GAMES101 10 Geometry 1 Introduction

Lecture 10 Geometry 1 Introduction 几何

1. About how to describe a stuff by geometry.
   1. A string -> fiber->ply->thread
   2. very complex geometry: a city a dog .etc
   3. Not every geometry can be described as triangles.
2. Many Ways to Represent Geometry
   1. 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.
   2. Explicit: 显式
      • All points are given directly or via parameter mapping
      • 全部用三角形表示出来
      • 或者用参数映射的方法 $f(u,v)=((2+cos u)cos v,(2+cos u)sin v, sin u)$, 每一个uv测一遍，uv 映射成x,y,z
      • Sample简单，inside/outside相对麻烦
3. CSG (constructive solid geometry) (implicit)
   • combine inplicit geometry via boolean operatioins
   • E.g. a is a cubic, b is a sphere. (a+b) can get a new stuff.
4. Distance Function (implicit)
   • instead of booleans, gradually blend surfaces together using Distance functions: giving minimum distance could be signed(有向) distance from anywhere to object

5. Fractals (implicit) 分形