Geometric Transformation (Maths)

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19 Terms

1
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What is geometric transformation?

The process of changing the position, orientation or size of a shape through model transformations.

2
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What is the Euclidian Plane?

A plan in which two values (x, y) and required to know the location of any point.

3
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What coordinate system does the Euclidian plane use?

Cartesian, with x-axis, y-axis, and origin.

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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.

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How can we convert a (x, y, w) homoegenous 3D point back to (x, y) cartesian?

(x/w, y/w)

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How do we add vectors?

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How do we multiply a matrix and a vector?

= a times x and 0 times y, then 0 times x and b times y.

<p>= a times x and 0 times y, then 0 times x and b times y.</p>
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What is the general 2D formula for scaling in terms of matrices?

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What is the general 2D formula for rotation in terms of matrices?

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What is the general 2D formula for mirroring in terms of matrices?

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How do we perform scaling in the homogeneous coordinate system?

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How do we perform rotation in the homogeneous coordinate system?

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From now on, w=1 as it usually does.

Ok!

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How do we perform a rotation around the z axis on a point?
modelMatrix.setRotate(q, 0, 0, 1)

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How do we perform a rotation around the y axis on a point?
modelMatrix.setRotate(q, 0, 1, 0)

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How do we perform a rotation around the x axis on a point?
modelMatrix.setRotate(q, 1, 0, 0)

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How do we translate a point?

Where (a,b,c) is the distance you are moving on each axis.

<p>Where (a,b,c) is the distance you are moving on each axis.</p>
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How do we scale a point?

Where (a,b,c) are the scaling factors for each axis.

<p>Where (a,b,c) are the scaling factors for each axis.</p>
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How do we shear a point?

Where in hxy, x = axis1 and y = axis2, “Shear along axis2 in direction of axis 1”

<p>Where in hxy, x = axis1 and y = axis2, “Shear along axis2 in direction of axis 1”</p>