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geom3d

  

homothety

  

Find the homothety of a geometric object

 

Calling Sequence

Parameters

Description

Examples

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 OP1OP=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

withgeom3d:

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

icosahedronp1,pointo,0,0,0,1

p1

(1)

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

stellatep2,p1,10

p2

(2)

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

homothetyp3,p2,3,o

p3

(3)

Plotting:

drawp2,p3,scaling=constrained,style=patch,lightmodel=light4,orientation=0,32,title=`homothety of a stellated icosahedron`

See Also

geom3d[draw]

geom3d[objects]

geom3d[transformation]

 


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