Geometry 1D Milestone

In computational geometry, we need to describe and manipulate geometric objects that are stored in the computer. To begin, we will look at geometry in one dimension, where we only have points and lines.

Topics we will need to learn include:

• representation of a point; representation of a line segment;
• distance between points; length of a line segment;
• "centroid" of a line segment; "centroid" of a set of N points;
• N evenly spaced points, or N random points, inside a line segment [A,B];
• is the point X inside the interval [A,B]?
• what is the smallest interval that contains a set of points?
• what point in that set of points is nearest this point?
• approximating an integral over [A,B] using evenly spaced or random points;