QCAD Bugtracker

Attached to Project: QCAD Bugtracker
Opened by CVH - 23.04.2024
Last edited by CVH - 28.02.2025

Andrew,

If a given point p is on the major axis then REllipse::getVectorTo(p) returns one of the major points. In the code this is handled as a special case when the point is in-line (collinear) with the major axis.
This is only correct for points outside the evolute.

On the major axis is defined by getAngle().
This may fail for a magnitude equal to or less than 1e-6.
A point that close to the center should not have a single solution at zero degrees.

The correct solutions are:
- If p is equal to the center ⇒ Two vectors to the two minor points.
- On the major axis and strictly inside the evolute ⇒ Two mirrored vectors.
- On the major axis and on or outside the evolute ⇒ The nearest major point.
- On the minor axis ⇒ The nearest minor point.

An additional problem is now what to return on a duality with full ellipses.
Or for an ellipse arc where both of two results are valid.
getVectorTo() typically returns but one unique result.

For example:
RCircle::getVectorTo(p) returns an invalid vector when the point is near the center.
Then there are an unlimited number of solutions.

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Further discovered that the point related to the returned vector may fail x²/a²+y²/b²=1
Although almost on the ellipse within 2.299e-10 ... f(x,y) may return 9.5310
This example would fail REllipse::contains while the border is considered as inside.

Meanwhile implemented a ‘simple method’ to find the nearest point(s) on an ellipse.
Fast converging in 3 steps, no trigs and very accurate, about 24 lines of code.
f(x,y) returns mostly 1.000 with so far:
- a minimum of 0.9999999999999997
- a maximum of 1.0000000000000007.
In other words, it is only off for the last meaningful decimal digit.

With this all methods that are based on REllipse::getVectorTo(p) can be implemented very reliable with tolerance, border flag, ... and so on.
By default the normal for a point is given with high accuracy and a tangent is that rotated.
...
..
.

Regards,
CVH