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 Wave and heatequation 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: Closetoconformal parametrizations of Hopf tori
 Tutorial 5: Lawson’s minimal surfaces and the Sudanese Möbius band
 The 3Sphere
 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
 ArclengthParametrized 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 arclength 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 highquality 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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