Spheres - Spheres are commonly represented in one of two ways:.Specialized or esoteric primitives, such as the Utah Teapot or Suzanne, Blender's monkey mascot.2D primitives, such as squares, triangles, and disks.This ensures that the model will be symmetrical.Īnother common method of creating a polygonal mesh is by connecting together various primitives, which are predefined polygonal meshes created by the modeling environment. In general, the artist will model half of the head and then duplicate the vertices, invert their location relative to some plane, and connect the two pieces together. This method is especially common for creating faces and heads. The user then uses a second image of the subject from a different angle and extrudes the 2D shape into 3D, again following the shape’s outline. In this method, the user creates a 2D shape which traces the outline of an object from a photograph or a drawing. Thus, performing the extrude operation on a square face would create a cube connected to the surface at the location of the face.Ī second common modeling method is sometimes referred to as inflation modeling or extrusion modeling. It creates a new face of the same size and shape which is connected to each of the existing edges by a face. The extrude tool is applied to a face or a group of faces.
For example, a square would be subdivided by adding one vertex in the center and one on each edge, creating four smaller squares. The subdivide tool splits faces and edges into smaller pieces by adding new vertices.One of the more popular methods of constructing meshes is box modeling, which uses two simple tools:
A wide variety of 3D graphics software packages are available for use in constructing polygon meshes. For some purposes it is important that the mesh be a manifold – that is, that it does not contain holes or singularities (locations where two distinct sections of the mesh are connected by a single vertex).Ĭonstruction of polygonal meshes Īlthough it is possible to construct a mesh by manually specifying vertices and faces, it is much more common to build meshes using a variety of tools. It is also desirable that the mesh not contain any errors such as doubled vertices, edges, or faces. Another way of looking at this is that the mesh cannot pierce itself. 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. If auto-cleanup is not present, however, they must be deleted manually.Ī group of polygons which are connected by shared vertices is referred to as a mesh. 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.