/// <summary>
/// Checks if vertex i is the tip of an ear in polygon defined by xv[] and yv[].
/// </summary>
/// <param name="i">The i.</param>
/// <param name="xv">The xv.</param>
/// <param name="yv">The yv.</param>
/// <param name="xvLength">Length of the xv.</param>
/// <remarks>
/// Assumes clockwise orientation of polygon.
/// </remarks>
/// <returns>
/// <c>true</c> if the specified i is ear; otherwise, <c>false</c>.
/// </returns>
private static bool IsEar(int i, float[] xv, float[] yv, int xvLength)
{
float dx0, dy0, dx1, dy1;
if (i >= xvLength || i < 0 || xvLength < 3)
{
return false;
}
int upper = i + 1;
int lower = i - 1;
if (i == 0)
{
dx0 = xv[0] - xv[xvLength - 1];
dy0 = yv[0] - yv[xvLength - 1];
dx1 = xv[1] - xv[0];
dy1 = yv[1] - yv[0];
lower = xvLength - 1;
}
else if (i == xvLength - 1)
{
dx0 = xv[i] - xv[i - 1];
dy0 = yv[i] - yv[i - 1];
dx1 = xv[0] - xv[i];
dy1 = yv[0] - yv[i];
upper = 0;
}
else
{
dx0 = xv[i] - xv[i - 1];
dy0 = yv[i] - yv[i - 1];
dx1 = xv[i + 1] - xv[i];
dy1 = yv[i + 1] - yv[i];
}
float cross = dx0 * dy1 - dx1 * dy0;
if (cross > 0)
return false;
Triangle myTri = new Triangle(xv[i], yv[i], xv[upper], yv[upper], xv[lower], yv[lower]);
for (int j = 0; j < xvLength; ++j)
{
if (j == i || j == lower || j == upper)
continue;
if (myTri.IsInside(xv[j], yv[j]))
return false;
}
return true;
}
/// <summary>
/// Triangulates a polygon using simple ear-clipping algorithm. Returns
/// size of Triangle array unless the polygon can't be triangulated.
/// This should only happen if the polygon self-intersects,
/// though it will not _always_ return null for a bad polygon - it is the
/// caller's responsibility to check for self-intersection, and if it
/// doesn't, it should at least check that the return value is non-null
/// before using. You're warned!
///
/// Triangles may be degenerate, especially if you have identical points
/// in the input to the algorithm. Check this before you use them.
///
/// This is totally unoptimized, so for large polygons it should not be part
/// of the simulation loop.
/// </summary>
/// <remarks>
/// Only works on simple polygons.
/// </remarks>
private static List<Vertices> TriangulatePolygon(Vertices vertices, float tolerance)
{
List<Vertices> results = new List<Vertices>();
//Recurse and split on pinch points
Vertices pA, pB;
Vertices pin = new Vertices(vertices);
if (ResolvePinchPoint(pin, out pA, out pB, tolerance))
{
List<Vertices> mergeA = TriangulatePolygon(pA, tolerance);
List<Vertices> mergeB = TriangulatePolygon(pB, tolerance);
if (mergeA.Count == -1 || mergeB.Count == -1)
throw new Exception("Can't triangulate your polygon.");
for (int i = 0; i < mergeA.Count; ++i)
{
results.Add(new Vertices(mergeA[i]));
}
for (int i = 0; i < mergeB.Count; ++i)
{
results.Add(new Vertices(mergeB[i]));
}
return results;
}
Vertices[] buffer = new Vertices[vertices.Count - 2];
int bufferSize = 0;
float[] xrem = new float[vertices.Count];
float[] yrem = new float[vertices.Count];
for (int i = 0; i < vertices.Count; ++i)
{
xrem[i] = vertices[i].X;
yrem[i] = vertices[i].Y;
}
int vNum = vertices.Count;
while (vNum > 3)
{
// Find an ear
int earIndex = -1;
float earMaxMinCross = -10.0f;
for (int i = 0; i < vNum; ++i)
{
if (IsEar(i, xrem, yrem, vNum))
{
int lower = Remainder(i - 1, vNum);
int upper = Remainder(i + 1, vNum);
Vector2 d1 = new Vector2(xrem[upper] - xrem[i], yrem[upper] - yrem[i]);
Vector2 d2 = new Vector2(xrem[i] - xrem[lower], yrem[i] - yrem[lower]);
Vector2 d3 = new Vector2(xrem[lower] - xrem[upper], yrem[lower] - yrem[upper]);
d1.Normalize();
d2.Normalize();
d3.Normalize();
float cross12;
MathUtils.Cross(ref d1, ref d2, out cross12);
cross12 = Math.Abs(cross12);
float cross23;
MathUtils.Cross(ref d2, ref d3, out cross23);
cross23 = Math.Abs(cross23);
float cross31;
MathUtils.Cross(ref d3, ref d1, out cross31);
cross31 = Math.Abs(cross31);
//Find the maximum minimum angle
float minCross = Math.Min(cross12, Math.Min(cross23, cross31));
if (minCross > earMaxMinCross)
{
earIndex = i;
earMaxMinCross = minCross;
}
}
}
// If we still haven't found an ear, we're screwed.
// Note: sometimes this is happening because the
// remaining points are collinear. Really these
// should just be thrown out without halting triangulation.
if (earIndex == -1)
{
for (int i = 0; i < bufferSize; i++)
{
results.Add(buffer[i]);
}
return results;
}
// Clip off the ear:
// - remove the ear tip from the list
--vNum;
float[] newx = new float[vNum];
float[] newy = new float[vNum];
int currDest = 0;
for (int i = 0; i < vNum; ++i)
{
if (currDest == earIndex) ++currDest;
newx[i] = xrem[currDest];
newy[i] = yrem[currDest];
++currDest;
}
// - add the clipped triangle to the triangle list
int under = (earIndex == 0) ? (vNum) : (earIndex - 1);
int over = (earIndex == vNum) ? 0 : (earIndex + 1);
Triangle toAdd = new Triangle(xrem[earIndex], yrem[earIndex], xrem[over], yrem[over], xrem[under],
yrem[under]);
buffer[bufferSize] = toAdd;
++bufferSize;
// - replace the old list with the new one
xrem = newx;
yrem = newy;
}
Triangle tooAdd = new Triangle(xrem[1], yrem[1], xrem[2], yrem[2], xrem[0], yrem[0]);
buffer[bufferSize] = tooAdd;
++bufferSize;
for (int i = 0; i < bufferSize; i++)
{
results.Add(new Vertices(buffer[i]));
}
return results;
}
public Triangle(Triangle t)
{
X = new float[3];
Y = new float[3];
X[0] = t.X[0];
X[1] = t.X[1];
X[2] = t.X[2];
Y[0] = t.Y[0];
Y[1] = t.Y[1];
Y[2] = t.Y[2];
}
private static Vertices AddTriangle(Triangle t, Vertices vertices)
{
// First, find vertices that connect
int firstP = -1;
int firstT = -1;
int secondP = -1;
int secondT = -1;
for (int i = 0; i < vertices.Count; i++)
{
if (t.X[0] == vertices[i].X && t.Y[0] == vertices[i].Y)
{
if (firstP == -1)
{
firstP = i;
firstT = 0;
}
else
{
secondP = i;
secondT = 0;
}
}
else if (t.X[1] == vertices[i].X && t.Y[1] == vertices[i].Y)
{
if (firstP == -1)
{
firstP = i;
firstT = 1;
}
else
{
secondP = i;
secondT = 1;
}
}
else if (t.X[2] == vertices[i].X && t.Y[2] == vertices[i].Y)
{
if (firstP == -1)
{
firstP = i;
firstT = 2;
}
else
{
secondP = i;
secondT = 2;
}
}
}
// Fix ordering if first should be last vertex of poly
if (firstP == 0 && secondP == vertices.Count - 1)
{
firstP = vertices.Count - 1;
secondP = 0;
}
// Didn't find it
if (secondP == -1)
{
return null;
}
// Find tip index on triangle
int tipT = 0;
if (tipT == firstT || tipT == secondT)
tipT = 1;
if (tipT == firstT || tipT == secondT)
tipT = 2;
Vertices result = new Vertices(vertices.Count + 1);
for (int i = 0; i < vertices.Count; i++)
{
result.Add(vertices[i]);
if (i == firstP)
result.Add(new Vector2(t.X[tipT], t.Y[tipT]));
}
return result;
}
/// <summary>
/// Triangulates a polygon using simple ear-clipping algorithm. Returns
/// size of Triangle array unless the polygon can't be triangulated.
/// This should only happen if the polygon self-intersects,
/// though it will not _always_ return null for a bad polygon - it is the
/// caller's responsibility to check for self-intersection, and if it
/// doesn't, it should at least check that the return value is non-null
/// before using. You're warned!
///
/// Triangles may be degenerate, especially if you have identical points
/// in the input to the algorithm. Check this before you use them.
///
/// This is totally unoptimized, so for large polygons it should not be part
/// of the simulation loop.
/// </summary>
/// <remarks>
/// Only works on simple polygons.
/// </remarks>
static List <Vertices> TriangulatePolygon(Vertices vertices, float tolerance)
{
//FPE note: Check is needed as invalid triangles can be returned in recursive calls.
if (vertices.Count < 3)
{
return(new List <Vertices>());
}
var results = new List <Vertices>();
//Recurse and split on pinch points
Vertices pA, pB;
var pin = new Vertices(vertices);
if (ResolvePinchPoint(pin, out pA, out pB, tolerance))
{
var mergeA = TriangulatePolygon(pA, tolerance);
var mergeB = TriangulatePolygon(pB, tolerance);
if (mergeA.Count == -1 || mergeB.Count == -1)
{
throw new Exception("Can't triangulate your polygon.");
}
for (int i = 0; i < mergeA.Count; ++i)
{
results.Add(new Vertices(mergeA[i]));
}
for (int i = 0; i < mergeB.Count; ++i)
{
results.Add(new Vertices(mergeB[i]));
}
return(results);
}
var buffer = new Vertices[vertices.Count - 2];
var bufferSize = 0;
var xrem = new float[vertices.Count];
var yrem = new float[vertices.Count];
for (int i = 0; i < vertices.Count; ++i)
{
xrem[i] = vertices[i].X;
yrem[i] = vertices[i].Y;
}
var vNum = vertices.Count;
while (vNum > 3)
{
// Find an ear
var earIndex = -1;
var earMaxMinCross = -10.0f;
for (int i = 0; i < vNum; ++i)
{
if (IsEar(i, xrem, yrem, vNum))
{
var lower = Remainder(i - 1, vNum);
var upper = Remainder(i + 1, vNum);
var d1 = new Vector2(xrem[upper] - xrem[i], yrem[upper] - yrem[i]);
var d2 = new Vector2(xrem[i] - xrem[lower], yrem[i] - yrem[lower]);
var d3 = new Vector2(xrem[lower] - xrem[upper], yrem[lower] - yrem[upper]);
Nez.Vector2Ext.Normalize(ref d1);
Nez.Vector2Ext.Normalize(ref d2);
Nez.Vector2Ext.Normalize(ref d3);
float cross12;
MathUtils.Cross(ref d1, ref d2, out cross12);
cross12 = Math.Abs(cross12);
float cross23;
MathUtils.Cross(ref d2, ref d3, out cross23);
cross23 = Math.Abs(cross23);
float cross31;
MathUtils.Cross(ref d3, ref d1, out cross31);
cross31 = Math.Abs(cross31);
//Find the maximum minimum angle
float minCross = Math.Min(cross12, Math.Min(cross23, cross31));
if (minCross > earMaxMinCross)
{
earIndex = i;
earMaxMinCross = minCross;
}
}
}
// If we still haven't found an ear, we're screwed.
// Note: sometimes this is happening because the
// remaining points are collinear. Really these
// should just be thrown out without halting triangulation.
if (earIndex == -1)
{
for (int i = 0; i < bufferSize; i++)
{
results.Add(buffer[i]);
}
return(results);
}
// Clip off the ear:
// - remove the ear tip from the list
--vNum;
float[] newx = new float[vNum];
float[] newy = new float[vNum];
int currDest = 0;
for (int i = 0; i < vNum; ++i)
{
if (currDest == earIndex)
{
++currDest;
}
newx[i] = xrem[currDest];
newy[i] = yrem[currDest];
++currDest;
}
// - add the clipped triangle to the triangle list
int under = (earIndex == 0) ? (vNum) : (earIndex - 1);
int over = (earIndex == vNum) ? 0 : (earIndex + 1);
var toAdd = new Triangle(xrem[earIndex], yrem[earIndex], xrem[over], yrem[over], xrem[under],
yrem[under]);
buffer[bufferSize] = toAdd;
++bufferSize;
// - replace the old list with the new one
xrem = newx;
yrem = newy;
}
var tooAdd = new Triangle(xrem[1], yrem[1], xrem[2], yrem[2], xrem[0], yrem[0]);
buffer[bufferSize] = tooAdd;
++bufferSize;
for (int i = 0; i < bufferSize; i++)
{
results.Add(new Vertices(buffer[i]));
}
return(results);
}
public Triangle(Triangle t)
{
x = new float[3];
y = new float[3];
x[0] = t.x[0];
x[1] = t.x[1];
x[2] = t.x[2];
y[0] = t.y[0];
y[1] = t.y[1];
y[2] = t.y[2];
}