CSC 543

We covered material from Chapter 2 of the textbook and from the second chapter
of Shekhar, Chawla's *Spatial Databases, a
Tour*. Along the way, I mentioned the
Jordan
Curve theorem in topology, and we looked at a nice
Google Earth Demo.

**Submission**: you can submit the homework by hardcopy
in class or by sending it to me as an email.

1. [Representation Modes, 30pt] Pick a country of your choice and represent it in the field and object models:

a) In the field model choose a 10 x 10 square grid, overlay it with a picture of the country you've chosen (stretched to the boundaries) and mark the cells that would be listed as belonging to the country.

b) For the object model choose a polygonal representation of the country using a polygon with at most 10 points.

c) For both representations calculate the following parameters:

- length of boundary (field: sum up borders of squares, polygon, sum up length of lines)
- area (field: sum of areas of squares, polygon, see below)

Compare both parameters to the real values. How accurate are your approximate
values? *Hint*: to compute the area of the polygon, first triangulate it,
and then sum up the areas of the triangles. To calculate the area of a triangle
you can use Heron's
formula.

d) In the 10 x 10 square grid field model, suppose you have a country that has an area of 1 unit square. How badly off could the area approximation in the field model be (assuming the, fictitious, country could be horribly shaped)? Can you suggest a modification of the model that would fix this?

2) [KML and Google Earth, 25pt] Take the polygonal representation of your country from problem 1 and write it as a KML file that can be loaded into Google Earth. Add to it some additional shape (e.g. a lake in the country or a river). Google maintains a detailed list of KML examples too that'll help you do this. You'll need to install Google Earth and the browser plug-in.

Marcus Schaefer

Last updated: April 9th, 2009.