A geometric criterion for smooth interpolation of curve networks

ABSTRACT

A key problem when interpolating a network of curves occurs at vertices: an algebraic condition called the vertex enclosure constraint must hold wherever an even number of curves meet. This paper recasts the constraint in terms of the local geometry of the curve network. This allows formulating a new geometric constraint, related to Euler's Theorem on local curvature, that implies the vertex enclosure constraint and is equivalent to it where four curve segments meet without forming an X.

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.2 Approximation

Additional Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Curve, surface, solid, and object representations

Keywords:
C¹ surface construction, Euler curvature constraint, local network interpolation, splines, vertex enclosure constraint