PNG1 triangles for tangent plane continuous surfaces on the GPU

Christoph Fünfzig, Kerstin Müller, Dianne Hansford, Gerald Farin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

22 Scopus citations


Improving the visual appearance of coarse triangle meshes is usually done with graphics hardware with per-pixel shading techniques. Improving the appearance at silhouettes is inherently hard, as shading has only a small influence there and the geometry must be corrected. With the new geometry shader stage released with DirectX 10, the functionality to generate new primitives from an input primitive is available. Also the shader can access a restricted primitive neighborhood. In this paper, we present a curved surface patch that can deal with this restricted data available in the geometry shader. A surface patch is defined over a triangle with its vertex normals and the three edge neighbor triangles. Compared to PN triangles, which define a curved patch using just the triangle with its vertex normals, our surface patch is G1 continuous with its three neighboring patches. The patch is obtained by blending two cubic Bézier patches for each triangle edge. In this way, our surface is especially suitable for efficient, high-quality tessellation on the GPU. We show the construction of the surface and how to add special features such as creases. Thus, the appearance of the surface patch can be fine-tuned easily. The surface patch is easy to integrate into existing polygonal modeling and rendering environments. We give some examples using Autodesk Maya®.

Original languageEnglish (US)
Title of host publicationProceedings - Graphics Interface 2008
Number of pages8
StatePublished - 2008
EventGraphics Interface 2008 - Windsor, ON, Canada
Duration: May 28 2008May 30 2008

Publication series

NameProceedings - Graphics Interface
ISSN (Print)0713-5424


OtherGraphics Interface 2008
CityWindsor, ON


  • Bézier surfaces
  • GPU based tessellation
  • Geometry shader
  • PN triangles

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design


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