geom3d
reflection
find the reflection of a geometric object in a point, in a line, or in a plane
Calling Sequence
Parameters
Description
Examples
reflection(Q, P, c)
Q
-
the name of the object to be created
P
geometric object
c
point, line, or plane
In reflection in a point, each point P of the set S of all points of unextended space is carried into the point P1 of S such that PP1 is bisected by a fixed point O of space.
In reflection in a line, each point P of S is carried into the point P1 of S such that PP1 is perpendicularly bisected by a fixed line l of space.
In reflection in a plane, each point P of S is carried into the point P1 of S such that PP1 is perpendicularly bisected by a fixed plane p of space.
For a detailed description of the object created Q, use the routine detail (i.e., detail(Q))
The command with(geom3d,reflection) allows the use of the abbreviated form of this command.
withgeom3d:
Define the plane oxy.
planeoxy,pointC,0,0,0,pointX,1,0,0,pointY,0,1,0:
Define the sphere with center (1,1,1) and radius 2.
spheres,pointo,1,1,1,2
s
Find the reflection of the sphere s in the plane oxy.
reflections1,s,oxy
s1
details1
name of the objects1form of the objectsphere3dname of the centercenter_s1_1coordinates of the center1,1,−1radius of the sphere2surface area of the sphere16πvolume of the sphere32π3equation of the sphere_x2+_y2+_z2−2_x−2_y+2_z−1=0
Check that s and s2, the reflection of s1, are the same.
reflections2,s1,oxy
s2
AreDistincts,s2
false
Plot the sphere, its reflection and the plane.
draws,s1,oxy,style=patch,lightmodel=light4
See Also
geom3d/objects
geom3d/transformation
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