CAD Curve Basics

A boundary representation (BREP) is a data structure used to represent all things topological: 3D meshes, 2d vector curves, volumes, etc. This post is about what makes a good boundary representation for CAD, tailored to support complex curves in a mathematically intutive (and correct) way.

What Is A Curve

What is a curve? A curve is a multidimensional function that is parameterized with one variable.

fx(t), fy(t)

Simple GPU Vector Graphics With Spatial Trees

Rendering 2D vector graphics on the GPU is a notoriously vexing problem. The most popular publicly available methods are either slow (stencil and cover) or highly memory intensive (cached prerendered buffers, e.g. most SVG renderers). In truth none of this is necessary; rendering vector graphics on the GPU is not hard if you use, as the saying goes, this one neat trick.

Bass Relief Modifier In Blender

For the Christmas holidays I decided to write a little bass-relief modifier for Blender.

Brush Tasks

The backend for Blender’s sculpt system is a simple coarse bounding volume hierarchy, which we call PBVH. It’s a KD-tree that uniquely assigns vertices to leaf nodes. To access node vertices we have a rather hideous C macro, BKE_pbvh_vertex_iter_begin. All of this had lead to a code pattern that’s fairly verbose with lots of copy-and-pasting of code.

Clothoid Splines

A century ago engineers had very good and robust means of drafting 2D curves using specialized spline sets and curve templates (e.g. French curves). But these proved difficult to replicate in early computers; the need for fast, simple algorithms drove first Bezier, and then de Boor to embrace the idea of polynomial-based splines.

Creating a spline from independent polynomial functions along the x/y/z axes has a number of problems. Such splines cannot be represented in arc length form and, more importantly, controlling their curvature functions is not easy. Polynomial splines are computationally simple but mathematically complex.

Dither Masks With Controlled Noise Spectra

Sampling is the bane of computer graphics. Aliasing, accuracy, and noise must all be traded off against each other. A sampling method that works well for low sample counts might be inferior at high sample counts.