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The boundary representation for a solid object, its surface, is a polygon mesh of vertices, edges and faces. Its topology is captured by the graph of the connections between faces. Its topology is captured by the graph of the connections between faces.
In solid modeling and computer-aided design, boundary representation (often abbreviated B-rep or BREP) is a method for representing a 3D shape [1] by defining the limits of its volume. A solid is represented as a collection of connected surface elements, which define the boundary between interior and exterior points.
In elementary geometry, a face is a polygon [note 1] on the boundary of a polyhedron. [3] [4] Other names for a polygonal face include polyhedron side and Euclidean plane tile. For example, any of the six squares that bound a cube is a face of the cube. Sometimes "face" is also used to refer to the 2-dimensional features of a 4-polytope.
A simple polygon is the boundary of a region of the plane that is called a solid polygon. The interior of a solid polygon is its body, also known as a polygonal region or polygonal area. In contexts where one is concerned only with simple and solid polygons, a polygon may refer only to a simple polygon or to a solid polygon.
A common compactness measure is the isoperimetric quotient, the ratio of the area of the shape to the area of a circle (the most compact shape) having the same perimeter. . In the plane, this is equivalent to the Polsby–Popper t
A supporting plane is a plane that intersects the boundary of D but not the interior of D. One defines the width of the body as before. If the width of D is the same in all directions, then one says that the body is of constant width and calls its boundary a surface of constant width, and the body itself is referred to as a spheroform.