Lecture20a-Fractals

Lecture20a-Fractals - CS 455 Computer Graphics Fractals in...

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CS 455 – Computer Graphics Fractals in Graphics
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Texturing with Images Texture maps with images are good because images are (sometimes) easy to create. In some cases, just taking a picture is easier than writing a program to generate the picture. But… Images are hard to get for things that aren’t real. Images consume space. Images have finite precision.
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Procedural Methods. Write a program to generate the texture. Save space. In some cases, can zoom in forever and retain precision But… Hard to write the right procedure. However, ideas based on fractals go a long way. Especially for objects in nature.
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Euclidean vs. Fractal Standard objects are represented in Euclidean geometry Described by equations This gives smooth, regular objects Spheres Polygons B-spline surfaces How do we model natural objects? Clouds Mountains Plants These kinds of objects are better represented with fractal geometry
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What is a Fractal? Benoit Mandelbrot, 1982, “clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.” Objects are represented as procedures rather than equations Repeating the fractal procedure produces more and more detail
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Properties of Fractals Self-similarity between object parts and the overall object features Fractional dimension No specific size or scaling Infinite detail: looks good at every resolution Generated by a function, so no data to store.
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