Monthly Archives: April 2016

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 arclength-parametrization $\gamma$ at evenly spaced points $t=\frac{mL}{n}$ for integer values of $m$ … Continue reading →

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 →

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 →

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 →

While (for good reasons) we have restricted our treatment of combinatorial cell complexes to the two-dimensional 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 →

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 →

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 →

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 →