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### Object Relative Position

The object relative position of a feature describes where it is with respect to the complete object. Position is defined in terms of the location of the feature and its orientation. Each of these is described in two ways: relative to the major and minor axes of the whole object, and relative to other features.

The location of a feature with respect to the whole object is described in terms of a reference point on the feature. The reference point for an edge, curve, or imple is the centre of the chord or waist axis, and the reference point for a vertex is the vertex point. The position of this point in a two dimensional space defined by the major and minor axes of the object is described by stating which end of each axis the point is nearest to, and how near it is.

The location of a feature with respect to other features is described by the order in which the features appear when the boundary of the object is being traversed in a clockwise direction. This description is independent of the overall shape of the object, but features which cannot be directly related to the boundary do not have any description of this type.

Orientation relative to the overall shape is specified in terms of a reference direction derived from the axes of individual features. The reference direction for curves and straight edges is the normal to the chord axis, the reference direction for vertices is the vertex axis, and imples are multiply defined in terms of several reference directions: the normal to the imple waist, the major axis of the imple shape itself, and the minor axis of that shape. The orientation of these feature reference directions with respect to the rest of the object can be described by a qualitative direction space oriented to the intersection of the major and minor axes. This qualitative centroid provides an origin by which four quadrants around the object centre can be defined. These four quadrants then produce a range of qualitative direction values with four distinguished directions, and four value ranges.

Orientation with respect to other features is only specified where there are special relationships between two features, since relating each feature to every other feature would become very complex for more than a few objects. The particular relationships defined are those between parallel, aligned, or perpendicular axes. Lists are maintained of every set of features in a scene which are parallel or aligned; where two of these sets are perpendicular to each other, that is also noted.

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