Tangent indicatrix information

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...

visualizes the distortion of a map Tangent indicatrix, an object in differential geometry related to a closed space curve Indicatrix, a special case of the index...

geometry, the Dupin indicatrix is a method for characterising the local shape of a surface. Draw a plane parallel to the tangent plane and a small distance...

{\displaystyle d} is the turning number of the stereographic projection of its tangent indicatrix. Its two values correspond to the two non-degenerate homotopy classes...

Sphere packing Spherical coordinates Spherical cow Spherical helix, tangent indicatrix of a curve of constant precession Spherical polyhedron Sphericity...

then the unit sphere bundle is the subbundle of the tangent bundle whose fiber at x is the indicatrix of F: U T x ( M ) = { v ∈ T x ( M ) | F ( v ) = 1...

of showing the distortion inherent in a projection is to use Tissot's indicatrix. Nicolas Tissot noted that the scale factors at a point on a map projection...

directions are the same as the asymptotes of the hyperbola of the Dupin indicatrix through a hyperbolic point, or the unique asymptote through a parabolic...

M is a bilinear form defined on the tangent space at p (that is, a bilinear function that maps pairs of tangent vectors to real numbers), and a metric...

of showing the distortion in projections. Like Tissot's indicatrix, the Goldberg-Gott indicatrix is based on infinitesimals, and depicts flexion and skewness...

fundamental form Second fundamental form Gauss–Codazzi–Mainardi equations Dupin indicatrix Asymptotic curve Curvature Principal curvatures Mean curvature Gauss curvature...

gnomonic projection, whereby global data expands from the center point of a tangent facet outward to the edges. Instead, each triangle edge of the Dymaxion...

north of 30°S. 15° graticule. The stereographic projection with Tissot's indicatrix of deformation. The stereographic is the only projection that maps all...

is coordinate-free. Applied to the Earth's surface, this is Tissot's indicatrix. In general, we want to specify tensor fields in a coordinate-independent...

geometry. He was the discoverer of conjugate tangents to a point on a surface and of the Dupin indicatrix. Dupin participated in the Greek science revival...

center, onto any plane not passing through the center, most commonly a tangent plane. Under gnomonic projection every great circle on the sphere is projected...

perspective (or azimuthal) projection in which the sphere is projected onto a tangent plane or secant plane. The point of perspective for the orthographic projection...

line of tangency with the equator. For the transverse Mercator, the axis of the cylinder lies in the equatorial plane, and the line of tangency is any...

projection. It corresponds to projecting the Earth's surface onto a cylinder tangent to the equator as if from a light source at Earth's center. The cylinder...

line of tangency with the equator. For the transverse Mercator, the axis of the cylinder lies in the equatorial plane, and the line of tangency is any...

asymmetric scaling horizontally and vertically. This yields a projection tangent to the sphere. Its formula is: x = R λ ; y = 2 R tan ⁡ φ 2 {\displaystyle...

coordinates Quasiregular map Pseudoanalytic function Teichmüller space Tissot's indicatrix Ahlfors, Lars (1935), "Zur Theorie der Überlagerungsflächen", Acta Mathematica...

The American polyconic projection can be thought of as "rolling" a cone tangent to the Earth at all parallels of latitude. This generalizes the concept...

azimuthal projections, meaning that the projection surface is a plane tangent to the sphere. This results in correct directions from the center to all...

meridian and φ is the latitude. When programming these equations, the inverse tangent function used is actually the atan2 function, with the first argument sin φ...