Mesh Processing Applications Research Articles

GPU accelerated grid-free surface tracking

We present the first GPU accelerated explicit surface tracker. Its speed and the fact that it does not use a grid makes it suitable for a wide range of applications including those that operate on a large, unbounded domain. The core idea for handling topological changes is to detect and delete overlapping triangles as well as triangles that lie inside the volume. The resulting holes are then joined or closed in a robust and efficient manner. We maintain a good quality mesh by using several improvement steps. The algorithm is guaranteed to produce a manifold mesh without boundary. In this paper we describe how all these steps can be parallelized to run efficiently on a GPU. Our results show the quality and efficiency of the method in Eulerian and Lagrangian liquid simulations, in solid simulations and in mesh processing applications. Our GPU implementation runs more than an order of magnitude faster than the CPU version.

Automatic Quad Patch Layout Extraction for Quadrilateral Meshes

ABSTRACTIn this paper, we present an automatic method to extract quad patch layout with monotone boundaries in a quadrilateral mesh. Our approach simplifies the separatrices and connectivity graph topologically compared with the previous work. The key idea of our method is firstly to find all the candidates of the short separatrices based on the safety turning areas, and secondly, the problem of finding proper separatrices to extract quad patch layout is formulated as a binary integer programming problem. In the process of solving this problem, each solution is detected whether to extract quad patch layout, and finally the one with the minimum energy is determined as the global optimal solution. The produced quad patch layout is well-shaped and the corresponding base complex is coarse, which can be further used for many mesh processing applications, such as texturing, NURBS fitting and so on.

Error diffusion on meshes

We consider the problem of quantization for surface graphs. In particular, we generalize the process of error diffusion to meshes and then compare different paths on the surface when used for error diffusion. We suggest paths for processing mesh elements that lead to better distributions of available neighbors for error diffusion. We demonstrate the potential benefit of error diffusion at several mesh processing applications: quantization of differential mesh coordinates, including an extension to animated geometry, and vertex subset selection for mesh simplification. These applications allow us to compare different paths objectively. We find that the linear time solution results in excellent overall performance, outperforming other traversals taken from the literature. We conclude that the proposed path can be taken as a starting point for any application of error diffusion on meshes.

Zipper: A compact connectivity data structure for triangle meshes

We propose Zipper, a compact representation of incidence and adjacency for manifold triangle meshes with fixed connectivity. Zipper uses on average only 6 bits per triangle, can be constructed in linear space and time, and supports all standard random-access and mesh traversal operators in constant time. Similarly to the previously proposed LR (Laced Ring) approach, the Zipper construction reorders vertices and triangles along a nearly Hamiltonian cycle called the ring. The 4.4× storage reduction of Zipper over LR results from three contributions. (1) For most triangles, Zipper stores a 2-bit delta (plus three additional bits) rather than a full 32-bit reference. (2) Zipper modifies the ring to reduce the number of exceptional triangles. (3) Zipper encodes the remaining exceptional triangles using 2.5× less storage. In spite of these large savings in storage, we show that Zipper offers comparable performance to LR and other data structures in mesh processing applications. Zipper may also serve as a compact indexed format for rendering meshes, and hence is valuable even in applications that do not require adjacency information.

Spin transformations of discrete surfaces

We introduce a new method for computing conformal transformations of triangle meshes in R 3 . Conformal maps are desirable in digital geometry processing because they do not exhibit shear , and therefore preserve texture fidelity as well as the quality of the mesh itself. Traditional discretizations consider maps into the complex plane, which are useful only for problems such as surface parameterization and planar shape deformation where the target surface is flat. We instead consider maps into the quaternions H, which allows us to work directly with surfaces sitting in R 3 . In particular, we introduce a quaternionic Dirac operator and use it to develop a novel integrability condition on conformal deformations. Our discretization of this condition results in a sparse linear system that is simple to build and can be used to efficiently edit surfaces by manipulating curvature and boundary data, as demonstrated via several mesh processing applications.

Sphere Image Representation of Triangular Mesh and its Application

Image processing algorithms are based on the idea that all pixels of it ranked over the orderly rows, which make the algorithms easier to be implemented. Extending image processing algorithms to triangular mesh is always an important idea for triangular mesh processing. But since the topology of a triangular mesh is not as simple as an image, triangular mesh processing is relatively difficult. This paper presented a new sphere image representation of a triangular mesh, which is an image as well as a graphic, and based on it, image processing algorithms can be easily extended to a triangular mesh. Experimental results show that by simply extending the image processing algorithms the presented sphere image representation can effectively reduce difficult of segmentation and mesh editing. Moreover the sphere image representation can be used for more triangular mesh processing applications.

Direct (Re)Meshing for Efficient Surface Processing

Abstract We propose a novel surface remeshing algorithm. While many remeshing algorithms are based on global parametrization or local mesh optimization, our algorithm is closely related to surface reconstruction techniques and it requires no explicit parameterization. Our approach is based on the advancing‐front paradigm, and it can be used to both incrementally remesh the complete surface, or simply to remesh a portion of it with a high‐quality mesh. It is accurate, fast, robust, and suitable for use with interactive mesh processing applications that require local remeshing. We show a number of applications, including matching the resolution of meshes when doing Boolean operations such as unions and intersections. We also show how to adapt the algorithm to blend and merge mixed‐mode objects — for example, to compute the union of a point‐set surface and a triangle mesh.

ABF++: fast and robust angle based flattening

Conformal parameterization of mesh models has numerous applications in geometry processing. Conformality is desirable for remeshing, surface reconstruction, and many other mesh processing applications. Subject to the conformality requirement, these applications typically benefit from parameterizations with smaller stretch. The Angle Based Flattening (ABF) method, presented a few years ago, generates provably valid conformal parameterizations with low stretch. However, it is quite time-consuming and becomes error prone for large meshes due to numerical error accumulation. This work presents ABF++, a highly efficient extension of the ABF method, that overcomes these drawbacks while maintaining all the advantages of ABF. ABF++ robustly parameterizes meshes of hundreds of thousands and millions of triangles within minutes. It is based on three main components: (1) a new numerical solution technique that dramatically reduces the dimension of the linear systems solved at each iteration, speeding up the solution; (2) a new robust scheme for reconstructing the 2D coordinates from the angle space solution that avoids the numerical instabilities which hindered the ABF reconstruction scheme; and (3) an efficient hierarchical solution technique. The speedup with (1) does not come at the expense of greater distortion. The hierarchical technique (3) enables parameterization of models with millions of faces in seconds at the expense of a minor increase in parametric distortion. The parameterization computed by ABF++ are provably valid, that is they contain no flipped triangles. As a result of these extensions, the ABF++ method is extremely suitable for robustly and efficiently parameterizing models for geometry-processing applications.

Robust Spherical Parameterization of Triangular Meshes

Parameterization of 3D mesh data is important for many graphics and mesh processing applications, in particular for texture mapping, remeshing and morphing. Closed, manifold, genus-0 meshes are topologically equivalent to a sphere, hence this is the natural parameter domain for them. Parameterizing a 3D triangle mesh onto the 3D sphere means assigning a 3D position on the unit sphere to each of the mesh vertices, such that the spherical triangles induced by the mesh connectivity do not overlap. This is called a spherical triangulation. In this paper we formulate a set of necessary and sufficient conditions on the spherical angles of the spherical triangles for them to form a spherical triangulation. We formulate and solve an optimization procedure to produce spherical triangulations which reflect the geometric properties of a given 3D mesh in various ways.