Definitions for conformal projection
con·for·mal pro·jec·tion

Princeton's WordNetRate this definition:0.0 / 0 votes

1. conformal projection, orthomorphic projectionnoun

   a map projection in which a small area is rendered in its true shape

WikipediaRate this definition:0.0 / 0 votes

1. conformal projection

   In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let U {\displaystyle U} and V {\displaystyle V} be open subsets of R n {\displaystyle \mathbb {R} ^{n}} . A function f : U → V {\displaystyle f:U\to V} is called conformal (or angle-preserving) at a point u 0 ∈ U {\displaystyle u_{0}\in U} if it preserves angles between directed curves through u 0 {\displaystyle u_{0}} , as well as preserving orientation. Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size or curvature. The conformal property may be described in terms of the Jacobian derivative matrix of a coordinate transformation. The transformation is conformal whenever the Jacobian at each point is a positive scalar times a rotation matrix (orthogonal with determinant one). Some authors define conformality to include orientation-reversing mappings whose Jacobians can be written as any scalar times any orthogonal matrix.For mappings in two dimensions, the (orientation-preserving) conformal mappings are precisely the locally invertible complex analytic functions. In three and higher dimensions, Liouville's theorem sharply limits the conformal mappings to a few types. The notion of conformality generalizes in a natural way to maps between Riemannian or semi-Riemannian manifolds.

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1. conformal projection

   A conformal projection is a type of map projection that maintains accurate angles locally. This means that all angles at every point on the map are true and match those on the globe, but the size and shape of areas can be distorted. This type of projection is often used in navigational purposes as they give an accurate depiction of the shape for small areas. Examples of conformal projections are Mercator and Stereographic projections.

Matched Categories

1. • Map Projection

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Numerology

1. Chaldean Numerology

   The numerical value of conformal projection in Chaldean Numerology is: 2

2. Pythagorean Numerology

   The numerical value of conformal projection in Pythagorean Numerology is: 6

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=conformal projection
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Conformal_Projection
3. ^ ChatGPT
   https://chat.openai.com