Re: [geometry] Points and Vectors Proposal

[Gilles]

Hi.

On Thu, 26 Apr 2018 21:19:08 +0000, Matt Juntunen wrote:

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.

That is annoying indeed.

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> {
    Vector<C> add(Vector<C> v);
    // ... 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();
}

The name of the above class should be "Cartesian2D".

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

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

The problem with the above is that it forces a coordinate
system on a class that represents the concept of vector
(which is coordinate-"agnostic").
If/when we want to introduce polar coordinates we'd need
something like
  class Vector2D implements Vector<Cartesian2D>, Vector<Polar2D>
which won't compile.

A straightforward way would be to include coordinate
accessors for all common systems:

interface Coordinates {
    int getDimensions();
}
interface Cartesian2D extends Coordinates {
    double getX();
    double getY();
}
interface Polar2D extends Coordinates {
    double getR();
    double getTheta();
}
class Vector2D implements Cartesian2D, Polar2D { ... }

What is the actual use of the "Vector" interface in the code?
Are there generic algorithms (I mean those that don't need
to "cast" to do some useful work, i.e. work at the "geometrical"
level rather than the "coordinate" level)?
If so, we'd have
  class Vector2D implements Vector, Cartesian2D, Polar2D { ... }

Regards,
Gilles

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 <gil...@harfang.homelinux.org>
Sent: Tuesday, April 24, 2018 7:55 AM
To: dev@commons.apache.org
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 <gil...@harfang.homelinux.org>
Sent: Monday, April 23, 2018 4:32 AM
To: dev@commons.apache.org
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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