Review Request 127364: improving CircleCircleIntersection (towards what geogebra does)

[Maurizio Paolini]

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https://git.reviewboard.kde.org/r/127364/
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Review request for KDE Edu, David Narváez and Rex Dieter.


Repository: kig


Description
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I am addressing two related issues: intersection points that jump, circles degenerating to lines.
When intersecting circles obtained as "circle by 3 points" it is possible that one or both degenerate into a straight line.  At present when dinamically moving one of the three defining points of a circle across the line through the other two, the two intersection points exchange position, possibly causing the subsequent constructions to change abruptly.
The other related issue is that at the moment the intersection point is not defined when one
of the two circles degenerate into a line.

Motivation: this situations naturally arise, for example, when trying to construct the Disk Poincare' model of the hyperbolic plane, in which case it is essential to allow for circles to become lines.

A sample kig file that exposes these issues is available as http://dmf.unicatt.it/~paolini/kig/bugs/test_circle_intersection_old.kig

The big black points can be moved across the other two defining one of the two circles, observe that the two intersection points exchange position.  Moreover, if a black point
is precisely aligned with the other two (press the shift key to force the point
onto the grid), then the two intersection points disappear.


Diffs
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  misc/builtin_stuff.cc e1de877 
  misc/common.cpp 2e1fac9 
  objects/circle_imp.h dc63e06 
  objects/circle_imp.cc 7450ef6 
  objects/circle_type.h 37cf400 
  objects/circle_type.cc 25ec233 
  objects/intersection_types.cc 2fd07be 
  objects/special_imptypes.cc 62e52a9 

Diff: https://git.reviewboard.kde.org/r/127364/diff/


Testing
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Unfortunately, to address the "abrupt intersection points exchange" it seems necessary to add a (hidden) circle orientation for CircleImp(s).  In the proposed patch this is achieved by allowing the "mradius" member to be negative (it is "private", so that we to not risk to expose this possibility; radius() method will now return the absolute value of mradius, and the new "orientation()" method returns the circle orientation).

The additional 'orientation' information can then be used inside the CircleCircleIntersection::calc to avoid the abrupt jump of the intersection points.

The new CircleBTPoType class constructs an "oriented" circle (note that the user will not
be able to directly access the orientation information), whereas the old CircleBTPType is left unchanges.  CircleBTPoType substitutes CircleBTPType in builtin_stuff.cc.
In this way we ensure backward compatibility for old saved kig files, whereas new constructions will take advantage of the orientation.

Alternatively we can simply substitute the present CircleBTP with the new version.


Thanks,

Maurizio Paolini

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