Sketch-based pruning of a solution space within a formal geometric constraint solver

A non-rigid cluster rewriting approach to solve systems of 3D geometric constraints

“…In fact, the problem of finding all real solutions of an arbitrary system of geometric constraints has been shown to be NP-complete [6]. Therefore, various solution selection schemes have been proposed, e.g., interactive approaches [5,18], genetic algorithms [19] and sketchbased methods [20]. Our solver supports two solution selection schemes, namely declarative solution selection [21] and prototype-based solution selection [22].…”

“…Typically, the prototype is obtained from a sketch created by the user. In [20] a formal framework is presented for sketch-based solution selection.…”

GA and CHC. Two Evolutionary Algorithms to Solve the Root Identification Problem in Geometric Constraint Solving

“…Possible different locations of geometric elements corresponding to different roots of systems of nonlinear algebraic equations can be distinguished by enumerating the roots with an integer index. For a more formal definition see [7,22].…”

“…Examples are: Selectively moving the geometric elements, conducting a dialogue with the constraint solver that identifies interactively the intended solution, and preserving the topology of the sketch input by the user. For a discussion of these approaches see, for example, references [1,7,20] and references therein.…”

Geometric Construction Problem Solving in Computer-Aided Learning

“…In education, the problems are given in a literal form, sometimes with an illustrative figure, and the teacher want the students to examine all the possible cases and in each case to find all the solutions . In CAD the statement of the problem is a dimensioned sketch and the user wants the solution which looks the most like the sketch (see [9] for more details on this subject).…”