victorliu.info

All articles

AI is making me a micromanager

In blog

I am a manager. I hate being a manager. Granted, I manage a whopping two people (two and half, if we're being realistic about job tasks), but I still don't enjoy it. I understand it is a necessary evil in a company of size greater than two, and on the …

First yard mowing of 2026

In blog

I mowed the yard today. Well, actually, it was with a weedeater, but the effect is the same. I am writing this note to remember for next year that this is too late by about two weeks. The last rain was about two weeks ago, and that was when the …

Circular arcs 4 - extrema

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 …

Circular arcs 3 - parameterization

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.

Parameters used for arc evaluation and parameterization.

To recap, we obtained the …

Circular arcs 2 - evaluation

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 …

Circular arcs 1 - representation

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 …