6533b873fe1ef96bd12d4c1f

RESEARCH PRODUCT

A comparison of local parametric C0 Bézier interpolants for triangular meshes

Christoph FünfzigGudrun AlbrechtLucia RomaniMaria Boschiroli

subject

Shape propertiesGeneral EngineeringBézier curveTopologyComputer Graphics and Computer-Aided DesignC0 local parametric interpolantRendering (computer graphics)Human-Computer InteractionComputer graphicsMAT/08 - ANALISI NUMERICABézier triangleTriangle meshPolygon meshComputingMethodologies_COMPUTERGRAPHICSParametric statisticsMathematics

description

Parametric curved shape surface schemes interpolating vertices and normals of a given triangular mesh with arbitrary topology are widely used in computer graphics for gaming and real-time rendering due to their ability to effectively represent any surface of arbitrary genus. In this context, continuous curved shape surface schemes using only the information related to the triangle corresponding to the patch under construction, emerged as attractive solutions responding to the requirements of resource-limited hardware environments. In this paper we provide a unifying comparison of the local parametric C^0 curved shape schemes we are aware of, based on a reformulation of their original constructions in terms of polynomial Bezier triangles. With this reformulation we find a geometric interpretation of all the schemes that allows us to analyse their strengths and shortcomings from a geometrical point of view. Further, we compare the four schemes with respect to their computational costs, their reproduction capabilities of analytic surfaces and their response to different surface interrogation methods on arbitrary triangle meshes with a low triangle count that actually occur in their real-world use.

yearjournalcountryeditionlanguage
2011-02-01
10.1016/j.cag.2010.09.011http://hdl.handle.net/10281/18898