Visualizing Geometric Uncertainty of Surface Interpolants

abstract Evaluating and comparing the quality of surface interpolants is an important problem in computer graphics, computer aided geometric design and scientiic visualization. We introduce geometric uncertainty as a measure of interpolation error, level of conndence or quality of an interpolant. Geometric uncertainty can be estimated as a scalar or a vector-valued function that depends upon geometric characteristics of interpolants associated with the underlying data. These characteristics include position, normals, isophotes, principal curvatures and directions, mean and Gaussian curvatures. We present several new techniques for visualizing geometric uncertainty of surface interpolants, that combine the strengths of traditional techniques such as pseudo-coloring, diierencing, overlay, and transparency with new glyph and texture-based techniques. The viewer can control an interactive query-driven toolbox to create a wide variety of graphics that allow probing of geometric information in useful and convenient ways. We demonstrate the eeectiveness of these techniques by visualizing geometric uncertainty of surfaces obtained by diierent interpolation techniques { bilinear, C 0 linear, C 2 bicubic B-spline, multiquadrics, inverse multiquadrics and thin plate splines.