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Re: [geometry] Points and Vectors Proposal


Hello.

On Sun, 29 Apr 2018 02:40:54 +0000, Matt Juntunen wrote:
Hi Gilles,

The generic Vector class is actually not used much but the generic
Point class is used throughout the core partitioning code and in the
high-level enclosing ball code. If we used a class like

class Vector2D implements Vector, Cartesian2D, Polar2D { ... }

We'd still need to cast internally on the Vector methods since they
accept the generic Vector type (eg, add(Vector<S> v)).

Do you mean that the code uses "instanceof" to check which
subclass of Vector is being passed?

A slightly different approach on the polar vs Cartesian thing would
be to use the same exact "spatial value" class to represent them both.
This makes sense conceptually since they're both just different
representations of the same underlying spatial value.

Does the codebase contain functionality that is purely
"geometric" (no assumption on the underlying coordinate system)
or is it a basic assumption that Cartesian coordinates are needed
for anything useful.

In the former case, it is not good to assume either Cartesian or
polar coordinates or even both, since other coordinate system are
possible.

If, say, the scope of this component is limited (to what?) and
explicitly requires a Cartesian coordinate system, then (and only
then, I guess), can the design be based on this assumption.

The main
interface might then look something like this (note that I'm playing
with the names a bit to see what fits best):

// Describes a value associated with a specific type of mathematical space.
// For an n-dimensional space, this will typically take the form of
an n-tuple, but no restrictions
// are placed on the representation at this level.
interface Spatial {
    int getDimension();
    boolean isNaN();
    boolean isInfinite();
}

// Point interface. This adds point semantics to an otherwise mathematically
// meaningless Spatial value.
interface Point<S extends Spatial> {
    S getValue();
    double distance(Point<S> p);
    // ...
}

// Vector interface. This adds vector semantics to an otherwise
mathematically
// meaningless Spatial value.
interface Vector<S extends Spatial> {
    S getValue();
    Vector<S> add(Vector<S> v);
    // ...
}

// Represents a value in Euclidean two-dimensional space.
class Euclidean2D implements Spatial {
    // Store coordinates internally in Cartesian form but expose
    // methods for getting and constructing the values in other
representations,
    // specifically polar.
    protected final double x;
    protected final double y;

    // Cartesian accessors
    double getX();
    double getY();

    // Polar accessors
    double getR();
    double getTheta();

    // ...
}

Unless there is a good reason (how to subclass should be
explained in the Javadoc), "protected" fields and methods
must be avoided.

As hinted above, we first have to decide whether specific
coordinate systems are a basic tenet of the component's
functionalities, or an implementation detail.

class Vector2D extends Euclidean2D implements Vector<Euclidean2D> {
    Euclidean2D getValue() {
        return this;
    }

    Vector2D add(Vector<Euclidean2D> v) {
        Euclidean2D val = v.getValue(); // no cast needed; we know
what types of values we're working with

        // perform operations in Cartesian coordinates; callers can
get the polar coordinate values
        // from the result if they want
        return new Vector2D(x + val.getX(), y + val.getY());
    }
}

I'm wary of
  Vector2D add(Vector<Euclidean2D> v)
where it should rather be
  Vector2D add(Vector2D v)

I'd imagine that an application developer will want to use
simple workflows:
 * create a vector (e.g. calling either a "Cartesian" or a
   "polar" factory method),
 * pass it to coordinate-system independent algorithms (it's
   up to those algorithm to make the necessary conversion if
   they are implemented in term of a specific system),
 * retrieve the result and be able to convert it to his system
   of choice.

How about something along the following lines?

public interface Vector2D {
  Vector2D add(Vector2D other);

  // etc.
}

public class Vector2DFactory {
  public static Cartesian2D toCartesian(Cartesian2D v) {
    return v;
  }
  public static Cartesian2D toCartesian(Polar2D v) { ... }

  // etc.
}

public class Cartesian2D implements Vector2D {
  private final double x;
  private final double y;

  public Cartesian2D add(Cartesian2D other) {
    return new Cartesian2D(x + other.x, y + other.y);
  }

  @Override
  public Vector2D add(Vector2D other) {
    return add(Vector2DFactory.toCartesian(other));
  }
}

public class Polar2D {
  private final double r;
  private final double theta;

  // etc.
}

Regards,
Gilles




________________________________
From: Gilles <gilles@xxxxxxxxxxxxxxxxxxxxx>
Sent: Saturday, April 28, 2018 7:28 AM
To: dev@xxxxxxxxxxxxxxxxxx
Subject: Re: [geometry] Points and Vectors Proposal

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 <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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