Computer Graphics

• Lighting simulation lighting simulation is important to create realistic simulations of how the interiors of buildings, interiors of rooms will look. How an automobile will look in an outdoor lighting environment. And computer graphics is used for all of these applications. It can be used for scientific visualization as well as medical visualization.
• future So, what we have seen here is that computer graphics has numerous applications and it involves fundamental intellectual and technical challenges which make it one of the most exciting areas to study and I hope you will join us in this course.

• 3D graphics pipeline he graphics pipeline consists of 3 stages: modeling, animation and rendering.

  • Modeling

• creating geometric models of objects

This could be a simple model of an object like a teapot. It could be a complicated mesh of an object like a cat sculpture. Or it could be a 2 billion polygon mesh of Michelangelo's David that was scanned several years ago by Professor Levoy and collaborators.

• Animation

The next step if you want the objects to actually move is to consider the animation or the motion of characters. And this is a rich area. We often want vibrant humanoid motion. In other cases we just want motion of objects from one place to another.

• Rendering

The final step is rendering or creating realistic images, given the geometry and the animation. And there we want to simulate the way the light propagates in the scene to create effects like realistic and intricate shadow details, such as what you see in images on the right.

• books The standard red book for OpenGL, and the orange book for the

GL shading language.

• Basic Math

  • linear algebra
  • vectors

• dot product

• cross product

  • matrix

• matrix-vector and matrix-matrix multiplication

  • 应用场景

Assume for example that you have a point that you want to translate to a different region. This comes up all the time, you have a character, you want to move it somewhere else in the scene. You can regard the point as a vector and we'll see how an operation like translation, rotation can be written as a matrix-vector mulitiplication.

• 点积
• scalar product

• 两种运算

  • k ・ a, 乘以常数 k
  • a ・ b, 两个向量相乘
  • 英语说法： a dot b
• 英语说法

• a*b + c a times b plus c
• cos<a,b> = (a ・ b)/(||a||・||b||)

叉积

正交基 与 坐标系框架 We use right-handed (standard) coordinates

分段曲线方程，间断点（连接点）数值相等

曲线段方程，连接点，一阶导数 “也” 相等

曲线段方程，连接点，一阶二阶导数 “都” 相等

与 0 阶参数连续性完全一致

• 注意

  • 0 阶，要数值，完全一致

1 阶导数成比例

1 阶导数成比例，并且曲率相等