The VXL Project

> The current implementation of angle in vnl_vector.txx is
>    acos( abs( cos_angle(a,b) ) )
> 
> Why is the abs there?

Apparently this is meant to give "symmetric" output, i.e.,
angle(a,b) == angle(b,a).

Should probably be documented.


	Peter.

> Apparently this is meant to give "symmetric" output, i.e.,
> angle(a,b) == angle(b,a).

By definition of the cos_angle, it is already symmetric:
cos_angle(a,b) = cos_angle(b,a) = a.b/(|a||b|). The current
implementation gives

                  ^
                 /
                /
             A / B
     <--------/.....

B as the "angle", which is the smallest angle provided the "vectors"
are undirected. Is this what is intended?  I think it should simply be
    acos( a.b / |a||b| )
since that is what most people refer to as the angle between two
vectors.

Amitha.

> Apparently 

In the sense of "obviously", or that you have 
other information?

A.

Amitha:
>  I think it should simply be
>     acos( a.b / |a||b| )
> since that is what most people refer to as the angle between two
> vectors.

Agreed.

I hate to ask, but are any test cases run on vxl?

> By definition of the cos_angle, it is already symmetric:
> cos_angle(a,b) = cos_angle(b,a) = a.b/(|a||b|).

Sure; sorry about the misunderstanding.
I meant "non-oriented" instead of "symmetric".

Forgive my ignorance: how is the angle between two complex vectors
defined? Is it  acos( |a.b| / |a||b| )  ?  If so, is there a clean way
to compute the norm for complex types, and not compute the norm for
real types? And does this lead to an inconsistency in the semantics of
the function call?

On Mon, Oct 29, 2001 at 08:13:33PM -0000, Andrew Fitzgibbon wrote:
> 
> Amitha:
> >  I think it should simply be
> >     acos( a.b / |a||b| )
> > since that is what most people refer to as the angle between two
> > vectors.
> 
> Agreed.

[vnl] angle(a,b) now returns acos( a.b / |a||b| ), but is not
instantiated for complex-valued vectors, since we lack an
implementation for acos(complex).

Amitha.


On Mon, Oct 29, 2001 at 03:03:29PM -0500, Amitha Perera wrote:
> > Apparently this is meant to give "symmetric" output, i.e.,
> > angle(a,b) == angle(b,a).
> 
> By definition of the cos_angle, it is already symmetric:
> cos_angle(a,b) = cos_angle(b,a) = a.b/(|a||b|). The current
> implementation gives
> 
>                   ^
>                  /
>                 /
>              A / B
>      <--------/.....
> 
> B as the "angle", which is the smallest angle provided the "vectors"
> are undirected. Is this what is intended?  I think it should simply be
>     acos( a.b / |a||b| )
> since that is what most people refer to as the angle between two
> vectors.
> 
> Amitha.