CS-511 - Assignment 5 (optional)

Particle system dynamics

Due by: December 4, 2008

Assignment Specifications

In this assignment you need to implement a mass-spring system containing multiple particles and multiple forces. The implementation should be done by forming and solving a system of differential equations, or by using Verlet integration (velocity-free implementation). The specific application targeted is that of a mass-spring system with a global gravitational force. Each spring used in the simulation should be accompanied by a damper. The springs and dampers are assumed to have identical spring/damping constants throughout the system and possibly different rest lengths. The mass of all the particles is assumed to be identical. The time step of the simulation should be set through a command line argument. Possible applications include ONE the following:

• Non-rigid cube simulation: Create a cube composed of identical springs along the edges and particles in the vertices. Add additional springs along the main diagonals of the cube with a rest length that preserves the shape of the cube. Position the cube on a ground plane. When pressing ``r'' on the keyboard a horizontal force parallel to the x-axis with a magnitude of $f$ should be applied to one of the top corners of the cube for a total of $n$ time steps. Assume friction between the cube and the ground plane with a friction coefficient of $k$. The constants $f$, $n$, $k$ should be set through command line arguments. Simulate the motion of the particles composing the cube and render its faces.

• Cloth simulation: Create a rectangular sheet composed of identical springs along a rectangular mesh of grid lines. Place particles at grid junctions. Add additional springs along the main diagonals of each square with a rest length that preserves the shape of the square. Position the sheet on the ground plane. When pressing ``r'' on the keyboard, a vertical force parallel to the y-axis with a magnitude of $f$ should be applied to the particle in the center of the sheet for a total of $n$ time steps. Assume friction between the sheet and the ground plane with a friction coefficient of $k$. The constants $f$, $n$, $k$ should be set through command line arguments. Simulate the motion of the particles composing the sheet and render its faces. Make sure to prevent self intersection by the cloth.

Common requirements

• Make sure to render the ground plane.
• Pressing the ``1''/''2'' keys should increase/decrease the spring constant.
• Pressing the ``3''/''4'' keys should increase/decrease the damper constant.
• Pressing the ``5''/''6'' keys should increase/decrease the gravitational constant.
• pressing the arrow keys should rotate the camera around the object.
• Pressing the ``+''/''-'' keys should zoom in/out.

General notes

• Late days are not allowed for this assignment.
• Use SVL/VL for vector operations and OpenGL for rendering.
• Support code for this assignment will be provided.
• Please follow the submission procedure of assignment 1.