Find the space homology of a geometric object - Maple Help

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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

withgeom3d:

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

tetrahedronp1,pointctr,0,0,0,1

p1

(1)

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

linem,0,0,t,t

m

(2)

homologyp2,p1,3,ctr,π2,m

p2

(3)

Plot the original tetrahedron and the result of the homology:

drawp2,p1,scaling=constrained,style=patch,transparency=0.7,orientation=0,32,title=`homology of a tetrahedron`

See Also

geom3d[homothety], geom3d[objects], geom3d[rotation]


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