GAMES101 12 Geometry 3 Mesh Operation
Geometry 3 Mesh Operationby @SankHyan24
Mesh Subdivision:
Loop Subdivision:(used only on triangle)
Add the number of triangle
Assign new vertex positions according to weight
New/old vertices updated differently
For new vertices: Updated to $\frac{3}{8}(A+B)+\frac{1}{8}(C+D)$
For old vertices: Updated to
$(1-nu)\times original position + u neighbor position sum$
$n: vertex degree$
$u:\frac{3}{16} if n=3, \frac{3}{8n} otherwise $
Catmull-Clark Subdivision (General Mesh)
Definition:
Quad fa ...
GAMES101 11 Geometry 2 Curves and Surface
11 Geometry 2 Curves and Surface 曲线和表面
Explicit Representations
Curves
Bezier Curves
De Casteljau’s Algorithm
B-splines, etc.
Surfaces
Bezier surfaces
Triangles & quads
Subdivision, simplification, regulation
Explicit Representations
Point Cloud (Explicit)
Easiest representation: list of points(x,y,z)
只要点足够密，表示任何面
经常被转化成多边形面
Polygon Mesh (Explicit)
Store vertices & polygons(一般是三角形/四边形)
更复杂的数据结构，更普遍的表达形式
The Wavefront Object File (.obj) Format
Curves
Bezier Curves 贝塞尔曲线
Defini ...
GAMES101 10 Geometry 1 Introduction
Lecture 10 Geometry 1 Introduction 几何
About how to describe a stuff by geometry.
A string -> fiber->ply->thread
very complex geometry: a city a dog .etc
Not every geometry can be described as triangles.
Many Ways to Represent Geometry
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.
Explicit: 显式
All points are given directly or ...
