Interpolation surfaces, such as Bezier or B-spline 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.

This paper proposes an Iterated Function System (IFS) which can reduce effects of quantization errors of the IFS parameters. The proposed method skips conventional analog-parameter search and directly selects optimum IFS parameters from pools of discrete IFS parameters. In conventional IFS-based image coding the IFS parameters are quantized after their analog optimum values are determined. The image reconstructed from the quantized parameters is degraded with errors that are traced back to quantization errors amplified in the iterated mappings. The effectiveness of this new realistic approach is demonstrated by simulation results over the conventional method.