Content

"Content" (also called hypervolume) is a dimension independent name for length, area, volume, etc. We supply functions to compute the content (hypervolume) of simplices. We group the functions according to distance, area and volume.

If the dimension of the simplex is equal to the dimension of its vertices, then the content is signed. If the dimension of the simplex is less than the dimension of the vertices, then the content is unsigned. (The content is not defined when the dimension of the simplex is greater than the dimension of its vertices.) Examples:

• The area of a triangle in 2-D is signed. (Simplex dimension = vertex dimension = 2.)
• The area of a triangle in 3-D is unsigned. (Simplex dimension = 2. Vertex dimension = 3.)
• A triangle is 1-D does not have a well-defined area. (Simplex dimension = 2. Vertex dimension = 1.)