COSC 89.18/189: Computational Methods for Physical Systems, Winter 2019

From Hollywood visual effects to EA game engines, from virtual dressing mirrors to drone design, and from soft exosuits to Origami robots, computer-based modeling and simulation of physical systems are essential in various fields related to entertainment, manufacturing, and scientific research. This course introduces mathematical and algorithmic techniques to simulate, design, and make various physical systems, with applications to computer graphics, animation, robotics, and 3D printing. We will introduce classical numerical algorithms to simulate rigid body, soft body, fluid, and cloth, as well as control and optimization algorithms to design drones and 3D printable objects. The theoretical underpinnings are formed by multi-variable calculus, linear algebra, unconstrained and constrained optimizations, and introductory-level topics in continuum mechanics.

This course will focus on the design and implementation of physical computing algorithms and their connections to the real world. You will learn how to progress from abstract mathematical models on to concise and efficient programs on to the fabrication of actual physical objects that can be grasped in one's hand. During the quarter, we will have a "Drone Day" to fly drones controlled by your own implemented simulation algorithm and a "3D Printing Day" to teach you 3D print your optimized designs.


[01/04/19] Lecture 1 slides and Assignment 0 were posted in Canvas.


Dartmouth COSC 89.18/189: Computational Methods for Physical Systems from Bo Zhu on Vimeo.


Instructor: Bo Zhu (Sudikoff 153)

Teaching assistant: Dario Seyb (Sudikoff 142)

Guest instructors: Tao Du (MIT CSAIL) -- Drone Day; Yuanming Hu (MIT CSAIL, the author of Taichi) -- Particle Fluid


Class Time: Tuesday/Thursday, 2:25pm-4:15pm

X-Hours: Wednesday, 4:35pm-5:25pm

Office Hours:, Professor, Tuesday/Thursday 4:30-5:30pm, Sudikoff 153; TA, TBD, Sudikoff 142

Location: Kemeny Hall 008


The course information will be posted on both Canvas ( and the public course website (


We will use Piazza for our class discussion. Here is the link: .

Reading Materials:

The reading materials for the course include a bunch of course notes and papers, covering the topics of rigid body, soft body, cloth, and fluid simulation.


This course assumes an understanding of multi-variable calculus and linear algebra. Students are recommended to take COSC 50 as a prerequisite or to show equivalent understanding and comfortableness with programming in C++.

Assignments and Projects:

Grading policies:: Programming Assignments:

There are four short programming assignments (100 lines C++ code) during the quarter, corresponding to the mathematical foundations, rigid body, deformable body, and fluid. In each assignment, you are expected to implement some critical parts of the numerical algorithm taught in class. A sample code will be delivered for each assignment.


You are expected to exercise two in-class presentations, including a presentation of a technical paper relevant to one of the class topics and a presentation for the final project at the end of the quarter.

Final Project:

We will send out an assignment for each simulation topic every one or two weeks. Each assignment includes 1-point, 2-point, and 3-point requirements. Typically, a 1-point assignment asks you to write a piece of C++ code to implement some critical parts of a simulation algorithm taught in class; a 2-point assignment requires implementing a more advanced algorithm with 2-300 lines of code; and for a 3-point assignment you need to finish the implementation of the central part a classical paper in physics simulation. You need to get 4 points in total for the full 40% assignment credits. You will obtain an up to 3% bonus if you finish 5 points or more for the programming assignments before the end of the quarter.

We encourage you to customize your path for programming practices. You may take four assignments in four different topics to get tastes of different simulation problems and then pick one theme for your final project. Or, You may also dive into one or two simulation topics that you are strongly interested in at the very beginning and fully develop your mathematical and programming skills by working on them intensively before you start your final project on the same topic.

You are encouraged to take advantage of your assignments and starter codes we have provided to help your final project. But the workloads for the assignments and the final projects need to be distinguished clearly and can't be double-counted.

Class Schedule:

The following is a tentative lecture schedule. It will be updated dynamically as the course proceeds.

Week 1: Introduction

Jan 3 (Th): Physical computing in animation, robotics, and fabricatoin

Week 2: Mathematical foundations

Jan 8 (Tu): Mathematical foundation of shape and motion

Jan 10 (Th): Particle system, collisions, and your first physics engine

Assignment 1 handed out

Week 3: Rigid body and drones

Jan 15 (Tu): Rigid body dynamics

Jan 17 (Th): PID control and Drones

Week 4: Articulation and character animation

Jan 22 (Tu): Articulation and inverse kinematics

Jan 24 (Th): Character animation, rigid-body robots

Week 5: Deformable body and 3D printing

Jan 29 (Tu): Deformable body and finite element method

Jan 31 (Th): Topology optimization, computational fabrication, and 3D printing

Assignment 3 handed out;Assignment 2 due

Week 6: Cloth and Origami

Feb 5 (Tu): Mass-spring model and cloth simulation

Feb 7 (Th): Thin shell, folding, and Origami

Week 7: Fluid and physically-based animation

Feb 12 (Tu): Introduction to fluid simulation

Feb 14 (Th): Particle fluid and visual special effects

Assignment 4 handed out;Assignment 3 due

Week 8: Multi-physics system and soft robots

Feb 19 (Tu): Solid-fluid interaction and soft robotic modeling

Feb 21 (Th): The 3D Printing Day, fabricate your own robot, in Thayer Machine Shop

Week 9: Real-time simulation

Feb 26 (Tu): Reduced models and fast simulations for games

Feb 28 (Th): The Drones Day, fly your own drone, location TBD

Assignment 4 due

Week 10: Not the end

Mar 5 (Tu): Summary: creating your own physical world

[Back to home]