geom3d - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Geometry : 3-D Euclidean : Transformations : geom3d/StereographicProjection

geom3d

  

StereographicProjection

  

find the stereographic projection of a point

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

StereographicProjection(P, P1, s)

Parameters

P

-

the name of the point to be created

P1

-

a point

s

-

a sphere

Description

• 

Let S and N be the south pole and the north pole of the sphere s, respectively. If P1 is a point on s, then the computed point P is the stereographic projection of P1 on s to the tangent plane sp at S, i.e., P is the intersection of the line l, which passes through N and P, and sp. If P1 is a point on the tangent plane sp, then the computed point P is a point on the sphere s such that P1 is the stereographic projection of P on s to the tangent plane sp.

• 

For a detailed description of the object created P, use the routine detail (i.e., detail(P))

• 

The command with(geom3d,StereographicProjection) allows the use of the abbreviated form of this command.

Examples

withgeom3d:

Define the point P(4/3,4/3,4/3) on the sphere s with center at (0,0,2) and radius 2

spheres,pointo,0,0,2,2,pointP,43,43,43

s,P

(1)

Find the stereographic projection P1 of P

StereographicProjectionP1,P,s

P1

(2)

Find the stereographic projection P2 of P1

StereographicProjectionP2,P1,s

P2

(3)

The points P and P2 should have the same coordinates

coordinatesP=coordinatesP2

43,43,43=43,43,43

(4)

See Also

geom3d[objects]

geom3d[transformation]

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam