✦ LIBER ✦

Computing View Graphs of Algebraic Surfaces

✍ Scribed by J.H. Rieger

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 496 KB
Volume: 16
Category: Article
ISSN: 0747-7171
DOI: 10.1006/jsco.1993.1044

No coin nor oath required. For personal study only.

✦ Synopsis

The "bad" directions or centres of projection, which yield degenerate projections of a smooth surface (S) embedded in 3-space, lie on a bifurcation set (\mathcal{B}) of positive codimension in view space (\mathcal{V}) (where (\mathcal{V}=\mathbb{P}^{2}) or (\mathbb{R}^{3} \backslash S) ). The connected components of (\mathcal{V} \backslash \mathcal{B}) are the nodes in the view graph of (S), and two nodes are connected by an edge if the corresponding components are separated by a branch of (\mathcal{B}) of dimension (\operatorname{dim} \mathcal{V}-1). The view graph of an algebraic surface of degree (d) has at most (O\left(d^{10 \operatorname{dim}} \mathcal{V}\right)) nodes. We describe an algorithm for computing the view graphs of surfaces defined as zero sets of polynomials with rational coefficients and present some examples.

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