MIT
Department of Ocean Engineering

13.016 Introduction to Geometric Modeling and Computation

Spring 1997

Problem Set 3

Assigned: February 20, 1997
Due: February 27, 1997

  1. The upper longitudinal profile curve of an AUV is represented by two cubic planar parametric curves and , where and

    1. Write the equations in the matrix form of Ferguson representation.
    2. Convert them to Hermite-Coons curves using matrix operations.
    3. Explain why the Hermite basis functions satisfy the boundary conditions stated in Section 4.3.2 in the course notes.
    4. Write a C program to create a new AUV profile by using the Hermite formulation derived above and by changing the magnitude of the tangent vectors at u=0 and v=1. Experiment with a few different values (2-3) of the tangent vectors and see what happens. Hand in the plots of two new shapes created by your program, with the tangent vectors specified at these two end points, using OpenGL.

  2. Use the source code of the transformation demo shown in class to create a simple wireframe model of an AUV by rotating the profile curve in problem 1 by , and around the x-axis, i.e. the model is represented by these four curves.

    The source code, named ``demo1-xform.c'', can be accessed in the course locker by

    Copy the file to your directory, and replace the part which draws a cube with code to draw the AUV. You need to draw the profile curve on XY-plane first, translate it in the x direction such that the origin of the coordinate system is at some point inside the model, and then rotate it to create the other three curves. Hand in your plots which include:

    and email your code (only the part which draws the four curves) to glshen@mit.edu.