Wrinkly Surface Generated on Irregular Mesh by Using IST Generalized on Code Space and Multi-Dimensional Space: Unification of Interpolation Surface and Fractal

摘要

Interpolation surfaces, such as Bezier or B-splirie surface, are usually used for representing smooth man-made objects and provide an excellent ability to control the shape of a surface by intuitively moving control points. In contrast, the fractal technique is used for creating various complex shapes, mainly of natural objects, that have self-similarity using simple procedures. We have proposed the "wrinkly surface (WR surface)" for combining the advantages of interpolation surfaces and fractals. In this paper, we propose the expansion of the construction scheme of the WR surface to irregular meshes. Control points of a WR surface are interpolated using the "Iterated Shuffle Transformation (IST)." Therefore, in order to achieve the expansion, we first generalize the IST on code spaces, and then propose multi-dimensional IST defined on geometric spaces. By creating various shape model examples, we demonstrate the usefulness of the WR surface as a modeling tool.