图形学基础几何

隐式几何

Sampling Can Be Hard
Inside/Outside Tests Easy
显式几何


CSG 布尔运算

距离函数


水平集（类似于等高线）

分型Fractals
隐式优缺点

显式
点云

多边形面

obj File

曲线
贝塞尔曲线Bézier Curves
de Casteljau Algorithm


Algebraic Formula




凸包Convex Hull

分段贝塞尔曲线

光滑\连续 C1连续

样条曲线Spline B-Spline


贝塞尔曲面

网格细分、简化、正规化

Mesh Subdivision (upsampling)Increase resolution
Mesh Simplification (downsampling)Decrease resolution; try to preserve shape/appearance
Mesh Regularization (same #triangles)Modify sample distribution to improve quality

Loop Subdivision三角形网格
Common subdivision rule for triangle meshes
First, create more triangles (vertices)
Second, tune their positions



Catmull-Clark Subdivision (General Mesh)一般网格
degree度点连接的线数量
Non-quad face 非四边形面
Extraordinary vertex(degree != 4)奇异点

第一次细分增加了非四边形面的奇异点，之后不增加


Mesh Simplification
Collapsing An Edge
Quadric Error Metrics⼆次误差度量


shadowmapping 分辨率不高、开销大、硬阴影
An Image-space Algorithm

• no knowledge of scene’s geometry during shadow computation
• must deal with aliasing artifacts
  Key idea:
• the points NOT in shadow must be seen both by the light and by the camera
  两次投影
  1、从光源看向场景，记录深度信息
  
  2、从摄像头看向场景，记录图像
  比较深度信息