Polygon mesh in the context of "Triangle mesh"

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⭐ Core Definition: Polygon mesh

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.

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In this Dossier

Polygon mesh in the context of 3D test model

This is a list of models and meshes commonly used in 3D computer graphics for testing and demonstrating rendering algorithms and visual effects. Their use is important for comparing results, similar to the way standard test images are used in image processing.

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Polygon mesh in the context of Wire-frame model

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.

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Polygon mesh in the context of Discrete differential geometry

Discrete differential geometry is the study of discrete counterparts of notions in differential geometry. Instead of smooth curves and surfaces, there are polygons, meshes, and simplicial complexes. It is used in the study of computer graphics, geometry processing and topological combinatorics.

Discrete differential geometry (DDG) aims not merely to discretize objects or equations, but to discretize the entire theory of classical differential geometry. In this context, classical differential geometry is expected to emerge as a limit of refinement of the discretization. Furthermore, in the process of refinement, DDG places an emphasis on the so-called “mimetic” viewpoint, that is, whether the essential properties of the system from the smooth setting are exactly preserved regardless of the size of the mesh elements.

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Polygon mesh in the context of Constructive solid geometry

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.

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Polygon mesh in the context of Hidden-line removal

In 3D computer graphics, solid objects are usually modeled by polyhedra. A face of a polyhedron is a planar polygon bounded by straight line segments, called edges. Curved surfaces are usually approximated by a polygon mesh. Computer programs for line drawings of opaque objects must be able to decide which edges or which parts of the edges are hidden by an object itself or by other objects, so that those edges can be clipped during rendering. This problem is known as hidden-line removal.

The first known solution to the hidden-line problem was devised by L. G. Roberts in 1963. However, it severely restricts the model: it requires that all objects be convex. Ruth A. Weiss of Bell Labs documented her 1964 solution to this problem in a 1965 paper.In 1966 Ivan E. Sutherland listed 10 unsolved problems in computer graphics. Problem number seven was "hidden-line removal". In terms of computational complexity, this problem was solved by Frank Devai in 1986.

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Polygon mesh in the context of Volumetric mesh

In 3D computer graphics and modeling, a volumetric mesh is a polyhedral representation of the interior region of an object. It is unlike polygon meshes, which represent only the surface as polygons.

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