Triangle Fans Research Articles

Polygon Laplacian Made Simple

AbstractThe discrete Laplace‐Beltrami operator for surface meshes is a fundamental building block for many (if not most) geometry processing algorithms. While Laplacians on triangle meshes have been researched intensively, yielding the cotangent discretization as the de‐facto standard, the case of general polygon meshes has received much less attention. We present a discretization of the Laplace operator which is consistent with its expression as the composition of divergence and gradient operators, and is applicable to general polygon meshes, including meshes with non‐convex, and even non‐planar, faces. By virtually inserting a carefully placed point we implicitly refine each polygon into a triangle fan, but then hide the refinement within the matrix assembly. The resulting operator generalizes the cotangent Laplacian, inherits its advantages, and is empirically shown to be on par or even better than the recent polygon Laplacian of Alexa and Wardetzky [AW11] — while being simpler to compute.

ARINC661 Graphics Rendering Based on OpenVG and Its Use Cases with Wireless Communications

ARINC 661 is a standard for the CDS (Cockpit Display Systems) defined by ARINC (Aeronautical Radio, Inc.) and used for application to communicate and display sensing data and information. ARINC 661 contains various two-dimensional GUI (Graphical User Interface) widget definitions. The widget set covers a variety of graphics elements including circles, arcs, crowns and others. Additionally, the symbol widgets provide rendering of user defined polygonal shapes which are typically described with triangle fans and triangle strips. ARINC 661 has various rendering features including text, image output, transformation of object and the halo effect which renders the outlines of graphics objects for highlighting. It is possible to use 3D graphics libraries like OpenGL and DirectX for implementation of graphics features. However those 3D graphics libraries are too heavy and over-powered to show 2D graphics primitives defined in ARINC 661. In this paper, we propose ARINC661 rendering based on OpenVG. OpenVG is a standard of 2D vector graphics API defined by the Khronos Group. OpenVG is designed for embedded system GUI rendering and its features are appropriate to implement ARINC661. Compare with OpenGL, OpenVG defined with fixed pipeline architecture without programmable shader. Therefore, OpenVG is cost effective to rendering and certification of software quality by reducing complexity of application source code. We also propose ARINC661 use cases for wireless application to communicate and display data from various sensor network, information gathered from unmanned aerial and land vehicles.

Interactive shape modeling using a skeleton-mesh co-representation

We introduce the Polar-Annular Mesh representation (PAM). A PAM is a mesh-skeleton co-representation designed for the modeling of 3D organic, articulated shapes. A PAM represents a manifold mesh as a partition of polar (triangle fans) and annular (rings of quads) regions. The skeletal topology of a shape is uniquely embedded in the mesh connectivity of a PAM, enabling both surface and skeletal modeling operations, interchangeably and directly on the mesh itself. We develop an algorithm to convert arbitrary triangle meshes into PAMs as well as techniques to simplify PAMs and a method to convert a PAM to a quad-only mesh. We further present a PAM-based multi-touch sculpting application in order to demonstrate its utility as a shape representation for the interactive modeling of organic, articulated figures as well as for editing and posing of pre-existing models.

An Algorithm for Large-Scale Terrain Generation Based on Quadtree

The paper puts forward an algorithm for multi-resolution terrain model generation based on quadtree. This algorithm puts elements as view-dependent and terrain relief into the evaluation standards for level of detail and raises appropriate methods to remove cracks in the course of terrain generation according to the law of node partition and rendering. In drawing terrain, optimized display technologies as frustum culling, backface culling, triangle fan and static data storage. Test results show, this algorithm can realize the real-time visualization of large-scale terrain.

Formula omitted] splines covering polar configurations

A polar configuration is a triangle fan in a quad-dominant mesh; it allows for many mesh lines to join at a single polar vertex. This paper shows how a single tensor-product spline of degree (3,6) can cap a polar configuration with a C2 surface. By design, this C2 polar spline joins C2 with surrounding bi-3 tensor-product splines and thereby complements algorithms that smoothly cap star-like, multi-sided regions.

Advancing fan-front: 3D triangle mesh compression using fan based traversal

Connectivity compression techniques for very large 3D triangle meshes are based on clever traversals of the graph representing the mesh, so as to avoid the repeated references to vertices. In this paper we present a new algorithm for compressing large 3D triangle meshes through the successive conquest of triangle fans. The connectivity of vertices in a fan is implied. As each fan is traversed, the current mesh boundary is advanced by the fan-front. The process is recursively continued till the entire mesh is traversed. The mesh is then compactly encoded as a sequence of fan configuration codes. The fan configuration code comprehensively encodes the connectivity of the fan with the rest of the mesh. There is no need for any further special operators like split codes and additional vertex offsets. The number of fans is typically one-fourth of the total number of triangles. Only a few of the fan configurations occur with high frequency, enabling excellent connectivity information compression using range encoding. A simple implementation shows significant improvements, on the average, in bit-rate per vertex, compared to earlier reported techniques.

An efficient 3D mesh compression technique based on triangle fan structure

In this paper, we propose an efficient compression algorithm for 3D triangular meshes, consisting of topology data and geometry data. First, the vertex degree warping technique is proposed to compress the topology data losslessly. The proposed algorithm exploits the geometrical information to efficiently encode the topology data, while most conventional algorithms process the topology data and the geometry data independently. Second, the dual parallelogram prediction technique is proposed as an effective geometry prediction scheme. By using forward and backward parallelograms, the proposed algorithm provides smaller prediction errors than the conventional parallelogram prediction scheme. Simulation results on various mesh models demonstrate that the proposed algorithm yields higher compression ratio than the conventional mesh compression algorithms proposed in Touma and Gotsman (Proceedings of the Graphics Interface ’98, June 1998, pp. 26–34) and MPEG-4 3D mesh coding (3DMC) standard ISO/IEC 14496-2 (Information Technology – Coding of Audio-Visual Objects – Part 2: Visual, July 2001. The 3DMC reference software is available from http://www.sait.samsung.co.kr/shhc).

Triangulating Convex Polygons Having T-Vertices

A technique to triangulate planar convex polygons having T-vertices is described. Simple strip or fan tessellation of a polygon with T-vertices can result in zero-area triangles and compromise the rendering process. Our technique splits such a polygon into one triangle strip and, at most, one triangle fan. The technique is particularly useful in multiresolution or adaptive representation of polygonal surfaces and the simplification of surfaces.