How to draw a circle tangent to two lines, trough two specific points?
Hi,
I suggest to try Geometric constraints which control the relationships of objects with respect to each other .
Imad Habash
Accepted solution
[Written before seeing Message 4's drawings] There will be a solution only if the two specific points are the same distance from the intersection of the Lines [or virtual intersection, if they don't meet each other]. There's a [white] Circle tangent to both [red] Lines at both [green] Points in the left arrangement that fits that description. But that's not possible in the other two, in which the [dashed white] Circle is tangent to the lower Line at the lower Point, and passes through the other Point, but clearly cannot be tangent to the other Line.
There would be an Ellipse that would be tangent to both Lines at both Points in the middle and right images. Finding it would be a challenge in the middle image, but easy in the right one where the Lines are perpendicular.
EDIT: An eye-balled approximation in your drawing:
Kent Cooper, AIA 
@Anonymous wrote:
How would I go about finding that elipse?
That's a real challenge, if even possible definitively, when the Lines are not perpendicular. In fact, there are an infinite number of solutions. My approximation is tangent to one Line at one of the Ellipse's quadrant points, which limits the solutions, but maybe that should not be assumed. And even given that assumption, that tangency condition could be at the Point on the other Line instead, with a different Ellipse. Even where a Circle solution is possible, there are an infinite number of possible Ellipse solutions at different aspect ratios, with an axis along the angle bisector:
I think at the very least you would need to come up with some more specific criteria, such as that it needs to be tangent at a quadrant point, and if so, at which of the two Points, or something.
Kent Cooper, AIA
Accepted solution
I would use a spline to draw your curve that is tangent at both ends at the indicated points. (screencast) . Although, in order to construct a "circle" that is tangent to both lines at specific points, the two points must have a perpendicular line that intersects at a line that bisects the angle of the two original lines.
Miljenko Hatlak
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@hak_vz wrote:
....
For ellipse consult this
That seems to be about finding the unknown tangency points D1 and D2 from known point A to an already-existing Ellipse, and therefore finding unknown tangent lines t1 and t2. What the OP is trying to do is to find the Ellipse, starting from already having known Lines t1 and t2 and known point A and known points D1 and D2. That's a very different animal, and not just some kind of reversal of the process, since that webpage's approach requires knowing where the focal points of the Ellipse are, but of course in what the OP wants, those are unknown. [And they can't be known, since there are infinite solutions at different Ellipse aspect ratios.]
Kent Cooper, AIA
@Kent1CooperThis image is about general rules of tangents for ellipse. As you say there are infinite numbers of ellipses that can be constructed. If nearly symmetrical triangle is created with nearly equal distance P1A P2A it leads to Steiner inellipse.
When two tangents are orthogonal this two points can be taken as vertex end co-vertex of a ellipse and it leads to construction of ellipse with center point method, as you have shown in your previous post. When tangents are not orthogonal solution require complex calculations.
Miljenko Hatlak
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