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- W126052077 abstract "In addition to isometries, there are two kinds of mappings that preserve lines: affine (Section 3.1) and projective (Section 3.2) transformations. Affine transformations f of ({mathbb{R}}^{n}) have the following property: If l is a line then f(l) is also a line, and if l ∥ k then f(l) ∥ f(k). A line in ({mathbb{R}}^{n}) means a set of the form {r 0+r:r∈W}, where ({mathbf{r}}_{0} in {mathbb{R}}^{n}) and (W subset {mathbb{R}}^{n}) is a one-dimensional subspace. Projective transformations f of ({mathbb{R}}^{n}) map lines to lines, preserving the cross-ratio of four points. We also use homogeneous coordinates (mathbf{x} = ({x}_{1} : ldots : {x}_{n+1})) in ({mathbb{R}}^{n+1}). Section 3.3 describes transformation matrices in homogeneous coordinates." @default.
- W126052077 created "2016-06-24" @default.
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- W126052077 date "2010-01-01" @default.
- W126052077 modified "2023-09-26" @default.
- W126052077 title "Affine and Projective Transformations" @default.
- W126052077 doi "https://doi.org/10.1007/978-0-387-71278-9_3" @default.
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