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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.
The points, lines, and polygons of a polyhedron are referred to as its vertices, edges, and faces, respectively. [1] A polyhedron is considered to be convex if: [2] The shortest path between any two of its vertices lies either within its interior or on its boundary. None of its faces are coplanar—they do not share the same plane and do not ...
A Johnson solid is a convex polyhedron whose faces are all regular polygons. [1] Here, a polyhedron is said to be convex if the shortest path between any two of its vertices lies either within its interior or on its boundary, none of its faces are coplanar (meaning they do not share the same plane, and do not "lie flat"), and none of its edges are colinear (meaning they are not segments of the ...
Solid modeling (or solid modelling) is a consistent set of principles for mathematical and computer modeling of three-dimensional shapes . Solid modeling is distinguished within the broader related areas of geometric modeling and computer graphics , such as 3D modeling , by its emphasis on physical fidelity. [ 1 ]
Another important class of simple polygons are the star-shaped polygons, the polygons that have a point (interior or on their boundary) from which every point is visible. [ 2 ] A monotone polygon , with respect to a straight line L {\displaystyle L} , is a polygon for which every line perpendicular to L {\displaystyle L} intersects the interior ...