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 Triangulated surfaces and domains
 Laplace operator 1
 Tutorial 10 – Discrete minimal surfaces
 Tutorial 9 – The Dirichlet problem
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 Tutorial 7 – Visualization of gradient fields
 Random Fourier polynomials
 Tutorial 6: Closetoconformal parametrizations of Hopf tori
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 Visualizing Discrete Geometry with Houdini II
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 Visualizing Discrete Geometry with Houdini I
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Monthly Archives: June 2016
Tutorial 9 – The Dirichlet problem
In the lecture we saw that the Dirichlet energy has a unique minimizer among all functions with prescribed boundary values. In this tutorial we want to visualize these minimizers in the discrete setting. Let \(\mathrm M\subset \mathbb R^2\) be a triangulated surface … Continue reading
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Tutorial 8 – Flows on functions
Last time we looked at the gradient flows of functions defined on the torus \(\mathrm T^n\). This time we will look at flows on the space of Fourier polynomials \(\mathcal F_N\). Let us first restrict ourselves to the realvalued Fourier polynomials \(\mathcal F_N^{\mathbb R} \subset … Continue reading
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Tutorial 7 – Visualization of gradient fields
In class we discussed how to generate smoothed random functions on the discrete torus and how to compute their discrete gradient and the symplectic gradient. In this tutorial we want to visualize the corresponding flow. As described in a previous … Continue reading
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Random Fourier polynomials
What is a typical function? The answer of this question certainly depends on the branch of mathematics you are into – while functions in differential geometry are usually smooth, the wiggling graphs appearing at the stock market are far from … Continue reading
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Tutorial 6: Closetoconformal parametrizations of Hopf tori
In this tutorial we want to construct Hopf cylinders and Hopf tori. These are flat surfaces in \(\mathrm S^3\) and allow for an easy conformal parametrization when mapped to Euclidean 3space by stereographic projection. For tori we will encounter a problem similar to … Continue reading
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