Abstract: The number and complexity of the individual computations required to automatically identify geometrical constraints in a two dimensional model are reduced by indexing line vectors associated with individual line segments and tangent vectors associated with individual circular arcs in a polar quadtree index separate and distinct from a Cartesian quadtree index used to index individual points and circles, as well as the end points of the individual line segments and arcs, and the centers of the individual arcs. The Cartesian quadtree is used to identify constraints between point elements, and the polar quadtree is used to identify constraints between line elements. In order to determine whether there is a point-on relationship between a point element and a line element, the line element (which may be a Circle or an arc) is used to define one or more search paths through adjoining nodes of the Cartesian quadtree.

Abstract: A computerized method of drawing provides sketching-type drawing capabilities in a computer-aided design (CAD) environment. Geometrical drawing parts or elements, sketched through a hand-controlled indicator and lacking in the precision criteria or standards associated with formal drawings, are recognized and interpreted as points, straight lines, open arcs, circles and ellipses. Delete and “areafill” symbols, similarly, are recognized and interpreted. The method also provides the capability to distinguish and interpret relatively complex, multiple-part or element strokes. This is done by determining break locations for the elements along the stroke, and by recognizing these elements before re-constituting a stroke meeting precision criteria. A variety of geometrical constraints which are important in a CAD environment, including coincidence, parallelism, tangency and relimitation, are also recognized and imposed.

Abstract: The number and complexity of the individual computations required to automatically identify geometrical constraints in a two dimensional model are reduced by indexing line vectors associated with individual line segments and tangent vectors associated with individual circular arcs in a polar quadtree index separate and distinct from a Cartesian quadtree index used to index individual points and circles, as well as the end points of the individual line segments and arcs, and the centers of the individual arcs. The Cartesian quadtree is used to identify constraints between point elements, and the polar quadtree is used to identify constraints between line elements. In order to determine whether there is a point-on relationship between a point element and a line element, the line element (which may be a circle or an arc) is used to define one or more search paths through adjoining nodes of the Cartesian quadtree.