Construction of Smooth Branching Surfaces using T-splines

A I Ginnis (1) , K V Kostas (2) , Panagiotis I Kaklis (3, 1, 4)

1 NTUA - National Technical University of Athens [Athens]
2 Nazarbayev University [Kazakhstan]
3 University of Strathclyde [Glasgow]
4 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes

The request for designing or reconstructing objects from planar cross sections arises in various applications, ranging from CAD to GIS and Medical Imaging. The present work focuses on the " one-to-many " branching problem, where one of the planes can be populated with many, possibly tortuous and densely packed, contours. The proposed method combines the proximity information offered by the Euclidean Voronoi diagram with the concept of surrounding curve, introduced in [1], and T-splines technology [2] for securing a flexible and portable representation. Our algorithm delivers a single T-spline that deviates from the given contours less than a user-specified tolerance, measured via the so-called discrete Fréchet distance [3] and is C 2 everywhere except from a finite set of point-neighborhoods. Subject to minor enrichment, the algorithm is also capable to handle the " many-to-many " configuration as well as the global reconstruction problem involving contours on several planes.

Mots clés: Branching surface; T-splines; Voronoi diagram; surrounding curve; discrete Fréchet distance

Domaines: Informatique [cs]; Ingénierie assistée par ordinateur

A I Ginnis, K V Kostas, Panagiotis I Kaklis. Construction of Smooth Branching Surfaces using T-splines. 2016. ⟨hal-01386105⟩