1. Modeling Transformations

2. Contents 2D-Transformations -Translation – 2D - Scaling – 2D
-Rotation – 2D
Mirror Reflection
Inverse 2D – Transformations
Homogeneous coordinates
-Translations with homogeneous
-Scaling with homogeneous
-Rotation with homogeneous

3. 2D-Transformations
Transformations are a fundamental part of computer graphics. Transformations are used to position objects, to shape objects, to change viewing positions, and even to change how something is viewed (e.g. the type of perspective that is used).
There are 4 main types of transformations that one can perform in 2 dimensions:
Translations
Scaling
Rotation
Reflection
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4. Translation – 2D
Shifting of an object from one position to anther is called translation
Translated coord. are ,
x’ = x + dx
y’ = y + dy
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5. Scaling – 2D
To scale an object by a vector v = (vx, vy, vz), each point p = (px, py, pz) would need to be multiplied with this scaling matrix:
Types of Scaling:
Differential ( sx != sy )
Uniform ( sx = sy )
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6. Rotation – 2D rotated original Coordinates before rotation
Coordinates after rotation
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7. Rotation – 2D
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8. Mirror Reflection
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9. Inverse 2D - Transformations
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10. Homogeneous coordinates
To perform a complex transformation, you usually make it by combining a number of basic transformations.
In order to represent all transformations in the same form, computer scientists have devised what are called homogeneous coordinates.
Add a third coordinate, z
A 2D point is a 3 coordinates vector:
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11. Translations with homogeneous
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12. Scaling with homogeneous
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13. Rotation with homogeneous
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14. Thanks !!!