Fractals and Solid Modeling

Fractals and Solid Modeling

Trying to combine fractal geometry and solid modeling seems to be a contradiction in itself, In this paper a new type of 3D objects is presented that accomplishes this combination in a specific way. Objects with a fractal macro structure and a 3D solid micro structure can be specified and rendered efficiently by using context free, attribute, geometric grammars. This new object type can be inco...

Shape Modeling with Fractals

Fractal phenomena are a source of geometric detail that can be difficult to harness for general purpose shape modeling. We present a method for modeling surfaces by warping a fractal onto a given mesh. The warp is specified by the user as a coarse displacement field and interpolated by triharmonic radial basis functions. Efficient methods for rendering the warped fractal by ray tracing and isos...

Geometric and Solid Modeling

Simplicial Complexes and Geometric Realization Since we de ned simplices as convex combinations of points, it is conceivable that this de nition is too narrow. That is, when constructing a simplicial complex, can we obtain more complicated structures using simplices that are only homeomorphic to convex combinations? From a topological point of view, the answer is no, and is justi ed as follows....

Solid and Physical Modeling

Selfsimilar Fractals and Selfsimilar Random Fractals

We survey the application of contraction mapping argments to selfsimilar (nonrandom) fractal sets, measures and functions. We review the results for selfsimilar random fractal sets and measures and show how the method and extensions also work for selfsimilar random fractal functions.