Question 3

How can you compute geometric relationships?

Every GIS user relies upon the calculation of:

• Perimeter
• Area
• Intersections (clipping, overlay, etc.)

Each of these depends on using coordinates to :

• represent lines (and sometimes as boundaries of areas)
• calculate local relationships

In other situations, the local relationships are used to construct the coordinates:

• coordinate geometry for parcels
• setbacks and offsets

• Find the parcel description for some piece of property that you care about. How would you use this to generate coordinates for this spatial object? What other information would be required? If you can visit this property, can you recover the corner markers? How would you measure the dimensions of the parcel and connect them to a coordinate system using different kinds of technology?
• ArcView wastes a huge amount of time redrawing the screen, particularly when zoomed in. Consider what software design (and data flow) you would need to provide quicker response to various kinds of graphic operations (zoom in, zoom out, pan, enlarge window, shrink window, etc.). Is a clipping engine the best tool for this?
• Examine the formulae used to calculate the area of a polygon (for example, see Warboys, page 214-215). Considering how computers store numbers, how would you implement this formula so that the result does not depend upon where the polygon is located with respect to the axis. HINT: consider what happens to the product of coordinates if you are within 1 KM of the origin versus being 20,000 km from the equator...
• It took some effort to move introduce the concept of "fuzzy intersections", but is a single tolerance enough? Think of some explanations for using a whole range of tolerances. How could these be implemented?

Your answers shouldn't be much longer than one page... See Lectures 7 and 8.