Abstract
A method to create a differentiable complex shapes from simple polygonal models is proposed. It is shown that classical schemes of “smooth” subdivision can be obtained from local self-similarity ratios if “deflection arrows” are scaled as s2, where s is the linear compression coefficient calculated for a flat regular grid of the same structure. The surfaces obtained by a smooth subdivision do not contain sharp features other than the vertices and edges of the original model, so in order to create a surface of more exotic shape one must use more complex model. The article describes an alternative approach, in which a fractal forecast of the position of embedded vertices, calculated using the local geometric self-similarity ratio, is used to obtain a pronounced surface shape. Fractal forecast transfers the properties of the original polygonal model to a smaller scale, thereby generating secondary sharp surface features that compose a large-scale texture. To ensure the differentiability of the surface, the fractal forecast is combined with the “smooth” one, and the proportion of the latter increases with decreasing scale.
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