QuadriFlow: A Scalable and Robust Method for Quadrangulation

Abstract

QuadriFlow is a scalable algorithm for generating quadrilateral surface meshes based on the Instant Field‐Aligned Meshes of Jakob et al. (ACM Trans. Graph. 34(6):189, 2015). We modify the original algorithm such that it efficiently produces meshes with many fewer singularities. Singularities in quadrilateral meshes cause problems for many applications, including parametrization and rendering with Catmull‐Clark subdivision surfaces. Singularities can rarely be entirely eliminated, but it is possible to keep their number small. Local optimization algorithms usually produce meshes with many singularities, whereas the best algorithms tend to require non‐local optimization, and therefore are slow. We propose an efficient method to minimize singularities by combining the Instant Meshes objective with a system of linear and quadratic constraints. These constraints are enforced by solving a global minimum‐cost network flow problem and local boolean satisfiability problems. We have verified the robustness and efficiency of our method on a subset of ShapeNet comprising 17,791 3D objects in the wild. Our evaluation shows that the quality of the quadrangulations generated by our method is as good as, if not better than, those from other methods, achieving about four times fewer singularities than Instant Meshes. Other algorithms that produce similarly few singularities are much slower; we take less than ten seconds to process each model. Our source code is publicly available.

3D Reconstruction and Geostatic Analysis of an Early Medieval Cemetery (Olonne-sur-Mer, France)

“…For each of the 174 polygons illustrating the contours of the graves, we extruded them downwards to the minimum altitude of the corresponding head-basin-foot points (Figure 7A). We then retopologized these same contours by applying the Quadriflow algorithm [63] to mesh them strongly. We then selected a longitudinal slice of vertex with the soft selection tool [64] to bulge the shape.…”

“…The creation of 3D heatmaps was done by finely retopologizing [63] a plane (Figure 8A), then applying a displace modifier (Figure 8C) [56] from a black and white image produced by QGIS with an outline for recalibration on site (Figure 8B). Extensive scaling was done to clearly distinguish the concentrations, including the lowest.…”

Automatic generation of global shell-element meshes for large-scale structural design optimization

“…Knoppel et al [9] further generate an algorithm for computing the stripe patterns on a surface which can be applied to create a mesh on the surface. By extending the idea of smooth orientation and position field [2], Huang et al [10] remove most of the singularities in the output mesh by formulating a minimum-cost network flow problem. However, they are all complicated, and some of them involve nonlinear programming which does not guarantee convergence or global minimum of the objective function.…”

FrameNet: Learning Local Canonical Frames of 3D Surfaces From a Single RGB Image

“…This can be achieved by optimizing a nonlinear energy by periodic functions [17,29] or a mixedinteger representation [30,5]. In our work, we use Quadri-Flow [21] to optimize the 4-RoSy field so that it aligns with the principal curvatures at the curved surface and ensures smoothness in flat regions (where principal directions are ill-defined) as well as robustness to noise.…”

“…Noises exist in both the geometry and the projections in images, as shown in (c). (b) computes the 4-RoSy field using QuadriFlow[21] and produces robust tangent principal directions, as shown in (d) as the projection in the image plane. Local Canonical Frames Dataset.…”