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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 …