Geometry

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) Definitio ...

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 D ...

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 gi ...