Course syllabus

 

Course PM

This page contains the program of the course: lectures, exercise sessions and computer labs. The primary course literature is the book "Architectural Geometry" by Pottmann et. al. As secondary literature, it is also useful with an entrance level textbook on classical differential geometry, such as "Classical Differential Geometry" by Struik.

Programming prerequisites

This course assumes some previous programming experience. If you are new to programming, I recommend that you read this online book. Most of the programming in the course is done in the Python language. If you are new to Python, but familiar with MATLAB, please have a look at this NumPy for MATLAB users tutorial. For Python, I also recommend the on-ramp course: https://cs231n.github.io/python-numpy-tutorial (I urge you to take this tutorial to test your skills).

Throughout the course we shall use Python via Rhino/Grasshopper version 8. It is therefore important that you have Rhino 8 installed on your computer. To install it on your personal laptop, visit the Rhino 3D download page and click "90-day Evaluation". This gives you full access to Rhino 8 for 90 days. You can also use Rhino via Chalmers' license server, but that requires VPN and is more complicated.

Mathematical prerequisites

This course assumes familiarity with basic linear algebra in 3 dimensions (dot products, cross products, matrices, determinants). It might be a good idea to go back to your old lecture notes from your own linear algebra course and repeat the concepts. There are also online material available, for example this on-line course:

Link between geometry and architecture

"Geometry links the art of building and the physics of space-time. Mathematical breakthroughs in geometry have led to new ways of designing our structures and our ability to visualise and describe the world, phenomena in nature and the universe. However, in contemporary architecture and structural engineering, a more profound understanding of geometry has been forgotten."
Emil Adiels, 2021

As an inspiration for the material we study in this course, I recommend you to read the introductory chapter in the licentiate thesis of Emil Adiels. Also, some time ago Emil gave an online seminar where he discussed how geometry is used in architectural workshops at Chalmers. I also recommend you to look at this video by Helmut Pottmann (about 50 min long).

Program

Each week has 2-3 sessions, where each session is typically a combination of lectures and computer exercises. The detailed schedule of the course is in TimeEdit.

Lectures

Week Contents Sections
1 Repetition of linear algebra in 3D, intro to Rhino/Grasshopper/Python, coordinate systems

Python in Rhino/Grasshopper
Appendix A
(Pottmann et al)
Chapter 1
Short lecture notes on 3D vectors

2 Plane curves, space curves, curvature, torsion, Frenet moving frame, Béizer curves, B-splines, NURBS Chapter 1.1
Section 7.2 and Chapter 8
Lecture notes
3 Polyhedral surfaces, triangular mesh, more on coordinate systems, transformations and projections

Chapter 3
Section 11.4
Section 6.6:
homogeneous coordinates
Chapters 5-6: rigid body motion (planar and 3D), linear and affine transformations, projective transformations
Chapter 2: orthographic projection, perspective projection

4 Classical differential geometry of surfaces, mean curvature, Gauss curvature, something about freeform surfaces

Chapter 7.4
Sections 11.1 - 11.4

5 Deformations, presentation of course projects Chapters 13.1-13.4: slice deformations, tapering, twisting
6 Presentation of course projects The Tent
Tsukiji Stadium
Principal Curvature
Quad-mesh Planarity
7 Work with course projects
8 Work with course projects
Exam week Hand in and present course projects

 

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Exercises and worksheets

Week Exercises
1 Diagnostic test
2 Worksheet 1
3 Worksheet 2
4 Worksheet 3
5 Worksheet 4
6 Course project
7 Course project
8 Presentations

 

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Computer labs

In this course we use Rhino+Grasshopper+Python to solve the assignments in the weekly worksheets. You're assumed to possess a basic understanding of these tools.

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Course summary:

Course Summary
Date Details Due