Each surface in DeskArtes can be considered to be made by taking a rectangular rubber sheet and stretching this over a framework of curves to form the correct shape. If the rubber sheet is removed and allowed to shrink to its original shape, this is called the parameter plane. The size of this parameter plane is determined by the number of points in the defining projection and cross-section curve.
For instance, a cylinder surface would be made by rolling the parameter plane around so that two of its boundaries meet each other. A torus would be made by bending the other two boundaries together, too.
The concept of the parameter plane is extremely important when dealing with trimmed surfaces. A trimmed surface is one where portions of the surface are cut away, normally by calculating an intersection with another surface. The cut is represented in DeskArtes by two-dimensional trim curves which are ‘drawn’ on the parameter plane. The trim curves can be considered as the lines which mark areas needed to be cut out in the rubber sheet before it is stretched into the shape of the surface. Since the rubber sheet is distorted during the stretching, so will the cut areas. The curves drawn on the parameter plane may not exactly be the shape of the final holes in the surface, though they will be similar.
In order to cut out a part of the surface, the trim curve must be closed. Closed trim curves are denoted in the Object Window as polygons.
Open trim curves (polylines) have no effect on the surfaces, thus, they are not taken into account in modeling or visualization computations, nor are they transported to the different data exchange formats.