Next: Relative Size Up: Describing 2D Shape With Previous: Describing 2D Shape With

### Primitive Shape

The basic components of the extended polygon boundary are ``segments'', and ``junctions'' between segments. A segment is a qualitatively homogeneous length of boundary corresponding to an edge of the extended polygon. A junction is the place where two homogeneous lengths of boundary meet, corresponding to a vertex in the extended polygon. Segments and junctions are both types of boundary ``element'' (in fact, all boundary elements are either segments, or junctions).

The term ``qualitatively homogeneous'' is used to describe either a straight line segment, a curve without discontinuities, or a wiggle, which is an untidy piece of boundary that is differentiated from other tidier segments by transitions at each end.4.2

These three types of boundary elements were derived from the shape features described above as part of the ASSF representation. Table 4.1 summarises the types of boundary element that are required to describe a wide range of 2D shape in a mechanical domain.

Table 4.1: Boundary Element Types
 Element Type Shape Attributes segment line length curve length angle concave/ convex bulge wiggle length period bulge junction angle concave/ convex

The range of values which can be assumed by the angle, bulge, and period attributes are the same as those used in the ASSF representation, and were chosen for the same reasons given in the previous section.

The EPB representation supports multiple levels of shape detail with a mechanism for defining one or more simple elements as an alternative to complex portions of the boundary.4.3 Operations which do not need exact data can then deal solely with the simplified boundary elements where it is appropriate. It is possible to nest these parallel representations, so that an overall shape can be progressively simplified.

Parallel representation can also be used to provide alternative descriptions of single shape features. For example, a knife with a serrated edge can be treated the same as a knife with a straight edge for most operations - the serrations are only a significant detail when the knife is sliding along that edge. The parallel representation can be used in this case to describe the knife-edge segment of the knife boundary as a line on the coarse branch of the parallel description, and as a wiggle on the fine branch.

The same approach can be used to describe manufacturing features such as fillets or chamfers. A curved boundary segment with a small radius can be described at a coarse level as a simple junction between the segments on either side of it. The transformation between curve and junction retains the angle of the curve in the junction description, and discards the curve size.

Next: Relative Size Up: Describing 2D Shape With Previous: Describing 2D Shape With
Alan Blackwell
2000-11-17