Project 5

Listing 232 on page 306 of the textbook outlines a file named problem-spec.c which contains the descriptions of four domains that are used to illustrate the various capabilities of Triangle. The file mesh-demo.c described in Section 23.7 provides the driver (function main()) that invokes those descriptions and triangulates all four domains.

In retrospect, defining four domains in a single file, and triangulating them all at once, is not such a great idea. It will make better sense to split the monolithic demo into four individual demos.

Consider, therefore, replacing problem-spec.c with four files

square-spec.c
triangle-with-hole-spec.c
annulus-spec.c
three-holes-spec.c,

that contain domain descriptions, and replacing mesh-demo.c with four individual drivers

square.c
triangle-with-hole.c
annulus.c
three-holes.c.

That simplifies the coding since the domains may be coded and debugged individually. It also makes it easy to add new domains without disturbing the existing ones.

Graphics in python

The book suggests producing graphical representation of the generated meshes through the supplied files mesh-to-eps.[ch]. These provide a function mesh_to_eps() that receives a mesh structure and an output file name, e.g., square.eps, it extracts the triangulation information from the mesh structure and writes a PostScript script into the file square.eps that can be fed into a PostScript viewer for viewing.

With the wide availability of python in these days, it may be convenient to use python's matplotlib plotting utility instead. That provides you the additional opportunity of writing your own equivalent of mesh-to-eps.[ch], let's call it mesh-to-py.[ch], which receives a mesh structure and an output file name. It extracts the triangulation information from the mesh structure and writes a python script, say square.py, that can be fed into python for viewing.

Here is a minimal sample of a python plotting script:

import matplotlib.pyplot as plt plt.rcParams['axes.prop_cycle'] = plt.cycler(color=['black']) plt.gca().set_aspect('equal') plt.plot([1,2],[4,7]) plt.plot([4,2],[0,4]) plt.show()

The first three lines and the last line are always the same. Each of the remaining two lines draws a line segment. The syntax for drawing a line from the point (x₁,y₁) to the point (x₂,y₂) is

plt.plot([x₁,x₂],[y₁,y₂])

You may repeat that line as many times as needed. If the script is written to a file try-me.py, you may view the graphics by entering

python try-me.py

on the Unix command-line.

Thus, write files mesh-to-py.[ch] that provide a function, say

void mesh_to_py(struct mesh *mesh, char *outfile);

that receives a mesh structure, walks through the mesh->edges array, determines the coordinates of the endpoints of each edge, and writes a python script in the outfile. for plotting the mesh.