A Method for Displaying Metaballs by using Bézier Clipping

For rendering curved surfaces, one of the most popular techniques is metaballs, an implicit model based on isosurfaces of potential fields. This technique is suitable for deformable objects and CSG model. For rendering metaballs, intersection tests between rays and isosurfaces are required. By defining the higher degree of functions for the field functions, richer capability can be expected, i.e., the smoother surfaces. However, one of the problems is that the intersection between the ray and isosurfaces can not be solved analytically for such a high degree function. Even though the field function is expressed by degree six polynomial in this paper (that means the degree six equation should be solved for the intersection test), in our algorithm, expressing the field function on the ray by Bézier functions and employing Bézier Clipping, the root of this function can be solved very effectively and precisely. This paper also discusses a deformed distribution function such as ellipsoids and a method displaying transparent objects such as clouds.