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Zed3D programming guide

A compact reference for 3d computer graphics

(by sébastien loisel)

A guide about 3d graphic programming which explains many arguments from a mathematical and programming point of view. The guide is 105 pages.
This article is online from 2658 days and has been seen 4345 times





Zed3D - A compact reference for 3d computer graphics programming
by Sébastien Loisel

Zed3D is a document about computer graphics, more particularly real-time 3d 
graphics. This document should be viewed as a practical reference for a first 
and perhaps second course in computer graphics.
The original Zed3D document grew out of my work notes. 
As a matter of fact, the original Zed3D, up to version 0.61beta, was my work 
notes. As such, it was messy, incomplete and often incorrect. I have attempted 
to correct this a bit now. I still consider these my work notes, but I have 
added more formal introductory material which was not in the original document.
In this document, I will attempt to describe various aspects of computer 
graphics in a clear, useful and complete fashion. You will find quite a bit 
of the theoretical aspects, copies of the calculations and proofs I made and 
so forth.
However, there is the painful fact that I am merely a student, trying to mark 
my territory in the university work, and since this work does not serve that 
purpose very well, Zed3D will oftentimes be lacking in areas that I wish I 
had more time to document. Also, I will attempt to distribute another nice 
portable graphics engine in the future, but that's only if I can find the time 
to make it.

Table of Contents                                                            6
Vector mathematics                                                          10
- Introduction                                                              10
- On notation                                                               10
- Vector operations                                                         11
- Exercises                                                                 12
- Answers                                                                   13
- Alcoholism and dependance                                                 13
- Exercises                                                                 14
- Answers                                                                   15
- On a plane (and of motion sickness)                                       15
- Exercises                                                                 16
- Answers                                                                   17
- Orthonormalizing a basis                                                  17

Matrix mathematics                                                          19
- Introduction                                                              19
- Matrix operations                                                         19
- Exercise                                                                  21
- Answer                                                                    22
- Matrix representation & linear transformations                            22

Affine transforms                                                           25
- Introduction                                                              25
- Affine transformations                                                    25
- Exercise                                                                  26
- Affine transform combination and inversion                                27
- Exercise                                                                  27
- Answer                                                                    28

Applications of linear transformations                                      30
- Introduction                                                              30
- World space, eye space, object space, outer space                         30
- Transformations in the hierarchy (or the French revolution)               31
- Some pathological matrices                                                31

Perspective                                                                 34
- Introduction                                                              34
- A simple perspectively incorrect projection                               35
- The perspective transformation                                            35
- Theorems                                                                  38
- Other applications                                                        39
- Constant Z                                                                41
- Texture mapping equations revisited                                       41
- Bla bla                                                                   43
- Reality strikes                                                           44

Interpolations and approximations                                           46
- Introduction                                                              46
- Forward differencing                                                      46
- Approximation function                                                    48

Polynomial Splines                                                          51
- Introduction                                                              51
- Basic splines                                                             51
- Parametrized splines                                                      54
- Uniform splines                                                           54
- Examples                                                                  57
- Frequently used uniform cubic splines                                     60
- Hermite splines                                                           60
- Bézier splines                                                            61
- Convex hull                                                               62
- Bernstein polynomials                                                     63
- Uniform nonrational B-spline                                              64
- Catmull-Rom splines: a non-uniform type of spline                         65

Rendering                                                                   66
- Introduction                                                              66
- The point                                                                 66
- Lines                                                                     69
- Polygon drawing                                                           70

Visible surface determination                                               73
- Introduction                                                              73
- Back-face culling                                                         74
- Sorting                                                                   75
- Painter's algorithm and depth sorting                                     77
- Z-Buffering                                                               79
- Binary Space Partitioning                                                 80
- Lighting models                                                           84
- Introduction                                                              84

Lighting models                                                             84
- Smooth shading                                                            86
- Texture mapping & variants on the same theme                              89

Computer graphics related problems                                          91
- Introduction                                                              91
- Generating edge normals                                                   91
- Triangulating a polygon                                                   92
- Computing a plane normal from vertices                                    93
- Generating correctly oriented normals for polyhedra                       94
- Polygon clipping against a line or plane                                  95

Quaternions                                                                 97
- Introduction                                                              97
- Preliminaries                                                             98
- Conversion between quaternions and matrices                               99
- Orientation interpolation                                                 99

Antialiasing                                                               101
- Introduction                                                             101
- Filtering                                                                101
- Pixel accuracy                                                           102
- Sub-pixel accuracy                                                       104
- Time antialiasing, a.k.a. motion blur                                    105
- Mipmapping                                                               106
- Uniform Mipmapping                                                       107
- Nonuniform Mipmapping                                                    108
- Summed area tables                                                       109
- Bi-linear interpolation                                                  110
- Tri-linear interpolation                                                 111

Glossary                                                                   112
Bibliography                                                               115




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