Functy
3D function rendering

• 3 September 2012

Implicit Representation of Parametric Curves and Surfaces

I’ve recently been working on the question of whether mathematical surfaces can be rendered entirely using Shaders in a resolution-independent way, by avoiding the need to simplify the curve using triangles first. As part of the research in to this I found myself reading Sederberg, Anderson and Goldman’s 1984 paper “Implicit Representation of Parametric Curves and Surfaces” (available from ScienceDirect). Although not a new paper by computing standards, it’s definitely one of the best papers I’ve read in a long time, and goes to show that previous work is important not just from a legacy perspective.

It’s not just the contemporary relevance of the paper that demonstrates this point, but also its content. As the authors explain at the end of the paper, they present “two important examples of problems deemed unsolvable in the CAD literature, which are, in fact, solvable using century-old theorems.”

I’m not sure why I’ve been quite so surprised by this; I’m sure most people will consider this obvious. I should also add that Sederberg is very well cited in the rasterisation literature. However, it’s nice to come across such a clear example of less recent research that remains essential (and enjoyable) reading today.

I recommend the paper if you’ve not already read it. It’s very well written and contains some fascinating but clearly explained work.

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