3D Reflection

The Reflection is a mirror image of the original object. We can differentiate 2D and 3D reflection by adding Z-axis. The Z-axis shows the depth of the surface. In the Reflection process, the size of the object does not change.

We can represent Reflection by using the following three ways-

  • Reflection along with xy Plane: In the xy plane reflection, the value of z is negative.

x1 = x0

y1 = y0

z1 = -z0

3D Reflection

Matrix of 3D Reflection-

3D Reflection
  • Reflection along with xz Plane: In the xz plane reflection the value of y is negative.

x1 = x0

y1 = -y0

z1 = z0

3D Reflection

Matrix of 3D Reflection-

3D Reflection
  • Reflection along with yz Plane: In the yz plane reflection the value of x is negative.

x1 = -x0

y1 = y0

z1 = z0

3D Reflection

Matrix of 3D Reflection-

3D Reflection

Example: A 3D triangle with coordinates points P (4, 5, 2), Q (7, 5, 3), R (6, 7, 4). Apply reflection on xy plane and find the new coordinates of triangle?

Solution: We have,

The initial coordinates of triangle = P (4, 5, 2), Q (7, 5, 3), R (6, 7, 4)

Reflection Plane = xy

Let the new coordinates of triangle = (x1, y1, z)

For Coordinate P (4, 5, 2)-

X1 = x0 = 4

y1 = y0 = 5

z1 = -z0= -2

The new coordinates = (4, 5, -2)

For Coordinate Q (7, 5, 3)-

X1 = x0 = 7

Y1 = y0 = 5

Z1 = -z0= -3

The new coordinates = (7, 5, -3)

For Coordinate P (6, 7, 4)-

X1 = x0 = 6

y1 = y0 = 7

z1 = -z0= -4

The new coordinates = (6, 7, 4)



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