Notes about 3D matrix primitives

In class we discussed 3D linear transformations using 4x4 matrices, which should largely be review for you, since you've already implemented 2D linear transformations using 3x3 matrices.

3D Transformation Matrices:

Here are the basic 3D matrix primitives (not including perspective):

identity:

1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

translationMatrix(a,b,c):

1 0 0 a
0 1 0 b
0 0 1 c
0 0 0 1

xRotationMatrix(θ):

1 0 0 0
0 cos(θ) -sin(θ) 0
0 sin(θ) cos(θ) 0
0 0 0 1

yRotationMatrix(θ):

cos(θ) 0 sin(θ) 0
0 1 0 0
-sin(θ) 0 cos(θ) 0
0 0 0 1

zRotationMatrix(θ):

cos(θ) -sin(θ) 0 0
sin(θ) cos(θ) 0 0
0 0 1 0
0 0 0 1

scaleMatrix(a,b,c):

a 0 0 0
0 b 0 0
0 0 c 0
0 0 0 1