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Here we distinguish two types of models, the geometric visual model (model):circles, points, lines, labels... and the geometric problem model (problem) points, lines, distances between points ... There are no circles as such.

A geometrical model whith one circle, the application gives a construction erroneous, though all its restrictions are well-defined. The error is, that not exist the circle-transformation of the model element to the problem, and continues to maintain the circle as a part of the problem. We say that solving the problem only works with:

Geometrics:

  • Points and lines

Constraints:

  • dpp (distance between points)
  • dpl (distance between point and line)
  • opl (point on line)
  • ...

So, a circle of the model must has to be transformed into another concept of the problem, such as a point (center), then for example, tangency between the two circles would be:

Circle c0 -> Point p1 (center c0)

Radius(c0) -> dpp(p1,p2), p2 belongs to c0

Circle c1 -> Point p3 (center c1)

Radius(c1) -> dpp(p3,p4), p4 belongs to c1

Tangency(c0,c1) -> dpp(p1,p3) = Radius(c0) +/- Radius(c1) = dpp(p1,p2) +/- dpp(p3,p4)

Defining the distance between points of the problem, the solution of the model will result in two circles united by a point. For example:

Model Problem Solution

As is not exist the transformation of a circle to a point, when we do the problem solution and it builds the Plan Construction, the element circle as is not a element of the problem (the problem only takes into account points and lines), returns null the Plan Construction, and as the evaluation analyzer is null, returns no solution.

Now we can to see attached a sequence diagram of the insertion of a circle as the first element of the model. We'll see all the way that makes the execution flow, and we'll see where it detects the failure of construction plan and it will not continues with the following assessments of the problem:

Sequence Diagram Paint Circle

Attachments