Quadrilateral Orbifold Splines

Orbifold spline surfaces are closed free form surfaces of any topological genus. Their patches have 𝐶𝑘 joints along common boundaries after linear rational reparametrizations, where k can be chosen arbitrarily. There are orbifold splines with rational triangular and—with certain restrictions on the patch layout—polynomial quadrilateral patches. Here, we present orbifold splines with rational quadrilateral patches without any restrictions on the patch layout. They are obtained from triangular orbifold splines by rational linear or bi-linear reparametrizations. With linear reparametrizations, we get discontinuously and otherwise continuously parametrized 𝐺𝑘 surfaces.