A Multi-sided Bézier Patch with a Simple Control Structure

A new n‐sided surface scheme is presented, that generalizes tensor product Bézier patches. Boundaries and corresponding cross‐derivatives are specified as conventional Bézier surfaces of arbitrary degrees. The surface is defined over a convex polygonal domain; local coordinates are computed from gen...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Computer graphics forum Jg. 35; H. 2; S. 307 - 317
Hauptverfasser: Várady, Tamás, Salvi, Péter, Karikó, György
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford Blackwell Publishing Ltd 01.05.2016
Schlagworte:
Algorithms
Analysis
and object representations
Bezier
Bezier patches
Boundaries
Categories and Subject Descriptors (according to ACM CCS)
Displacement
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Curve
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations
Image processing systems
Mathematical analysis
Mathematical models
Representations
solid
Studies
surface
Topological manifolds
ISSN:0167-7055, 1467-8659
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:A new n‐sided surface scheme is presented, that generalizes tensor product Bézier patches. Boundaries and corresponding cross‐derivatives are specified as conventional Bézier surfaces of arbitrary degrees. The surface is defined over a convex polygonal domain; local coordinates are computed from generalized barycentric coordinates; control points are multiplied by weighted, biparametric Bernstein functions. A method for interpolating a middle point is also presented. This Generalized Bézier (GB) patch is based on a new displacement scheme that builds up multi‐sided patches as a combination of a base patch, n displacement patches and an interior patch; this is considered to be an alternative to the Boolean sum concept. The input ribbons may have different degrees, but the final patch representation has a uniform degree. Interior control points—other than those specified by the user—are placed automatically by a special degree elevation algorithm. GB patches connect to adjacent Bézier surfaces with G1continuity. The control structure is simple and intuitive; the number of control points is proportional to those of quadrilateral control grids. The scheme is introduced through simple examples; suggestions for future work are also discussed.
Bibliographie:istex:9CFD8C5195D60D984E92EB60F3AB89F94B0B33CF
ark:/67375/WNG-MHMXLRTC-9
ArticleID:CGF12833
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-1
ObjectType-Feature-2
content type line 23
ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12833