Geometric transformation
A geometric transformation is a mapping or operation that changes or expresses the position, orientation, scale, shape, or coordinate representation of geometric objects.
Geometry for Programmers
A mapping that changes the position, orientation, size, shape, or other geometric properties of an object.
- How it is used
- Positions, renders, projects, deforms, and models geometric objects in applications such as games, CAD, 3D printing, and image processing.
- How deep it goes
- Defines point-to-point mappings, develops projective matrix composition and inverses, then extends transformations to nonlinear page unbending and surfaces.
- Examples
- Uses quadrilateral page projection, curved-page unbending with linear-cubic interpolation, plane-to-surface mapping, vector translation, and vector scaling.
- What you can do after
- Build it from scratch as matrix-based or interpolated point mappings when framework routines are insufficient or inefficient.
Read how Geometry for Programmers explains geometric transformation →
Deep Learning with R, Third Edition
A geometric transformation is a mapping that changes the position, scale, orientation, or representation of geometric objects.
- How it is used
- Frames neural networks as chains of geometric operations that transform vectorized inputs into target representations.
- How deep it goes
- Explains layered composition, parameter updates, and differentiability, but stops short of formal mathematical derivations.
- Examples
- Uses crumpled colored paper, class separation, vector spaces, and layer-by-layer manifold uncrumpling.
- What you can do after
- Evaluate/understand why deep networks suit perceptual mappings and struggle with discrete algorithms.
Read how Deep Learning with R, Third Edition explains geometric transformation →
Related concepts
- mathematical functionkind of · A mathematical function is a mapping that assigns exactly one output to each permitted input in its domain.
- linear transformationincludes · A linear transformation is a mapping between vector spaces that preserves vector addition and scalar multiplication.
- coefficientincludes · A coefficient is a numerical multiplier that scales a quantity, term, or contribution in a mathematical or computational operation.
- language modelused by · A language model is a computational model that represents patterns in linguistic tokens to estimate sequence probabilities and predict or generate language from context.
- tensor operationincludes · A tensor operation is a mathematical or computational transformation applied to one or more tensors, producing tensor or scalar values.
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