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1 .A BRIEF INTRODUCTION TO 3D Selected topics with focus on Flash, Unity and WebGL
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
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
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
29 .Programmable pipeline Illustration from db-in.com
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