Solid modeling in the context of Polygon (computer graphics)

In 3D computer graphics, a wire-frame model (also spelled wireframe model) is a visual representation of a three-dimensional (3D) physical object. It is based on a polygon mesh or a volumetric mesh, created by specifying each edge of the physical object where two mathematically continuous smooth surfaces meet, or by connecting an object's constituent vertices using (straight) lines or curves.

The object is projected into screen space and rendered by drawing lines at the location of each edge. The term "wire frame" comes from designers using metal wire to represent the three-dimensional shape of solid objects. 3D wireframe computer models allow for the construction and manipulation of solids and solid surfaces. 3D solid modeling efficiently draws higher quality representations of solids than conventional line drawing.

In 3D computer graphics and solid modeling, a polygon mesh is a collection of vertices, edges and faces that defines the shape of a polyhedral object's surface. It simplifies rendering, as in a wire-frame model. The faces usually consist of triangles (triangle mesh), quadrilaterals (quads), or other simple convex polygons (n-gons). A polygonal mesh may also be more generally composed of concave polygons, or even polygons with holes.

The study of polygon meshes is a large sub-field of computer graphics (specifically 3D computer graphics) and geometric modeling. Different representations of polygon meshes are used for different applications and goals. The variety of operations performed on meshes includes Boolean logic (Constructive solid geometry), smoothing, and simplification. Algorithms also exist for ray tracing, collision detection, and rigid-body dynamics with polygon meshes. If the mesh's edges are rendered instead of the faces, then the model becomes a wireframe model.

Geometric dimensioning and tolerancing (GD&T) is a system for defining and communicating engineering tolerances via a symbolic language on engineering drawings and computer-generated 3D models that describes a physical object's nominal geometry and the permissible variation thereof. GD&T is used to define the nominal (theoretically perfect) geometry of parts and assemblies, the allowable variation in size, form, orientation, and location of individual features, and how features may vary in relation to one another such that a component is considered satisfactory for its intended use. Dimensional specifications define the nominal, as-modeled or as-intended geometry, while tolerance specifications define the allowable physical variation of individual features of a part or assembly.

There are several standards available worldwide that describe the symbols and define the rules used in GD&T. One such standard is American Society of Mechanical Engineers (ASME) Y14.5. This article is based on that standard. Other standards, such as those from the International Organization for Standardization (ISO) describe a different system which has some nuanced differences in its interpretation and rules (see GPS&V). The Y14.5 standard provides a fairly complete set of rules for GD&T in one document. The ISO standards, in comparison, typically only address a single topic at a time. There are separate standards that provide the details for each of the major symbols and topics below (e.g. position, flatness, profile, etc.). BS 8888 provides a self-contained document taking into account a lot of GPS&V standards.

Constructive solid geometry (CSG; formerly called computational binary solid geometry) is a technique used in solid modeling. Constructive solid geometry allows a modeler to create a complex surface or object by using Boolean operators to combine simpler objects, potentially generating visually complex objects by combining a few primitive ones.

In 3D computer graphics and CAD, CSG is often used in procedural modeling. CSG can also be performed on polygonal meshes, and may or may not be procedural and/or parametric.