public static bool TestLineLineIntersection(Math.Vector2 a1, Math.Vector2 a2, Math.Vector2 b1, Math.Vector2 b2, out Math.Vector2 intersection)
{
float denom = (b2.Y - b1.Y) * (a2.X - a1.X) - (b2.X - b1.X) * (a2.Y - a1.Y);
if (denom == 0)
{
intersection = Math.Vector2.Zero;
return(false); // lines are parallel
}
Math.Vector2 u;
u.X = ((b2.X - b1.X) * (a1.Y - b1.Y) - (b2.Y - b1.Y) * (a1.X - b1.X)) / denom;
//u.Y = ((a2.X - a1.X) * (a1.Y - b1.Y) - (a2.Y - a1.Y) * (a1.X - b1.X)) / denom;
intersection.X = a1.X + u.X * (a2.X - a1.X);
intersection.Y = a1.Y + u.X * (a2.Y - a1.Y);
return(true);
}
public static bool IsPointInTriangle(Math.Vector2 point, Math.Vector2 a, Math.Vector2 b, Math.Vector2 c, out Math.Vector2 uv)
{
Math.Vector2 v0 = c - a;
Math.Vector2 v1 = b - a;
Math.Vector2 v2 = point - a;
float dot00 = v0.Dot(v0);
float dot01 = v0.Dot(v1);
float dot02 = v0.Dot(v2);
float dot11 = v1.Dot(v1);
float dot12 = v1.Dot(v2);
float invDenom = 1.0f / (dot00 * dot11 - dot01 * dot01);
uv.X = (dot11 * dot02 - dot01 * dot12) * invDenom;
uv.Y = (dot00 * dot12 - dot01 * dot02) * invDenom;
return(uv.X >= 0 && uv.Y >= 0 && uv.X + uv.Y < 1.0f);
}
public static bool TestTriangleBoxAndGetCenterOfMassUV(Math.Vector2 a, Math.Vector2 b, Math.Vector2 c, Math.Vector2 boxMin, Math.Vector2 boxMax, out Math.Vector2 centerUV)
{
if (TestTriangleBox(a, b, c, boxMin, boxMax) == false)
{
centerUV = Math.Vector2.Zero;
return(false);
}
// we know the box and the triangle intersect, but do we need to find the cetroid?
centerUV.X = (boxMin.X + boxMax.X) * 0.5f;
centerUV.Y = (boxMin.Y + boxMax.Y) * 0.5f;
if (IsPointInTriangle(centerUV, a, b, c, out centerUV))
{
return(true);
}
if (float.IsNaN(centerUV.X) || float.IsNaN(centerUV.Y))
{
// ugh... whatever... just keep going
return(true);
}
// apparently the texel intersects 1 or more triangle edges, which means we need
// to clip the triangle and square.
List <Math.Vector2> subject = new List <Math.Vector2>();
subject.Add(boxMin);
subject.Add(new Math.Vector2(boxMin.X, boxMax.Y));
subject.Add(boxMax);
subject.Add(new Math.Vector2(boxMax.X, boxMin.Y));
List <Math.Vector2> outputList = subject;
// UV coords may be mirrored, which means winding order is backwards, will screw up everything below.
// So check to see if they are, and if they are, rearrange them so they aren't.
Math.Vector2 center = (a + b + c) / 3.0f;
Math.Plane2D ab = Math.Plane2D.CreateFromEdge(a, b);
Math.Plane2D bc = Math.Plane2D.CreateFromEdge(b, c);
Math.Plane2D ca = Math.Plane2D.CreateFromEdge(c, a);
bool reversed = false;
if (Math.Plane2D.IsPointInFrontOfPlane(ab, center) == false ||
Math.Plane2D.IsPointInFrontOfPlane(bc, center) == false ||
Math.Plane2D.IsPointInFrontOfPlane(ca, center) == false)
{
// doh, winding order seems to be reversed. Swap c and a.
Math.Vector2 d = a;
a = c;
c = d;
ab = Math.Plane2D.CreateFromEdge(a, b);
bc = Math.Plane2D.CreateFromEdge(b, c);
ca = Math.Plane2D.CreateFromEdge(c, a);
reversed = true;
}
// side A
List <Math.Vector2> inputList = new List <Math.Vector2>(outputList);
outputList.Clear();
Math.Vector2 S = inputList[inputList.Count - 1];
foreach (Math.Vector2 E in inputList)
{
if (Math.Plane2D.IsPointInFrontOfPlane(ab, E))
{
if (Math.Plane2D.IsPointInFrontOfPlane(ab, S) == false)
{
Math.Vector2 i;
TestLineLineIntersection(S, E, a, b, out i);
outputList.Add(i);
}
outputList.Add(E);
}
else if (Math.Plane2D.IsPointInFrontOfPlane(ab, S))
{
Math.Vector2 i;
TestLineLineIntersection(S, E, a, b, out i);
outputList.Add(i);
}
S = E;
}
if (outputList.Count == 0)
{
return(true);
}
// side B
inputList = new List <Math.Vector2>(outputList);
outputList.Clear();
S = inputList[inputList.Count - 1];
foreach (Math.Vector2 E in inputList)
{
if (Math.Plane2D.IsPointInFrontOfPlane(bc, E))
{
if (Math.Plane2D.IsPointInFrontOfPlane(bc, S) == false)
{
Math.Vector2 i;
TestLineLineIntersection(S, E, b, c, out i);
outputList.Add(i);
}
outputList.Add(E);
}
else if (Math.Plane2D.IsPointInFrontOfPlane(bc, S))
{
Math.Vector2 i;
TestLineLineIntersection(S, E, b, c, out i);
outputList.Add(i);
}
S = E;
}
if (outputList.Count == 0)
{
return(true);
}
// side C
inputList = new List <Math.Vector2>(outputList);
outputList.Clear();
S = inputList[inputList.Count - 1];
foreach (Math.Vector2 E in inputList)
{
if (Math.Plane2D.IsPointInFrontOfPlane(ca, E))
{
if (Math.Plane2D.IsPointInFrontOfPlane(ca, S) == false)
{
Math.Vector2 i;
TestLineLineIntersection(S, E, c, a, out i);
outputList.Add(i);
}
outputList.Add(E);
}
else if (Math.Plane2D.IsPointInFrontOfPlane(ca, S))
{
Math.Vector2 i;
TestLineLineIntersection(S, E, c, a, out i);
outputList.Add(i);
}
S = E;
}
if (outputList.Count == 0)
{
return(true);
}
// at this point we've got a clipped list of points, so now we need to find the "center of mass"
centerUV = Math.Vector2.Zero;
float area = 0;
outputList.Add(outputList[0]);
for (int i = 0; i < outputList.Count - 1; i++)
{
float second = outputList[i].X * outputList[i + 1].Y - outputList[i + 1].X * outputList[i].Y;
centerUV += (outputList[i] + outputList[i + 1]) * second;
area += second;
}
centerUV /= 6 * area * 0.5f;
// if we reversed the windings, undo it, so that the output UV coords are correct
if (reversed)
{
Math.Vector2 d = a;
a = c;
c = d;
}
if (float.IsNaN(centerUV.X) || float.IsNaN(centerUV.Y))
{
centerUV = boxMax;
}
IsPointInTriangle(centerUV, a, b, c, out centerUV);
return(true);
}
public static bool TestTriangleBox(Math.Vector2 a, Math.Vector2 b, Math.Vector2 c, Math.Vector2 boxMin, Math.Vector2 boxMax)
{
Math.Vector2 ab = (b - a).Normalize();
Math.Vector2 ac = (a - c).Normalize();
Math.Vector2 bc = (c - b).Normalize();
// calc the normals
/*Utils.Swap(ref ab.X, ref ab.Y);
* Utils.Swap(ref ac.X, ref ac.Y);
* Utils.Swap(ref bc.X, ref bc.Y);
* ab.X = -ab.X;
* ac.X = -ac.X;
* bc.X = -bc.X;*/
// project the triangle onto the 1st axis of the triangle
float dotA = a.Dot(ab);
float dotB = b.Dot(ab);
float dotC = c.Dot(ab);
float dotMax = System.Math.Max(dotA, System.Math.Max(dotB, dotC));
float dotMin = System.Math.Min(dotA, System.Math.Min(dotB, dotC));
// project the box onto 1st axis of triangle
float boxA = boxMin.X * ab.X + boxMin.Y * ab.Y;
float boxB = boxMax.X * ab.X + boxMin.Y * ab.Y;
float boxC = boxMax.X * ab.X + boxMax.Y * ab.Y;
float boxD = boxMin.X * ab.X + boxMax.Y * ab.Y;
float boxDotMax = System.Math.Max(boxA, System.Math.Max(boxB, System.Math.Max(boxC, boxD)));
float boxDotMin = System.Math.Min(boxA, System.Math.Min(boxB, System.Math.Min(boxC, boxD)));
if (boxDotMax < dotMin || dotMax < boxDotMin)
{
return(false);
}
// project the triangle onto 2nd axis of triangle
dotA = a.Dot(ac);
dotB = b.Dot(ac);
dotC = c.Dot(ac);
dotMax = System.Math.Max(dotA, System.Math.Max(dotB, dotC));
dotMin = System.Math.Min(dotA, System.Math.Min(dotB, dotC));
// project the box onto 1st axis of triangle
boxA = boxMin.X * ac.X + boxMin.Y * ac.Y;
boxB = boxMax.X * ac.X + boxMin.Y * ac.Y;
boxC = boxMax.X * ac.X + boxMax.Y * ac.Y;
boxD = boxMin.X * ac.X + boxMax.Y * ac.Y;
boxDotMax = System.Math.Max(boxA, System.Math.Max(boxB, System.Math.Max(boxC, boxD)));
boxDotMin = System.Math.Min(boxA, System.Math.Min(boxB, System.Math.Min(boxC, boxD)));
if (boxDotMax < dotMin || dotMax < boxDotMin)
{
return(false);
}
// project the triangle onto 3rd axis of triangle
dotA = a.Dot(bc);
dotB = b.Dot(bc);
dotC = c.Dot(bc);
dotMax = System.Math.Max(dotA, System.Math.Max(dotB, dotC));
dotMin = System.Math.Min(dotA, System.Math.Min(dotB, dotC));
// project the box onto 1st axis of triangle
boxA = boxMin.X * bc.X + boxMin.Y * bc.Y;
boxB = boxMax.X * bc.X + boxMin.Y * bc.Y;
boxC = boxMax.X * bc.X + boxMax.Y * bc.Y;
boxD = boxMin.X * bc.X + boxMax.Y * bc.Y;
boxDotMax = System.Math.Max(boxA, System.Math.Max(boxB, System.Math.Max(boxC, boxD)));
boxDotMin = System.Math.Min(boxA, System.Math.Min(boxB, System.Math.Min(boxC, boxD)));
if (boxDotMax < dotMin || dotMax < boxDotMin)
{
return(false);
}
return(true);
}
