Add a basic Sphere3D element

[Vectornaut]

Summary

This addresses #616 by adding an element, Sphere3D, representing a sphere in 3D space. It also adds a usage example, sphere3d.html.

Implementation

The interface is based on Circle, but I use ideas from Line3D and ParametricSurface3D to link the 3D geometric representation to the 2D display representation (stored in element2D).

Pitfalls

• In the example, the lack of depth cues makes it hard to see where the control points are in relation to the sphere.
• My implementation of Sphere3D isn't consistent with the elements it's based on, because those elements aren't implemented consistently with each other. For example:
  • To measure the distance between points, Circle uses the CoordsElement.Dist method that Point inherits. However, there's no 3D analogue of CoordsElement: the class Point3D descends directly from GeometryElement. I therefore added a distance function, Point3D.distance, directly to the Point3D class.
  • The new type check function isPointType3D is inconsistent with both the 2D analogue isPointType, and it also doesn't match the type check done in createLine3D. Ideally, it would be nice to use the same type check for createSphere3D and createLine3D, but I don't understand the latter well enough to change it.

[alfredwassermann]

Thanks a lot, this is very helpful! You probably saw that there is a lot of work ahead for 3D ...

The 2D CoordsElement contains methods which can be used for points, images and texts The position of these elements consist of a single coordinate array. There is no analog (yet) in 3D, so it does not exist yet.

The problem with isPointType and now also with isPointType3D is that internally we work with homogeneous coordinates (i.e. in 3D these are arrays of length 4) but from the users we mostly require affine coordinates (i.e. in 3D an array of length 3). Therefore, the test with >.

[Vectornaut]

The problem with isPointType and now also with isPointType3D is that internally we work with homogeneous coordinates (i.e. in 3D these are arrays of length 4) but from the users we mostly require affine coordinates (i.e. in 3D an array of length 3). Therefore, the test with >.

If it's worth refactoring these a bit, I can put that on my to-do list. I'd just need to know more about what the desired behavior is: I couldn't find any isPointType unit tests, so I'm not totally sure what should count as point type.