = new Vector3(XZofVertices[ii1].x, 0, XZofVertices[ii1].y);
}
GameObject OurNewMesh = new GameObject("OurNewMesh1");
Mesh mesh = new Mesh();
mesh.vertices = Vertices;
mesh.uv = XZofVertices;
mesh.triangles = TriangulatePolygon(XZofVertices);
mesh.RecalculateNormals();
MeshFilter mf = OurNewMesh.AddComponent < MeshFilter > ();
OurNewMesh.AddComponent < MeshRenderer > ();
//OurNewMesh.GetComponent().castShadows = false;
//OurNewMesh.GetComponent().receiveShadows = false;
mf.mesh = mesh;
return OurNewMesh;
}
int[] TriangulatePolygon(Vector2[] XZofVertices) {
int VertexCount = XZofVertices.Length;
float xmin = XZofVertices[0].x;
float ymin = XZofVertices[0].y;
float xmax = xmin;
float ymax = ymin;
for (int ii1 = 1; ii1 < VertexCount; ii1++) {
if (XZofVertices[ii1].x < xmin) {
xmin = XZofVertices[ii1].x;
} else if (XZofVertices[ii1].x > xmax) {
xmax = XZofVertices[ii1].x;
}
if (XZofVertices[ii1].y < ymin) {
ymin = XZofVertices[ii1].y;
} else if (XZofVertices[ii1].y > ymax) {
ymax = XZofVertices[ii1].y;
}
}
float dx = xmax - xmin;
float dy = ymax - ymin;
float dmax = (dx > dy) ? dx : dy;
float xmid = (xmax + xmin) * 0.5f;
float ymid = (ymax + ymin) * 0.5f;
Vector2[] ExpandedXZ = new Vector2[3 + VertexCount];
for (int ii1 = 0; ii1 < VertexCount; ii1++) {
ExpandedXZ[ii1] = XZofVertices[ii1];
}
ExpandedXZ[VertexCount] = new Vector2((xmid - 2 * dmax), (ymid - dmax));
ExpandedXZ[VertexCount + 1] = new Vector2(xmid, (ymid + 2 * dmax));
ExpandedXZ[VertexCount + 2] = new Vector2((xmid + 2 * dmax), (ymid - dmax));
List < Triangle > TriangleList = new List < Triangle > ();
TriangleList.Add(new Triangle(VertexCount, VertexCount + 1, VertexCount + 2));
for (int ii1 = 0; ii1 < VertexCount; ii1++) {
List < Edge > Edges = new List < Edge > ();
for (int ii2 = 0; ii2 < TriangleList.Count; ii2++) {
if (TriangulatePolygonSubFunc_InCircle(ExpandedXZ[ii1], ExpandedXZ[TriangleList[ii2].p1], ExpandedXZ[TriangleList[ii2].p2], ExpandedXZ[TriangleList[ii2].p3])) {
Edges.Add(new Edge(TriangleList[ii2].p1, TriangleList[ii2].p2));
Edges.Add(new Edge(TriangleList[ii2].p2, TriangleList[ii2].p3));
Edges.Add(new Edge(TriangleList[ii2].p3, TriangleList[ii2].p1));
TriangleList.RemoveAt(ii2);
ii2--;
}
}
if (ii1 >= VertexCount) {
continue;
}
for (int ii2 = Edges.Count - 2; ii2 >= 0; ii2--) {
for (int ii3 = Edges.Count - 1; ii3 >= ii2 + 1; ii3--) {
if (Edges[ii2].Equals(Edges[ii3])) {
Edges.RemoveAt(ii3);
Edges.RemoveAt(ii2);
ii3--;
continue;
}
}
}
for (int ii2 = 0; ii2 < Edges.Count; ii2++) {
TriangleList.Add(new Triangle(Edges[ii2].p1, Edges[ii2].p2, ii1));
}
Edges.Clear();
Edges = null;
}
for (int ii1 = TriangleList.Count - 1; ii1 >= 0; ii1--) {
if (TriangleList[ii1].p1 >= VertexCount || TriangleList[ii1].p2 >= VertexCount || TriangleList[ii1].p3 >= VertexCount) {
TriangleList.RemoveAt(ii1);
}
}
TriangleList.TrimExcess();
int[] Triangles = new int[3 * TriangleList.Count];
for (int ii1 = 0; ii1 < TriangleList.Count; ii1++) {
Triangles[3 * ii1] = TriangleList[ii1].p1;
Triangles[3 * ii1 + 1] = TriangleList[ii1].p2;
Triangles[3 * ii1 + 2] = TriangleList[ii1].p3;
}
return Triangles;
}
}
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