find the inversion of a point, plane, or sphere with respect to a given sphere. - Maple Help

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geom3d[inversion] - find the inversion of a point, plane, or sphere with respect to a given sphere.

Calling Sequence

inversion(Q, P, s)

Parameters

Q

-

the name of the object to be created

P

-

point, line, or sphere

s

-

sphere

Description

• 

If P is a point that is not the same as the center O of sphere sr, the inverse of P in, or with respect to, sphere sr is the point Q lying on the line OP such that OPOQ=r2.

• 

Sphere sr is called the sphere of inversion, point O the center of inversion, r the radius of inversion, and r2 the power of inversion.

• 

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

• 

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

Examples

withgeom3d:

Define the sphere s with center (0,0,0), radius 1

spheres,pointo,0,0,0,1

s

(1)

Define a plane passing through A, B, C

planep,pointA,1,0,1,pointB,0,0,1,pointC,0,1,1

p

(2)

Find the inversion of the plane with respect to the sphere s

inversions1,p,s

s1

(3)

Sine the plane p does not pass through the center of inversion, its inversion is a sphere through the center of inversion.

Checking:

details1

Warning, assume that the name of the axes are _x, _y and _z

name of the objects1form of the objectsphere3dname of the centercenter_s1_1coordinates of the center0,0,12radius of the sphere12surface area of the sphereπvolume of the sphereπ6equation of the sphere_x2+_y2+_z2+_z=0

(4)

IsOnObjecto,s1

true

(5)

Plotting:

draws,s1,pstyle=patchnogrid,color=maroon,style=wireframe,view=1..1,1..1,2..1,title=`inversion of a plane with respect to a sphere`

See Also

geom3d[objects], geom3d[transformation]


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