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Ray Shooting, Depth Orders and Hidden Surface Removal

  • Book
  • © 1993

Overview

Editors:
  1. Mark Berg

Part of the book series: Lecture Notes in Computer Science (LNCS, volume 703)

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About this book

Computational geometry is the part of theoretical computer science that concerns itself with geometrical objects; it aims to define efficient algorithms for problems involving points, lines, polygons, and so on. The field has gained popularity very rapidly during the last decade. This is partly due to the many application areas of computational geometry and partly due to the beauty of the field itself. This monograph focuses on three problems that arise in three-dimensional computational geometry. The first problem is the ray shooting problem: preprocess a set of polyhedra into a data structure such that the first polyhedron that is hit by a query ray can be determined quickly. The second problem is that of computing depth orders: we want to sort a set of polyhedra such thatif one polyhedron is (partially) obscured by another polyhedron then it comes first in the order. The third problem is the hidden surface removal problem: given a set of polyhedra and a view point, compute which parts of the polyhedra are visible from the view point. These three problems involve issues that are fundamental to three-dimensional computational geometry. The book also contains a large introductory part discussing the techniques used to tackle the problems. This part should interest not only those who need the background for the rest of the book but also anyone who wants to know more about some recent techniques in computational geometry.

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Table of contents (17 chapters)

  1. Front Matter

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  2. Computational geometry and computer graphics

    Pages 2-9

  3. Preliminaries

    Pages 11-35

  4. Introduction

    Pages 38-41

  5. A general strategy

    Pages 43-51

  6. Ray shooting from a fixed point

    Pages 53-65

  7. Ray shooting into a fixed direction

    Pages 67-84

  8. Ray shooting with arbitrary rays

    Pages 85-106

  9. Conclusions

    Pages 107-108

  10. Introduction

    Pages 110-113

  11. Depth orders in the plane

    Pages 115-133

  12. Depth orders in three dimensions

    Pages 135-144

  13. Conclusions

    Pages 145-146

  14. Introduction

    Pages 148-154

  15. Non-intersecting polyhedra

    Pages 155-162

  16. Intersecting polyhedra

    Pages 163-168

  17. Dynamization

    Pages 169-180

  18. Conclusions

    Pages 181-183

  19. Back Matter

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