A computational approach to joint line detection on triangular meshes

Abstract

In this paper, we present formulae for evaluating differential quantities at vertices of triangular meshes that may approximate potential piecewise smooth surfaces with discontinuous normals or discontinuous curvatures at the joint lines. We also define the C 1 and C 2 discontinuity measures for surface meshes using changing rates of one-sided curvatures or changing rates of curvatures across mesh edges. The curvatures are computed discretely as of local interpolating surfaces that lie within a tolerance to the mesh. Together with proper estimation of local shape parameters, the obtained discontinuity measures own properties like sensitivity to salient joint lines and being scale invariant. A simple algorithm is finally developed for detection of C 1 or C 2 discontinuity joint lines on triangular meshes with even highly non-uniform triangulations. Several examples are provided to demonstrate the effectiveness of the proposed method.