/// <summary>
/// Computes from a <see cref="V3d"/> point (origin) and
/// a <see cref="V3d"/> normal the transformation matrix
/// and its inverse.
/// </summary>
/// <param name="origin">The point which will become the new origin.</param>
/// <param name="normal">The normal vector of the new ground plane.</param>
/// <param name="local2global">A <see cref="M44d"/>The trafo from local to global system.</param>
/// <param name="global2local">A <see cref="M44d"/>The trafofrom global to local system.</param>
public static void NormalFrame(V3d origin, V3d normal,
out M44d local2global, out M44d global2local
)
{
V3d min;
double x = Fun.Abs(normal.X);
double y = Fun.Abs(normal.Y);
double z = Fun.Abs(normal.Z);
if (x < y)
{
if (x < z)
{
min = V3d.XAxis;
}
else
{
min = V3d.ZAxis;
}
}
else
{
if (y < z)
{
min = V3d.YAxis;
}
else
{
min = V3d.ZAxis;
}
}
V3d xVec = Vec.Cross(normal, min);
xVec.Normalize(); // this is now guaranteed to be normal to the input normal
V3d yVec = Vec.Cross(normal, xVec);
yVec.Normalize();
V3d zVec = normal;
zVec.Normalize();
local2global = new M44d(xVec.X, yVec.X, zVec.X, origin.X,
xVec.Y, yVec.Y, zVec.Y, origin.Y,
xVec.Z, yVec.Z, zVec.Z, origin.Z,
0, 0, 0, 1);
M44d mat = new M44d(xVec.X, xVec.Y, xVec.Z, 0,
yVec.X, yVec.Y, yVec.Z, 0,
zVec.X, zVec.Y, zVec.Z, 0,
0, 0, 0, 1);
var shift = M44d.Translation(-origin);
global2local = mat * shift;
}
public static Trafo3d Translation(double dx, double dy, double dz)
{
return(new Trafo3d(M44d.Translation(dx, dy, dz),
M44d.Translation(-dx, -dy, -dz)));
}
public static Trafo3d Translation(V3d v)
{
return(new Trafo3d(M44d.Translation(v),
M44d.Translation(-v)));
}
public static Trafo3d Translation(V3d v) => new Trafo3d(M44d.Translation(v), M44d.Translation(-v));
