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geometry

  

GlideReflection

  

find the glide-reflection of a geometric object

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

GlideReflection(Q, P, l, AB)

Parameters

Q

-

the name of the object to be created

P

-

geometric object

l

-

line

AB

-

directed segment on l

Description

• 

Let l be a fixed line of the plane and AB a given directed segment on l. By the glide-reflection Gl,AB we mean the product RlTAB where Rl is the reflection with respect to the line l, and TAB is the translation with respect to the directed segment AB. The line l is called the axis of the glide-reflection, and the directed segment AB on l is called the vector of the glide-reflection.

• 

For a detailed description of Q (the object created), use the routine detail (i.e., detail(Q))

• 

The command with(geometry,GlideReflection) allows the use of the abbreviated form of this command.

Examples

withgeometry:

dsegmentdsg,pointM,0,0,pointN,1,1:linel1,M,N:

GlideReflectionAgli,pointAA,1,0,l1,dsg:

coordinatesAgli

1,2

(1)

dsegmentdsg,pointM,0,0,pointN,1,0:linel,M,N:

circlec1,pointOO,0,1,1:

translate c1 with respect to the directed segment MN, then reflect this object with respect to the line l

GlideReflectioncgli,c1,l,dsg:

detailcgli

assume that the names of the horizontal and vertical axes are _x and _y, respectively

name of the objectcgliform of the objectcircle2dname of the centercenter_cglicoordinates of the center1,1radius of the circle1equation of the circle_x2+_y22_x2_y+1=0

(2)

drawc1color=blue,cglicolor=green,printtext=true

See Also

geometry[draw]

geometry[objects]

geometry[reflection]

geometry[transformation]

geometry[translation]

 


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