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"Sinwave 4"
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While the basic idea behind this scene is fairly simple, the function defining the surface is a complex one. For this and the next image, a grid of spheres is created using a doubly nested while loop, and then they are translated up by the value of the function in space. The surface will be different if you change the range of values over which it is being evaluated. You can have a 100 by 100 grid of spheres if you have the loop go from -50 to +50 through both of the loops, and have a step of 1, or you can have it go from -.5 to +.5 with a step of .01. You will of course have to change the size of the spheres as well.
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Scene file for viewing here: sinwave-4.txt
Scene file for downloading: sinwave-4.pov | | by Ben Scheele -- initial 4-26-00, intermediate 6-12-00, final 12-2-02
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"Sinwave 2"
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The iridescent quality of the surface is created by using the same marble texture on each of the spheres, and using a huge number of them with very small radius. The number of spheres in both of these is almost 300,000. The colors are determined both by the original orientation of the texture and by which angle the surface is at and how the light is hitting it. I used an ultra wide angle camera in order to distort these surfaces.
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Scene file for viewing here: sinwave-2.txt
Scene file for downloading: sinwave-2.pov | | by Ben Scheele -- initial 4-25-00, final 3-6-03
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"Vector Valued Equation"
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AKA parametric equation. Here the form is created by using a sine function for z and cosine for y so that a circular motion is generated. Then it is translated along the third axis by the sum of a linear function and a sinusoidal function. An additional motion is created by adding the product of an exponential function and sinusoidal functions to the z term. All of these are functions of a single parameter, which is what is being changed by the loop.
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Scene file for viewing here: vector-valued-equation.txt
Scene file for downloading: vector-valued-equation.pov | | by Ben Scheele -- initial 7-18-02, final 3-20-03
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"Dfield2d Sinex"
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This image was created using my directional field plotter for systems of differential equations which I created in order to avoid having to go in to the labs to finish my Differential Equations and Linear Algebra homework. I placed switches in the file so that I could produce the result seen here, and then turn off the out-of-plane translation, color, and scaling, and turn on a grid and axes when I was using it for my assignments. It looked a lot more like the output from the lab program that way: boring. It is much more interesting like this I think. Also check out my shortened version of the code, and some examples of its use in the short gallery.
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Scene file for viewing here: dfield2d-sinex.txt
Scene file for downloading: dfield2d-sinex.pov
| | by Ben Scheele -- initial 2-27-02, intermediate 12-9-02, final 4-6-03
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"Harmonics Set5 b"
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I have often done polar coordinate "spirograph" like images using harmonic functions or products of them. I hadn't tried sums of harmonics until I got the idea from a book on functions and graphs. I created an array of shapes whose form is governed by a sum of harmonics, with a different frequency for each function. The ones down the sides have a value of one for one of the functions, and are counting up for the other. Therefore the diagonal has the same value for both functions, and is increasing towards the upper right corner. The thumbnail is a close up of one of the interesting ones, click on it to see all of them.
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Wallpaper version
Scene file for viewing here: harmonics-set-5b.txt
Scene file for downloading: harmonics-set-5b.pov | | by Ben Scheele -- initial 11-17-01, final 1-4-03
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