Computer representation of surfaces

Open surfaces are not closed in either direction. This means moving in any direction along the surface will cause an observer to hit the edge of the surface. The top of a car hood is an example of a surface open in both directions.

Surfaces closed in one direction include a cylinder, cone, and hemisphere. Depending on the direction of travel, an observer on the surface may hit a boundary on such a surface or travel forever.

Surfaces closed in both directions include a sphere and a torus. Moving in any direction on such surfaces will cause the observer to travel forever without hitting an edge.

Places where two boundaries overlap (except at a point) are called a seam. For example, if one imagines a cylinder made from a sheet of paper rolled up and taped together at the edges, the boundaries where it is taped together are called the seam.

Some open surfaces and surfaces closed in one direction may be flattened into a plane without deformation of the surface. For example, a cylinder can be flattened into a rectangular area without distorting the surface distance between surface features (except for those distances across the split created by opening up the cylinder). A cone may also be so flattened. Such surfaces are linear in one direction and curved in the other (surfaces linear in both directions were flat to begin with). Sheet metal surfaces which have flat patterns can be manufactured by stamping a flat version, then bending them into the proper shape, such as with rollers. This is a relatively inexpensive process.

Other open surfaces and surfaces closed in one direction, and all surfaces closed in both directions, can't be flattened without deformation. A hemisphere or sphere, for example, can't. Such surfaces are curved in both directions. This is why maps of the Earth are distorted. The larger the area the map represents, the greater the distortion. Sheet metal surfaces which lack a flat pattern must be manufactured by stamping using 3D dies (sometimes requiring multiple dies with different draw depths and/or draw directions), which tend to be more expensive.

Surfaces closed in one or two directions frequently must also be broken into two or more surface patches by the software.

Surfaces and surface patches can only be trimmed at U and V flow lines. To overcome this severe limitation, surface faces allow a surface to be limited to a series of boundaries projected onto the surface in any orientation, so long as those boundaries are collectively closed. For example, trimming a cylinder at an angle would require such a surface face.

A single surface face may span multiple surface patches on a single surface, but can't span multiple surfaces.

Planar faces are similar to surface faces, but are limited by a collectively closed series of boundaries projected to an infinite plane, instead of a surface.

Volumes can be filled in to build a solid model (possibly with other volumes subtracted from the interior). Skins and faces can also be offset to create solids of uniform thickness.

A surface's patches and the faces built on that surface typically have point continuity (no gaps) and tangent continuity (no sharp angles). Curvature continuity (no sharp radius changes) may or may not be maintained.

Skins and volumes, however, typically only have point continuity. Sharp angles between faces built on different supports (planes or surfaces) are common.