In 3D computer graphics, polygonal modeling is an approach for modeling objects by representing their surfaces using polygons. The basic object used in polygonal modeling is a vertex, a point in three dimensional space. Two vertices connected by a straight line become an edge. Three vertices, connected to the each other by three edges, define a triangle, which is the simplest polygon. Four sided polygons (generally referred to as quads) and triangles are the most common shapes used in polygonal modeling. A group of polygons which are connected together by shared vertices is referred to as a mesh. As shown in the figure below, meshes are comprised of flat, faceted faces.
T-spline surfaces can be viewed as meshes or as smooth surfaces. The following is an example of a T-spline displayed as a mesh and as a smooth surface.
Box modeling (also known as subdivision modeling) starts with a simple box, and then modifies the box using extrusion to gradually add detail to the model. The final surface is a smoothed version of the box model.
Box modeling and basic polygonal modeling are not independent from each other and are often used together on the same model. While box modeling can be easier and faster to use, polygonal modeling is more versatile and allows for more detailed modeling and shape control. A design process that uses both these approaches can be adapted to many particular modeling situations.
How T-Splines modeling differ from other polygonal modeling methods