3. Geometric Theory

Geometric theory is the 3D software interpreting a 2d screen, using a Cartesian coordinates to represent geometry in 3D space. When using a 3D Cartesian coordinate system, which you can find in 3DS Max, is that it consists of 3 axis which is X, Y and Z.

 A polygon mesh is a collection of vertices, edges and faces that defines the shape of a polyhedral object. The faces usually consist of triangles, quadrilaterals or other simple polygons, but it may also me composed of more general concave polygons, or polygons with holes. Various operations can be performed on meshes; these include Boolean logic, smoothing, simplification and many others. Polygon meshes are made up of different elements, these include, vertices, edges, faces, polygons and surfaces.

The basic object used in mesh modeling is vertex, a point in three dimensional space. Two vertices connected by a straight line become an edge. Three vertices, connected to each other by three edges, define a triangle, which is the simplest polygon in Euclidean space. More complex polygons can be created out of multiple triangles, or as a single object with more than 3 vertices. Four sided polygons (generally referred to as quads) and triangles are the most common shapes used in polygonal modeling. A group of polygons, connected to each other by shared vertices, is generally referred to as an element. Each of the polygons making up an element is called a face.

A group of polygons which are connected by shared vertices is referred to a mesh.
In order for a mesh to appear attractive when rendered, it is desirable that it be non-self-intersecting, meaning that no edge passes through a polygon. Another way of looking at this is that the mesh cannot pierce itself. It is also desirable that the mesh not contain any errors such as doubled vertices, edges, or faces.