顶点 边 面 数目的关系

今天看模型时候观察到了一个规律，原来这个规律还有理论支持。

三角面local frame上的tangent

两个向量的夹角

不同local frame之间的角度值

weekly update

- row-major vs. column-major, affine transform. some history, http://fgiesen.wordpress.com/2011/05/04/row-major-vs-column-major-and-gl-es .

- a trip through the graphics pipeline 2011, http://fgiesen.wordpress.com/2011/07/09/a-trip-through-the-graphics-pipeline-2011-index/

- "Obligatory FXAA Post", what is AA/MSAA/MLAA (doing AA as a post-process, depth based)/FXAA (post-process, luminosity based technique)? 例如对FXAA最好的理解是你之前尝试过了其他AA方法并知道有什么问题然后去看新技术是否克服了旧问题;// "Image Space for Beginners" Render a Quad with the texture you want to do sth on, shader code. A distortion example with code.// "Moving beyond the Linear Bezier" linear, quadratic and bezier curve equations. level of continuity C0/C1/..., how to obtain a piecewise bezier with C1 continuity(meaning that the first derivative is continuously defined), how to obtain a cubic beizer curve that has C2 continuity with deBoor points.// "Little more theory with your mesh", Euler Characteristic, Closure/Link/Star of simplicial complex. http://jonmanatee.blogspot.com/

- book [A New Kind Of Science by Stephen Wolfram, 2002].

- [Procedural Textures Mapping using Geodesic Distance 2011]

- from twitter, ID_AA_Carmack John Carmack "I would like to use reference and const object fields more, but it can require awkward dances in initialization lists." 复习了有两种东西需要在初始化列表中完成初始化的.

三角形法向 - 两个frame之间的angle

叉积的方向

weekly update

- What is the OpenGL Context look like? A structure in C? An object is attached to a target (a pointer in C), then the state machine use the target to get and set the value of the object? http://www.arcsynthesis.org/gltut/Basics/Intro%20What%20is%20OpenGL.html

- profiling. Mac上的shark比较流行，可惜在windows上没有.

Download Windows SDK, v7.1, to get the xperf application and play with it.

xperf http://msdn.microsoft.com/en-us/performance/cc825801.aspx and Process Explorer.

Debugging Tools for Windows (x64)

Microsoft Windows Performance Toolkit

Microsoft Windows SDK v7.1

a similar profiler from AMD http://developer.amd.com/tools/CodeAnalyst/Pages/default.aspx

- 继续看[Introduction to Linear Algebra]里面的subspace, column space, null space的概念。

Column space contains all the right hand sides, in which case the Ax = b is solvable. The Null space N(A) contains all the solutions of Ax = 0.

- 继续读[Scientific Computing: An Introductory Survey by Michael Heath]

1. 在书中解nonlinear equations system or optimization的例子时候终于知道跟linear system ( system of linear equations )的关系了, 用iterative methods解前者的问题时候每一步都迭代中很可能需要解一个线性方程组来得到下一步走向的信息. 例如在P158 5.2.3, Newton's Method for One dimension nonlinear equation: use a linear line to fit the curve at every step.

2. 怎么求解minimization of quadratic function/energy (which is quadratic object function without constraints)?, for example min||Bx - b||^2 -> f(x) = x^t*B^t*B*x - B^t*b*x -> A = B^t * B, a = B^t * b,

Ax=b, which A is spd, can be solved by conjugate gradient method.