This paper describes a method for finding the rectangle of minimum area in which a given arbitrary plane curve can be contained. The method is of interest in certain packing and optimum layout problems. It consists of first determining the minimal-perimeter convex polygon that encloses the given curve and then selecting the rectangle of minimum area capable of containing this polygon. Three theorems are introduced to show that one side of the minimum-area rectangle must be collinear with an edge of the enclosed polygon and that the minimum-area encasing rectangle for the convex polygon is also the minimum-area rectangle for the curve.
This paper describes a new technique for modeling 3D objects that is applicable to recognition tasks in advanced automation.Objects are represented in terms of canonic 2D models which can be used to determine the identity, location and orientation of an unknown object. The reduction in dimensionality is achieved by factoring the space of all possible perspective projections of an object into a set of characteristic views, where each such view defines a characteristic -view domain within which all projections are topologically identical and related by a linear transformation. The characteristic views of an object can then be hierarchically structured for efficient classification. The line -junction labelling constraints are used to match a characteristic view to a given unknown -object projection, and determination of the unknown -object projection -to-characteristic view transformation then provides information about the identity as well as the location and orientation of the object.
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