Feature Enhancement by Vertex Flow for 3D Shapes

We present a new method for enhancing shape features of a mesh surface by moving mesh vertices from low-curvature regions to high-curvature regions or feature regions. The movement of the vertices, also called vertex flow, is driven by minimizing an objective function defined to take into account several important considerations in mesh improvement. First, a new edge-based energy term is used to measure the uniformity of the approximation error of a target shape by a mesh surface. Clearly, given a fixed number of triangle faces of a mesh surface approximating an underlying target surfaces, the approximation is made more uniform by placing more faces are used in higher-curvature regions and fewer faces in lower-curvature regions. Therefore, the minimization of this edge-based energy term provides a strong force to move mesh vertices towards high-curvature regions. Second, to maintain faithful shape approximation during vertex flow, a distance-error term is included to penalize the displacement of mesh vertices along normal directions of the underlying surface, and a novel local quadratic model is employed to efficiently minimize this term. Third, a fairing term is used to ensure the smoothness of the resulting mesh surface. Our method enhances significantly shape features even at a low sampling rate and is useful to several feature-aware geometry processing operations, such as simplification and perceptual line drawing.