// creates an arbitrary Caresian coordinate system with given plane xy
public static RotoTranslation3 CoordinateSystemWithPlaneXY(Plane plane)
{
var x = Vector3Utils.VectorOrthogonalTo(plane.Normal);
var y = plane.Normal.Cross(x);
return(new RotoTranslation3(Rotation3Utils.GramSchmidt(x, y), plane.ProjectOrigin()));
}
public void GramSchmidt_reconstructs_rotation_from_its_x_column_and_a_linear_combination_of_the_x_and_y_columns([ValueSource("GramSchmidt_TestCases")] Rotation3 rot)
{
var x = 4.3 * rot.ColX();
var y = 3.4 * rot.ColY() + 0.123 * x;
var result = Rotation3Utils.GramSchmidt(x, y);
ExpectEqualRotations(result, rot);
}