Real Time Render 4

【Real Time Render 4】

1、Radiometry（辐射测试） deals with the measurement of electromagnetic（电磁） radiation（辐射）. Such radiation consists of a flow of photons（光子）.

　　Photons behave as either particles or waves, depending on circumstance. 

　　光子可以表现为粒子或波。

　　One wave-related property of photons that cannot be disregarded is the fact that each has an associated frequency or wavelength.  The energy of each photon is proportional to its frequency. Different frequencies of photons are perceived as light of different colors.

　　波有频率、波长属性， 能量正比于频率。不同频率的光子对应不同的颜色。

2、The relationships between a photon’s wavelength λ (in meters), frequency ν (in Hertz, or cycles per second) and energy Q (in joules) are：

　　　　

　　where c is the speed of light (2.998×108 meters/second) and h is Planck’s constant (6.62620 × 10−34 joule-seconds).

　　

3、In radiometry, the basic unit is energy or radiant energy Q, measured in joules (abbreviated “J”).

　　能量单位是焦耳（joule），简写为 J。

　　The radiant flux（辐射流） or radiant power（辐射能量）, Φ or P, of a light source is equalto the number of joules per second emitted (i.e., dQ/dt).  The watt (W) is another term for joules per second.

　　辐射流等于每秒的joules。简称为watt（瓦）。

　　Irradiance （辐照度） is the density of radiant flux with respect to area.dΦ/dA.  irradiance E is used to measure light flowing into a surface and exitance M (also called radiosity or radiant exitance) is used to measure light flowing out of a surface.

　　辐照度是单位面积的辐射强度。

　　

　　I, is called intensity or radiant intensity.  If the distance r equals 1, then intensity is the same as irradiance—in other words, intensity is flux density with respect to area on an enclosing radius-1 sphere.

　　辐射强度，等于半径为1时的辐照度。

　　

　　

　　A solid angle is a three-dimensional extension of the concept—a continuous set of directions, measured with steradians （弧度）(abbreviated “sr”).  intensity is actually flux density with respect to solid angle (dΦ/dω), unlike irradiance, which is flux density with respect to area.  Intensity is measured in watts per steradian.

　　强度单位是 w/sr。

　　"five-times" rule of thumb.   If the distance from the light source is five times or more that of the light's width, then the inverse square law is a reasonable approximation and so can be used.

　　五倍定律，到光源的距离大于光源宽度时，上述Intesity公式可以使用。

4、In two dimensions, an angle of 2π radians covers the whole unit circle. Extending this to three dimensions, a solid angle of 4π steradians would cover the whole area of the unit sphere.

　　球的表面积是4πr2，所以，整个球面有4π球面度。

　　　　

5、Radiance measures the illumination in a single ray of light—it is flux density with respect to both area and solid angle.

　　　　

　　　　

　　对于上图：

　　　　This irradiance is the flux density per area at a surface point— it represents photons hitting that point from all parts of the light bulb, covering a range of directions represented by the solid angle ω.

　　An important property of radiance is that it is not affected by distance.

6、Light from a given direction consists of a set of photons in some distribution of wavelengths. This distribution is called the light’s spectrum.

　　光由一群不同波长的光子组成，这些不同波长的光子的分布叫作 spectrum。

　　So for a given spectrum, the brain itself then receives only three different signals from these receptors. This is why just three numbers can be used to precisely represent any spectrum seen.

　　对于给定的 spectrum，大脑只会接收3种不同的信号。所以只要3种颜色就能表示任意的 spectrum。

　　不同的光强可以组成任意的颜色。在 645、526、444上，分别是单色。

　　　　

7、Given an arbitrary spectrum, these curves can be multiplied by the spectrum and the area under each resulting curve (i.e., the integral) gives the relative amounts to set the colored lights to match the perceived color produced by the spectrum.

　　对于任意的光（spectrum），分别用上图中的 r、g、b 乘以 spectrum。各个面积的值就是各RGB值。

　　　　The three weighted r, g, and b values cannot directly represent all visible colors, as their color matching curves have negative weights for various wavelengths.

　　　　RGB无法代表所有颜色，因为有负数。

 　　     The CIE proposed three different hypothetical light sources that did not use monochromatic light.

　　　　　

　　　　Given a surface reflectance and light source, the product of these two defines a color function C(λ), i.e., a spectrum. By again multiplying this spectrum by a color matching curve and integrating a single value is computed for each curve:

　　　　　　

　　　　让 X+Y+Z=1，则可以省略Z轴。

　　　　　　

　　　　从而得到CIE色彩图：

　　　　　　

　　　　The curvedline in the diagram shows where the colors of the spectrum lie, and the straight line connecting the ends of the spectrum is called the purple line.

　　　　曲线是 spectrum。

　　　　白色是 1/3，1/3，1/3。

　　　　

　　　　Given a color point (x,y), draw a line from the white point through this point to the spectral line. The relative distance of the color point compared to the distance to the edge of the region is the saturation of the color.

　　　　饱和度。指颜色的纯度。

　　　　The point on the region edge defines the hue of the color.

　　　　色调。指颜色。

　　　　The third dimension needed to fully describe a color is the Y value, luminance. These then define what is called the xyY coordinate system.

　　　　亮度。最右侧图中，竖轴表示亮度。指黑白程度。

　　　　　　

　　　　参考：https://blog.csdn.net/u011399342/article/details/79656855　　

　　　　The triangle in the chromaticity diagram represents the gamut of a typical computer monitor.

8、Conversion from XY Z to RGB space is linear and can be done with a matrix.

　　　　

　　The inverse RGB to XYZ conversion is:

　　　　

　　A common conversion is to transform an RGB color to a grayscale luminance value, which is simply the middle row of the previous equation:

　　　　

　　Photometric curve  multiplied by the spectra of the three phosphors,  The three resulting weights are what form the luminance equation above.

9、 Multiplying two RGB colors to obtain an RGB result is not the same as multiplying two spectra together and then converting the resulting spectrum to RGB.

　　

　　Other color systems common in computer graphics include HSB (hue, saturation, brightness)。

　　计算机图形也常用 HSB来表示颜色。即前文所述，Hue色调，Saturation饱和度，Brightness亮度。

　　CMYK (cyan, magenta, yellow, black) is for the inks used in standard four-color printing.

　　CMYK用在四色印刷行业。

10、Omni Lights（常量点光源）

　　Point lights are defined by their position pL and intensity IL. Point lights with a constant value for IL are known as omni lights.

　　

　　　It is often preferable to use a different function to describe how EL decreases with distance. Such functions are called distance falloff function.

　　　

　　　　A much simpler distance falloff function is often used in games and graphical modeling applications:

　　　　

11、Spotlight

　　IL varies with direction. The spotlight function used in the OpenGL fixed-function pipeline is:

　　　　

　　　　

　　　　We call θu the umbra angle, the angle at which the intensity reaches 0. 

　　　　The exponent and cutoff behavior in the DirectX fixed-function pipeline is more flexible:

　　　　　　

　　　　The angle θp defines the penumbra angle of the spotlight, or the angle at which its intensity starts to decrease.

12、Textured Lights

　　　　For lights that are not limited to a frustum but illuminate in all directions, a cube map can be used to modulate the intensity, instead of a two-dimensional projective texture.