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Graphics: Polygonal Math
Geometric Anti-Aliasing Methods |
Triangle Mesh Tangent Space Calculation |
Skin Splitting for Optimal Rendering |
CSG Construction Using BSP Trees |
Using Geometric Algebra for Computer Graphics |
Fast Setup for Bilinear and Biquadratic Interpolation over Triangles |
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Tony Barrera (Barrera Kristiansen AB), Anders Hast (Creative Media Lab, University of G�vle), and Ewert Bengtsson (Center for Image Analysis, Uppsala University)
Graphics Programming Methods, 2003. |
Using Vector Fractions for Exact Geometry |
T-Junction Elimination and Retriangulation |
Abstract: This article describes how to detect possible sources of these seams in complex 3D scenes and how to modify static geometry so that visible artifacts are avoided. Since T-junction elimination adds verticies to existing polygons (that are not necessarily convex), we also discuss a method for triangulating arbitrary concave polygons.
Triangle Strip Creation, Optimizations, and Rendering |
Abstract: This article focuses on how to generate triangle strips from arbitrary 3D polygonal models. We will describe and provide source code for developing long triangle strips. After describing the triangle strip algorithm, we will explain the benefits of triangle strips, the possible pitfalls encountered when creating them, and how to submit them to the graphics API. In addition, several other triangle strip creation algorithms will be reviewed and critiqued.
Subdivision Surfaces for Character Animation |
Abstract: This article introduces subdivision surfaces as a means of improving the appearance of game characters. First, we will present the different schemes available, focusing on two implementations of subdivision surfaces. Then, we will explore a number of optimization methods based on culling and preprocessing.
Tweaking a Vertex's Projected Depth Value |
Abstract: The goal is to find a way to offset a polygon's depth in a scene without changing its projected screen coordinates or altering its texture mapping perspective. Most 3D graphcs libraries contain some kind of polygon offset function to help achieve this goal. However, these solutions generally lack fine control and usually incur a per-vertex performance cost. This article presents an alternative method that modifies the projection matrix to achieve the depth offset effect.
Computing the Distance into a Sector |
Abstract: This article describes a simple and fast algorithm for determining where a point is between the edges of a 2D quad (or sector). The result is a unit floating point number, where 0 indicates that the point lies on the leading edge, and where 1 indicates that the point lies on the opposite edge. The sector may be any four-sided, 2D convex shape.
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