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GPU Gems
2004

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2005

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2007

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2002

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2003

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2004

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2006

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2006

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2008

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2009

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2010

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2011

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2012

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Graphics: Polygonal Math


Geometric Anti-Aliasing Methods

Emil Persson
GPU Pro 3, 2012.

Triangle Mesh Tangent Space Calculation

Martin Mittring
ShaderX4, 2006.

Skin Splitting for Optimal Rendering

Dominic Filion
Game Programming Gems 6, 2006.

CSG Construction Using BSP Trees

Octavian Marius Chincisan
Game Programming Gems 5, 2005.

Using Geometric Algebra for Computer Graphics

Chris Lomont
Game Programming Gems 5, 2005.

Fast Setup for Bilinear and Biquadratic Interpolation over Triangles

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

Thomas Young (PathEngine)
Game Programming Gems 3, 2002.

T-Junction Elimination and Retriangulation

Eric Lengyel (Terathon Software)
Game Programming Gems 3, 2002.
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

Carl S. Marshall (Intel Labs)
Game Programming Gems 3, 2002.
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

William Leeson (Trinity College, Dublin)
Game Programming Gems 3, 2002.
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

Eric Lengyel (C4 Engine)
Game Programming Gems, 2000.
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

Steven Ranck (Midway Home Entertainment)
Game Programming Gems, 2000.
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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