b/Surf: Interactive Bézier Splines on Surface Meshes

We present a practical framework to port Bzier curves to surfaces. We support the interactive drawing and editing of Bzier splines on manifold meshes with millions of triangles, by relying on just repeated manifold averages. We show that direct extensions of the de Casteljau and Bernstein evaluation...

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Veröffentlicht in:IEEE transactions on visualization and computer graphics Jg. 29; H. 7; S. 1
Hauptverfasser: Mancinelli, Claudio, Nazzaro, Giacomo, Pellacini, Fabio, Puppo, Enrico
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States IEEE 01.07.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
Approximation algorithms
Bezier patches
Computer graphics
Curves
Editing
geometric meshes
Geometry
geometry processing
Manifolds
Measurement
Robustness
spline curves
Spline functions
Splines (mathematics)
user interfaces
Visualization
ISSN:1077-2626, 1941-0506, 1941-0506
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Zusammenfassung:We present a practical framework to port Bzier curves to surfaces. We support the interactive drawing and editing of Bzier splines on manifold meshes with millions of triangles, by relying on just repeated manifold averages. We show that direct extensions of the de Casteljau and Bernstein evaluation algorithms to the manifold setting are fragile, and prone to discontinuities when control polygons become large. Conversely, approaches based on subdivision are robust and can be implemented efficiently. We implement manifold extensions of the recursive de Casteljau bisection, and an open-uniform Lane-Riesenfeld subdivision scheme. For both schemes, we present algorithms for curve tracing, point evaluation, and approximated point insertion. We run bulk experiments to test our algorithms for robustness and performance, and we compare them with other methods at the state of the art, always achieving correct results and superior performance. For interactive editing, we port all the basic user interface interactions found in 2D tools directly to the mesh. We also support mapping complex SVG drawings to the mesh and their interactive editing.
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ISSN:1077-2626
1941-0506
1941-0506
DOI:10.1109/TVCG.2022.3171179