Light Falloff(Point Light)

Introduction

The light of the point light source is diffused outward in the shape of a sphere. As the diffusion distance increases, the amount of light energy per unit surface area of the sphere becomes smaller and smaller.

What is the calculation for light energy?

Calculation

GAMES 101

In the figure, the unit light energy of a sphere at radius 1 is set to $I_1$, and at radius r is set to $I_2$.

According to the law of conservation of energy, the total energy is constant, so we obtain the equation

$$I_1 4\pi 1^2 = I_24\pi r^2 \\[5px] I_2 = \frac{I_14\pi}{4\pi r^2} \\[5px] I_2 = \frac{I_1}{r^2}$$

References

GAMES 101-現代計算機圖形學入門-闫令琪