Injectivity conditions of rational Bézier surfaces

Rational Bézier surface is a common fitting tool in Computer Aided Geometric Design. The injectivity of curve/surface implies the one-to-one property and there is no self-intersection of curve/surface. In this paper, we propose a geometric method for checking the injectivity of rational Bézier surface based on its control points. [Display omitted] •Well-posedness of control points set of rational Bézier surface is defined.•Well-posed control points set guarantees the injectivity of the surface.•Non-well-posedness implies that the surface has self-intersection for some weights.