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geom3d[inversion] - find the inversion of a point, plane, or sphere with respect to a given sphere.
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Calling Sequence
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inversion(Q, P, s)
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Parameters
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Q
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the name of the object to be created
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P
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point, line, or sphere
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s
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sphere
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Description
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Sphere  is called the sphere of inversion, point O the center of inversion, r the radius of inversion, and  the power of inversion.
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For a detailed description of Q the object created, use the routine detail (i.e., detail(Q))
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The command with(geom3d,inversion) allows the use of the abbreviated form of this command.
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Examples
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Define the sphere s with center (0,0,0), radius 1
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![sphere(s, [point(o, 0, 0, 0), 1])](/support/helpjp/helpview.aspx?si=5969/file04013/math109.png)
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Define a plane passing through A, B, C
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![plane(p, [point(A, 1, 0, -1), point(B, 0, 0, -1), point(C, 0, 1, -1)])](/support/helpjp/helpview.aspx?si=5969/file04013/math118.png)
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Find the inversion of the plane with respect to the sphere s
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Sine the plane p does not pass through the center of inversion, its inversion is a sphere through the center of inversion.
Checking:
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Warning, assume that the name of the axes are _x, _y and _z
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Plotting:
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![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`)](/support/helpjp/helpview.aspx?si=5969/file04013/math157.png)
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