Pure Core Flashcards
Matrix transformation that takes a 3D vector and makes it 2D (discards z-value)
(1 0 0)
(0 1 0)
Matrix transformation in the line y = x
(0 1)
(1 0)
General matrix for enlargement, centre origin, scale factor k
(k 0)
(0 k)
General matrix for rotation, θ degrees about the origin (ACW)
(cosθ –sinθ)
( sinθ cosθ )
General matrix for stretch, scale factor k parallel to the x-axis
(k 0)
(0 1)
General matrix for stretch, scale factor k parallel to the y-axis
(1 0)
(0 k)
General matrix for shear with x-axis fixed
(1 k)
(0 1)
General matrix for shear with y-axis fixed
(1 0)
(k 1)
Matrix for reflection in the x-axis
(1 0)
(0 -1)
Matrix for reflection in the y-axis
(-1 0)
(0 1)
Matrix transformation in the line y = -x
(0 -1)
(-1 0)
What does it mean if a shear is fixed to an axis?
The points of the shape that go through that axis do not change. The shape is transformed parallel to that axis.
Rotation θ about x-axis (3 x 3 matrix)
(1 0 0 )
(0 cosθ -sinθ)
(0 sinθ cosθ)
Rotation θ about y-axis
( cosθ 0 sinθ )
( 0 1 0 )
( -sinθ 0 cosθ)
Rotation θ about z-axis
(cosθ -sinθ 0 )
(sinθ cosθ 0 )
( 0 0 1 )
