Radiometry
Irradiance
Definition: The irradiance is the power per unit area incident on a surface point.
A指的是投影的面积
Radiance
Radiance is the fundamental field quantity that describes the distribution of light in an environment
• Radiance is the quantity associated with a ray
• Rendering is all about computing radiance
Definition: The radiance (luminance) is the power emitted, reflected, transmitted or received by a surface,
per unit solid angle, per projected unit area.
Recall
• Irradiance: power per projected unit area
• Intensity: power per solid angle
So
• Radiance: Irradiance per solid angle
• Radiance: Intensity per projected unit area
Incident Radiance
Incident radiance is the irradiance per unit solid angle arriving at the surface.
i.e. it is the light arriving at the surface along a given ray
(point on surface and incident direction).
Exiting Radiance
Exiting surface radiance is the intensity per unit projected area leaving the surface.
e.g. for an area light it is the light emitted along a given ray
(point on surface and exit direction).
Irradiance vs. Radiance
Light transport
Bidirectional Reflectance Distribution Function (BRDF)
Radiance from direction ωi turns into the power E that dA receives
Then power E will become the radiance to any other direction ω
f_r 即BRDF 定义了光从一个方向到达接触点后，向另一个方向的反射的强度
The Reflection Equation
Challenge: Recursive Equation
光线会弹射多次
Reflected radiance depends on incoming radiance
But incoming radiance depends on reflected radiance (at another point in the scene)
The Rendering Equation
Note: now, we assume that all directions are pointing outwards
Understanding the rendering equation
一个点光源
多个点光源
面光源：
面光源带反射光源：
Rendering Equation as Integral Equation
Linear Operator Equation
Global illumination
分解为不同的弹射次数，得到全局光照（不同弹射次数光照的集合）