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CGT511-09-Procedural

CGT511-09-Procedural - CGT511 ProceduralMethods 3D Volume...

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11/15/2011 1 CGT 511 Procedural Methods Bed ř ich Beneš, Ph.D. Purdue University Department of Computer Graphics Technology © Bedrich Benes 3D object representation Voxels Oct tree CSG Volume representation Wire frame Polygonal Bézier surfaces NURBS Implicit surfaces Free form Surfaces Boundary representation Fractals Particle systems Grammars Procedural 3D object representation © Bedrich Benes Procedural Techniques Three classes: fractals particle systems grammars Used when shape cannot be represented as a surface (fire, water, smoke, flock of birds, explosions, model of mountain, grass, clouds, plants, etc.) Used for Simulation of Natural Phenomena © Bedrich Benes Procedural Techniques Model is generated by a piece of code Model is not represented as data! The generation can take some time and of course the data can be precalculated
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11/15/2011 2 © Bedrich Benes The Mandelbrot Set – the big logo The Mandelbrot set discovered in 1970 by Benoit Mandelbrot It is a non linear deterministic fractal It is graph of a solution of a dynamic system © Bedrich Benes The Mandelbrot Set Take the equation where: z i and c are complex numbers and z 0 =0+i0 Explore c complex numbers from the complex plane Measure the speed of divergence of the z n i.e., measure when |z n | > 2 (predefined value) z n+1 = z n 2 +c © Bedrich Benes The Mandelbrot Set Explore c complex numbers from the complex plane Measure the speed of divergence of the z n i.e., measure when |z n | > 2 (predefined value) there are two kinds of points: |z n | < 2 for n > , (stable points) |z n | > 2 for certain n and n greater (unstable points) © Bedrich Benes The Mandelbrot Set a) stable points displayed in black b) unstable points color=f(n) for every point c in the plane < 2 2i>, <2+2i> do set z = 0+i0 set n=0 while (n<MAX) and (|z|<2) do z=z 2 +c end of while if (n==MAX) Draw Point(Black) else Draw Point(n) end of for
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11/15/2011 3 © Bedrich Benes The Mandelbrot Set Zooming into the Mandelbrot set © Bedrich Benes The Mandelbrot Set Zooming into the Mandelbrot set © Bedrich Benes The Mandelbrot Set Zooming into the Mandelbrot set © Bedrich Benes The Mandelbrot Set Zooming into the Mandelbrot set
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