/// <summary>
/// Calculates normal.
/// </summary>
/// <returns>The normal.</returns>
/// <param name="a">The alpha component.</param>
/// <param name="b">The blue component.</param>
/// <param name="c">C.</param>
public static Vector3d CalculateTriangleNormal(
Vector3d a,
Vector3d b,
Vector3d c)
{
Vector3d v1 = b - a;
Vector3d v2 = c - a;
double x = (v1.y * v2.z) - (v1.z * v2.y);
double y = -((v2.z * v1.x) - (v2.x * v1.z));
double z = (v1.x * v2.y) - (v1.y * v2.x);
return(Vector3d.Normalize(new Vector3d(x, y, z)));
}
/// <summary>
/// Normalizes the matrix rows.
/// </summary>
/// <returns>The rows.</returns>
/// <param name="a">The alpha component.</param>
public static Matrix3x3 NormalizeRows(Matrix3x3 a)
{
var r1 = new Vector3d(a.r1c1, a.r1c2, a.r1c3);
var r2 = new Vector3d(a.r2c1, a.r2c2, a.r2c3);
var r3 = new Vector3d(a.r3c1, a.r3c2, a.r3c3);
r1 = Vector3d.Normalize(r1);
r2 = Vector3d.Normalize(r2);
r3 = Vector3d.Normalize(r3);
return(new Matrix3x3(
r1.x, r1.y, r1.z,
r2.x, r2.y, r2.z,
r3.x, r3.y, r3.z));
}
public static Matrix3x3 GetRotationMatrix(Vector3d a, Vector3d b)
{
a = a.Normalize();
b = b.Normalize();
if (a != b &&
a.Length() > 0 &&
b.Length() > 0)
{
Vector3d c = a.Cross(b);
return(new Matrix3x3(
a.x, b.x, c.x,
a.y, b.y, c.y,
a.z, b.z, c.z));
}
return(new Matrix3x3());
}
/// <summary>
/// Projects the vector on plane.
/// </summary>
/// <returns>The vector on plane.</returns>
/// <param name="normal">Normal.</param>
public static Vector3d ProjectVectorOnPlane(Vector3d normal)
{
if (Math.Abs(normal.x) < 0.000000001)
{
return(new Vector3d(1.0, 0.0, 0.0));
}
if (Math.Abs(normal.y) < 0.000000001)
{
return(new Vector3d(0.0, 1.0, 0.0));
}
if (Math.Abs(normal.z) < 0.000000001)
{
return(new Vector3d(0.0, 0.0, 1.0));
}
double z = -(normal.x + normal.y) / normal.z;
return(Vector3d.Normalize(new Vector3d(1.0, 1.0, z)));
}