find the reflection of a geometric object in a point, in a line, or in a plane
reflection(Q, P, c)
the name of the object to be created
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.
Define the plane oxy.
Define the sphere with center (1,1,1) and radius 2.
Find the reflection of the sphere s in the plane oxy.
name of the objects1form of the objectsphere3dname of the centercenter_s1_1coordinates of the center1,1,−1radius of the sphere2surface area of the sphere16⁢πvolume of the sphere32⁢π3equation 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.
Plot the sphere, its reflection and the plane.
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