find the inversion of a point, plane, or sphere with respect to a given sphere.
inversion(Q, P, s)
the name of the object to be created
point, line, or sphere
If P is a point that is not the same as the center O of sphere s⁡r, the inverse of P in, or with respect to, sphere s⁡r is the point Q lying on the line OP such that OP⁢OQ=r2.
Sphere s⁡r 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.
Define the sphere s with center (0,0,0), radius 1
Define a plane passing through A, B, C
Find the inversion of the plane with respect to the sphere s
Sine the plane p does not pass through the center of inversion, its inversion is a sphere through the center of inversion.
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
draw⁡s,s1,p⁡style=patchnogrid,color=maroon,style=wireframe,view=−1..1,−1..1,−2..1,title=`inversion of a plane with respect to a sphere`
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