
Recent Posts
 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
Recent Comments
Archives
Categories
Meta
Monthly Archives: April 2016
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
Posted in Tutorial
Comments Off on Parallel Frame for Curves
ArclengthParametrized Curves
A parametrized curve $\gamma_[0,L]\to\mathbb{R}^3$ is called parametrized by arclength provided that $\gamma(t)$ moves with unit speed if we interpret $t$ as time: $\left\gamma'(t)\right=1$ for all $t\in [0,L]$. Sampling an arclengthparametrization $\gamma$ at evenly spaced points $t=\frac{mL}{n}$ for integer values of $m$ … Continue reading
Posted in Lecture
Comments Off on ArclengthParametrized Curves
Sampled Parametrized Curves
In the last post we created geometric objects from scratch, including the underlying combinatorics. In most situations it is much more convenient to start with already existing geometry and transform it. This approach is similar to the standard way of … Continue reading
Posted in Lecture
Comments Off on Sampled Parametrized Curves
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
Posted in Tutorial
Comments Off on Tutorial 1: Implicit Surfaces with Houdini
Creating Geometry From Scratch
Here we explain how to generate geometry procedurally. There are two node types that allow tho do this: Nodes of type Attribute Wrangle allow to specify geometry using the programming language VEX. Nodes of type Python allow to do the same in the … Continue reading
Posted in Lecture
Comments Off on Creating Geometry From Scratch
Combinatorial Geometry in Houdini
As primitive geometric objects (objects that do not arise as combinations of other objects) Houdini supports also round spheres, cylinders (called tubes in Houdini), volumes and other things. We will focus here on Houdini’s implementation of the combinatorial complexes described … Continue reading
Posted in Lecture
Comments Off on Combinatorial Geometry in Houdini
Combinatorial Geometry: Simplicial Complexes
While (for good reasons) we have restricted our treatment of combinatorial cell complexes to the twodimensional case, the theory of $n$dimensional simplicial complexes is rather straightforward: Definition: A simplicial complex is a finite set $P$ together with a set $\mathcal{S}$ … Continue reading
Posted in Lecture
Comments Off on Combinatorial Geometry: Simplicial Complexes
Combinatorial Geometry: Cell Complexes
Roughly speaking, Combinatorial complexes play a similar role in the discrete world as differentiable manifolds in the smooth world. They are able to capture the “intrinsic” properties of a geometric object, i.e. those properties that are independent of any embedding … Continue reading
Posted in Lecture
Leave a comment
Scenes with White Background
In a scientific context a very common task is to prepare figures for manuscripts. In most cases the objects in the foreground are the sole focus of attention, and in such cases it is desirable that the figure should blend naturally with … Continue reading
Posted in Lecture
Leave a comment
Simple Ambient Scenes
Visual perception is always slightly irritated when it is confronted with understanding objects that are just floating in empty space, with no clues concerning the surrounding environment. For this reason the slight gradient in Houdinis Scene View is already helpful: The … Continue reading
Posted in Lecture
Leave a comment