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The point-slope form of a line through the point (x_1,y_1) with slope m in the Cartesian plane is given by y-y_1=m(x-x_1).

The diameter of a polygon is the largest distance between any pair of vertices. In other words, it is the length of the longest polygon diagonal (e.g., straight line segment ...

The breaking up of self-intersecting polygons into simple polygons (illustrated above) is also called tessellation (Woo et al. 1999).

A line segment where two faces of a polyhedron meet, also called a side.

A point at which three or more polyhedron edges of a polyhedron meet. The concept can also be generalized to a polytope.

A one-dimensional line segment where two two-dimensional faces of an n-dimensional polytope meet, also called a side.

A polytope in n-dimensional Euclidean space R^n whose vertices are integer lattice points but which does not contain any other lattice points in its interior or on its ...

At each point on a given a two-dimensional surface, there are two "principal" radii of curvature. The larger is denoted R_1, and the smaller R_2. The "principal directions" ...

A polygon vertex x_i of a simple polygon P is a principal polygon vertex if the diagonal [x_(i-1),x_(i+1)] intersects the boundary of P only at x_(i-1) and x_(i+1).

The volume of a prismatoid is equal to the sum of the volumes of a pyramid, a wedge, and a parallelepiped.