indicatrix

A single indicatrix describes the distortion at a single point.

In dealing with a Tissot indicatrix, different notions of radius come into play.

Tissot's indicatrix is often used to illustrate the variation of point scale across a map.

Lastly, the size that the indicatrix gets drawn for human inspection on the map is arbitrary.

The figure illustrates the Tissot indicatrix for this projection.

The classic way of showing the distortion inherent in a projection is to use Tissot's indicatrix.

Then the tangent indicatrix of is the closed curve on the unit sphere given by .

In differential geometry, the Dupin indicatrix is a method for characterising the local shape of a surface.

The distortion ellipse is known as Tissot's indicatrix.

One tool for examining distortions is Tissot's indicatrix, a series of small, identical circles drawn on a globe.

The Dupin indicatrix is the result of the limiting process as the plane approaches the tangent plane.

The indicatrix was invented by Charles Dupin.

He was the discoverer of conjugate tangents to a point on a surface and of the Dupin indicatrix.

When viewing the indicatrix of biaxial minerals, both optic axes are always perpendicular to one of the two circular sections.

The direction of the asymptotic direction are the same as the asymptotes of the hyperbola of the Dupin indicatrix.

The following examples illustrate three normal cylindrical projections and in each case the variation of scale with position and direction is illustrated by the use of Tissot's indicatrix.

Because distortion varies across a map, generally Tissot's indicatrices (plural of indicatrix) are placed across a map to illustrate the spatial change in distortion.

In differential geometry, the tangent indicatrix of a closed space curve is a curve on the unit sphere intimately related to the curvature of the original curve.

This mineral belongs to the uniaxial (+) optical class, which means its indicatrix has a prolate sphenoid shape with a circular section, principal section, and one optic axis.

He devised Tissot's indicatrix, or distortion circle, which when plotted on a map will appear as an ellipse whose elongation depends on the amount of distortion by the map at that point.

In Figure 1, ABCD is a circle with unit area defined in a spherical or ellipsoidal model of the Earth, and A'B'C'D' is the Tissot's indicatrix that results from its projection on the plane.

Specifically, if M is a manifold equipped with a Finsler metric F : TM R, then the unit sphere bundle is the subbundle of the tangent bundle whose fiber at x is the indicatrix of F:

Goldberg and Gott show that the Winkel tripel fares well against several other projections analyzed against their measures of distortion, producing small distance errors, small combinations of Tissot indicatrix ellipticity and area errors, and the smallest skewness of any of the projections they studied.

Tissot's indicatrix (Tissot indicatrix, Tissot's ellipse, Tissot ellipse, ellipse of distortion) is a mathematical contrivance presented by French mathematician Nicolas Auguste Tissot in 1859 and 1871 in order to characterize distortions due to map projection.