Sketcher: Ellipse support

[marktaff]

Have a look here: viewtopic.php?f=10&t=7520&start=40#p61810

git clone URL your_directory
should do the job.

Ulrich

That did not have the expected results; I must be doing something wrong or misunderstanding something.

I currently have the main master in /home/mark/freecad/freecad, building in /home/mark/freecad/freecad-build.
I put the ellipse stuff in /home/mark/freecad/freecad-ellipse via:

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git clone https://github.com/abdullahtahiriyo/FreeCAD_sf_master.git freecad-ellipse

and building in /home/mark/freecad/freecad-ellipse-build.

freecad-ellipse configured, built, and ran just fine, but there was none of the ellipse stuff apparently in it--no way to draw an ellipse, no ellipse icons in the resource file, etc. I'd appreciate any help pointing out my error(s). Thanks.

[quick61]

Once you have cloned the source, cd into your ~/freecad-ellipse directory and do -

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git branch

This will tell you which branch your in. It should return -

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* master

Now do -

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git branch -r

And you will see a list of all the branches that are included in your clone, the ones that are of intrest for Sketcher: Ellipse support look like -

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origin/sketcher_elipse
origin/sketcher_ellipse2
origin/sketcher_ellipse2_tangent_circunf_ulrich1a_original_pointonellipse
origin/sketcher_ellipse2_tangent_circunf_ulrich1a_squared_pointonellipse
origin/sketcher_ellipse_master

Decide which branch you want to build - and for this example we'll use "sketcher_ellipse_master" and do -

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git checkout sketcher_ellipse_master

and you will see the message -

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Switched to a new branch 'sketcher_ellipse_master'

If you now do -

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git branch

You will now see -

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  master
* sketcher_ellipse_master

With the * noting which branch you are in.

From this point, now configure your build with cmake or cmake-gui and compile as always.

Edit - now my question is, which branch should we be building if we want to look and test? Is sketcher_ellipse_master the current one?

Mark

[marktaff]

Thank you so much Mark! I am now on the correct branch.

[quick61]

Thank you so much Mark! I am now on the correct branch.

Your welcome. While I do not even come close to resembling a programmer, I have been using git enough while bug testing different FeeeCAD branches to know some of the git basics.

Mark

[abdullah]

You picked the right branch out of 5 possilities Mark-quick61!! ... you should play lotto this week!!!

Because all the solver parameters are going to change, I would welcome a general equation of the ellipse based on those parameters. Let's say we pick the one of the eccentricity... I need an ellipse equation based only on those parameters. Why? To derive the error function and the gradient, the partials, that now have to be with respect to this new parameters, as they are the solver params... for example part(error)/part(e)...

... when I started, I chose phi, also because I was using the cartesian parametric equation, which is a function of phi...

[ulrich1a]

I need an ellipse equation based only on those parameters.

The ellipse equation for this parametrization is:
2*a=sqrt((yF2−yp)^2+(xF2−xp)^2)+sqrt((yF1−yp)^2+(xF1−xp)^2)
xp and yp are the points on an ellipse.
F1 and F2 are the foci
a is the major radius.
See this post: viewtopic.php?f=10&t=7520&start=110#p62721

It may work also with this equation:
0=−(−yF2^2+2*yp*yF2+yF1^2−2*yp*yF1−xF2^2+2*xp*xF2+xF1^2−2*xp*xF1−4*a^2)^2/(16*a^2)+yF2^2−2*yp*yF2+
xF2^2−2*xp*xF2+yp^2+xp^2
See this post: viewtopic.php?f=10&t=7520&start=160#p63282
The ellipse equation is just equal to the point on ellipse error equation with the error set to zero.

So I thought it would not be so much work to use the parametrization of F1, F2 and a, as the last added constraints are already based on the new parametrization.

The existing drawing method may be reused:
Center_point = (F1 + F2) / 2
b^2 = a^2 - (|(F1 + F2)/2|)^2

Ulrich

[DeepSOIC]

Sorry, I don't have time today to properly craft my posts.
The ellipse eq in brand new polar (perifocal) coordinates and brand new eccentricity-based parameterization is:

universal equation for conics

ellipse_eq_polar.gif (2.35 KiB) Viewed 2803 times

It should be valid for all conics.
I got it by substituting a=d/(1-e) into the previously mentioned polar equation of ellipse based on a.

[abdullah]

I wanted to summarize what I did today and which design decisions I took and why.

I have been thinking about the representation and I decided to give a try first to UlrichDeepSOIC approach. Why? because this representation is much closer to the current work done (further reasons follow). Can't we use the perifocal approach? Yes, we can solve the equations using the perifocal if this is more convenient, however, the basic parameters in this approach has to be well, continue reading...

...then I coded all those changes (yes including calculations of PoE and Line tangent to Ellipse) and realized (yes it should have come to my mind earlier) that because the center is a UI point to which a constraint can be set (for example, a coincident constraint), and the sketcher solving relies on a midpoint,startpoint,endpoint (yes, also so deep inside) and maps UI midpoint to sketcher solving midpoint, it follows that the center point has to be a parameter of the ellipse. (side note: could we have painted in the UI a focus and constraint a focus? theoretically yes, but this would mean that for the UI it would be a "center" or middle point, while obviously would not be the point in the center)...

... so I modified the UlrichDeepSOIC to use a focus (the positively defined one) and the center. This way the parameters are:
Center x,y
Focus1 x,y
Minor radius r (5 DoF)

...I have just finished the changes (yes including calculations of PoE and Line tangent to Ellipse) . It does compile, but I think I made a mistake when mapping parameters, because the constraints do not work properly (tangent is a secant and point on ellipse is point far away from the ellipse, a total success ) (but they converge nicely in the solver )... I will take a look when I have time...

This is the code:

https://github.com/abdullahtahiriyo/Fre ... master.git
* [new branch] sketcher_ellipse_solver_modified_ulrich1a_proposal


Calculus (sage worksheets) are attached...

I still do not dispose the perifocal approach, I just want to see if this solves our problems...

[DeepSOIC]

I still do not dispose the perifocal approach, I just want to see if this solves our problems...

You don't. But I do. Here is why.
I have written an error function in perifocal coordinates for point-on-object constraint. The error function is very simple - it is just an ellipse equation with all terms thrown into the right side (i.e. equality is substituted by subthaction). It is fine for ellipse and parabola, but it is an epic fail for hyperbola. The reason for that is that if a point happens to be slightly off but enough to cross the asymptote (which can be very close to the hyperbola!), the error function will switch to the other branch of hyperbola. This is absolutely unacceptable..

This doesn't rule out the perifocal approach completely, but it turns out that math there is not as simple as I expected, it will unlikely be universal to all conics and I don't see any advantages anymore compared to our previous path with vector/cartesian math.

[marktaff]

I have written an error function in perifocal coordinates for point-on-object constraint. The error function is very simple - it is just an ellipse equation with all terms thrown into the right side (i.e. equality is substituted by subthaction). It is fine for ellipse and parabola, but it is an epic fail for hyperbola. The reason for that is that if a point happens to be slightly off but enough to cross the asymptote (which can be very close to the hyperbola!), the error function will switch to the other branch of hyperbola. This is absolutely unacceptable..

This doesn't rule out the perifocal approach completely, but it turns out that math there is not as simple as I expected, it will unlikely be universal to all conics and I don't see any advantages anymore compared to our previous path with vector/cartesian math.

Some things will vertainly be easier in cartesian coords than polar coords. To be clear, a perifocal frame doesn't imply using polar or cartesian--it is just a question of how you place the basis vectors.

Your point about the hyperbola asymptote and error functions is quite interesting--I suppose this is an issue we will have with any function with asymptotes. I'm going to start digging in to abdullah's code to see if I can get a better handle on it.

Cheers!