/// <summary>
/// Gets whether a given point is inside a triangle
/// </summary>
/// <param name="p">Point</param>
/// <param name="triangle">Triangle defined by 3 points</param>
/// <returns>True if the point is inside given triangle</returns>
public static bool IsPointInTriangle(Point3D p, Tuple <Point3D, Point3D, Point3D> triangle)
{
// taken from http://www.blackpawn.com/texts/pointinpoly/default.html
// Compute vectors
Point3D a = triangle.Item1;
Point3D b = triangle.Item2;
Point3D c = triangle.Item3;
Point3D v0 = c - a;
Point3D v1 = b - a;
Point3D v2 = p - a;
// Compute dot products
float dot00 = v0.DotProduct(v0);
float dot01 = v0.DotProduct(v1);
float dot02 = v0.DotProduct(v2);
float dot11 = v1.DotProduct(v1);
float dot12 = v1.DotProduct(v2);
// Compute barycentric coordinates
double invDenom = 1F / (dot00 * dot11 - dot01 * dot01);
double u = (dot11 * dot02 - dot01 * dot12) * invDenom;
double v = (dot00 * dot12 - dot01 * dot02) * invDenom;
// Check if point is in triangle
return((u >= 0) && (v >= 0) && (u + v <= 1));
}
/// <summary>
/// Gets the line fragment intersection with a triangle (if any).
/// </summary>
/// <param name="triangle">Triangle defined by 3 points</param>
/// <param name="line">Line fragment defined by 2 points</param>
/// <returns>First item = 0 --> no intersetion; first item = 1 --> one
/// intersection in the second item; first item = 2 --> line is on the
/// plane</returns>
public static Tuple <int, Point3D> GetTriangleIntersection(Tuple <Point3D, Point3D, Point3D> triangle, Vector3D line)
{
#if DIAG
_IntersectCounter++;
#endif
Point3D vU1U2 = line.Point2 - line.Point1;
Point3D vU1P1 = triangle.Item2 - line.Point1;
Point3D norm = GetPlanesNormal(triangle);
float lenNormU1U2 = norm.DotProduct(vU1U2);
float lenNormU1P1 = norm.DotProduct(vU1P1);
// normala dotProduct usecka => kdyz je to 0, jsou kolme, normala je kolma na plochu, tedy usecka a plocha jsou paralelni
if (lenNormU1U2.EqEps(0))
{
if (lenNormU1P1.EqEps(0))
{
// usecka lezi v rovine definovane trojuhelnikem.... detekuj si prunik usecky strojuhelnikem sam :-)
return(Tuple.Create <int, Point3D>(2, null));
}
else
{
// usecka je paralelni s rovinou, takze nic se nikdy neprotne
return(Tuple.Create <int, Point3D>(0, null));
}
}
// 0 zacatek, 1 konec usecky... uzavreny interval [0;1] == na usecce :-)
float position = lenNormU1P1 / lenNormU1U2;
if (0 <= position && position <= 1)
{
// ha!, usecka protina rovinu definovanou trojuhelnikem.... ted jen zjistit jestli ten bod je v tom trojuhelniku
// měla by platit rovnost pro všechny 4 body roviny:
// NBx = ZjistiNormaluPlochuDefinovanouTremiBodyVole(plocha)
// NBx.Item1.DotProduct( [ plocha.Item1 ...až plocha.Item3 a bodPruniku] ) == NBx.Item3
// jestli ne, mám něco blbě, což by nebylo nic zvláštního :)
Point3D intersection = line.Point1 + vU1U2 * position;
if (IsPointInTriangle(intersection, triangle))
{
return(Tuple.Create(1, intersection));
}
return(Tuple.Create <int, Point3D>(0, null));
}
// usecka NEprotina plochu, ale kdybys ji prodlouzil (kdyby to byla primka), tak by rovinu protnula v bode (usecka.Item1 + vU1U2 * pozice)
return(Tuple.Create <int, Point3D>(0, null));
}