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A mesh edge is defined by a pair of integers hv0,v1i, each integer corresponding to an end point of the edge. To support edge maps, the edges are stored so that v0 = min(v0,v1). A triangle component is defined by a triple of integers hv0,v1,v2i, each integer corresponding to a vertex of the triangle.
Face-vertex meshes represent an object as a set of faces and a set of vertices. This is the most widely used mesh representation, being the input typically accepted by modern graphics hardware. Face-vertex meshes improve on VV mesh for modeling in that they allow explicit lookup of the vertices of a face, and the faces surrounding a vertex.
In the edge (x, y) directed from x to y, the vertices x and y are called the endpoints of the edge, x the tail of the edge and y the head of the edge. The edge is said to join x and y and to be incident on x and on y. A vertex may exist in a graph and not belong to an edge. The edge (y, x) is called the inverted edge of (x, y).
This is a remake of "Ecke Kante Fläche" by Klaus-Dieter Keller, modified to be a bit more accessible: the vertex and edge highlights are bigger, and all the higlights have some white space around them so that they stand out even when the difference in colour can't be seen.
Most attributes of a vertex represent vectors in the space to be rendered. These vectors are typically 1 (x), 2 (x, y), or 3 (x, y, z) dimensional and can include a fourth homogeneous coordinate (w). These values are given meaning by a material description. In real-time rendering these properties are used by a vertex shader or vertex pipeline.
In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes . For example, a square vertex arrangement is understood to mean four points in a plane, equal distance and angles from a center point.
A face is a bounded portion of a surface; an edge is a bounded piece of a curve and a vertex lies at a point. Other elements are the shell (a set of connected faces), the loop (a circuit of edges bounding a face) and loop-edge links (also known as winged edge links or half-edges) which are used to create the edge circuits. [2]
graph join: . Graph with all the edges that connect the vertices of the first graph with the vertices of the second graph. It is a commutative operation (for unlabelled graphs); [2] graph products based on the cartesian product of the vertex sets: