Dexel is a concept used for a discretized representation of functions defined on surfaces used in geometrical modeling and physical simulation, sometimes also referred to as multilevel Z-map. Dexel is a nodal value of a scalar

Scalar

Scalar may refer to:*Scalar , a quantity used to multiply vectors in the context of vector spaces*Scalar , a quantity which is independent of specific classes of coordinate systems...

 or vector field

Vector field

In vector calculus, a vector field is an assignmentof a vector to each point in a subset of Euclidean space. A vector field in the plane for instance can be visualized as an arrow, with a given magnitude and direction, attached to each point in the plane...

 on a meshed surface. Dexels are used in simulation

Simulation

Simulation is the imitation of some real thing available, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system....

 of manufacturing

Manufacturing

Manufacturing is the use of machines, tools and labor to produce goods for use or sale. The term may refer to a range of human activity, from handicraft to high tech, but is most commonly applied to industrial production, in which raw materials are transformed into finished goods on a large scale...

 processes (such as turning

Turning

Turning is the process whereby a single point cutting tool is parallel to the surface. It can be done manually, in a traditional form of lathe, which frequently requires continuous supervision by the operator, or by using a computer controlled and automated lathe which does not. This type of...

, milling

Milling machine

A milling machine is a machine tool used to machine solid materials. Milling machines are often classed in two basic forms, horizontal and vertical, which refers to the orientation of the main spindle. Both types range in size from small, bench-mounted devices to room-sized machines...

 or rapid prototyping

Rapid prototyping

Rapid prototyping is the automatic construction of physical objects using additive manufacturing technology. The first techniques for rapid prototyping became available in the late 1980s and were used to produce models and prototype parts. Today, they are used for a much wider range of applications...

), when workpiece surfaces are subject to modifications. It is practical to express the surface evolution by dexels especially when the surface evolution scale is very different from the structural finite element 3D model discretization step (e.g. in machining the depth of cut variation is often several orders of magnitude smaller (1..10 microns) than the FE model mesh step (1 mm)).