Piecewise smooth surface reconstruction

ABSTRACT

We present a general method for automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data. The method can be used in a variety of applications such as reverse engineering—the automatic generation of CAD models from physical objects. Novel aspects of the method are its ability to model surfaces of arbitrary topological type and to recover sharp features such as creases and corners. The method has proven to be effective, as demonstrated by a number of examples using both simulated and real data.

A key ingredient in the method, and a principal contribution of this paper, is the introduction of a new class of piecewise smooth surface representations based on subdivision. These surfaces have a number of properties that make them ideal for use in surface reconstruction: they are simple to implement, they can model sharp features concisely, and they can be fit to scattered range data using an unconstrained optimization procedure.

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Index Terms

• Applied computing

  • Arts and humanities

    • Architecture (buildings)

      • Computer-aided design

  • Physical sciences and engineering

    • Engineering

      • Computer-aided design

• Computing methodologies

  • Computer graphics

    • Shape modeling

      • Parametric curve and surface models

      • Volumetric models

• Mathematics of computing

  • Mathematical analysis

    • Functional analysis

      • Approximation

    • Numerical analysis

      • Computations on polynomials