1.
This chapter defines a set of classes for describing the way that light scatters at surfaces. Recall that in Section 5.6.1 we introduced the bidirectional reflectance distribution function (BRDF) abstraction to describe light reflection at a surface, the BTDF to describe transmission at a surface, and the BSDF to encompass both of these effects. In this chapter, we will start by defining a generic interface to these surface reflection and transmission functions. Scattering from realistic surfaces is often best described as a mixture of multiple BRDFs and BTDFs;
（BRDF 是描述 光在表面上是怎么放射的， BTDF 是描述光是在表面上怎么传输的，BSDF 就是 包含 这两种效果）
2.
Before we define the relevant interfaces, a brief review of how they fit into the overall system is in order. In the common case where the SamplerRenderer is used, the renderer is first responsible for determining which surface is first visible along a ray. It then calls the integrator classes, defined in Chapter 15, which call the surface shader that is bound to the surface. The surface shader is a method in subclasses of the Material class and is responsible for deciding what the BSDF is at a particular point on the surface (see Chapter 9); it returns a BSDF object that holds BRDFs and BTDFs that it has allocated and initialized for that point. The integrator then uses the BSDF to compute the scattered light at the point, based on the incoming illumination fromthe light sources in the scene. (The process where the MetropolisRenderer is used rather than the SamplerRenderer is similar, but without the use of separate Integrators.)
（以上是 BSDF在整个PBRT系统的作用，主要是 Integrator 使用 BSDF 来计算一个点的散射）
3.
Reflection from surfaces can be split into four broad categories(大类): diffuse, glossy specular, perfect specular, and retro-reflective (Figure 8.1).Most real surfaces exhibit(展示) reflection that is a mixture of these four types.
Diffuse surfaces scatter light equally in all directions. Although a perfectly diffuse surface isn’t physically realizable, examples of near-diffuse surfaces include dull chalkboards(黑板) and matte paint(油漆).
Glossy specular surfaces such as plastic or high-gloss paint scatter light preferentially in a set of reflected directions—they show blurry reflections of other objects.
Perfect specular surfaces scatter incident light in a single outgoing direction. Mirrors and glass are examples of perfect specular surfaces.
Finally, retro-reflective surfaces like velvet or the Earth’s moon scatter light primarily back along the incident direction.
（反射模型的分类， diffuse，glossy specular，perfect specular retro-reflective）
4.
Given a particular category of reflection, the reflectance distribution function may be isotropic(各向同性) or anisotropic(各向异性). Most objects are isotropic: if you choose a point on the surface and rotate it around its normal axis at that point, the amount of light reflected doesn’t change.
In contrast, anisotropic materials reflect different amounts of light as you rotate them in this way. Examples of anisotropic surfaces include brushed metal, phonographic records, and compact disks.
（什么是isotropic(各向同性) or anisotropic(各向异性).）
1.
Reflection computations in pbrt are evaluated in a reflection coordinate system wherethe two tangent vectors and the normal vector at the point being shaded are aligned with the x, y, and z axes, respectively (Figure 8.2). All direction vectors passed to and returned from the BRDF and BTDF routines will be defined with respect to this coordinate system. It is important to understand this coordinate system in order to understand the BRDF and BTDF implementations in this chapter.
The shading coordinate system is defined by the orthonormal basis vectors (s, t, n). We will orient these vectors such that they lie along the x, y, and z axes in this coordinate system. Direction vectors ω in world space are transformed into the shading coordinate system before any of the BRDF or BTDF methods are called.
（pbrt的反射的计算 是在 reflection coordinate system 空间下进行的，reflection coordinate system空间就由一个点的两条切线和一条法线构成的，传入 BRDF和BTDF 的 向量或者从 BRDF和BTDF 传出的 向量 都是 关于定义在 reflection coordinate system空间 上的，所以，一个世界坐标向量 w， 在传入 BRDF 或者 BTDF之前，需要先转换到 reflection coordinate system 空间上 ）
2.
The shading coordinate system also gives a frame for expressing directions in spherical coordinates (θ , φ); the angle θ is measured from the given direction to the z axis, and φ is the angle formed with the x axis after projection of the direction onto the xy plane. Given a direction vector ω in this coordinate system, it is easy to compute quantities like the cosine of the angle that it forms with the normal direction:
The value of sin θ can be found by computing the length of the dotted line, which is the magnitude of the xy components of the vector. (Recall that the length of the vector ω is one.) The sin φ and cos φ values can be computed using the circular coordinate equations x = r cos φ and y = r sin φ, where r, the length of the dashed line, is equal to sin θ.
（这里就是用球坐标来表示一个向量w，
x = sin θ cos φ => cos φ = x / sin θ
y = sin θ sin φ => sin φ = y / sin θ
z = cos θ
）
inline float CosTheta(const Vector &w) { return w.z; } inline float AbsCosTheta(const Vector &w) { return fabsf(w.z); } inline float SinTheta2(const Vector &w) { return max(0.f, 1.f - CosTheta(w)*CosTheta(w)); } inline float SinTheta(const Vector &w) { return sqrtf(SinTheta2(w)); } inline float CosPhi(const Vector &w) { float sintheta = SinTheta(w); if (sintheta == 0.f) return 1.f; return Clamp(w.x / sintheta, -1.f, 1.f); } inline float SinPhi(const Vector &w) { float sintheta = SinTheta(w); if (sintheta == 0.f) return 0.f; return Clamp(w.y / sintheta, -1.f, 1.f); }
3. 细节
Another convention we will follow is that the incident light direction ωi and the outgoing viewing direction ωo will both be normalized and outward facing after being transformed into the local coordinate system at the surface. By convention, the surface normal n always points to the “outside” of the object, which makes it easy to determine if light is entering or exiting transmissive objects: if the incident light direction ωi is in the same hemisphere as n, then light is entering; otherwise, it is exiting.
（wi 和 wo 都是要 normalized，并且 向外（outward facing），法线也是向外（outside））
Therefore, one detail to keep in mind is that the normal may be on the opposite side of the surface than one or both of the ωi and ωo direction vectors. Unlike many other renderers, pbrt does not flip the normal to lie on the same side as ωo. Therefore, it is important that BRDFs and BTDFs be implemented so that they don’t expect otherwise.
Furthermore, note that the local coordinate system used for shading may not be exactly the same as the coordinate system returned by the Shape::Intersect() routines from Chapter 3; they can be modified between intersection and shading to achieve effects like bump mapping. See Chapter 9 for examples of this kind of modification.
One final detail to be aware of when reading this chapter is that BRDF and BTDF implementations should not concern themselves with whether ωi and ωo lie in the same hemisphere. For example, although a reflective BRDF should in principle detect if the incident direction is above the surface and the outgoing direction is below and always return no reflection in this case, here we will expect the reflection function to instead compute and return the amount of light reflected using the appropriate formulas for their reflection model, ignoring the detail that they are not in the same hemisphere. Higher-level code in pbrt will ensure that only reflective or transmissive scattering routines are evaluated as appropriate.
