homothety - Maple Help

geom3d

 homothety
 Find the homothety of a geometric object

 Calling Sequence homothety(Q, P, k, O)

Parameters

 Q - the name of the object to be created P - geometric object k - number which is the ratio of the homothety O - point which is the center of the homothety

Description

 • In homothety, each point P of the set S of all points of unextended space is carried into the point P1 of S collinear with P and a fixed point O of space, and such that $\frac{\mathrm{OP1}}{\mathrm{OP}}=k$, where k is a nonzero real number. Note that OP1, OP denote the sensed magnitudes of OP1 and OP.
 • For a detailed description of the object created Q, use the routine detail (i.e., detail(Q))
 • The command with(geom3d,homothety) allows the use of the abbreviated form of this command.

Examples

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

Define an icosahedron with center (0,0,0), radius of the circum-sphere 1

 > $\mathrm{icosahedron}\left(\mathrm{p1},\mathrm{point}\left(o,0,0,0\right),1\right)$
 ${\mathrm{p1}}$ (1)

Construct a stellate (#10 in this example) of the given icosahedron

 > $\mathrm{stellate}\left(\mathrm{p2},\mathrm{p1},10\right)$
 ${\mathrm{p2}}$ (2)

Apply homothety transformation to p2 with ratio 3, and o being the center of the homothety

 > $\mathrm{homothety}\left(\mathrm{p3},\mathrm{p2},3,o\right)$
 ${\mathrm{p3}}$ (3)

Plotting:

 > $\mathrm{draw}\left(\left[\mathrm{p2},\mathrm{p3}\right],\mathrm{scaling}=\mathrm{constrained},\mathrm{style}=\mathrm{patch},\mathrm{lightmodel}=\mathrm{light4},\mathrm{orientation}=\left[0,32\right],\mathrm{title}=\mathrm{homothety of a stellated icosahedron}\right)$