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 FunctionDescribe how light is reflected from a surfacePreliminary forBRDFBRDF: definition andPropertiesBRDFModelsBRDF Measurement

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 orglobal.is concerned with howLocalilluminationobjects are directly illuminated by lightsources.- Global illumination includes how objects areilluminated by light from locations other thanlight sources, Including by reflection of otherobjects and refraction through objects

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 orglobal.Localillumination is concerned with howobjects are directly illuminated by lightsources.Today's Topic: a physical description of howlightisreflected from a surface,whichisknownasBRDF

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 somepreliminary concepts.-SphericalCoordinate(球面坐标)- Solid Angle(立体角)ForeshortenedArea（投影面积）Radiant Energy (光能)-RadiantFlux(光通量)Irradiance（辉度）一Intensity（发光强度）一Radiance（光亮度）

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 ofdirections, it is generally more convenient todescribe them by spherical coordinates rather thanby cartesian coordinate vectors.Z0OX

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 ofdirections, it is generally more convenient todescribe them by spherical coordinates rather thanby cartesian coordinate vectors.As illustrated in the figure, a vector in sphericalcoordinates is specified by three elements.magnituder denotesthelength ofthevector.- measures the angle between the vector and the z-axis,- represents the counterclockwise angle on the x-y planefrom the X-axis to the projection of the vector onto the X-yplane

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, 0, y)A· Conversion= sqrt(x^2+y^2+z^2)0 = acos(z/r); = atan2(y,x);0: z=r cos(o); y = r sin(O)sin(y);: x = r sin(o)cos(y);dx

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 surfacepoint from a range of directions that isdenoted by solid angles. solid anglesrepresents a 3D generalization of angleformed by a region on a sphere.dsdo=2. Max value of arsinesolid angle is 4元which is given bya sphere.(b)(a)

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 bydifferential angles do,dp in the ,Φdirections, its differential area dA on thesphere isdA =(rdO)(r sinOdp) = r? sinOd0dp: From the solid angle definition, thedifferential solid angle is given by:dAdosinddp

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 accordingto the angle at which it is viewed For a surface patch of area A, its foreshortenedarea from direction Ois given as A cos(), sinceits apparent length in the x direction is scaledby cos(0).nA,coseAForeshortenedArea = Acos 0area=AcosoAArea=A=AxA

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