CS451: Advanced Computer Graphics

CS451: Advanced Computer Graphics
Spring 2008

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Programming Assignment 2: Procedural seashells

Due Thursday, Mar. 13

Overview

For this assignment, you will implement a procedural technique for generating geometric models of seashells described by Fowler et al. 92.

0. Starter Code

Download the starter code and get it to compile. You'll need to install the GLUT and FLTK libraries. The mouse/key functions are as follows:

Left mouse button: rotate
Middle mouse button (or left and right held together): translate
Right mouse button: zoom
Space bar: reset to the initial view
'e' key: toggle drawing mesh edges
'c' key: toggle drawing coordinate system axes
'm' key: toggle between viewing modes (shell view or curve view)
'q' or 'Esc' key: quit

1. Splines (20%)

Write code to compute and draw a B-spline using the 10 control points that may be positioned in the 'curve' viewing mode.

2. Frenet Frames (30%)

Write code to compute the orthonormal axes defining the Frenet frame at an arbitrary position along the helico spiral (i.e., for an arbitrary value of the parameter t).
Extend your program to visualize the Frenet frame at an arbitrary parameter value (e.g., simply draw the coordinate axes as small line segments).
Write code for transforming points defined in the coordinate system in which the generating curve is defined to the coordinate system defined by the Frenet frame at an arbitrary position along the helico spiral. In the notation used in Fowler 92, this transformation allows mapping points in the (u,v,w) coordinate system to the (e_1, e_2, e_3) coordinate system. It's OK to support only 2D generating curves (i.e., w=0).
Extend your program to draw the generating curve appropriately scaled and aligned to the Frenet frame at an arbitrary parameter value along the helico spiral.

3. Swept Surfaces (40%)

Write code to triangulate the surface of the shell by sweeping the generating curve along the helico spiral. This is done by first identifying n+1 evenly spaced points on the generating curve (including its endpoints). Next, connect corresponding points for consecutive positions of the generating curve along the spiral. Store the resulting vertices and faces in the simple indexed face data structure included in the starter code so that the shell will be displayed during the normal rendering cycle. You may also want to re-triangulate the surface whenever the parameters change that determine its shape.

Ensure that you select the n+1 points so that they are evenly spaced in terms of arc length, using the procedure outlined in Section 2.4 of the paper.

Also implement support for modulating the radial distance of the generating curve as it is swept along the helico spiral as described in Section 2.5 of the paper. This allows giving the surface a sculpted shape like the examples in Figures 7, 8, 9, and 10.

4. Writeup and Analysis (10%)

Please submit your source code together with a writeup (as HTML) that contains a description of the design decisions you made and results. At a minimum, you should include screenshots of three different shells you created with your system. Feel free to either try and model some of the examples shown in the paper, create entirely new and interesting shapes, or do a bit of both.

Extra Credit: Activator-Substrate Model for Pattern Generation (10%)

Implement the activator-substrate model described in Section 3.1 (or the activator-inhibitor model described in Section 3.2) to generate color patterns for your shells. Experiment with the various rates of decay and growth and include a discussion of these decisions (along with screenshots) in your write-up.

Submitting

Please make your writeup and code accessible via the web, and send the URL to rpw7e@cs.virginia.edu with "CS451" in the subject line. Please see the general notes on submitting your assignments, as well as the late policy and the collaboration policy.