/// <summary> //Can only be done in Matrix4X4 b/c it uses the 3rd row
/// Build a world space to camera space matrix - Based on OpenTK.Matrix4.LookAt
/// </summary>
/// <param name="eye">Eye (camera) position in world space</param>
/// <param name="target">Target position in world space</param>
/// <param name="unitUpVector">Up vector in world space (should not be parallel to the camera direction, that is target - eye)</param>
public void SetLookAt(Vector3H1 eye, Vector3H1 target, Vector3H1 unitUpVector)
{
//unitUpVector.SetUnitVector()
Vector3H1 z = eye - target;
z.SetUnitVector();
Vector3H1 x = Vector3H1.CrossProduct(unitUpVector, z);
x.SetUnitVector();
Vector3H1 y = Vector3H1.CrossProduct(z, x);
y.SetUnitVector();
Data[0, 0] = x.X;
Data[0, 1] = y.X;
Data[0, 2] = z.X;
Data[0, 3] = 0;
Data[1, 0] = x.Y;
Data[1, 1] = y.Y;
Data[1, 2] = z.Y;
Data[1, 3] = 0;
Data[2, 0] = x.Z;
Data[2, 1] = y.Z;
Data[2, 2] = z.Z;
Data[2, 3] = 0;
Data[3, 0] = -((x.X * eye.X) + (x.Y * eye.Y) + (x.Z * eye.Z));
Data[3, 1] = -((y.X * eye.X) + (y.Y * eye.Y) + (y.Z * eye.Z));
Data[3, 2] = -((z.X * eye.X) + (z.Y * eye.Y) + (z.Z * eye.Z));
Data[3, 3] = 1;
}
/// <summary>
/// QuickSolve3D
/// Solves matrix equation [A] * x = N for x based on Cramer's Rule
/// where A is a Matrix, N is a vector (usually a normal)
/// -----------------------------------------------------------------
/// Marix A is typed as IMatrix so that Matrix3X3, Matrix3H4 or Matrix4X4 can be used
/// extra data is ignored, but Matrix2X2 would cause an error (but it doesn't exist yet)
/// </summary>
/// <param name="A">IMatrix</param>
/// <param name="N">IVector3H1</param>
/// <param name="bUnitize">bool</param>
/// <returns></returns>
public static Vector3H1 QuickSolve3D(IMatrix A, IVector3H1 N, bool bUnitize = true)
{
float determinate = Determinate3D(A);
//if the determinate comes out to zero, it's probably b/c this is actually a small
if (determinate == 0) //2X2 matrix in a larger object w/ the rest zeros, so just
{
determinate = Determinate2D(A); //go ahead & take the 2X2 determinate
A.Data[2, 2] = 1; //but you aldo have to set the Z-identity
} //this works, but it it good to change the matrix????????
Vector3H1 V = new Vector3H1();
V.X = ((A.Data[2, 2] * A.Data[1, 1] - A.Data[1, 2] * A.Data[2, 1]) * N.X
+ (A.Data[2, 1] * A.Data[0, 2] - A.Data[0, 1] * A.Data[2, 2]) * N.Y
+ (A.Data[0, 1] * A.Data[1, 2] - A.Data[1, 1] * A.Data[0, 2]) * N.Z)
/ determinate;
V.Y = ((A.Data[1, 2] * A.Data[2, 0] - A.Data[2, 2] * A.Data[1, 0]) * N.X
+ (A.Data[0, 0] * A.Data[2, 2] - A.Data[2, 0] * A.Data[0, 2]) * N.Y
+ (A.Data[1, 0] * A.Data[0, 2] - A.Data[0, 0] * A.Data[1, 2]) * N.Z)
/ determinate;
V.Z = ((A.Data[2, 1] * A.Data[1, 0] - A.Data[1, 1] * A.Data[2, 0]) * N.X
+ (A.Data[0, 1] * A.Data[2, 0] - A.Data[0, 0] * A.Data[2, 1]) * N.Y
+ (A.Data[0, 0] * A.Data[1, 1] - A.Data[0, 1] * A.Data[1, 0]) * N.Z)
/ determinate;
if (bUnitize)
{
V.SetUnitVector();
}
return(V);
}
