清华大学：《计算机图形学基础》课程教学资源（授课教案）双向反射分布函数

BRDF(双向反射分布函数) • BRDF – Bidirectional Reflectance Distribution Function – Describe how light is reflected from a surface • Preliminary for BRDF • BRDF：definition and Properties • BRDF Models • BRDF Measurement

Illumination(光照、照明) • Illumination can be classified as local or global. – Local illumination is concerned with how objects are directly illuminated by light sources. – Global illumination includes how objects are illuminated by light from locations other than light sources, Including by reflection of other objects and refraction through objects. Local illumination

Illumination(光照、照明) • Illumination can be classified as local or global. – Local illumination is concerned with how objects are directly illuminated by light sources. – Global illumination includes how objects are illuminated by light from locations other than light sources, Including by reflection of other objects and refraction through objects. Today’s Topic: a physical description of how light is reflected from a surface, which is known as BRDF

Preliminary • Before introducing BRDF, we review some preliminary concepts. – Spherical Coordinate (球面坐标) – Solid Angle (立体角) – Foreshortened Area (投影面积) – Radiant Energy (光能) – Radiant Flux (光通量) – Irradiance （辉度） – Intensity （发光强度） – Radiance （光亮度）

Spherical Coordinate (球面坐标) • Since light are mostly expressed in terms of directions, it is generally more convenient to describe them by spherical coordinates rather than by cartesian coordinate vectors

Spherical Coordinate (球面坐标) • Since light are mostly expressed in terms of directions, it is generally more convenient to describe them by spherical coordinates rather than by cartesian coordinate vectors. • As illustrated in the figure, a vector in spherical coordinates is specified by three elements. – magnitude r denotes the length of the vector. – Θ measures the angle between the vector and the z-axis, – ψ represents the counterclockwise angle on the x-y plane from the x-axis to the projection of the vector onto the x￾y plane

Spherical Coordinate (球面坐标) • Relationship between Cartesian(笛卡尔) and spherical coordinates – (x,y,z)  (r, Θ, ψ) • Conversion • r = sqrt(x^2+y^2+z^2) • Θ = acos(z/r); • ψ = atan2(y,x); • z = r cos(Θ); • y = r sin(Θ)sin(ψ); • x = r sin(Θ)cos(ψ);

Solid Angle(立体角) • Light generally arrives at or leaves a surface point from a range of directions that is denoted by solid angles. solid angles represents a 3D generalization of angle formed by a region on a sphere. • Max value of a solid angle is , which is given by a sphere. 4 2 ds d r  

Solid Angle(立体角) • For a differential solid angle described by differential angles in the directions, its differential area dA on the sphere is • From the solid angle definition, the differential solid angle is given by: 2 sin dA d d d r       2 dA rd r d r d d   ( )( sin ) sin       d,d ,

Foreshortened Area（投影面积） • The apparent area of a surface patch according to the angle at which it is viewed • For a surface patch of area A, its foreshortened area from direction θis given as A cos(θ), since its apparent length in the x direction is scaled by cos(θ). Area A  cos