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.


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


Instructor: Bo Zhu, office hours Wednesday 1pm-3pm (Sudikoff 153)

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


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

Location: TBD


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:

You will work on a final project either individually or in a group (with up to two members). The goal of the project is to build a small computational system to solve a physical problem, with some concrete application related to animation, robotics, design, fabrication, etc. The workload per person is approximately three times larger than one programming assignment. You can start from one of the programming assignments and extend it to a self-contained system, but you are always encouraged to start from scratch to work for your own ideas. A project proposal is required before the mid-term week to ensure the project take off on time.

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

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