TY - JOUR
T1 - Similarity maps and field-guided T-Splines
T2 - ACM SIGGRAPH 2017
AU - Campen, Marcel
AU - Zorin, Denis
N1 - Funding Information:
This work is supported by the National Science Foundation, under grant IIS-1320635. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. © 2017 Copyright held by the owner/author(s). Publication rights licensed to ACM. 0730-0301/2017/7-ART91 $15.00 DOI: http://dx.doi.org/10.1145/3072959.3073647
Publisher Copyright:
© 2017 Copyright held by the owner/author(s).
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
KW - Conformal maps
KW - Holonomy
KW - Interval assignment
KW - Seamless parametrization
KW - T-NURCCS
KW - T-mesh
UR - http://www.scopus.com/inward/record.url?scp=85030771703&partnerID=8YFLogxK
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U2 - 10.1145/3072959.3073647
DO - 10.1145/3072959.3073647
M3 - Conference article
AN - SCOPUS:85030771703
VL - 36
JO - ACM Transactions on Graphics
JF - ACM Transactions on Graphics
SN - 0730-0301
IS - 4
M1 - 91
Y2 - 30 July 2017 through 3 August 2017
ER -