https://bugs.kde.org/show_bug.cgi?id=505842
Bug ID: 505842
Summary: Intersection of a cubic and a vertical line is highly
unstable
Classification: Applications
Product: kig
Version First 25.04.2
Reported In:
Platform: KDE Linux
OS: Linux
Status: REPORTED
Severity: normal
Priority: NOR
Component: general
Assignee: [email protected]
Reporter: [email protected]
Target Milestone: ---
Created attachment 182419
--> https://bugs.kde.org/attachment.cgi?id=182419&action=edit
Construction corresponding to the description above
SUMMARY
With all the hype about elliptic functions and cryptography it comes handy the
possibility of kig
for the computation of the intersections of a cubic (actually a specific kind
of cubic) with a vertical line.
Of specific interest is the case where the vertical line is constructed through
a point that is itself constrained to the cubic. This triggers in kig the
computation of "other two intersections". If the cubic is symmetric about the
x-axis, then one of the intersections happens to be at infinity. This is not
actually taken into account by kig, which causes the instability of the result.
STEPS TO REPRODUCE
1. Construct the x-axis (line through two points with zero y-component)
2. Construct one point constrained on the x-axis and four points with positive
y-component with their reflection about the x-axis for a total of 9 points
3. Construct a cubic through those 9 points
4. Construct a point A constrained to the cubic
5. Construct the line through A perpendicular to the x-axis
6. Ask for the intersections of this line with the cubic
OBSERVED RESULT
The resulting visible intersection is highly unstable wrt perturbations of the
points defining the cubic.
EXPECTED RESULT
If the visible other intersection is named B, then we espect to continue to see
this point when we
move the defining points.
SOFTWARE/OS VERSIONS
Linux box with Fedora 41
ADDITIONAL INFORMATION
A patch that solves (or at least alleviates) the problem is available
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