Design-driven quadrangulation of closed 3D curves

Abstract

(e) design-driven quadrangulation AbstractWe propose a novel, design-driven, approach to quadrangulation of closed 3D curves created by sketch-based or other curve modeling systems. Unlike the multitude of approaches for quad-remeshing of existing surfaces, we rely solely on the input curves to both conceive and construct the quad-mesh of an artist imagined surface bounded by them. We observe that viewers complete the intended shape by envisioning a dense network of smooth, gradually changing, flow-lines that interpolates the input curves. Components of the network bridge pairs of input curve segments with similar orientation and shape. Our algorithm mimics this behavior. It first segments the input closed curves into pairs of matching segments, defining dominant flow line sequences across the surface. It then interpolates the input curves by a network of quadrilateral cycles whose iso-lines define the desired flow line network. We proceed to interpolate these networks with all-quad meshes that convey designer intent. We evaluate our results by showing convincing quadrangulations of complex and diverse curve networks with concave, non-planar cycles, and validate our approach by comparing our results to artist generated interpolating meshes.

Flow-complex-based shape reconstruction from 3D curves

“…Work focused on surfacing designer curve cycles already identified for surfacing, such as [Bessmeltsev et al 2012], works well for many designer curve cycles but unlike our approach, is not intersection-free and fails for more complex or arbitray curve cycles like Figure 20, 21.…”

“…One advantage of our approach is that we do not require a pre- cisely connected network of input curves, but can handle an arbitrary collection including unconnected curves representing surface holes (see Figure 5), feature lines, or even additional points (see Figure 21) to be interpolated. In contrast approaches strongly driven by the topological connectivity of curves [Abbasinejad et al 2011] [Bessmeltsev et al 2012] are sensitive to how well the input curves are processed into a single curve network (see Section 4.1) and have no way of incorporating floating curves and points into the resulting surface.…”

“…These approaches may fail for complicated boundary curves and are best-suited to well-shaped convex curve cycles. Recently [Bessmeltsev et al 2012] surface complex curve loops by quadrangulating them into multiple 4-sided patches. None of these approaches however, provide a complete solution to the intersection-free surfacing of an unorganized set of 3D curves.…”

“…The boundary of a target patch is a curve cycle in Γ, potentially with inner cycles representing holes (see Figure 5). As all surface detail must be represented by input curves, it is reasonable to assume that a target patch has simple topology, homeomorphic to an open disk, possibly with holes [Bessmeltsev et al 2012]. Although our algorithm uses a point-set P representation of the curves Γ, we base the following discussion and the proposed sampling conditions on Γ itself and not on P .…”

Interactive shape modeling using a skeleton-mesh co-representation

“…Quad-meshing: methods attempt to define the flow-lines of shape [Bessmeltsev et al 2012] and are often based on establishing a vector field guided, periodic parametrization on a triangle mesh. The quad faces are then formed by tracing isoparameter curves in this parametrization, sometimes using an interactive workflow [Krishnamurthy and Levoy 1996;Takayama et al 2013].…”