Computational Geometry

Welcome:wave:

<div align="center">God ever geometrizes. - PLATO </div>

Welcome to this repo. As the development of geometric deep learning and geometry processing, geometry is playing an ever-growing important role in the field of architecture, computational design, and robotic fabrication. Although I am able to write geometric algorithm from time to time, I aim to have a big and thorough picture over this topic. Therefore, I felt compelled to study computational geometry across different subject.

Structure🧩

In light of different sources of materials, this repo is organized as follows:

• Book:books: the must read books
• Lecture:school: the popular online lecture
• Library:computer: the popular geometry processing library
• Paper:page_with_curl: the must read paper
• Workshop:video_camera: the short-period of workshop

Recommended Material:thumbsup:

My recommended study material is followed:

| Name | Type | Link | | --------------------------------------------------- | ----------------------- | ------------------------------------------------------------ | | Discrete Differential Geometry, Keenan Crane | Online Lecture | http://geometry.cs.cmu.edu/ddg | | Digital Geometry Processing, FU Xiaoming | Online Lecture(Chinese) | http://staff.ustc.edu.cn/~fuxm/course/2020_Spring_DGP/index.html | | Computational Conformal Geometry | Online Lecture | https://www3.cs.stonybrook.edu/~gu/lectures/2020/ | | Computational Geometry: Algorithms and Applications | Book | https://www.amazon.com/dp/3540779736/ref=cm_sw_em_r_mt_dp_TN2TN09Q61YS2C2D344T |

Learning progress

Book:books:

Lecture:school:

Discrete Differential Geometry: :arrow_right:(navigate here)

• [x] Chapter 01 Overview
• [x] Chapter 02 Combinatorial Surfaces
• [x] Chapter 03 Intro to Differential Geometry
• [ ] Chapter 04 Intro to Exterior Calculus
• [ ] Chapter 05 Curvature of Discrete Surfaces
• [ ] Chapter 06 The Laplacian
• [ ] Chapter 07 Surface Parameterization
• [ ] Chapter 08 Vector Field Decomposition and Design

Geometry Modeling and Processing::arrow_right: (navigate here)

Library:computer:

libigl

CGAL

Paper:page_with_curl:

:arrow_right:(navigate here)

• Mark Meyer, Mathieu Desbrun, Peter Schröder and Alan H. Barr, Discrete Differential-Geometry Operators for Triangulated 2-Manifolds, 2003.

Workshop:video_camera:

//TODO

Outputs

| <img src="Lecture/DiscreteDifferentialGeometry/img/orbits_faces.gif" width="310"/> | <img src="Lecture/DiscreteDifferentialGeometry/img/why-tangent-normal-ortho.gif" width="310"/> | | :----------------------------------------------------------: | :----------------------------------------------------------: | | "Next" Operation in HalfEdge data structure | Why tangent vector is orothogonal to normal vector |

| <img src="Lecture/DiscreteDifferentialGeometry/img/why-tangent-normal-ortho1.gif" width="310"/> | <img src="Lecture/DiscreteDifferentialGeometry/img/curvature-of-curve.gif" height="310"/> | | :----------------------------------------------------------: | :----------------------------------------------------------: | | Why tangent vector is orothogonal to normal vector | Visualize the curvature of a curve |

| <img src="Lecture/DiscreteDifferentialGeometry/img/simplicial-operator-preview.gif" width="310"/> | | | :----------------------------------------------------------: | :--: | | Simplicial Operator written in C++ | |

Disclaimer

1.This repo is merely a collection of notes and I highly recommend YOU to learn by yourself.

2.The update of this repo may be very very very slow...

3.Please cite the authors for their contribution!