tangent to two entities, through a point, when the point belongs to one of the two entities

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mangel
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tangent to two entities, through a point, when the point belongs to one of the two entities

Post by mangel » Mon Sep 27, 2021 6:32 pm

When I use the tool: tangent to two entities, through a point, and the point belongs to one of the two entities, Qcad does not solve the problem.

Works well if there are two lines,
but if it is a line and a circle gives false solutions,
and if it is two circles say that there is not solutions.

Tested in Debian Gnu/linux 10 and Qcad 3.26.4.0

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Husky
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Re: tangent to two entities, through a point, when the point belongs to one of the two entities

Post by Husky » Mon Sep 27, 2021 7:08 pm

mangel wrote:
Mon Sep 27, 2021 6:32 pm
When I use the tool: tangent to two entities, through a point, and the point belongs to one of the two entities, Qcad does not solve the problem.
Sorry, never heard about a tool called "Tangent to two entities". I know about a tool called "Tangent two circle (LT2) which works between two circle. Is that the tool what you refer to?
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andrew
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Re: tangent to two entities, through a point, when the point belongs to one of the two entities

Post by andrew » Mon Sep 27, 2021 8:19 pm

mangel: please attach your drawing file with the two tangential entities and indicate which exact tool you are using, thanks.

CVH
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Re: tangent to two entities, through a point, when the point belongs to one of the two entities

Post by CVH » Tue Sep 28, 2021 7:23 am

mangel wrote:
Mon Sep 27, 2021 6:32 pm
When I use the tool: tangent to two entities, through a point, and the point belongs to one of the two entities, Qcad does not solve the problem.
Husky wrote:
Mon Sep 27, 2021 7:08 pm
Sorry, never heard about a tool called "Tangent to two entities".
Draw circle tangential to two entities, through a point (CT2).
Andrew, all my findings are in the attached dxf files ... Not limiting. :wink:

- With 2 lines and a point on one of the lines QCAD presents 2 correct solutions.
The indicated point is then the (forced) tangent point with that line.
Solutions reduce to one unique if the lines are parallel.

- With a circle, a line and a point on the line QCAD may present 4 solutions of which none is correct.
If the indicated point is exactly the center projected perpendicular on the line, a lucky shot or by an auxiliary line, ...
... then 2 correct solutions are presented.
With 4 solutions it is clearly visible that the indicated point is an intersection with the line and that all the solutions intersect twice.
CT2-Line-Circle-Point.dxf
(103.38 KiB) Downloaded 27 times
For the correct solutions:
The tangent point of two circles is on a line through both centers. (Cyan)
And the center of a circle tangent to a line is on a line orthogonal in the tangent point. (Blue)
One can find these correct solutions by the intersection of 2 incorrect solutions. :P :wink:

- Analog with a line, a circle and a point on the circle.

- With two circles there will not be a solution for a point inside one of the circles.
The solution can't be and tangent to and crossing the circle at the same time.
For a point outside the circles 4 solutions may be presented. Not all 4 are correct in all cases.
CT2-Circle-Circle-Point-1.dxf
(101.41 KiB) Downloaded 24 times
For a point on one of the circles there are no solutions presented.
These can be found by mirroring the other circle over the symmetry axis center - point and matching solutions of 3 tangents (CT3). :P :wink:
CT2-Circle-Circle-Point-2.dxf
(101.88 KiB) Downloaded 31 times

This knowledge is gathered in the past few months while I investigated how to round all corners of bulging polylines.
It boils down to what is considered tangent, what is the intersection of two circles, and how arc segments are prepended/appended to a polyline.
The tool is perfectly functional up to a point where the numbers don't add up anymore. They should mathematically.

Regards,
CVH


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