Exploring the Laplacian in Computer Graphics

EN 500.111.40

Fall 2023, 1 credit


Crane He Chen

Email: hchen136@jhu.edu

Website: http://cranehechen.com/

Office: Hackerman Hall 136

Office hours: by appointment


Th 9:00AM - 10:15AM, Homewood Campus, Bloomberg 178

Zoom Link



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No prerequisites. Course is designed primarily for freshmen at Johns Hopkins University.

Course Information

This course provides a practical, hands-on introduction to computer graphics, serving as an inspiring stepping stone towards the advanced 3 credit course in Computer Graphics. Central to this study is the fundamental concept of "the Laplacian" in computer graphics, an important topic, but not addressed in the 3-credit course. This technology has many practical applications, including computer game modeling, animation, and visual effects in movie production. The concept will be illuminated from both an algebraic and geometric perspective, accompanied by real-life examples and practical exercises. This course is designed to offer an expansive understanding of the role of the Laplacian in computer graphics, further enriched by hands-on opportunities coding with C++.

Course Goals

Specific outcomes for this course are that


Learning Environment

Course Schedule

Date Lecture Slides Codebase / Other Resources Video
Week 1 Overview and motivation Introduction to USD coming soon
Week 2 Data Pelican,Lizard,Beetle, Rebel, HappyDragon, Solution
Week 3 CMake HelloGraphics
Week 4 “The Laplacian" Basics, 1D, 2D, 3D
Week 5 “The Laplacian” for 3D models part1
Week 6 “The Laplacian” for 3D models part2
Week 7 “The Laplacian” as second derivative
Week 8 Guest Lecture (Ruben Wiersma from TU Delft)
Week 9 Lab
Week 10 Art Contest (opening speech: Cary Philips from ILM)

Extra Gears for Art


SweptVolumes (by Silvia Sellan, Noam Aigerman, Alec Jacobson) code more info CubicStylization (by Derek Liu, Alec Jacobson) code more info


coming soon...

Resources for Reference

Don’t need to freak out if you find the contents below quite advanced.

Note: Our course has no prerequisites, focuses on intuitions, so we are doing lots of handwavings here and there when it comes to math. But it would be beneficial to point you to resources mathematically rigorous in case you are interested in digging further in the future. Lectures I mentioned are the most relevant. In general, the whole playlists are good contents. The books are rigorous to another level. Those are super well-written textbooks though. You might find them not that hard to follow.

Optional lectures

Optional textbooks