Parametrization of translational surfaces
Sonia Perez-Diaz, Liyong Shen
TL;DR
This paper provides a necessary and sufficient condition for algebraic translational surfaces to have a standard parametric form, along with a constructive proof and a method to compute such parametrizations.
Contribution
It introduces a precise criterion for translational surfaces to admit standard parametrizations and offers a constructive approach to compute them.
Findings
Established a necessary and sufficient condition for standard parametrization
Provided a constructive proof for the parametrization process
Enabled computation of parametric representations for translational surfaces
Abstract
The algebraic translational surface is a typical modeling surface in computer aided design and architecture industry. In this paper, we give a necessary and sufficient condition for that algebraic surface having a standard parametric representation and our proof is constructive. If the given algebraic surface is translational, then we can compute a standard parametric representation for the surface.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Computer Graphics and Visualization Techniques · Computational Geometry and Mesh Generation