Ellipsoid3d

[g-belmonte]

Pull request related to #135

Pull request checklist:

• Is the pull request from a dedicated branch in your fork instead of
  master?
• Have you added yourself to the AUTHORS file?
• Is "Allow edits from maintainers" enabled?
• Is the code formatted using the same version of elm-format as the rest of
  elm-geometry?
• Is code (mostly) wrapped to 80 columns?
• BONUS POINTS: Have you added tests for new functionality?
• EXTRA BONUS POINTS: Have you added documentation for new functionality?

Proposed API:

• Ellipsoid3d type

Constructors

• with

Properties

• centerPoint
• axes
• xAxis
• yAxis
• zAxis
• xDirection
• yDirection
• zDirection
• xRadius
• yRadius
• zRadius
• volume
• surfaceArea
• boundingBox

Queries

• contains

Measurement

• signedDistanceAlong

Transformations

• scaleAbout
• rotateAround
• translateBy
• translateIn
• mirrorAcross

Unit conversions

• at
• at_

Coordinate conversions

• relativeTo
• placeIn

[ianmackenzie]

Just did a brief skim but looking pretty good so far!

[g-belmonte]

@ianmackenzie take a look at the formula for the surface area: wikipedia or wolfram
The analytical solution seems to require elliptic integrals. Should I try to implement it like this, or should I go for the approximate solutions?

[ianmackenzie]

Oof didn't realize that, I would just leave it out then =) I don't think it's a particularly important operation, just for spheres it's so simple it seemed silly not to include it.

[g-belmonte]

@ianmackenzie the code is mostly done. We're missing top-level docs and tests.
About the tests, is there anything special you want tested? I was thinking on covering basic usage of all public functions. Wdyt?

[ianmackenzie]

Hey @g-belmonte, sorry for the delay! This one took a bit of thought 🙂 Here are some cool and useful tests I can think of:

• If you apply a random translateBy, rotateAround, scaleAbout, mirrorAcross, placeIn or relativeTo to an Ellipsoid3d, and the matching transformation to a Point3d, do you get the same result from Ellipsoid3d.contains before and after? For example if you have a random ellipsoid and a random point and you both move them the same amount, then if the point is contained in the ellipsoid before the transformation it should also be contained in the ellipsoid after both are transformed, and vice versa.
• Same for signedDistanceAlong - if you apply a particular transformation to an ellipsoid and the same transformation to an Axis3d then you should get (within roundoff error) the same signed distance range before and after.
• If you scale an ellipsoid about an arbitrary point by a scale factor k, does the volume increase by a factor of k^3?

For the first couple of tests, you can check out modules like Tests.Generic.Curve3d and tests like Tests.CubicSpline3d which use it - there are a bunch of similar tests like "if I evaluate a curve at t=0.5 and then rotate the point, it should be the same as rotating the curve and then evaluating the rotated curve at t=0.5" (which tests both curve evaluation and rotation).

Let me know if that makes sense!

[g-belmonte]

Yes, it does make sense! I'll work on it 😁

[ianmackenzie]

One more thought, you could probably make a couple tests based on an Ellipsoid3d with 3 equal radii being equivalent to a Sphere3d with that radius...volume should be the same, point containments results should be the same, etc. But only if you have time and it seems interesting, I don't think those are mandatory 🙂

[g-belmonte]

@ianmackenzie this was the very first test I added 😁 I also wanted to compare an Ellipsoid3d having 2 equal radii with an Ellipse3d, but the latter doesn't have a volume function 😅

I had little time the last days, so I'll try to finish the tests today :)

[g-belmonte]

I'm getting this message while trying to implement Fuzz.ellipsoid3d:

Should I create a new Fuzz.frame3d without local coordinates, or should I tweak the type of Ellipsoid3d?

[g-belmonte]

Docs and tests added. The Fuzzer thing I solved by adding the globalFrame3d to the Geometry.Fuzz module, but I haven't exposed it.

[ianmackenzie]

Haven't looked through everything in detail but I think a better solution for the frame type issue would be to have Ellipsoid3d.with accept an arbitrary Frame3d units coordinates defines argument instead of a Frame3d units coordinates {}, and then use Frame3d.copy inside the constructor to make the types work out (see the implementation of Rectangle2d.centeredOn as an example). Then I think you should be able to drop the globalFrame3d fuzzer and just use frame3d.

[g-belmonte]

@ianmackenzie done! 😄

I think that the PR is now ready for a thorough review. Let me know if anything!

[ianmackenzie]

I think this looks good now - thanks for all your work on this!

[ianmackenzie]

Anything else you were planning to do before merging? I was about to just merge but then I noticed the title was still set to 'WIP' =)

[g-belmonte]

@ianmackenzie Oh, I forgot about the WIP! You can proceed with merging :)