Empathy List Archives

JW

Joe Weinpert

Mon, May 2, 2022 9:58 PM

How do you find the X/Y tangent positions of circles tangent to an ellipse?

The ellipse is 3x4
The .655 dia circle on the outside is at 3.000x
The 1.200 dia circle on the inside is at 2.000x

How would the Y positions of those circles be determined?

How would the X/Y positions of the tangents be determined?

What would the proper formula be?

[image: ellipseTangents.png]

How do you find the X/Y tangent positions of circles tangent to an ellipse? The ellipse is 3x4 The .655 dia circle on the outside is at 3.000x The 1.200 dia circle on the inside is at 2.000x How would the Y positions of those circles be determined? How would the X/Y positions of the tangents be determined? What would the proper formula be? [image: ellipseTangents.png]

BL

Bryan Lee

Mon, May 2, 2022 10:35 PM

Thus Joe Weinpert hast written on Mon, May 02, 2022 at 05:58:42PM -0400, and, according to prophecy, it shall come to pass that:

How do you find the X/Y tangent positions of circles tangent to an ellipse?

The ellipse is 3x4
The .655 dia circle on the outside is at 3.000x
The 1.200 dia circle on the inside is at 2.000x

How would the Y positions of those circles be determined?

How would the X/Y positions of the tangents be determined?

What would the proper formula be?

ellipseTangents.png

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Ellipse related: https://www.youtube.com/watch?v=5nW3nJhBHL0 Thus Joe Weinpert hast written on Mon, May 02, 2022 at 05:58:42PM -0400, and, according to prophecy, it shall come to pass that: > How do you find the X/Y tangent positions of circles tangent to an ellipse? > > The ellipse is 3x4 > The .655 dia circle on the outside is at 3.000x > The 1.200 dia circle on the inside is at 2.000x > > How would the Y positions of those circles be determined? > > How would the X/Y positions of the tangents be determined? > > What would the proper formula be? > > > > ellipseTangents.png > > > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org

JW

Joe Weinpert

Mon, May 2, 2022 11:05 PM

That was fun ... but it doesn't answer my question.

On Mon, May 2, 2022 at 6:35 PM Bryan Lee leebc11@acm.org wrote:

Thus Joe Weinpert hast written on Mon, May 02, 2022 at 05:58:42PM -0400,
and, according to prophecy, it shall come to pass that:

How do you find the X/Y tangent positions of circles tangent to an

ellipse?

The ellipse is 3x4
The .655 dia circle on the outside is at 3.000x
The 1.200 dia circle on the inside is at 2.000x

How would the Y positions of those circles be determined?

How would the X/Y positions of the tangents be determined?

What would the proper formula be?

ellipseTangents.png

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To unsubscribe send an email to discuss-leave@lists.openscad.org

That was fun ... but it doesn't answer my question. On Mon, May 2, 2022 at 6:35 PM Bryan Lee <leebc11@acm.org> wrote: > Ellipse related: > > https://www.youtube.com/watch?v=5nW3nJhBHL0 > > > > Thus Joe Weinpert hast written on Mon, May 02, 2022 at 05:58:42PM -0400, > and, according to prophecy, it shall come to pass that: > > How do you find the X/Y tangent positions of circles tangent to an > ellipse? > > > > The ellipse is 3x4 > > The .655 dia circle on the outside is at 3.000x > > The 1.200 dia circle on the inside is at 2.000x > > > > How would the Y positions of those circles be determined? > > > > How would the X/Y positions of the tangents be determined? > > > > What would the proper formula be? > > > > > > > > ellipseTangents.png > > > > > > > > > _______________________________________________ > > OpenSCAD mailing list > > To unsubscribe send an email to discuss-leave@lists.openscad.org > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

DP

David Phillip Oster

Mon, May 2, 2022 11:22 PM

A quick review of high school algebra, the equation for points on a circle
is:
when the origin is at the point [h,k]
( x - h )^2 + ( y - k )^2 = r^2,

so you fill in what you know:

( x - 3 )^2 + ( y - k )^2 = 0.655^2

and do the same for the ellipse, and solve for 'k'. Note: there are two
circles that satisfy the condition that there is an [x,y] pair that is both
on the circle and the ellipse. You get to pick the one you want.

The other circle ellipse pair is solved the same way.

On Mon, May 2, 2022 at 3:02 PM Joe Weinpert joe.weinpert@gmail.com wrote:

How do you find the X/Y tangent positions of circles tangent to an ellipse?

The ellipse is 3x4
The .655 dia circle on the outside is at 3.000x
The 1.200 dia circle on the inside is at 2.000x

How would the Y positions of those circles be determined?

How would the X/Y positions of the tangents be determined?

What would the proper formula be?

[image: ellipseTangents.png]

OpenSCAD mailing list
To unsubscribe send an email to discuss-leave@lists.openscad.org

A quick review of high school algebra, the equation for points on a circle is: when the origin is at the point [h,k] *( x - h )^2 + ( y - k )^2 = r^2*, so you fill in what you know: *( x - *3* )^2 + ( y - k )^2 = *0.655*^2* and do the same for the ellipse, and solve for 'k'. Note: there are two circles that satisfy the condition that there is an [x,y] pair that is both on the circle and the ellipse. You get to pick the one you want. The other circle ellipse pair is solved the same way. On Mon, May 2, 2022 at 3:02 PM Joe Weinpert <joe.weinpert@gmail.com> wrote: > How do you find the X/Y tangent positions of circles tangent to an ellipse? > > The ellipse is 3x4 > The .655 dia circle on the outside is at 3.000x > The 1.200 dia circle on the inside is at 2.000x > > How would the Y positions of those circles be determined? > > How would the X/Y positions of the tangents be determined? > > What would the proper formula be? > > > > [image: ellipseTangents.png] > > > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

AM

Adrian Mariano

Tue, May 3, 2022 1:05 AM

You have too many uknowns to solve for k. Or in other words, the equations
don't determine a unique k, but the set of all k such that the circle and
ellipse intersect at all. How do you constrain the solution to produce a
TANGENT intersection?

Maybe the analysis here is useful?
https://math.stackexchange.com/questions/272606/find-a-circle-tangent-to-an-ellipse

On Mon, May 2, 2022 at 7:23 PM David Phillip Oster <
davidphilliposter@gmail.com> wrote:

A quick review of high school algebra, the equation for points on a circle
is:
when the origin is at the point [h,k]
( x - h )^2 + ( y - k )^2 = r^2,

so you fill in what you know:

( x - 3 )^2 + ( y - k )^2 = 0.655^2

and do the same for the ellipse, and solve for 'k'. Note: there are two
circles that satisfy the condition that there is an [x,y] pair that is both
on the circle and the ellipse. You get to pick the one you want.

The other circle ellipse pair is solved the same way.

On Mon, May 2, 2022 at 3:02 PM Joe Weinpert joe.weinpert@gmail.com
wrote:

How do you find the X/Y tangent positions of circles tangent to an
ellipse?

The ellipse is 3x4
The .655 dia circle on the outside is at 3.000x
The 1.200 dia circle on the inside is at 2.000x

How would the Y positions of those circles be determined?

How would the X/Y positions of the tangents be determined?

What would the proper formula be?

[image: ellipseTangents.png]

OpenSCAD mailing list
To unsubscribe send an email to discuss-leave@lists.openscad.org

You have too many uknowns to solve for k. Or in other words, the equations don't determine a unique k, but the set of all k such that the circle and ellipse intersect at all. How do you constrain the solution to produce a TANGENT intersection? Maybe the analysis here is useful? https://math.stackexchange.com/questions/272606/find-a-circle-tangent-to-an-ellipse On Mon, May 2, 2022 at 7:23 PM David Phillip Oster < davidphilliposter@gmail.com> wrote: > A quick review of high school algebra, the equation for points on a circle > is: > when the origin is at the point [h,k] > *( x - h )^2 + ( y - k )^2 = r^2*, > > > so you fill in what you know: > > *( x - *3* )^2 + ( y - k )^2 = *0.655*^2* > > > and do the same for the ellipse, and solve for 'k'. Note: there are two > circles that satisfy the condition that there is an [x,y] pair that is both > on the circle and the ellipse. You get to pick the one you want. > > > The other circle ellipse pair is solved the same way. > > > On Mon, May 2, 2022 at 3:02 PM Joe Weinpert <joe.weinpert@gmail.com> > wrote: > >> How do you find the X/Y tangent positions of circles tangent to an >> ellipse? >> >> The ellipse is 3x4 >> The .655 dia circle on the outside is at 3.000x >> The 1.200 dia circle on the inside is at 2.000x >> >> How would the Y positions of those circles be determined? >> >> How would the X/Y positions of the tangents be determined? >> >> What would the proper formula be? >> >> >> >> [image: ellipseTangents.png] >> >> >> _______________________________________________ >> OpenSCAD mailing list >> To unsubscribe send an email to discuss-leave@lists.openscad.org >> > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

DP

David Phillip Oster

Tue, May 3, 2022 2:17 AM

Thank you for teaching me.
On Mon, May 2, 2022 at 6:06 PM Adrian Mariano avm4@cornell.edu wrote:

You have too many uknowns to solve for k. Or in other words, the
equations don't determine a unique k, but the set of all k such that the
circle and ellipse intersect at all.

Thank you for teaching me. On Mon, May 2, 2022 at 6:06 PM Adrian Mariano <avm4@cornell.edu> wrote: > You have too many uknowns to solve for k. Or in other words, the > equations don't determine a unique k, but the set of all k such that the > circle and ellipse intersect at all. >

DM

Douglas Miller

Tue, May 3, 2022 3:20 AM

Each circle is tangent to the ellipse at exactly one point -- and that
point is a solution to /both/ the equation of the circle, and the
equation of the ellipse. So:

Determine the equations of the ellipse and one circle.
Solve each equation for y in terms of x.
Now replace y in one equation by the expression in x from the other
equation, giving you expressions in x on each side of the equation.
Solve for x.
Solve for y.
Repeat for the other circle.

On 5/2/2022 5:58 PM, Joe Weinpert wrote:

How do you find the X/Y tangent positions of circles tangent to an
ellipse?

The ellipse is 3x4
The .655 dia circle on the outside is at 3.000x
The 1.200 dia circle on the inside is at 2.000x

How would the Y positions of those circles be determined?

How would the X/Y positions of the tangents be determined?

What would the proper formula be?

Each circle is tangent to the ellipse at exactly one point -- and that point is a solution to /both/ the equation of the circle, and the equation of the ellipse. So: 1. Determine the equations of the ellipse and one circle. 2. Solve each equation for y in terms of x. 3. Now replace y in one equation by the expression in x from the other equation, giving you expressions in x on each side of the equation. 4. Solve for x. 5. Solve for y. 6. Repeat for the other circle. On 5/2/2022 5:58 PM, Joe Weinpert wrote: > How do you find the X/Y tangent positions of circles tangent to an > ellipse? > > The ellipse is 3x4 > The .655 dia circle on the outside is at 3.000x > The 1.200 dia circle on the inside is at 2.000x > > How would the Y positions of those circles be determined? > > How would the X/Y positions of the tangents be determined? > > What would the proper formula be? > > >

JW

Joe Weinpert

Tue, May 3, 2022 10:35 PM

Thanks for all the help. This was needed to make a CAD drawing and to
determine some X/Y points in an Inkscape SVG project.

On Mon, May 2, 2022 at 11:21 PM Douglas Miller doug@milmac.com wrote:

Each circle is tangent to the ellipse at exactly one point -- and that
point is a solution to both the equation of the circle, and the
equation of the ellipse. So:

1. Determine the equations of the ellipse and one circle.
2. Solve each equation for y in terms of x.
3. Now replace y in one equation by the expression in x from the other
equation, giving you expressions in x on each side of the equation.
4. Solve for x.
5. Solve for y.
6. Repeat for the other circle.

On 5/2/2022 5:58 PM, Joe Weinpert wrote:

How do you find the X/Y tangent positions of circles tangent to an ellipse?

The ellipse is 3x4
The .655 dia circle on the outside is at 3.000x
The 1.200 dia circle on the inside is at 2.000x

How would the Y positions of those circles be determined?

How would the X/Y positions of the tangents be determined?

What would the proper formula be?

OpenSCAD mailing list
To unsubscribe send an email to discuss-leave@lists.openscad.org

Thanks for all the help. This was needed to make a CAD drawing and to determine some X/Y points in an Inkscape SVG project. On Mon, May 2, 2022 at 11:21 PM Douglas Miller <doug@milmac.com> wrote: > Each circle is tangent to the ellipse at exactly one point -- and that > point is a solution to *both* the equation of the circle, and the > equation of the ellipse. So: > > 1. Determine the equations of the ellipse and one circle. > 2. Solve each equation for y in terms of x. > 3. Now replace y in one equation by the expression in x from the other > equation, giving you expressions in x on each side of the equation. > 4. Solve for x. > 5. Solve for y. > 6. Repeat for the other circle. > > > > On 5/2/2022 5:58 PM, Joe Weinpert wrote: > > How do you find the X/Y tangent positions of circles tangent to an ellipse? > > The ellipse is 3x4 > The .655 dia circle on the outside is at 3.000x > The 1.200 dia circle on the inside is at 2.000x > > How would the Y positions of those circles be determined? > > How would the X/Y positions of the tangents be determined? > > What would the proper formula be? > > > > > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

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Ellipse tangents formula