/// <summary>
/// tested on 30-Aug-10
/// </summary>
/// <param name="eq"></param>
/// <param name="p"></param>
/// <returns></returns>
public static Point3D GetPtOnPlanePassingThroughAPtOnItsNormal(PlaneEquation eq, Point3D p)
{
//x = x1 + Ak
//y = y1 + Bk
//z = z1 + Ck
//Ax + By + Cz + D = 0
//A(x1 + Ak) + B(y1 + Bk) + C(z1 + Ck) + D = 0
//(A*A + B*B + C*C)k = -Ax1 - By1 - Cz1 - D
var k = -(eq.A * p.X + eq.B * p.Y + eq.C * p.Z + eq.D) / (eq.A * eq.A + eq.B * eq.B + eq.C * eq.C);
return(new Point3D(p.X + eq.A * k, p.Y + eq.B * k, p.Z + eq.C * k));
}
public static double ValueInPlaneEquation(PlaneEquation p, Point3D pt)
{
return(pt.X * p.A + pt.Y * p.B + pt.Z * p.C + p.D);
}
public static double ValueInPlaneEquation(Point3D pt, double a, double b, double c, double d)
{
var p = new PlaneEquation(a, b, c, d);
return(pt.X * p.A + pt.Y * p.B + pt.Z * p.C + p.D);
}
/// <summary>
/// gets a box for a triangle
/// </summary>
/// <param name="triangle"></param>
/// <returns></returns>
public static GeometryModel3D GetBoxForATriange(Triangle triangle)
{
//Get the equation of the triangle plane
var trianglePlane = new PlaneEquation(triangle.V1, triangle.V2, triangle.V3);
//todo: logic to decide how far the second plane should be
//make a parallel plane
var parallelPlane = new PlaneEquation(trianglePlane.A, trianglePlane.B, trianglePlane.C, trianglePlane.D + .02);
var p1 = PlaneEquation.GetPtOnPlanePassingThroughAPtOnItsNormal(parallelPlane, triangle.V1);
var p2 = PlaneEquation.GetPtOnPlanePassingThroughAPtOnItsNormal(parallelPlane, triangle.V2);
var p3 = PlaneEquation.GetPtOnPlanePassingThroughAPtOnItsNormal(parallelPlane, triangle.V3);
var mesh = new MeshGeometry3D();
//add the triangle positions
mesh.Positions.Add(triangle.V1);
mesh.Positions.Add(triangle.V2);
mesh.Positions.Add(triangle.V3);
mesh.Positions.Add(p1);
mesh.Positions.Add(p2);
mesh.Positions.Add(p3);
//add the triangle indices for the first triangle
mesh.TriangleIndices.Add(0);
mesh.TriangleIndices.Add(1);
mesh.TriangleIndices.Add(2);
//add the indices for the second triangle
mesh.TriangleIndices.Add(3);
mesh.TriangleIndices.Add(5);
mesh.TriangleIndices.Add(4);
//first side 031 341
mesh.TriangleIndices.Add(0);
mesh.TriangleIndices.Add(3);
mesh.TriangleIndices.Add(1);
mesh.TriangleIndices.Add(3);
mesh.TriangleIndices.Add(4);
mesh.TriangleIndices.Add(1);
//second side 142 452
mesh.TriangleIndices.Add(1);
mesh.TriangleIndices.Add(4);
mesh.TriangleIndices.Add(2);
mesh.TriangleIndices.Add(4);
mesh.TriangleIndices.Add(5);
mesh.TriangleIndices.Add(2);
//third side 502 530
mesh.TriangleIndices.Add(5);
mesh.TriangleIndices.Add(0);
mesh.TriangleIndices.Add(2);
mesh.TriangleIndices.Add(5);
mesh.TriangleIndices.Add(3);
mesh.TriangleIndices.Add(0);
//Add a default material
var material = new DiffuseMaterial(new SolidColorBrush(Colors.SteelBlue));
return(new GeometryModel3D(mesh, material));
}