Graphics

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 ...

Texture Mapping 纹理映射Interpolation Across Triangles: Barycentric Coordinates 重心坐标 A coordinate system for triangles ( $\alpha ,\beta ,\gamma$ ) $(x,y)=\alpha A+\beta B+\gamma C, where \alpha ,\beta ,\gamma>0 and \alpha ,\beta ,\gamma+1=0$ How to Calculate them? Use the triangle area: $$ \alpha = \frac{A_A}{A_A+A_B+A_C}, \ \beta = \frac{A_B}{A_A+A_B+A_C}, \ \gamma = \frac{A_C}{A_A+A_B+A_C} $$ 重心坐标不具有投影变换不变性，所以先三维插值，再投影到二维面上去 Texture Magnification: What if the textu ...

08 Shading 着色Blinn-Phong Reflection Model Specular highlights Term 高光 Intensity depends on view direction Bright near mirror reflection direction V close to mirror direction <–> half vector near normal(h) Measure “near” by dot productof unit vectors Formula: $L_s = k_s(I/r^2)max(0,<n,h>)^p$ What is the p in $max(0,<n,h>)^p$ for? Make it real: If $\alpha $ is too big, $<n,h>^p$ is small. Ambient Term 环境光照 Assumption: Shading that does not depend on any ...

07 Shading 着色解决遮挡(Visibility)与着色的问题———Z-bufferingBlinn-Phong Reflection Model现在只针对于一个点的着色1.Painter’s Algorithm 遮挡和覆盖overwrite 但是对于物体，填充顺序是个问题 nlog(n) 2.Z-Buffer 深度缓存,n triangle idea ：存储min.z-value, for every pixel Frame buffer Depth buffer Algorithm 维护当前看到的最浅深度的信息 initialize depth buffer to infinity zbuffer[x,y] denotes the screen’s pixel buffer framebuffer[x,y] denotes the information(r,g,b) of the pixel for(every triangle) for(every sample(x,y,z)in Triangle) if(z<zbuffer[x,y]) framebuffe ...

反走样（应对取样带来的模糊）空间上走样 锯齿 摩尔纹时间上走样 车轮效应 方法：先模糊，再采样傅里叶变换边界：高频率波 Low Pass filter 低通滤波，模糊 High Pass filter 高通滤波，留下边界 Filter out low and high frequency 保留中间信号 Filter = Convolution = AverageConvolution: 用Filter（卷积核）对signal一个点的周围区域进行加权平均，生成一个新的信号（一般都变小了） 卷积定理：直接卷积（时域上），和先傅里叶变换（变到频域上）再与卷积核傅里叶变换的结果进行乘积再逆傅里叶变换回去，结果是一样的。 采样，频域上就是复制波，采样约密集，复制出来的波差的越远 高频信号的频谱更长，采样之后更容易覆盖 抗锯齿处理： 增加采样率 模糊化，本质上砍掉高频信息，让频谱覆盖面小一些 实际运用： MSAA抗锯齿: 几个像素模糊化 代价:更大的计算量 其他应用： FXAA：图像层面抗锯齿，找边界抗锯齿 TAA： Temporal AA 与时间相关，时间上复用 ...

不是很难，所以没怎么记，就当个目录放这里吧 1 Overview of Computer Graphics2 Review of Linear Algebra3 Transformation4 Transformation Cont5 Raterization 1 Triangles