the map of the points and polygons of a model laid out in a 2 dimensial shape is brainly

Situations such as these are usually not desired and many packages support an auto-cleanup function. It is also possible for two vertices to exist at the same spatial coordinates, or two faces to exist at the same location. Many modeling programs do not strictly enforce geometric theory for example, it is possible for two vertices to have two distinct edges connecting them, occupying exactly the same spatial location. In many systems only one of these normals is considered valid – the other side of the polygon is referred to as a backface, and can be made visible or invisible depending on the programmer’s desires. Note that every triangle has two face normals, which point to opposite directions from each other. Some rendering systems use vertex normals instead of face normals to create a better-looking lighting system at the cost of more processing. Surface normals are useful for determining light transport in ray tracing, and are a key component of the popular Phong shading model. The flat nature of triangles makes it simple to determine their surface normal, a three-dimensional vector perpendicular to the triangle's surface. This is not necessarily true of more complex polygons, however. For this reason, triangles always inhabit a single plane. In Euclidean geometry, any three non-collinear points determine a plane. Each of the polygons making up an element is called a face. A group of polygons, connected to each other by shared vertices, is generally referred to as an element.

Four sided polygons (generally referred to as quads) and triangles are the most common shapes used in polygonal modeling. More complex polygons can be created out of multiple triangles, or as a single object with more than 3 vertices. Three vertices, connected to each other by three edges, define a triangle, which is the simplest polygon in Euclidean space. Two vertices connected by a straight line become an edge. The basic object used in mesh modeling is a vertex, a point in three-dimensional space. Alternate methods of representing 3D objects include NURBS surfaces, subdivision surfaces, and equation-based (implicit surface) representations used in ray tracers. Polygonal modeling is well suited to scanline rendering and is therefore the method of choice for real-time computer graphics. In 3D computer graphics, polygonal modeling is an approach for modeling objects by representing or approximating their surfaces using polygon meshes.

The map of the points and polygons of a model laid out in a 2 dimensial shape is brainly