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geom3d[homology] - Find the space homology of a geometric object
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Calling Sequence
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homology(Q, P, K, O, theta, l )
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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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a geometric object
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K
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ratio of the homothety
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O
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center of the homothety
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theta
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angle of rotation
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l
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the axis of rotation
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Description
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A space homology is the product of a homothety and a rotation about an axis passing through the center of the homothety.
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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,homology) allows the use of the abbreviated form of this command.
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Examples
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Define a tetrahedron with center (0,0,0), radius of the circum-sphere 1
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Apply a homology transformation to p1 with ratio 3, center of the homothety ctr, and rotation Pi/2 about the z-axis.
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![line(m, [0, 0, t], t)](/support/helpjp/helpview.aspx?si=5966/file04009/math130.png)
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Plot the original tetrahedron and the result of the homology:
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![draw([p2, p1], scaling = constrained, style = patch, transparency = .7, orientation = [0, 32], title = `homology of a tetrahedron`)](/support/helpjp/helpview.aspx?si=5966/file04009/math146.png)
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