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geom3d[reflection] - find the reflection of a geometric object in a point, in a line, or in a plane
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Calling Sequence
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reflection(Q, P, c)
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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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geometric object
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c
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point, line, or plane
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Description
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In reflection in a point, each point P of the set S of all points of unextended space is carried into the point P1 of S such that PP1 is bisected by a fixed point O of space.
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In reflection in a line, each point P of S is carried into the point P1 of S such that PP1 is perpendicularly bisected by a fixed line l of space.
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In reflection in a plane, each point P of S is carried into the point P1 of S such that PP1 is perpendicularly bisected by a fixed plane p of space.
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For a detailed description of the object created Q, use the routine detail (i.e., detail(Q))
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The command with(geom3d,reflection) allows the use of the abbreviated form of this command.
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Examples
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Define the plane oxy.
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![plane(oxy, [point(C, 0, 0, 0), point(X, 1, 0, 0), point(Y, 0, 1, 0)])](/support/helpjp/helpview.aspx?si=5971/file04028/math123.png)
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Define the sphere with center (1,1,1) and radius 2.
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![sphere(s, [point(o, 1, 1, 1), 2])](/support/helpjp/helpview.aspx?si=5971/file04028/math129.png)
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Find the reflection of the sphere s in the plane oxy.
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Warning, assume that the name of the axes are _x, _y and _z
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Check that s and s2, the reflection of s1, are the same.
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Plot the sphere, its reflection and the plane.
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![draw([s, s1, oxy], style = patch, lightmodel = light4)](/support/helpjp/helpview.aspx?si=5971/file04028/math173.png)
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Download Help Document
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