# Re: [geometry] Points and Vectors Proposal

```Hi,

I think one of the main issues here is that implementations of Point and Vector need to have access to coordinate values in order to do work, but the generic interfaces don't make that information accessible. We end up having to constantly cast from inputs like Vector<Euclidean2D> to Cartesian2D in the implementation classes. This is true in the current code as well as in my updated branch. This makes it difficult to allow for other coordinate systems. So, what would you say to an interface structure like this:

interface Coordinates {
int getDimensions();
}

interface Spatial<C extends Coordinates> {
C getCoordinates();
}

interface Vector<C extends Coordinates> extends Spatial<C> {
// ... other methods
}

interface Point<C extends Coordinates> extends Spatial<C> {
Vector<C> subtract(Point<C> p);
// ... other methods
}

class Euclidean2D implements Coordinates {
double getX();
double getY();
}

class Vector2D extends Euclidean2D implements Vector<Euclidean2D>
Euclidean2D c = v.getCoordinates();
return new Vector2D(x + c.getX(), y + c.getY());
}

Euclidean2D getCoordinates() {
return this;
}
// ...
}

This is using your idea of having the coordinates be available through an accessor method in order to avoid the need to cast types and make assumptions about the coordinate system. Also, note that I'm not even using the Space interface here. The only method that seems to be used in that class is getDimensions() and that can easily be placed in the Coordinates interface.

-Matt

________________________________
From: Gilles <gilles@xxxxxxxxxxxxxxxxxxxxx>
Sent: Tuesday, April 24, 2018 7:55 AM
To: dev@xxxxxxxxxxxxxxxxxx
Subject: Re: [geometry] Points and Vectors Proposal

Hi.

[Note: there is a problem with the quoted part in your
message.]

On Tue, 24 Apr 2018 01:31:43 +0000, Matt Juntunen wrote:
> Hi Gilles,
>
> The hierarchy would be wrong from a conceptual POV: A vector can be
> described by Cartesian coordinates, but it should be possible to
> introduce new coordinate systems (polar in 2D, spherical in 3D) ...

> This approach doesn't limit the coordinate system at all. We can
> still make implementations of Point<EuclideanXD> and
> Vector<EuclideanXD> based on other coordinate systems. I think it'll
> actually be easier in this structure, since the details of the system
> are explicitly defined in a single base class. For example, to create
> polar vectors and points, we would create a PolarCoordinate2D base
> class and PolarPoint2D and PolarVector2D subclasses.

What you propose (in the branch) is:
public class Point3D extends Cartesian3D

Then if we'd implement spherical coordinates, we'd have (similarly):
public class Point3D extends Spherical3D

Obviously, that will not work; so I may be missing what you
are trying to achieve...

> ...algorithms that use vectors would/should still work (transparently
> doing the appropriate conversions if necessary).

> This is a general issue with the current code, separate from the
> changes I'm proposing here. I'm not introducing a new issue.

What is the general issue?  That the code assumes Cartesian
coordinates?
My understanding is that your proposal exposes an "implementation
detail" (a set choice of the coordinate system).

> I understand (and agree with) the performance goal, but let's
> be careful to not define an API that does not correspond to
> the underlying concepts.

> Agreed. One vote in favor of having these utility methods is that I
> used some of them while transitioning the other geometry classes for
> my proof-of-concept. For example,
> o.a.c.geometry.euclidean.threed.Plane uses the
> Vector3D.dotProduct(Cartesian3D, Cartesian3D) method to compute the
> origin offset directly from the origin point and plane normal.

I think that two issues are compounded here; one is the static
"utility" functions (whether they are more performant then
"pure" OO methods should be demonstrated, with benchmarks),
the other is the OO hierarchy, which should make sense from a
subject domain (i.e. geometry) POV.  Here I was again referring
to the fact that e.g. a vector in Euclidean 3D-space is equally
well represented by
(x, y, z)
or
(r, theta, phi)
or
(r, theta, z)
or
...

Perhaps a "Cartesian3D" instance should be returned by an
accessor, rather than be the parent (?).

> What will happen when we introduce
>    Spherical3D(r, theta, phi)
> alongside
>    Cartesian3D(x, y, z)
> ?
> They should be able to get along just fine. They would each have
> subclasses that perform point and vector operations using their
> respective coordinate systems. The only issue would be trying to mix
> them, which as I mentioned above, is an existing issue with the
> current code base. However, I think having the coordinate systems
> encapsulated in base classes is a good first step in solving this.

[See above.]

> If "Cartesian3D" _implements_ "Point3D" and "Vector3D", it
> would still work (i.e. refactor so that "Point3D" becomes
> an interface and does not assume that the coordinates are
> Cartesian).

> I'm not quite sure what you're picturing for the Point3D interface
> here. Even so, if Cartesian3D implemented both interfaces, the
> compiler wouldn't be any help in catching simple programming errors.

IMO, a design is not primarily aimed at detecting programming
errors but should help the user avoid them. ;-)

Regards,
Gilles

>
> Thanks,
> Matt
> ________________________________
> From: Gilles <gilles@xxxxxxxxxxxxxxxxxxxxx>
> Sent: Monday, April 23, 2018 4:32 AM
> To: dev@xxxxxxxxxxxxxxxxxx
> Subject: Re: [geometry] Points and Vectors Proposal
>
> Hi.
>
> On Mon, 23 Apr 2018 05:36:09 +0000, Matt Juntunen wrote:
>> Hi all,
>>
>> I'd like to propose an update to the Euclidean Point/Vector classes
>> in the geometry project. We currently have a single CartesianXD
>> class
>> per dimension (eg, Cartesian2D) that implements both the Point and
>> Vector interfaces. This is similar to the previous commons-math
>> version where we had VectorXD classes that were also both Points and
>> Vectors. The change to the current version was through discussion on
>> MATH-1284 (https://issues.apache.org/jira/browse/MATH-1284). My
>> proposal is to flip the current inheritance hierarchy so that the
>> CartesianXD classes become the base classes for separate PointXD and
>> VectorXD classes.
>
> The hierarchy would be wrong from a conceptual POV: A vector can be
> described by Cartesian coordinates, but it should be possible to
> introduce new coordinate systems (polar in 2D, spherical in 3D) and
> algorithms that use vectors would/should still work (transparently
> doing the appropriate conversions if necessary).
>
>> PointXD classes only implement the Point interface
>> and VectorXD classes only implement Vector. The Cartesian base
>> classes
>> contain the actual x, y, z coordinate values along with a few other
>> common methods (such as getSpace()). For performance and
>> convenience,
>> we can create static methods in the VectorXD classes that accept the
>> Cartesian base class instances, so that users can perform common
>> vector operations using either type. For example, if you have a
>> giant
>> list of Points, these static methods would allow you to compute dot
>> products without needing to convert the Point instances to Vectors
>> first.
>
> I understand (and agree with) the performance goal, but let's
> be careful to not define an API that does not correspond to
> the underlying concepts.
>
> What will happen when we introduce
>    Spherical3D(r, theta, phi)
> alongside
>    Cartesian3D(x, y, z)
> ?
>
>> I've partially implemented this in a branch so you can get a better
>> idea of what I'm picturing:
>> https://github.com/darkma773r/commons-geometry/tree/point-vector.
>> The
>> commons-geometry-core and commons-geometry-euclidean sub-modules
>> contain the changes.
>>
>>
>> [https://avatars1.githubusercontent.com/u/3809623?s=400&v=4]<https://github.com/darkma773r/commons-geometry/tree/point-vector>
>>
>>
>>
>> darkma773r/commons-geometry<https://github.com/darkma773r/commons-geometry/tree/point-vector>
>> commons-geometry - Apache Commons Geometry
>> github.com
>>
>>
>>
>> The main benefit I see from this approach is code clarity. The
>> intent
>> of the code seems much clearer to me when the names of the types
>> exactly match what they represent mathematically. For example, one
>> of
>> the constructors for the Plane class currently looks like this:
>>
>> public Plane(final Cartesian3D p, final Cartesian3D normal, final
>> double tolerance)
>>
>> With my proposed changes, it would look like this:
>>
>> public Plane(final Point3D p, final Vector3D normal, final double
>> tolerance)
>>
>> The code is easier to read and the compiler will also help prevent
>> algorithm errors.
>
> That API is better indeed.
>
> If "Cartesian3D" _implements_ "Point3D" and "Vector3D", it
> would still work (i.e. refactor so that "Point3D" becomes
> an interface and does not assume that the coordinates are
> Cartesian).
>
> Best regards,
> Gilles
>
>>
>> Thoughts?
>>
>> Regards,
>> Matt Juntunen
>
>

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