Triangles Milestone

In the 2D geometry milestone, we already saw how to represent points, and how to describe a polygonal shape by a sequence of points called vertices. The most basis interesting polygon is the triangle, and we can understand a lot about any polygon if we first learn about triangles.

Topics we will need to learn include:

• representing a triangle as a 3x2 array of coordinates; as a list of the coordinates of 3 points; as a list of the indexes of 3 points whose coordinates are listed elsewhere;
• the counter-clockwise convention for describing triangles;
• the length of each edge of a triangle;
• the angles of a triangle;
• the centroid of a triangle;
• the area of a triangle;
• generating a regular grid of points in a triangle;
• generating random points in a triangle;
• is a point inside a triangle?
• the barycentric coordinates of a point with respect to a triangle.
• estimating an integral over a triangle;