geometry - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Geometry : 2-D Euclidean : Transformations : geometry/reflection

geometry

  

reflection

  

find the reflection of a geometric object with respect to a given point or line

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

reflection(Q, P, c)

Parameters

Q

-

the name of the object to be created

P

-

geometric object

c

-

point or line

Description

• 

Let c be a fixed point in the plane. By the reflection (or half-turn) Rc in  point c we mean the transformation of S onto itself which carries each point P of the plane into the point Q of the plane such that c is the midpoint of PQ. Point c is called the center of the reflection.

• 

Let c be a fixed line in the plane. By the reflection Rc about line c we mean the transformation of S onto itself which carries each point P of the plane into the point Q of the plane such that c goes through the midpoint of PQ and is perpendicular to PQ.

• 

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

• 

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

Examples

withgeometry:

reflection of a point with respect to a line

pointP,2,3,linel,a+b=1,a,b

P,l

(1)

reflectionQ,P,l

Q

(2)

coordinatesQ

2,1

(3)

reflection of a line with respect to a line

linex_axis,y=0,x,y:

reflectionl1,l,x_axis:

drawl,l1

reflection of a circle with respect to a line

circlec,pointOO,0,0,1:

detailc

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

name of the objectcform of the objectcircle2dname of the centerOOcoordinates of the center0,0radius of the circle1equation of the circle_x2+_y21=0

(4)

linel1,pointa1,1,0,pointa2,0,1:

linel2,pointb1,1,0,pointb2,0,1:

linel3,pointc1,1,0,pointc2,0,1:

linel4,pointd1,0,1,pointd2,1,0:

reflectionc1,c,l1:reflectionc2,c,l2:

reflectionc3,c,l3:reflectionc4,c,l4:

drawccolor=orange,c1,c2,c3,c4,color=blue,axes=BOX,style=POINT,symbol=DIAMOND

See Also

geometry[objects]

geometry[transformation]

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam