3D繪圖流程依照處理性大致分為 : 幾何轉換子系統 ( Geometry Subsystem )以及著色子系統( Render Subsystem )。幾何轉換子系統包含基本的座標轉換( Transformation )、光源照射( Lighting )以及刪除多餘運算的Backface Culling及Clipping。Clipping主要是針對跨越可視範圍的物件做裁切的動作，針對部分在可視範圍內、部分在可視範圍外的物件做處理，將位於可視範圍外的部分做裁切的動作，而此裁切動作往往會是幾何轉換子系統效能上的瓶頸。本論文主要實踐幾何轉換子系統中裁切( Clipping )動作的硬體設計，硬體設計上以提高裁切動作的產能( throughput )、減少裁切動作對於幾何轉換子系統效能上的瓶頸，並應用於幾何轉換子系統。另外，提出一個可以減少多餘運算的pre-clipping方法，此方法運用在幾何轉換子系統上可以減少由於裁切動作而造成效能上的瓶頸。

A 3D graphics system usually consists of two major subsystems: geometry subsystem and rendering subsystem. The geometry subsystem performs transformation, lighting, backface culling, and clipping. The clipping is to remove the part of a triangle that is outside of the view volume by calculating the intersections of the triangle edges with view planes. The clipping operation turns out to be a time-consuming procedure in the geometry subsystem. In this thesis, we present several clipping algorithms and their hardware implementations, and compare the performance in the geometry subsystem. Furthermore, a new pre-clipping algorithm is also proposed to reduce the number of triangles that need to go through the clipping operations in order to reduce the burden of clipping operations in the whole geometry subsystem. The whole geometry system including the pre-clipping and clipping hardware is verified in a complete 3G graphics system in the Versatile FPGA demonstration board.

Chapter1 論文簡介 14
1.1 動機 14
1.2 本文大綱 14
Chapter2 Geometry Operations in OpenGL ES 15
2.1 OpenGL ES 1.1概要 15
2.2 Geometry Operations 18
2.2.1 Geometry System 介紹 18
2.2.2 座標運算 ( transformation ) 19
2.2.2.1 Model transformation 21
2.2.2.2 View transformation 22
2.2.2.3 Projection transformation 22
2.2.2.4 Perspective division 24
2.2.2.5 Viewport transformation 24
2.2.3 顏色運算 ( lighting ) 25
2.2.4 Culling 27
2.2.5 Clipping 27
Chapter3 Performance Improvement In Geometry System 28
3.1 Geometry system architecture 28
3.1.1 Fully pipeline geometry system 28
3.1.2 Overall architecture of geometry system 31
3.2 Pre-clipping 33
3.3 Guard Band 35
3.4 Proposed Pre-clipping Method 37
3.4.1 pre-clipping algorithm 37
3.4.2 pre-clipping module硬體架構與效能分析 43
Chapter4 Clipping Module In Geometry System 49
4.1 Survey of Clipping Algorithms 49
4.1.1 Cohen-Sutherland line clipping algorithm (CS Clipping Method) 49
4.1.2 Cyrus-Beck line clipping algorithm (CB Clipping Method) 57
4.1.3 Sutherland-Hodgman polygon clipping algorithm (SH Clipping Method) 65
4.2 Proposed Clipping Algorithm I 73
4.2.1 proposed clipping algorithm 73
4.2.2 proposed clipping module 硬體架構與效能分析 82
4.3 Proposed Clipping Algorithm II 84
4.3.1 proposed clipping algorithm 84
4.3.2 proposed clipping module 硬體架構與效能分析 91
4.3.3 proposed clipping module效能改善 97
4.4 效能比較 101
4.4.1 Proposed clipping algorithm VS. SH clipping algorithm 101
4.4.2 Geometry system不同架構效能比較 103
4.4.3 Improved Modified SH clipping algorithm VS. other papers 108
Chapter5 Geometry System驗證 115
5.1 Clipping module驗證 115
5.2 Geometry System驗證 117
Chapter6 結論與未來展望 121
6.1 結論 121
6.2 未來展望 121
參考文獻 122

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