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- Wave- and heat-equation on surfaces
- Partial differential equations involving time
- Tutorial 11 – Electric fields on surfaces
- Laplace operator 2
- Triangulated surfaces with metric and the Plateau problem
- Dirichlet energy 2
- Gradient and Dirichlet energy on triangulated domains.
- Triangulated surfaces and domains
- Laplace operator 1
- Tutorial 10 – Discrete minimal surfaces
- Tutorial 9 – The Dirichlet problem
- Tutorial 8 – Flows on functions
- Tutorial 7 – Visualization of gradient fields
- Random Fourier polynomials
- Tutorial 6: Close-to-conformal parametrizations of Hopf tori
- Tutorial 5: Lawson’s minimal surfaces and the Sudanese Möbius band
- The 3-Sphere
- Tutorial 4: Hyperbolic helicoids
- Tutorial 3: Framed Closed Curves
- Conformal maps III: Stereographic Projection
- Conformal Maps II: Inversions
- Quaternions
- Tutorial 2: Framed Discrete Curves
- Mandelbrot Set
- Conformal Maps I: Holomorphic Functions
- Conformal Parametrizations of Surfaces
- Parallel Frame for Curves
- Arclength-Parametrized Curves
- Sampled Parametrized Curves
- Tutorial 1: Implicit Surfaces with Houdini
- Creating Geometry From Scratch
- Combinatorial Geometry in Houdini
- Combinatorial Geometry: Simplicial Complexes
- Combinatorial Geometry: Cell Complexes
- Scenes with White Background
- Simple Ambient Scenes
- Visualizing Discrete Geometry with Houdini II
- Rendering and Working with Cameras
- Visualizing Discrete Geometry with Houdini I
- Using Houdini on MacBooks
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Category Archives: Tutorial
Mandelbrot Set
If you google “mathematics visualization”, the resulting wikipedia page shows the Mandelbrot set as a famous example. The Mandelbrot set \(M\subset{\Bbb C}\) is defined as the following. For each \(c\in {\Bbb C}\), consider the iteration \(z_{n+1}(c) = ({z_n}(c))^2+c\), \(n=0,1,2,\ldots\) and \(z_0(c) = … Continue reading
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Parallel Frame for Curves
If you have a polygonal curve, say arc-length parameterized, you might want to visualize the curve as the following rendering This can be done in Houdini by the “copy” SOP node. The “copy” node has two input and one output. The … Continue reading
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Tutorial 1: Implicit Surfaces with Houdini
It is amazingly simple to create high-quality renderings with Houdini. Several small tricks to achieve nice renderings of geometries in a mathematical context are already described in the first posts of this blog. If you not have looked at it yet you should … Continue reading
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