GAMES101

19 Cameras, Lenses and Light Fields 相机棱镜和光场Camera Structure shutter 快门 sensor 传感器，感知Irradiance 针孔相机 Pinhole Image Formation没有模糊 Feild of view (FOV) 视场取决于Lens和Sensor（宽度是h）的距离（f）。 $Fov=2 arctan(\frac{h}{2f})$ Exposure 曝光 $ H=T\times E$ exposure=time*irradiance Aperture size 光圈（E）f数（F-Number F-STop）直径分之一，越大光圈越小。光圈大远景模糊，浅景深(景深是光像清晰的一段范围) Shutter speed 快门曝光时间（T）Motion Blur 运动模糊 ISO Gain 感光度。太大放大噪声 F-Stop和Shutter时间要Trade off Gauss Ray Tracing Construction / Thin lens equation$\fr ...

18 Advanced Topics in RenderingAdvanced Light TransportUnbiased light transport methodsBidirectional Path Tracing (BDPT)生成两个子路径，分别从光源和摄像机出发光线，并将两者断电连接起来。 Metropolis Light Transport (MLT) 用马尔可夫链生成样本，给一条路径，生成一系列相似的路径。被积函数和pdf形状一致的时候variance最小。(马尔可夫链可以用任何函数生成样本) 适用于局部取样、复杂光路、焦散、SDS(Specular-Diffuse-Specular) 缺点是收敛速度问题不清楚、有些像素收敛快，有的慢 Biased light transport methodPhoton Mapping caustics(焦散)， Step 1 Photon Tracing 光子一直跑，知道遇到diffuse的地方 Step 2 photon collecting 从视角跑，直到遇到diffuse的地方 Step 3 Calculation - ...

17 Material and AppearanceMaterial = BRDF Diffuse / Lambertain Material albedo (color): $f_r=\rho/\pi,albedo\ is\ \rho $ Glossy MaterialIdeal Reflective / Refractive Material 反射和折射材料Snell’s Law Law of Refraction 斯涅尔定律（折射定律） Snell’s Circle (水中的全反射，一个锥形) Fresnel Reflection / Term 菲涅尔项 Reflectance depends on incident angle (and polarization of light) 不同角度反射和折射的量不同。也取决于光的偏振方向。但是太不好算了 菲涅尔项的approximation: schlick’s approximation Microfacet Theory 微表面模型 基于物理 对于细节很多的材质。远 ...

Ray Tracing 4 Path TracingMonte Carlo Integration Definite intergral: $\int_{a}^{b}{f(x)dx}$ Random variable: $X_i\sim pdf(x)$ , pdf is the Probability Distribution Function Monte Carlo estimator: $F_N=\frac{1}{N}\sum_{i=1}^{N}{\frac{f(x_i)}{pdf(x_i)}}$ 我自己证明一下：中心极限定理，当 $ N\rightarrow \infty $ $\frac{1}{N}\sum_{i=1}^{N}{\frac{f(x_i)}{pdf(x_i)}}\rightarrow E(\frac{f(x_i)}{pdf(x_i)})$ $= \int_{a}^{b}{pdf(x_i)\times \frac{f(x_i)}{pdf(x_i)}}dx$ $=\int_{a}^{b}{f(x_i)}dx$ $& ...

15 Ray Tracing 3 BRDFBasic Radiometry 辐射度量学基础Irradiance Definition: Power pur unit area. $ E(x) \equiv \frac{d\Phi_{\perp}(x)}{dA}=\frac{\Phi}{A}cos\theta $ 单位面积上接收到的能量 Radiance Definition: Power pur unit solid angle pur unit area $L(p,\omega)\equiv \frac{d^2\Phi(p,\omega)}{d\omega dAcos\theta}$ 单位立体角单位面积上接收到的能量 Radiance 对单位立体角积分，就是Irradiance: $E_i(\omega_i)=L_i(\omega_i)cos\theta_i d\omega_i$ Bidirectional Reflectance Distribution Function (BRDF)Reflection at a Point 光在一个点的反射 可以理解成， ...

14 Ray Tracing 2 AccelerateAcceleration: Bounding Volumes Ray-Intersection With a Box Understanding : box is the intersection of 3 pairs of slabs. Axis-Aligned Bounding Box: AABB 轴对齐包围盒 光线进入所有包围面，进入盒子。出去其中一个包围面，出去包围盒。 $t_{enter}=max{t_{min}}, t_{exit}=min{t_{max}}$ If $t_{enter}<t_{exit}$, ray stay a while in the box. $t_{enter}<t_{exit} and t_{exit}>=0$, ray and AABB intersection. Grid Solution: 在bounding box 里面再弄一堆格子 Spatial Partitioning Examples Oct-Tree KD-Tree BSP- ...

13 Ray Tracing 1 Whitted-StyleShadow Mapping before we move onTBD Whitted-Style Ray TracingTBD Why Ray Tracing? Rasterization couldn’t handle global effects well Soft shadow Light bounces more than once Ray Tracing is accurate, but is very slow Rasterization: real-time, ray tracing: offline ~10k CPU core hours to render one frame in production. Definition: Light Rays: Light travels in straight lines 直线传播 Light rays do not collide with each other if they cross 不相互影响 Light rays travel from th ...

Geometry 3 Mesh Operationby @SankHyan24 Mesh Subdivision: Loop Subdivision:(used only on triangle) Add the number of triangle Assign new vertex positions according to weight New/old vertices updated differently For new vertices: Updated to $\frac{3}{8}(A+B)+\frac{1}{8}(C+D)$ For old vertices: Updated to $(1-nu)\times original position + u neighbor position sum$ $n: vertex degree$ $u:\frac{3}{16} if n=3, \frac{3}{8n} otherwise $ Catmull-Clark Subdivision (General Mesh) Definitio ...

11 Geometry 2 Curves and Surface 曲线和表面 Explicit Representations Curves Bezier Curves De Casteljau’s Algorithm B-splines, etc. Surfaces Bezier surfaces Triangles & quads Subdivision, simplification, regulation Explicit Representations Point Cloud (Explicit) Easiest representation: list of points(x,y,z) 只要点足够密，表示任何面 经常被转化成多边形面 Polygon Mesh (Explicit) Store vertices & polygons(一般是三角形/四边形) 更复杂的数据结构，更普遍的表达形式 The Wavefront Object File (.obj) Format Curves Bezier Curves 贝塞尔曲线 D ...

Lecture 10 Geometry 1 Introduction 几何 About how to describe a stuff by geometry. A string -> fiber->ply->thread very complex geometry: a city a dog .etc Not every geometry can be described as triangles. Many Ways to Represent Geometry Implicit: 隐式 points satisfy some specified relationship, E.g. sphere:all points in 3D, where $x^2+y^2+z^2=1$ more generally, $f(x,y,z)=0$ Implict Surface: Sampling can be hard, Inside/Outside tests is easy. Explicit: 显式 All points are gi ...