3D技术介绍

计算机3D技术,本质上就是数学,本文从线性代数,矩阵,空间,投影等基础知识入手,进入到图形pipeline,渐变处理,渲染处理,光照处理等基本概念。没有太多的公式运算,纯概念的普及,科普入门。
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1.A BRIEF INTRODUCTION TO 3D Selected topics with focus on Flash, Unity and WebGL

2.

3.MATH & ALGEBRA

4.VECTOR

5.Length Pythagorean Formula | V | = sqrt (x 2  + y 2 )

6.Addition A = (1, 2) B = (4, 0) A + B = (1+4, 2+0) = (5, 2)

7.Subtraction A = (1, 2) B = (4, 0) A - B = A + (-B ) A - B = ( 1-4 , 2-0) = (-3, 2)

8.Subtraction A = (1, 2) B = (4, 0) A - B = A + (-B ) A - B = ( 1-4 , 2-0) = (-3, 2)

9.Dot Product A = (A x , A y , A z ) B = ( B x , B y , B z ) A · B = A x B x  + A y B y  + A z B z A · B = |A|| B| cos θ  

10.Cross Product AxB = ( A y B z  - A z B y , A z B x  - A x B z , A x B y  - A y B x )  

11.Real world examples In which  direction should the missile  be fired  to hit the target ? Is the enemy visible in the field of view? How far is the bullet from the window?

12.Solutions Solutions have been done by many before. Know the basics to find them quicker. Use utils and classes like: Vector3D Vector3DUtils Plane3D, Ray (4.0) Vector3

13.SPACES

14.Spaces Euclidean space using Cartesian coordinates. (X , Y and Z) Local/Model Space World Space View/Camera Space (Point-of-view) Screen space (2D)

15.Left- and right-handed systems

16.MATRICES AND SPACES ENTER THE MATRIX

17.Matrices Matrix = Transformation placeholder So again: Local/Model matrix World matrix View/Camera matrix WVP = world * view * projection

18.Classes/Utils Matrix3D Matrix3DUtils Matrix4x4

19.TRANSFORMATIONS

20.Linear transformation Translation

21.Linear transformation Scale

22.Linear transformation Skew

23.Linear transformation Eulers Quaternions Avoids gimbal lock Slerp (Smooth interpolated rotation) Matrix – memory intensive Rotation

24.Multi linear transformation Stack of matrices Apply all at once to an object The order is importent Identity matrix

25.Nonlinear transformations Sin curve displacement Warp

26.PROJECTIONS Converting a three-dimensional graphics object or scene into two dimensions

27.Most common projections

28.GRAPHICS PIPELINE

29.Programmable pipeline Illustration from db-in.com