a new reflectance model for rendering computer synthesized images is presented. the mode accounts for the relative brightness of different materials and light sources in the same scene. it describes the directional distribution of the reflected light and a color shift that occurs as the reflectance changes with incidence angle. a method for obtaining the spectral energy distribution of the light reflected from an object made of a specific real material is presented, and a procedure for accurately reproducing the color associated with the spectral enery distribution is discussed. the model is applied to the simulation of a metal and a plastic.
introduction
the rendering of realistic images in computer graphics requires a model of how objects reflect light. the reflectance model must describe both the color and the spatial distribution of the reflected light. the model is independent of the other aspects of image synthesis, such as the surface geometry representation and the hidden surface algorithm.
most real surfaces are neither ideal specular (mirrolike) reflectors nor ideal diffuse (Lambertian) reflectors. Phong proposed a reflectance model for computer graphics that was a linear combination of specular and diffsue reflection. the specular component was spread out around the specular direction by using a cosine function raised to a power. subsequent, blinn used similar ideas together with a specular reflection model from, which accounts for the off-specular peaks that occur when the incident light is at a grazing angle relative to the surface normal. whitted extended these methods by adding a term for idea specular reflection from perfectly smooth surfaces. all of these models are based on geometrical optics (ray theory).
the foregoing models treat reflection as consisting of three components: ambient, diffuse, and specular. the ambient component represents light that is assumed to be uniformly incident from the environment and that is reflected equally in all directions by the surface. the diffuse and specular components are associated with light from specific light sources. the diffuse component represents light that is scattered equally in all directions. the specular component represents highlights, light that is concentrated around the mirror direction. the specular component was assumed to be the color of the light source; 呢？这句话的是是高光分量，被认为是光源的颜色？？
the Fresnel equation was used to obtain the angular variation of the intensity, but not the color, of the specular component. the ambient and diffuse components were assumed to be the color of the material. the resulting models produce images that look realistic for certain types of materials.
this paper presents a reflectance model for rough surfaces that is more general than previous models. it is based on geometrical optics and is applicable to a broad range of materials, surface conditions, and lighting situations. the basis of this model is a reflectance definition that relates the brightness of an object to the intensity and size of each light source that illuminates it. the model predicts the directional distribution and spectral composition of the reflected light. a procedure is described for calculating red, green, and blue (RGB) values from the spectral energy distribution. the new reflectance model is then applied to the simulation of a metal and a plastic, with an explanation of why images rendered with previous models often look plastic, and how this plastic appearance can be avoided.
the reflectance model
given a light source, a surface, and an observer, a reflectance model describes the intensity and spectral composition of the reflected light reaching the observer. the intensity of the reflected light is determined by the intensity and size of the light source and by the reflecting ability and surface properties of the material.
the spectral 光谱 composition of the reflected light is determined by the spectral composition of the light source and the wavelength-selective reflection of the surface. in this section the appropriate reflectance definitions are introduced and combined into a general reflectance model. figure 1 contains a summary of the symbols used in this model.
the geometry of reflection is shown in figure 2. an observer is looking at a point P on a surface. v is the unit vector in the direction of the viewer, n is the unit normal to the surface, and l is the unit vector in the direction of specific light source. h is a normalized vector in the direction of the angular bisector 平分线 of v and l, and is defined by
which is the unit normal to a hypothetical 假设 surface that would reflect light specularly from the light source to the viewer. a is the angle between H and N, and θ is the angle between H and V, so that cos(θ) = V.H = L.H.
the energy of the incident light is expressed as energy per unit time and per unit area of the reflecting surface. the intensity of the incident light is similar, but is expressed per unit projected area and, in addition, per unit solid angle. (solid angle is the projected area of the light source divided by the square of the distance to the light source and can be treated as a constant for a distant light source.) the energy in an incoming beam of light is
except for mirros or near-mirros, the incoming beam is reflected over a wide range of angles. for this reason, the reflected intensity in any given direction depends on the incident energy, not just on the incident intensity. the ratio of the reflected intensity in a given direction to the incident energy from another direction (within a small solid angle) is called the bidirectional reflectance. this reflectance is fundamental for the study of reflection. for each light source, the bidirectional reflectance R is thus
the reflected intensity reaching the viewer from each light source is then
the bidirectional reflectance may be split into two components, specular and diffuse. The specular component represents light that is reflected from the surface
of the material. The diffuse component originates from internal scattering (in
which the incident light penetrates beneath the surface of the material) or from
multiple surface reflections (which occur if the surface is sufficiently rough). The
specular and diffuse components can have different colors if the material is not
homogeneous. The bidirectional reflectance is thus
In addition to direct illumination by individual light sources, an object may be
illuminated by background or ambient illumination. All light that is not direct
illumination from a specific light source is lumped together into ambient illumination.
The amount of light reflected toward the viewer from any particular
direction of ambient illumination is small, but the effect is significant when
integrated over the entire hemisphere of illuminating angles. Consequently, it is
convenient to introduce an ambient (or hemispherical-directional) reflectance,
R,. This reflectance is an integral of the bidirectional reflectance R and is thus a
linear combination of Rs and Rd. For simplicity, we assume that R, is independent
of viewing direction. In addition we assume that the ambient illumination is
uniformly incident. The reflected intensity due to ambient illumination is defined
by
The term f is the fraction of the illuminating hemisphere that is not blocked by
nearby objects (such as a corner) [25]. It is given by
where the integration is done over the unblocked part of the illuminating
hemisphere.
The total intensity of the light reaching the observer is the sum of the reflected
intensities from all light sources plus the reflected intensity from any ambient
illumination. Assuming that f = 1, the basic reflectance model used in this paper
becomes