One basic operation upon shapes is to compute bounding regions. For a shape made up of pieces of simple curves, this amounts to computing directional extrema on the curve. In other words, given a curve and a direction vector \(d\) (without loss of generality we assume it is normalized), determine …

In the last article, we discussed how to compute a point on the arc given a parameter value. In this article, we explore the inverse problem of computing the parameter value given a point (approximately) on the arc.

To recap, we obtained the …

Continuing the series on circular arc representations, we next discuss the most fundamental operation of curve representation: evaluation at an arbitrary parameter value.

The typically most desirable parameterization is arc length parameterization. We will use instead a parameter \(s\in[0,1]\) that is proportional to the arc length parameterization …

I have written a short note on circular arcs, but I feel it would be a good idea to revisit much of that material and explain some of the rationale and derivations. We will begin this series with this article on arc representation.

The goal is to represent an arc …