Reuse of B-spline-based shape interrogation tools for triangular mesh models

Yuji Kobashi, Junya Suzuki, Han Kyul Joo, Takashi Maekawa*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In many engineering applications, a smooth surface is often approximated by a mesh of polygons. In a number of downstream applications, it is frequently necessary to estimate the differential invariant properties of the underlying smooth surfaces of the mesh. Such applications include first-order surface interrogation methods that entail the use of isophotes, reflection lines, and highlight lines, and second-order surface interrogation methods such as the computation of geodesics, geodesic offsets, lines of curvature, and detection of umbilics. However, we are not able to directly apply these tools that were developed for B-spline surfaces to tessellated surfaces. This article describes a unifying technique that enables us to use the shape interrogation tools developed for B-spline surface on objects represented by triangular meshes. First, the region of interest of a given triangular mesh is transformed into a graph function (z=h(x,y)) so that we can treat the triangular domain within the rectangular domain. Each triangular mesh is then converted into a cubic graph triangular Bézier patch so that the positions as well as the derivatives of the surface can be evaluated for any given point (x,y) in the domain. A number of illustrative examples are given that show the effectiveness of our algorithm.[Figure not available: see fulltext.]

Original languageEnglish
Article number4
Pages (from-to)1-15
Number of pages15
Journal3D Research
Issue number2
Publication statusPublished - 2012
Externally publishedYes


  • B-spline surface
  • PN triangles
  • Shape interrogation
  • Triangular mesh

ASJC Scopus subject areas

  • Software
  • Electrical and Electronic Engineering


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