Reflection in 3D space is quite similar to the reflection in 2D space, but a single difference is there in 3D, here we have to deal with three axes (x, y, z). Reflection is nothing but a mirror image of an object.
Three kinds of Reflections are possible in 3D space:
- Reflection along the X-Y plane.
- Reflection along Y-Z plane.
- Reflection along X-Z plane.
1. Reflection along the X-Y plane: This is shown in the following figure –
Reflection along x-y plane
The Reflection transformation matrix is used to perform the reflection operation over the 3D image, which is as follows:
Consider, a point P[x, y, z] which is in 3D space is made to reflect along X-Y direction after reflection P[x, y, z] becomes P'[x’ ,y’ ,z’].
2. Reflection along the Y-Z plane: This is shown in the following figure –
Reflection along the Y-Z plane
The reflection transformation matrix for y-z axes is as follows:
Consider, a point P[x, y, z] which is in 3D space is made to reflect along Y-Z direction, after reflection P[x, y, z] becomes P'[x’ ,y’ ,z’].
3. Reflection along the X-Z plane: This is shown in the following figure –
Reflection along the X-Z plane:
The Reflection transformation matrix for z-x axes is as follows:
Consider, a point P[x, y, z] which is in 3D space is made to reflect along Z-X direction, after reflection P[x, y, z] becomes P'[x’, y’, z’].
Consider a cube ‘OABCDEFG’, which is given below, perform reflect transformation over it along X-Y plane.
The given cube is as follows:
Fig.1
So, Matrix representation condition of Reflection transformation along X-Y axis:
Point O[0 0 0] becomes O’ after performing Reflection transformation:
Point A[0 4 0] becomes A’ after performing Reflection transformation:
Point B[0 4 4] becomes B’ after performing Reflection transformation:
Point C[-4 4 0] becomes C’ after performing Reflection transformation:
Point D[4 4 4] becomes D’ after performing Reflection transformation:
Point E[4 0 0] becomes E’ after performing Reflection transformation:
Point F[0 0 4] becomes F’ after performing Reflection transformation:
Point G[4 0 4] becomes G’ after performing Reflection transformation:
After performing Reflection Transformation over the above figure (Fig.1) would look like:
Reflected 3D image