Computer Graphic Course (by LSR)

纪念Steve Jobs 1955-2011

2011-10-07T23:14:00.003+08:00

This is a prepared text of the Commencement address delivered by Steve Jobs, CEO of Apple Computer and of Pixar Animation Studios, on June 12, 2005.

I am honored to be with you today at your commencement from one of the finest universities in the world. I never graduated from college. Truth be told, this is the closest I've ever gotten to a college graduation. Today I want to tell you three stories from my life. That's it. No big deal. Just three stories.

The first story is about connecting the dots.

I dropped out of Reed College after the first 6 months, but then stayed around as a drop-in for another 18 months or so before I really quit. So why did I drop out?
It started before I was born. My biological mother was a young, unwed college graduate student, and she decided to put me up for adoption. She felt very strongly that I should be adopted by college graduates, so everything was all set for me to be adopted at birth by a lawyer and his wife. Except that when I popped out they decided at the last minute that they really wanted a girl. So my parents, who were on a waiting list, got a call in the middle of the night asking: "We have an unexpected baby boy; do you want him?" They said: "Of course." My biological mother later found out that my mother had never graduated from college and that my father had never graduated from high school. She refused to sign the final adoption papers. She only relented a few months later when my parents promised that I would someday go to college.
And 17 years later I did go to college. But I naively chose a college that was almost as expensive as Stanford, and all of my working-class parents' savings were being spent on my college tuition. After six months, I couldn't see the value in it. I had no idea what I wanted to do with my life and no idea how college was going to help me figure it out. And here I was spending all of the money my parents had saved their entire life. So I decided to drop out and trust that it would all work out OK. It was pretty scary at the time, but looking back it was one of the best decisions I ever made. The minute I dropped out I could stop taking the required classes that didn't interest me, and begin dropping in on the ones that looked interesting.
It wasn't all romantic. I didn't have a dorm room, so I slept on the floor in friends' rooms, I returned coke bottles for the 5¢ deposits to buy food with, and I would walk the 7 miles across town every Sunday night to get one good meal a week at the Hare Krishna temple. I loved it. And much of what I stumbled into by following my curiosity and intuition turned out to be priceless later on. Let me give you one example:
Reed College at that time offered perhaps the best calligraphy instruction in the country. Throughout the campus every poster, every label on every drawer, was beautifully hand calligraphed. Because I had dropped out and didn't have to take the normal classes, I decided to take a calligraphy class to learn how to do this. I learned about serif and san serif typefaces, about varying the amount of space between different letter combinations, about what makes great typography great. It was beautiful, historical, artistically subtle in a way that science can't capture, and I found it fascinating.
None of this had even a hope of any practical application in my life. But ten years later, when we were designing the first Macintosh computer, it all came back to me. And we designed it all into the Mac. It was the first computer with beautiful typography. If I had never dropped in on that single course in college, the Mac would have never had multiple typefaces or proportionally spaced fonts. And since Windows just copied the Mac, it's likely that no personal computer would have them. If I had never dropped out, I would have never dropped in on this calligraphy class, and personal computers might not have the wonderful typography that they do. Of course it was impossible to connect the dots looking forward when I was in college. But it was very, very clear looking backwards ten years later.
Again, you can't connect the dots looking forward; you can only connect them looking backwards. So you have to trust that the dots will somehow connect in your future. You have to trust in something — your gut, destiny, life, karma, whatever. This approach has never let me down, and it has made all the difference in my life.

My second story is about love and loss.

I was lucky — I found what I loved to do early in life. Woz and I started Apple in my parents garage when I was 20. We worked hard, and in 10 years Apple had grown from just the two of us in a garage into a $2 billion company with over 4000 employees. We had just released our finest creation — the Macintosh — a year earlier, and I had just turned 30. And then I got fired. How can you get fired from a company you started? Well, as Apple grew we hired someone who I thought was very talented to run the company with me, and for the first year or so things went well. But then our visions of the future began to diverge and eventually we had a falling out. When we did, our Board of Directors sided with him. So at 30 I was out. And very publicly out. What had been the focus of my entire adult life was gone, and it was devastating.
I really didn't know what to do for a few months. I felt that I had let the previous generation of entrepreneurs down - that I had dropped the baton as it was being passed to me. I met with David Packard and Bob Noyce and tried to apologize for screwing up so badly. I was a very public failure, and I even thought about running away from the valley. But something slowly began to dawn on me — I still loved what I did. The turn of events at Apple had not changed that one bit. I had been rejected, but I was still in love. And so I decided to start over.
I didn't see it then, but it turned out that getting fired from Apple was the best thing that could have ever happened to me. The heaviness of being successful was replaced by the lightness of being a beginner again, less sure about everything. It freed me to enter one of the most creative periods of my life.
During the next five years, I started a company named NeXT, another company named Pixar, and fell in love with an amazing woman who would become my wife. Pixar went on to create the worlds first computer animated feature film, Toy Story, and is now the most successful animation studio in the world. In a remarkable turn of events, Apple bought NeXT, I returned to Apple, and the technology we developed at NeXT is at the heart of Apple's current renaissance. And Laurene and I have a wonderful family together.
I'm pretty sure none of this would have happened if I hadn't been fired from Apple. It was awful tasting medicine, but I guess the patient needed it. Sometimes life hits you in the head with a brick. Don't lose faith. I'm convinced that the only thing that kept me going was that I loved what I did. You've got to find what you love. And that is as true for your work as it is for your lovers. Your work is going to fill a large part of your life, and the only way to be truly satisfied is to do what you believe is great work. And the only way to do great work is to love what you do. If you haven't found it yet, keep looking. Don't settle. As with all matters of the heart, you'll know when you find it. And, like any great relationship, it just gets better and better as the years roll on. So keep looking until you find it. Don't settle.

My third story is about death.

When I was 17, I read a quote that went something like: "If you live each day as if it was your last, someday you'll most certainly be right." It made an impression on me, and since then, for the past 33 years, I have looked in the mirror every morning and asked myself: "If today were the last day of my life, would I want to do what I am about to do today?" And whenever the answer has been "No" for too many days in a row, I know I need to change something.
Remembering that I'll be dead soon is the most important tool I've ever encountered to help me make the big choices in life. Because almost everything — all external expectations, all pride, all fear of embarrassment or failure - these things just fall away in the face of death, leaving only what is truly important. Remembering that you are going to die is the best way I know to avoid the trap of thinking you have something to lose. You are already naked. There is no reason not to follow your heart.
About a year ago I was diagnosed with cancer. I had a scan at 7:30 in the morning, and it clearly showed a tumor on my pancreas. I didn't even know what a pancreas was. The doctors told me this was almost certainly a type of cancer that is incurable, and that I should expect to live no longer than three to six months. My doctor advised me to go home and get my affairs in order, which is doctor's code for prepare to die. It means to try to tell your kids everything you thought you'd have the next 10 years to tell them in just a few months. It means to make sure everything is buttoned up so that it will be as easy as possible for your family. It means to say your goodbyes.
I lived with that diagnosis all day. Later that evening I had a biopsy, where they stuck an endoscope down my throat, through my stomach and into my intestines, put a needle into my pancreas and got a few cells from the tumor. I was sedated, but my wife, who was there, told me that when they viewed the cells under a microscope the doctors started crying because it turned out to be a very rare form of pancreatic cancer that is curable with surgery. I had the surgery and I'm fine now.
This was the closest I've been to facing death, and I hope it's the closest I get for a few more decades. Having lived through it, I can now say this to you with a bit more certainty than when death was a useful but purely intellectual concept:
No one wants to die. Even people who want to go to heaven don't want to die to get there. And yet death is the destination we all share. No one has ever escaped it. And that is as it should be, because Death is very likely the single best invention of Life. It is Life's change agent. It clears out the old to make way for the new. Right now the new is you, but someday not too long from now, you will gradually become the old and be cleared away. Sorry to be so dramatic, but it is quite true.
Your time is limited, so don't waste it living someone else's life. Don't be trapped by dogma — which is living with the results of other people's thinking. Don't let the noise of others' opinions drown out your own inner voice. And most important, have the courage to follow your heart and intuition. They somehow already know what you truly want to become. Everything else is secondary.
When I was young, there was an amazing publication called The Whole Earth Catalog, which was one of the bibles of my generation. It was created by a fellow named Stewart Brand not far from here in Menlo Park, and he brought it to life with his poetic touch. This was in the late 1960's, before personal computers and desktop publishing, so it was all made with typewriters, scissors, and polaroid cameras. It was sort of like Google in paperback form, 35 years before Google came along: it was idealistic, and overflowing with neat tools and great notions.
Stewart and his team put out several issues of The Whole Earth Catalog, and then when it had run its course, they put out a final issue. It was the mid-1970s, and I was your age. On the back cover of their final issue was a photograph of an early morning country road, the kind you might find yourself hitchhiking on if you were so adventurous. Beneath it were the words: "Stay Hungry. Stay Foolish." It was their farewell message as they signed off. Stay Hungry. Stay Foolish. And I have always wished that for myself. And now, as you graduate to begin anew, I wish that for you.

Stay Hungry. Stay Foolish.
Thank you all very much.

怀念下传说

2009-12-21T12:39:00.003+08:00

如今，这里已是传说，也不见杂草丛生。只有一片荒芜，无处寻找后续故事的踪迹。

GLFW

2008-09-25T10:46:00.007+08:00

时间过的真快，这个博客又可以访问了，真是太棒了，发一个跨平台GL框架的helloworld.

希望大家能重新把这个站点建立起来，用了那么多平台后发现还是这个好。

#include <GL/gl.h>

#include <GL/glu.h>

#include <GL/glext.h>

#include <GL/glfw.h>

int main(int argc,char** argv){

int running = GL_TRUE; glfwInit(); if(!glfwOpenWindow(300,300,0,0,0,0,0,0,GLFW_WINDOW)){

glfwTerminate();

return 0;

}

while(running){

glClear(GL_COLOR_BUFFER_BIT);

glfwSwapBuffers();

running=!glfwGetKey(GLFW_KEY_ESC&&

glfwGetWindowParam(GLFW_OPENED);

}

glfwTerminate();

return 0;

}

理想主义者的站点

2007-05-30T02:28:00.000+08:00

交了一个新朋友，发现又一个理想主义者的论坛。
一群为了blender在中国的发展而奔波的年轻人。很值得支持他们一下。
大家有空多去逛逛。
CG世界风光无限哦^_^
http://bbs.blendercn.org

资源分享

2007-04-24T22:30:00.000+08:00

一篇很好的文章
《高质量c++编程》
http://oss.org.cn/man/develop/c&c++/c/c.htm

资源分享

2007-04-19T22:59:00.000+08:00

突然间好无方向感
在eclipse那烂烂的cdt下呆了一周半，沉迷在改彭玉的代码中，装库装的麻木了，一个粗糙的半成品框架丢在那里，突然间方向感丢失了，在兴趣与现实之间游荡，不知道是因为我是个超现实主义者，还是周期性的低迷，总之，方向感丢了，一个晚上的荒芜足够心痛了，就这样吧，继续为性格付出代价吧，忍者无敌.

以下所有这些我都是刚用的，我是个彻底的菜鸟，给出来希望可以给大家一点方便：

/--------------------------------------/
SDL即Simple DirectMedia Layer，类似DirectX，是完整的游戏、多媒体开发包，但不同的是它跨越几乎所有的平台，有各种语言的接口，多种语言的文档，而这一切都是广大志愿者完成的。目前扩展部分还没有正式的文档，以下为核心部分文档的向导部分。
相关网址：
http://tech.itdb.cn/n/200608/10/n20060810_52768.shtml
http://www.libsdl.org/intro.cn/toc.html
http://www.libsdl.org/faq.php?action=listentries&category=2
http://blog.csdn.net/snaill/archive/2005/02/05/282000.aspx
http://popul.jqcq.com/computer/gdev/1154046338.shtml
http://www.daniweb.com/techtalkforums/post337926.html

推荐指数：*****
评价：不要以为上面的文档都是正确的，bug到处有，自己慢慢调吧，不要怕遇到问题，学习的模式就是
问题->搜索答案->解决？下一个问题：搜索|自己解决->下一个问题

/--------------------------------------/
eclipse 自然不用我多说了，不懂的话自己google
eclipse SDK 下载：
http://www.eclipse.org/downloads/
eclipse上可以装一大堆插件，不嫌繁琐的话慢慢试试吧，晕死你：
http://hw.cnblogs.com/articles/251148.html
eclipse 下安装cdt+mingw的文档找啊睿要吧，他那边好东西多的是，别浪费了，当然只有你很好的使用才会得到更好的后续资源.
恩，添加库的include 和lib类似于vc6，大同小异，想想IDE的目的就知道了，恩，要不然你可以想想不要vc或者eclipse的话你在txt文档里写的代码如何编译，生成目标文件，链接，生成可执行文件，流程弄清楚了自然就明白了.

/--------------------------------------/
opencv 图像处理库
官方文档上十分详细的介绍和例子
资源：
http://www.opencv.org.cn/index.php/%E9%A6%96%E9%A1%B5

/--------------------------------------/
audiere音频库：
http://audiere.sourceforge.net/
还没开始用，所以没有中文文档资源，你用到的话发到这边吧

/--------------------------------------/
c++标准stl库学习：
呵呵，这个当然是Stephen Prata的c plusplus最详细了，需要整本书的程序电子版本的话找a睿吧
或者发我emial:mhsy2003@gmail.com

/--------------------------------------/

最后，去读懂彭玉的基于sdl+opengl编写的游戏代码吧，完了之后就不用再说c++的哪个东西没用过了
要看原著，好像在218.193.53.74上有专门放置在某个旮旯角落.openglguide那书也是很简单明了的.

...
依旧的追寻，
未知的梦想.
...

【李胜睿说……】如何访问课程blog

2007-04-16T12:28:00.000+08:00

如何访问课程blog
1.www.blogger.com可以访问，并没有被禁掉。所以我们依然可以正常的编辑文章。
2.www.blogspot.com被大陆禁掉了，所以我们无法直接访问blog的页面。

因此采用如下的域名访问blog:
pkblogs.com/XXXXXX
其中XXXXXX.blogspot.com 为你要访问的blog。

例如： pkblogs.com/xmugradeone
就可以访问本页面，呵呵，欢迎大家继续支持本课程。

OpenGL学习笔记2007-4-16

2007-04-16T12:16:00.000+08:00

在8.1，也就是第一个粒子系统

glBegin(GL_TRIANGLE_STRIP); //
绘制粒子
glTexCoord2f(1.0f, 1.0f); glVertex3f(x + 0.5f, y + 0.5f, z);
glTexCoord2d(0.0f, 1.0f); glVertex3f(x - 0.5f, y + 0.5f,
z);
glTexCoord2d(1.0f, 0.0f); glVertex3f(x + 0.5f, y - 0.5f,
z);
glTexCoord2d(0.0f, 0.0f); glVertex3f(x - 0.5f, y - 0.5f,
z);
glEnd();

就是画个正方形，然后绑定纹理？
用三角形去凑不容易理解。
直接

glBegin(GL_QUADS); //
绘制粒子
glTexCoord2d(0.0f, 1.0f); glVertex3f(x - 0.5f, y +
0.5f, z);
glTexCoord2f(1.0f, 1.0f); glVertex3f(x + 0.5f, y + 0.5f,
z);
glTexCoord2d(1.0f, 0.0f); glVertex3f(x + 0.5f, y - 0.5f,
z);
glTexCoord2d( 0.0f, 0.0f); glVertex3f(x - 0.5f, y - 0.5f, z);
glEnd();

直接画正方形即可

另外关于8.2有一点要注意
在VC6下是不能编译通过的。
在8.2中
void Font01Init()函数里面有这么一段代码，

for (int i = 0 ; i 《 30; ++i) dropSpeed[i] =
float(rand()%50 + 20); // 通道的下降速度
for (int i=0;
i《FONT_COUNT; ++i)
{
for (int j=0; j《FONT_COUNT; ++j)
{

我很确定，作者不是在Visual C++ 6中写出来的。
因为这个是标准的C语法
而VC用的不是标准C编译器，而是带有M$风格的。MS编译器会认为这样的代码，i重定义了。可是标准C规定，在for里面定义的变量，只有在该循环里面才有效。
换句话，这段代码只有在标准的C++编译器里面才能编译通过
如果要在M$的VC里面编译通过，必须放弃第二个i的定义声明，直接使用。

[转载]分形数学的沟通

2007-03-19T14:03:00.000+08:00

分形数学的沟通

2007-3-10FranPeking / WudaokouSculpting in Time / Speakeasy Café
人的思维 / 个体或单位的意识
确定存在一个规律法则 / 可用迭代函数系统表述
自变量取一合适值 / 函数值则存在分形思维中的自相似信息

一直的认为以家庭为单位的存在和发展
与一个村庄和城镇 / 一个城市和区域 / 一个民族和国家的存在发展有着必然的相似性
比如怎样的发展和富裕
比如怎样的与邻里和周围的社会保持或战争或和谐的关系
有时候觉得国家之间的外交就像小时候玩的过家家 / Hehe
而从这些都是自然的存在来讲 / 确实应该具有相似性
因为确认的是 / 自然中的所有东西具有严格的规律
也可以表述为 / 自然并不是混沌中随意的自然
比如自然数e的存在 / 比如黄金分割点 / 是规律性的东东
另一类的 / 很多形状的排列
比如含羞草的树叶 / 比如玫瑰花的层层含苞怒放
比如大陆的海岸线 / 比如划破夜空的闪电 / 比如层层分支的人体血管
比如分子光谱分布 / 比如动植物的DNA
太多的 / 也可以说所有自然的东东 / 都符合其一定的规律

一直的思考 / 也提及过数次 / 当然没有专门的论证和表述
当下一直做的一件事情
那就是用数学的语言来表述诸如我想到的这些东东
也就是我所确定的一个课题 / 文理在数字世界的沟通 / 简称文理的沟通

近段时间看数学 / 发现开始提及的那些规律性东东
有一种非常艺术和美丽的数学语言来表述
那就是三十多年前刚刚确立的 / 分形数学

数学上定义的分形数学
说它的研究对象是自然界和非线性系统中没有特征长度的几何形体
这里分形理论的数学基础是分形几何
广义一些 / 那就是自然界中
有许多东东都在某种程度上存在自相似特性
即它们中的一个部分和它的整体或者其它部分都十分形似
这个自相似性是分形的灵魂
它使得分形的任何一个片段都包含了整个分形的信息

可惜啊偶没早存在那怕五十年 / Haha
不过的 / 偶所关注的 / 不是分形几何 / 以及分形的物体
而是隶属整个自然的分形思维 / 比如这段文字开始提到的家庭与国家等的关系
另外的 / 当然还包括个体人的思维
和一个群体 / 或者不同时期不同地域群体之间的关系

用数学的语言来表述分形的存在大概是 / 分形之间的关系是一种递归和迭代 / 可以用迭代函数系统来表述
也就是说 / 这里存在一个函数 / 这个函数 / 表述的就是其中的规律和法则
用思维的语言来讲
人的思维 / 个体或单位的意识
确定存在一个规律法则 / 可用迭代函数系统表述
自变量取一合适值 / 函数值则存在分形思维中的自相似信息

分形的世界是美丽的 / 艺术的 / 和谐的
比如一个国家如果掌握了国家结构Essential分形单位
建立和谐国家的愿望肯定能实现那么一个区域 / 一个城市 / 一个村庄 / 一个家庭也是
只是这是一件非常不易得的东东
而再加上规律法则结构必然相应的有反规律法则结构存在
所以的目前阶段 / 和谐还是人们的美好愿望
如果能找到国家结构Essential分形单位 / 那就好喽 / Hehe

http://frankriel.spaces.live.com/blog/cns!99D98DF6F3835E6E!178.entry?_c=BlogPart

OpenGL学习笔记

2007-03-14T22:57:00.000+08:00

3月14日，白色情人节。黄昏，放学路上，广播女孩用甜美的声音主持着白色情人节专题。Kiss the rain的曲子回响耳边，我却不由自主得咧了咧嘴。我怎么能感伤呢？犯贱，绝对不行！我是光棍，但是光棍也应该是幸福的！

今天初步掌握了光源的设置

步骤如下：

一、初始化变量(当窗口建立时=>全局)：

定义光源位置
定义环境光的颜色
定义漫反射光的颜色
定义镜面反射光的颜色

二、把光源变量和光源控制联系起来(你定义了光源变量,但是计算机怎么知道呢?所以必须关联起来,这个不知道能不能叫做把变量实体化??)(当窗口重新加载时=>Initialize() )：

创建光源位置
创建环境光
创建漫反射光
创建镜面反射光

三、开启光源(重绘图像时 => WinMain => DrawSceneGL):

开启光源(就像拉开电源总开关)
开启指定光源(然后开启某个家电的电源)

具体实现如下(照搬阿睿的例子)

定义全局变量

// 定义位置在屏幕右上方的光源

GLfloat light_position0[] = {2.0f, 2.0f, 2.0f, 1.0f}; // 设置光源的位置
GLfloat light_ambient0[] = {1.0f, 1.0f, 1.0f, 1.0f}; // 定义环境光的颜色
GLfloat light_diffuse0[] = {1.0f, 0.1f, 0.1f, 1.0f}; // 定义漫反射光的颜色
GLfloat light_specular0[] = {1.0f, 0.3f, 0.3f, 1.0f}; // 定义镜面反射光的颜色

这样是定义了四个GLfloat型的数组,理解不?

在Initialize()函数中关联这四个变量

glLightfv(GL_LIGHT0, GL_POSITION, light_position0); // 创建光源位置
glLightfv(GL_LIGHT0, GL_AMBIENT, light_ambient0); // 创建环境光
glLightfv(GL_LIGHT0, GL_DIFFUSE, light_diffuse0); // 创建漫反射光
glLightfv(GL_LIGHT0, GL_SPECULAR, light_specular0); // 创建镜面反射光

最后在DrawSceneGL()函数中实现光源

glEnable(GL_LIGHTING); //启用光源
glEnable(GL_LIGHT0); //启用光源LIGHT0

最后：
遗憾的是，目前这个方法实现光源有一个缺点，那就是光照的alpha值是100%的，也就是说给照到的物体颜色会变成和光源一样，这样就太假了。我们需要的是透明的自然光。事情总是有办法的，我们一起摸索。
加油吧。

还有，因为我比较菜，心得难免会有一些错误或者不足，请大家发现了不要吝啬，告诉我哦。

另外，关于坐标系旋转的体会。

坐标系三个参数是x, y, z
但是不是说是说物体按x, y, z方向转动，而是物体绕着x, y, z轴转动。

也就是说如果你在x这里加参数，那么其实物体是竖着，如自行车方向着你开来或者驶去的方向转动的。

OpenGL学习笔记

2007-03-13T14:16:00.001+08:00

今天初步掌握了绘制立方体的两种方法。
其中一种是用

glVertex3f()

定义各个面，由面组成体。

另外一种是利用辅助函数库gl\glaux.h里面的

auxSolidBox()

直接定义立方体的三围。

auxSolidBox（）

比较方便，但是遇到了一个问题：

#include 〈gl\glaux〉

调用

guxSolibBox()

编译通过，链接出错。
提示如下：

--------------------Configuration: OpenGL_1_1 - Win32 Debug--------------------
Linking...
5DG'S Win32 Framework.obj : error LNK2001: unresolved external symbol _auxSolidBox@24
Debug/OpenGL_1_1.exe : fatal error LNK1120: 1 unresolved externals
Error executing link.exe.

OpenGL_1_1.exe - 2 error(s), 0 warning(s)

经过baidu,发现是因为没有链接到glaux.lib

加入以下代码，问题解决。

#pragma comment( lib, "glaux.lib" )

bug提交

2007-03-13T13:37:00.000+08:00

对象：课本附带光盘例1.7香皂模型
描述：F1全屏后，盒子里面的香皂只剩下两个贴图，长方体不见了，切换回来也没用。
推测：
1.代码有问题
2.我的电脑有问题
3.我人品有问题

本周上课思路

2007-03-12T00:44:00.000+08:00

还是没有改变临时写课件的习惯，因为自己的思路总是在变，学生也在变^_^
今晚的思路如下：

介绍google sketchUp，并且让大家完成2个tutorial，直观的了解3D场景的建模
介绍OpenGL的3D场景的基本要素，包括世界坐标系、视角坐标系、纹理坐标系
介绍基本的坐标变换操作、学会glPushMatrix(), glPopMatrix()等。
解释课本1.2--1.6的要点，进一步熟悉提供的框架(引入4.1的阅读要求）
宣布第一个工程：钟，并且声明创作规则。

本来打算用新海诚的星之声开场，时间原因只能挪到下回了。
这段时间，如果代码有熟悉的同学，马上就可以开始动手写工程了。呵呵，创作开心哦。

NEHE站点资源推荐

2007-03-10T22:31:00.000+08:00

NEHE是OpenGL入门的鼻祖了，提供了各种编程框架。课本的5DG框架也是源于早期的nehe版本的：http://nehe.gamedev.net/
另外，清华大学的小孩把这个站点的lesson全部汉化了，大家可以参考：
http://www.owlei.com/DancingWind/

分形_1.1.1 Von Koch(冯.科克)曲线

2007-03-09T09:33:00.000+08:00

参考书：李水根编著《分形》
图文编辑：@－荷默
程序： @－荷默

1. Euclide Geometry（欧几里得几何）
空间维数是整数维的:点（0维），线（1维），面（2维），体（3维），...
分别得到他们的定常度量：点的个数，线的长度，面的面积，体的体积，...
2 Fractal Geometry（分形几何）空间维数是非整数维，在欧几里得空间中不可度量.
3 1904 年，瑞典数学家Von Koch 设计了一条被称之为 Koch 的曲线.
步骤如下：
>>1:设 E0 为一单位区间【0，1】.

>>2:以E0的中间三分之一线段为底，向上作一个等边三角形，然后去掉区间(1/3,2/3),得到一条4折线段的多边形E1，它有3个不可微点.

>>3:对E1的4条折线段重复上述过程，得到一条16折线段多边形E2，它有15个不可微点.

>>...
>>8:

>>n=∞时几乎处处不可微.

△1.Von_Koch曲线在（R1，Euclidean）空间中的长度：
Length(E0)=1, Length(E1 )=4/3,
Length(E2)=16/9, Length(En )=pow(4/3,n),
Length(E )=lim(pow(4/3,n))=∞.
△2.Von_Koch曲线在（R2，Euclidean）空间中的面积：

S＝lim(sqrt(3)/12*pow(4/9,n)=0;
由上分析得Von_Koch曲线在1维Euclid空间的度量（长度）为∞,在2维Euclid空间中的度量（面积）为0.换言之，Von_Koch曲线在传统的Euclid几何领域不可度量.
4.附：Von_Koch曲线的绘制子程序（in OpenGL framwork)：
坐标计算：

已知Ax,Ay,Bx,By;Length(AD),Length(CD);Length(AB);
求 Cx,Cy:
Key:
设复数Z1，Z2，Z3分别为A，B，C.
则：令Z4=（Length(AD)+i*Length(CD)）/Length(AB),
则 Z3=Z1+(Z2-Z1)*Z4;
然后展开即得Cx，Cy.

Cx＝Ax+((Bx-Ax)*Length(AD)-(By-Ay)*Length(CD))/Length(AB);
Cy＝Ay+((By-Ay)*Length(AD)+(Bx-Ax)*Length(CD))/Length(AB);
/**************************/
//Von_koch 曲线
GLfloat xVon_Koch[MAX],yVon_Koch[MAX];//存储节点
void Von_Koch(GLint n=8,GLfloat a=0.5f,GLfloat b=sqrt(3.0f)/6)
{
int i,m=1;
GLfloat x1[MAX],y1[MAX];
xVon_Koch[0]=-90.0f;
yVon_Koch[0]=0.0f;
xVon_Koch[1]=90.0f;
yVon_Koch[1]=0.0f;
while (m＜n)
{
for(i=0;i＜pow(4,m);i++)
{//存储上次迭代节点
x1[i]=xVon_Koch[i];
y1[i]=yVon_Koch[i];
}
for(i=0;i＜pow(4,m);i++)
{//计算迭代后的新节点
xVon_Koch[i*4]=x1[i];
xVon_Koch[i*4+1]=x1[i]+(x1[i+1]-x1[i])*(1.0f/3);
xVon_Koch[i*4+3]=x1[i]+(x1[i+1]-x1[i])*(2.0f/3);
xVon_Koch[i*4+2]=x1[i]+(x1[i+1]-x1[i])*a-b*(y1[i+1]-y1[i]);

yVon_Koch[i*4]=y1[i];
yVon_Koch[i*4+1]=y1[i]+(y1[i+1]-y1[i])*(1.0f/3);
yVon_Koch[i*4+3]=y1[i]+(y1[i+1]-y1[i])*(2.0f/3);
yVon_Koch[i*4+2]=y1[i]+(y1[i+1]-y1[i])*a+b*(x1[i+1]-x1[i]);
}
xVon_Koch[i*4]=x1[i]; yVon_Koch[i*4]=y1[i];
m++;
}
glColor3f(1.0f, 1.0f, 0.0f);
for(i=0;i＜pow(4,n-1);i++)
{//绘制，连接前后两个节点
glBegin(GL_LINES );
glVertex2f(xVon_Koch[i],yVon_Koch[i]);
glVertex2f(xVon_Koch[i+1],yVon_Koch[i+1]);
glEnd();
}
}
/**************************/

讲义纠正

2007-03-06T08:38:00.001+08:00

要参与共同建设此空间的同学请发信到：lishengrui+computergraphic@gmail.com
我是白痴，上课讲义给的地址反了。

第一周的必读资料

2007-03-05T01:29:00.000+08:00

1. 框架代码必须熟悉，同时懂得如何将课本的.net代码移植到vc6下。
2. 课本1.1 -- 1.4的必须熟读，同时完成服务器上 OpenGL相关资料的中文资料OpenGLGuide.chm的前2部分——引导篇以及基础篇
3.学有余力的同学不妨阅读另外的1分中文资料 OpenGL相关资料中的 nehe的中文教程Lesson1-lesson5
注意：第一周的资料阅读尤其重要，同时框架代码的熟悉直接决定下周以后第一个工程的质量。请入门的同学加油了:)

使用OpenGL的几点说明

2007-03-02T20:28:00.000+08:00

近几年OpenGL在国内的游戏和3D开发中所占用的比例越来越小，单独的图形库而没有音频库，开发平台让它越来越原来游戏工业的开发。
但是OpenGL规整的语法，相当容易理解的操作，以及网上大量的参考资料，为大家学习OpenGL提供了相当大的便利。另外，初学者可以在短期内将注意力集中到图形库本身的学习，逐步搭建音频库和平台等概念，养成DIY工程的习惯。
最后，由于课程积累以及本人水平的原因，只能暂时使用OpenGL作为主要的工具授课。

Computer Graphic Course (by LSR)

纪念Steve Jobs 1955-2011

怀念下 传说

GLFW

理想主义者的站点

资源分享

资源分享

【李胜睿说……】如何访问课程blog

OpenGL学习笔记2007-4-16

[转载]分形数学的沟通

OpenGL学习笔记

OpenGL学习笔记

bug提交

本周上课思路

NEHE站点资源推荐

分形_1.1.1 Von Koch(冯.科克)曲线

推荐一个网站，附一篇文章－－

讲义纠正

第一周的必读资料

使用OpenGL的几点说明

怀念下传说