skull - THE SKULL SURFACE Oliver Knill Math21a Surfaces are...

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Unformatted text preview: THE SKULL SURFACE, Oliver Knill , Math21a Surfaces are usually represented in a triangulated form. where a few points on the surface are given and triples of points form triangles. This illustrates the concept of linear approximation . Every triangle is close to the actual surface. HOW TO PRODUCE THE SKULL SURFACE. We found on the web a file skull.dat , which contains data 0 -0.02 0.02 0.29 0.65 0.08 0.4 0.53 0.06 0 -0.02 0.02 0.4 0.53 0.06 0.53 0.41 0.02 0 -0.02 0.02 ... ... These data encode points in space: every line is a point, three points in a row represent a triangle in space. So, the first 3 lines from the datafile represent the triangle { P,Q,R } = { (0 ,- . 02 , . 02), (0 . 29 , . 65 , . 02), (0 . 4 , . 65 , . 08) } . In to- tal, the file contains 3729 points which means that there are 1243 triangles encoded. PLOTTING THE SURFACE. To the right is a small Mathemat- ica program which produces a sur- face from these data. The data are first read, then packed into groups of 3 to get the points, then packed...
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