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point at infinity
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Point at infinity
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point at infinity
名詞
point at infinity (複数形 points at infinity)
- An asymptotic point in 3-dimensional space, viewed from some point, at which parallel lines appear to meet and which in perspective drawing is represented as a vanishing point.
- (geometry, Euclidean projective 幾何学) Any point added to a space to achieve projective completion.
- 1960, Roger A. Johnson, Advanced Euclidean Geometry, Republished 2007, page 45,
In the geometry of inversion, therefore, it is usual to sacrifice the line of points at infinity which is so useful in other fields, and adopt the convention of a single point at infinity, the inverse of the center of the circle of inversion. - 1997, Susan Addington, Stuart Levy, Lost in the Fun House: An Application of Dynamic Projective Geometry, James King, Doris Schattschneider, Geometry Turned On: Dynamic Software in Learning, Teaching, and Research, page 159,
To unify the treatment of concurrent and parallel lines, define a point at infinity for each family of parallel lines, and declare each point at infinity to lie on each of the parallel lines that define it. […] Now parallel lines meet at infinity, and vanishing points are the images of points at infinity.
- 1960, Roger A. Johnson, Advanced Euclidean Geometry, Republished 2007, page 45,
- (geometry, hyperbolic 幾何学) An ideal point.
- 2007, Maurice Margenstern, Cellular Automata in Hyperbolic Spaces, Volume 1: Theory, page 66,
As we have seen, points at infinity behave as ordinary points: a single line passes through two distinct points at infinity or through a point in the plane and a point at infinity.
This representation of the points at infinity is a difference between the disc and the half-plane models of Poincaré, […] . - 2012, Norbert A'Campo, Athanase Papadopoulos, Notes on non-Euclidean Geometry, Athanase Papadopoulos (editor), Strasbourg Master Class on Geometry, page 126,
To describe a parabolic transformation f of the hyperbolic plane, we consider two parallel lines l and _l_’ and we call ω their common point at infinity.
- 2007, Maurice Margenstern, Cellular Automata in Hyperbolic Spaces, Volume 1: Theory, page 66,
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