Double partial said-ball curves: a new type of generalized ball curves

Ball curves and surfaces play a crucial role in modeling 3D objects with varying shapes. This paper presents theorems and algorithms for the generation of a new type of generalized Ball curves: double partial Said-Ball curves. The authors also investigate the properties of the new curves, including nonnegative, interpolation at the end points and partition of unity, give the detailed proof of the latter. Furthermore, the shape differences between the new curves and the other existent generalized Ball curves are demonstrated through image.