Similarity maps and field-guided T-Splines: A perfect couple

Marcel Campen, Denis Zorin

Research output: Contribution to journalArticle

Abstract

A variety of techniques were proposed to model smooth surfaces based on tensor product splines (e.g. subdivision surfaces, free-form splines, T-splines). Conversion of an input surface into such a representation is commonly achieved by constructing a global seamless parametrization, possibly aligned to a guiding cross-field (e.g. of principal curvature directions), and using this parametrization as domain to construct the spline-based surface. One major fundamental difficulty in designing robust algorithms for this task is the fact that for common types, e.g. subdivision surfaces (requiring a conforming domain mesh) or T-spline surfaces (requiring a globally consistent knot interval assignment) reliably obtaining a suitable parametrization that has the same topological structure as the guiding field poses a major challenge. Even worse, not all fields do admit suitable parametrizations, and no concise conditions are known as to which fields do. We present a class of surface constructions (T-splines with halfedge knots) and a class of parametrizations (seamless similarity maps) that are, in a sense, a perfect match for the task: for any given guiding field structure, a compatible parametrization of this kind exists and a smooth piecewise rational surface with exactly the same structure as the input field can be constructed from it. As a byproduct, this enables full control over extraordinary points. The construction is backward compatible with classical NURBS. We present efficient algorithms for building discrete conformal similarity maps and associated T-meshes and T-spline surfaces.

Original languageEnglish (US)
Article number91
JournalACM Transactions on Graphics
Volume36
Issue number4
DOIs
StatePublished - 2017

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Splines
Tensors
Byproducts

Keywords

  • Conformal maps
  • Holonomy
  • Interval assignment
  • Seamless parametrization
  • T-mesh
  • T-NURCCS

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

Cite this

Similarity maps and field-guided T-Splines : A perfect couple. / Campen, Marcel; Zorin, Denis.

In: ACM Transactions on Graphics, Vol. 36, No. 4, 91, 2017.

Research output: Contribution to journalArticle

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