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What is geometric transformation?
The process of changing the position, orientation or size of a shape through model transformations.
What is the Euclidian Plane?
A plan in which two values (x, y) and required to know the location of any point.
What coordinate system does the Euclidian plane use?
Cartesian, with x-axis, y-axis, and origin.
How do you convert cartesian coordinates to a homogenous 3D coordinate system?
point in cartesian + weight ‘w’ = point in 3D.
A line L is formed in the 3D to represent ‘w’’s effects on the coordinates provided. All homogenous points on L represent the same 2D cartesian point.
How can we convert a (x, y, w) homoegenous 3D point back to (x, y) cartesian?
(x/w, y/w)
How do we add vectors?
How do we multiply a matrix and a vector?
= a times x and 0 times y, then 0 times x and b times y.
What is the general 2D formula for scaling in terms of matrices?
What is the general 2D formula for rotation in terms of matrices?
What is the general 2D formula for mirroring in terms of matrices?
How do we perform scaling in the homogeneous coordinate system?
How do we perform rotation in the homogeneous coordinate system?
From now on, w=1 as it usually does.
Ok!
How do we perform a rotation around the z axis on a point?
modelMatrix.setRotate(q, 0, 0, 1)
How do we perform a rotation around the y axis on a point?
modelMatrix.setRotate(q, 0, 1, 0)
How do we perform a rotation around the x axis on a point?
modelMatrix.setRotate(q, 1, 0, 0)
How do we translate a point?
Where (a,b,c) is the distance you are moving on each axis.
How do we scale a point?
Where (a,b,c) are the scaling factors for each axis.
How do we shear a point?
Where in hxy, x = axis1 and y = axis2, “Shear along axis2 in direction of axis 1”