Space subdivision for fast polygonization of implicit surfaces

Journal of Computing and Information Technology, 2011

Problem statement: Displaced subdivision representation possesses a number of attractive features for efficient and convenient processing tasks like editing, geometry compression, animation, scalability and adaptive rendering of polygonal models. In this representation, a detailed surface model was built as a scalar-valued displacement map over a smooth domain surface. The construction of the smooth domain surface from a polygonal model was a challenging task in the conversion process. Approach: For building the smooth domain surface, we proposed an efficient algorithm that was based on √3-subdivision scheme, memory efficient simplification and a linear time optimization technique. Results: At some fixed level of detail, the vertex and triangle complexity of the displaced surface generated by the proposed algorithm was far less and so it resulted in better compression ratios and transmission speed. Conclusion: The proposed algorithm created surfaces of better quality, computationally more efficient and occupied less memory as compared to the original algorithm by Lee.

1992

We present d i s c r e t e p h ysically-based methods for generating polygonal approximations of implicit surfaces. These methods not only generate a combinatorial manifold approximating the surface, but also produce a structure that is well suited to numerical simulations in physically-based modeling and animation systems.

International Journal of Shape Modeling, 1996

A polygonisation algorithm is presented which extends an existing skeletal implicit surface technique to include operations based on Constructive Solid Geometry between blended groups of implicit surface objects. The result is a surface definition (to be called Boolean Compound Soft Object, or BCSO for short) which consists of a boolean expression with union, intersection, and set difference operators. The geometric primitives that form the operands are soft objects bounded by the iso-surfaces resulting from suitable potential fields. These potential fields are parameterized by configurations of so called skeletal elements. The resulting system, unlike most CSG systems, combines blended and unblended primitives. The polygonisation algorithm produces a mesh of triangles to facilitate fast viewing and rendering.

Programming and Computer Software, 2017

A ray-tracing algorithm for interactive visualization of very large and structurally complicated scenes presented in the constructive solid geometry (CSG) form is suggested. The algorithm is capable of visualizing such scenes in real time by using a graphic processor. As primitives, classical shapes and objects represented in an analytical form (in particular, second-order surfaces and implicit functions) are used. Unlike other similar algorithms, our algorithm produces the final image in a single pass and has no constraints on the maximum number of primitives and on the CSG tree depth. The key feature of the algorithm is a method for optimizing CSG models, which converts the input tree to an equivalent spatially coherent and well-balanced form (a completely balanced equivalent tree may not exist). The performance of visualization after applying the optimization technique is shown to depend on only the computational resource of the GPU (in contrast to multi-pass algorithms whose performance is restricted by memory capacity). It has been shown experimentally that our algorithm is capable of rendering CSG models consisting of more than a million CSG primitives with the tree depth up to 24.

Eurographics Workshop on Parallel Graphics and Visualization, 2012

In this research we tackle the problem of rendering complex models which are created using implicit primitives, blending operators, affine transformations and constructive solid geometry in a design environment that organizes all these in a scene graph data structure called BlobTree. We propose a fast, scalable, parallel polygonization algorithm for BlobTrees that takes advantage of multicore processors and SIMD optimization techniques available on modern architectures. Efficiency is achieved through the usage of spatial data structures and SIMD optimizations for BlobTree traversals and the computation of mesh vertices and other attributes. Our solution delivers interactive visualization for modeling systems based on BlobTree scene graph.

Proceedings of the …, 2002

We present an algorithm for interactively extracting and rendering isosurfaces of large volume datasets in a view-dependent fashion. A recursive tetrahedral mesh refinement scheme, based on longest edge bisection, is used to hierarchically decompose the data into a multiresolution structure. This data structure allows fast extraction of arbitrary isosurfaces to within user specified view-dependent error bounds. A data layout scheme based on hierarchical space filling curves provides access to the data in a cache coherent manner that follows the data access pattern indicated by the mesh refinement.

2003

The synthesis of computer models from real objects is a usual procedure in medical image processing and reverse engineering. In both cases, the main issues are to reach a topologically consistent and geometrically precise object reconstruction. Implicit surfaces provide a solution to this problem. They define a smooth surface surrounding objects which must be polygonized for an efficient visualization. Due to the increasing size of the application generated data, it becomes necessary to use precise and efficient methods. This work presents a modified method of implicit surface polygonization based on “Marching Triangles”. This modification assures the topological consistency with the initial dataset during the progressive reconstruction of the surface, avoiding overlapping triangles. In addition, a comparison of our method with the marching cubes and the adaptive skeleton climbing algorithms is provided.

Graphical Models, 2005

This paper presents DigitalSculpture, an interactive sculpting framework founded upon isosurfaces extracted from recursively subdivided, 3D irregular grids. Our unique implicit surface model arises from an interpolatory, volumetric subdivision scheme that is C 1 continuous across the domains defined by arbitrary 3D irregular grids. We assign scalar coefficients and color to each control vertex and allow these quantities to participate in the volumetric subdivision of irregular grids. In the subdivision limit, a virtual sculpture is obtained by extracting the zero-level from the volumetric, scalar field defined over the irregular grid. This novel shape geometry extends concepts from solid modeling, recursive subdivision, and implicit surfaces; facilitates many techniques for interactive sculpting; permits rapid, local evaluation of iso-surfaces; and affords level-of-detail control of the sculpted surfaces. (K.T. McDonnell). www.elsevier.com/locate/gmod Graphical Models 67 (2005) 347-369

Computers & Graphics, 2004

The language of geometric algebra can be used in the development of computer graphics applications. This paper proposes a method to describe a 3D polygonal mesh model using a representation technique based on geometric algebra and the conformal model of the 3D Euclidean space. It describes also the stages necessary to develop an application that uses this formalism. The current application was used to validate the implementation of the main abstract operations characteristic to a geometric algebra computational environment (programming module GAP). The data structures that characterize this geometric algebra based modeling approach as well as the implementation of geometric algebra based methods for model visualization/transformation are developed in detail. The paper emphasizes the elegance and generality of the geometric algebra approach referring also to the necessary computational resources.

We present a new technique for generating surface meshes from a uniform set of discrete samples. Our method extends the well-known marching cubes algorithm used for computing polygonal isosurfaces. While in marching cubes each vertex of a cubic grid cell is binary classified as lying above or below an isosurface, in our approach an arbitrary number of vertex classes can be specified. Consequently the resulting surfaces consist of patches separating volumes of two different classes each.

2007

Visualising implicit surfaces with the ray casting method is a slow procedure. The design cycle of a new implicit surface is, therefore, fraught with long latency times as a user must wait for the surface to be rendered before being able to decide what changes should be introduced in the next iteration. In this paper, we present an attempt at reducing the design cycle of an implicit surface modeler by introducing a progressive refinement rendering approach to the visualisation of implicit surfaces. This progressive refinement renderer provides a quick previewing facility. It first displays a low quality estimate of what the final rendering is going to be and, as the computation progresses, increases the quality of this estimate at a steady rate. The progressive refinement algorithm is based on the adaptive subdivision of the viewing frustrum into smaller cells. An estimate for the variation of the implicit function inside each cell is obtained with an affine arithmetic range estimation technique. Overall, we show that our progressive refinement approach not only provides the user with visual feedback as the rendering advances but is also capable of completing the image faster than a conventional implicit surface rendering algorithm based on ray casting.

This paper presents an adaptive approach for polygonization of implicit surfaces. The algorithm generates a well-shaped triangular mesh with respect to a given approximation error. The error is proportional to a local surface curvature estimation. Polygonization of surfaces of high curvature, as well as surfaces with sharp features, is possible using a simple technique combined with a particle system approach. The algorithm is based on a surface tracking scheme, and it is compared with other algorithms based on a similar principle, such as the marching cube and the marching triangle algorithms.

Generating subdivision surfaces from polygonal meshes requires the complete topological information of the original mesh, in order to find the neighbouring faces, and vertices used in the subdivision computations. Normally, winged-edge type data-structures are used to maintain such information about a mesh. For rendering meshes, most of the topological information is irrelevant, and winged-edge type data-structures are inefficient due to their extensive use of dynamical data structures. A standard approach is the extraction of a rendering mesh from the winged-edge type data structure, thereby increasing the memory footprint significantly. We introduce a mesh data-structure that is efficient for both tasks: creating subdivision surfaces as well as fast rendering. The new data structure maintains full topological information in an efficient and easily accessible manner, with all information necessary for rendering optimally suited for current graphics hardware. This is possible by dis...

Proceedings - GRAPHITE 2006: 4th International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast Asia, 2006

Figure 1: (x 2 + y 2 + z 2 − 2) 2 • (sin(x) + y + 1) = 0.

Sistemas y Telemática, 2008

Polygonal meshes and particularly triangular meshes are the most used structure for 3D modelling. The 'direct edges' data structure is the most efficient way to represent them and subdivision surfaces is an appropri-SISTEMAS & TELEMÁTICA Vol. 6 No. 12 • Julio-Diciembre de 2008 ate method to generate them. From a review of subdivision surfaces we chose the '√3 subdivision' method for mesh generation. Our main challenge was to take advantage of the direct edges data structure and to find the right formulas for an efficient implementation. We decided to use files in the 3DS file format and convert them to the direct edges data structures for use in our application. We tested our algorithm with arbitrary mesh topologies and calculated efficiency. Our implementation will be used in the creation of a virtual dog head.