Matrix lecture (Sep 11)

In class we discussed linear transformations, which should largely be review for most of you. After reviewing the form of the basic matrix primitives, below, do the homework assignment, which is here. That assignment page contains extensive notes and hints about implementation.

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