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Geometric Transformation- All that you must know
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What is geometric transformation?
The geometric transformation is the bijection of set possessing some kind of geometric structure. Particularly, geometric transformation is the operation whose range and domain are the sets of point.
Classifications of geometric transformations
- These transformations have following classifications-
- The displacements conserve oriented angles and distances
- Isometrics conserve distances and angles
- Similarities conserve ratios between distances and angles
- Affine transformations conserve parallelism
- The Projective transformations conserve co-linearity
Each of the sections containsprevious one
The circle inversion conserves set of the circles and lines in planar case. Mobius transformations preserve all spheres and planes in the 3rd dimension.
- Diffeomorphisms are transformation, which are affine in primary order. They contain the previous ones as the special ones.
- The conformal transformations conserve areas in planar volumes and case in three cases that are dimensional.
- Homeomorphisms conserve neighbourhoods of the points.
- Transformations of similar kind of groups, which may be the sub-divisions of the other groups of transformations
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Geometric transformations are one of the most important sub-topics of geometry. It helps in building the base of understanding the different dimensions of the shape. Hence, neglecting assignments on such subject can be harmful.
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