homology - Maple Help

geom3d

 homology
 Find the space homology of a geometric object

 Calling Sequence homology(Q, P, K, O, theta, l )

Parameters

 Q - the name of the object to be created P - a geometric object K - ratio of the homothety O - center of the homothety theta - angle of rotation l - the axis of rotation

Description

 • A space homology is the product of a homothety and a rotation about an axis passing through the center of the homothety.
 • For a detailed description of Q (the object created), use the routine detail (i.e., detail(Q))
 • The command with(geom3d,homology) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$

Define a tetrahedron with center (0,0,0), radius of the circum-sphere 1

 > $\mathrm{tetrahedron}\left(\mathrm{p1},\mathrm{point}\left(\mathrm{ctr},0,0,0\right),1\right)$
 ${\mathrm{p1}}$ (1)

Apply a homology transformation to p1 with ratio 3, center of the homothety ctr, and rotation Pi/2 about the z-axis.

 > $\mathrm{line}\left(m,\left[0,0,t\right],t\right)$
 ${m}$ (2)
 > $\mathrm{homology}\left(\mathrm{p2},\mathrm{p1},3,\mathrm{ctr},\frac{\mathrm{\pi }}{2},m\right)$
 ${\mathrm{p2}}$ (3)

Plot the original tetrahedron and the result of the homology:

 > $\mathrm{draw}\left(\left[\mathrm{p2},\mathrm{p1}\right],\mathrm{scaling}=\mathrm{constrained},\mathrm{style}=\mathrm{patch},\mathrm{transparency}=0.7,\mathrm{orientation}=\left[0,32\right],\mathrm{title}=\mathrm{homology of a tetrahedron}\right)$