[Insight-developers] itk::Vector Normalize method

[Arnaud Gelas]

Let's imagine, you need to normalize the sum of n vectors and compute  
a dot product with another one.
In this case the dot product is supposed to be null, right? or am I  
missing something (maybe) ?

In such a case, what do you suggest?
Do you think it is better to try to normalize the sum of this n  
vectors, return inf, check with with vnl_math_isinf and then return 0?

Regarding the performance of this little modification, I'll run a test  
with calling 10^9 times both code and check the time difference.

Arnaud

On Jan 14, 2010, at 1:36 PM, Bradley Lowekamp wrote:

> I object to these changes.
>
> Why do you expect the normalize value of a zero vector to be 0 as  
> apposed to "inf"? Can you not check for the "inf" value with  
> vnl_math_isinf() function?
>
> Why do you think you GetNorm methods improves performance? Did you  
> actually check?
>
> I also strongly object to exception being thrown in low level  
> numerical methods.
>
>
> Brad
>
> On Jan 14, 2010, at 1:17 PM, Arnaud Gelas wrote:
>
>> I would agree with you about throwing an exception in the case of  
>> NULL
>> vector.
>> However, when computing mesh normals on a mesh with boundaries it
>> sometimes
>> happens on some point of the boundary. In such a case, I am not sure
>> an exception
>> should be thrown.
>>
>> But how should we define normalization for NULL vectors?
>> (I have just checked in VTK, the normalization of a NULL vector is a
>> NULL vector and it returns the norm).
>>
>> Can I proceed and test these changes? any suggestions / thoughts?
>>
>> Arnaud
>>
>> On Jan 14, 2010, at 12:43 PM, Luis Ibanez wrote:
>>
>>> Hi Arnaud,
>>>
>>> All your suggestions sound very reasonable to me.
>>>
>>> I would just add that when checking for NULL in the
>>> Normalize() method we probably should use the
>>> Assert and Throw Exception macro (or a variant of it).
>>>
>>> In your current suggested modification, calling Normalize
>>> in a Null vector will still return a null vector.... well... I guess
>>> it comes down to picking a mathematical definition of what
>>> should be the normalization of a null vector...
>>>
>>>
>>> I would vote for throwing an Exception in that case....
>>>
>>>
>>>   Any thoughts ?
>>>
>>>
>>>          Luis
>>>
>>>
>>> --------------------------------
>>> On Thu, Jan 14, 2010 at 10:47 AM, Gelas, Arnaud Joel Florent
>>> <Arnaud_Gelas at hms.harvard.edu> wrote:
>>>> Hi guys,
>>>>
>>>> I was going through the implementation of the normalize method of
>>>> itk::Vector, and I was wondering if there is any reason not to test
>>>> if the norm is null (see the implementation below)?
>>>> I guess it can create some problems when trying to normalize null
>>>> vector...
>>>>
>>>> /**
>>>> * Divide vector's components by vector's norm
>>>> */
>>>> template<class T, unsigned int TVectorDimension>
>>>> void
>>>> Vector<T, TVectorDimension>
>>>> ::Normalize( void )
>>>> {
>>>> const RealValueType norm = this->GetNorm();
>>>> for( unsigned int i=0; i<TVectorDimension; i++)
>>>>   {
>>>>   (*this)[i] = static_cast<T> (static_cast<RealValueType>((*this)
>>>> [i]) / norm);
>>>>   }
>>>> }
>>>>
>>>> What about the following modification?
>>>>
>>>> /**
>>>> * Divide vector's components by vector's norm
>>>> */
>>>> template<class T, unsigned int TVectorDimension>
>>>> void
>>>> Vector<T, TVectorDimension>
>>>> ::Normalize( void )
>>>> {
>>>> const RealValueType norm = this->GetNorm();
>>>> if( norm > 0 )
>>>>   {
>>>>   for( unsigned int i=0; i<TVectorDimension; i++)
>>>>     {
>>>>     (*this)[i] = static_cast<T> (static_cast<RealValueType>((*this)
>>>> [i]) / norm);
>>>>     }
>>>>   }
>>>> }
>>>>
>>>> I also think that the method GetNorm could be slightly optimized in
>>>> the case where the norm is null.
>>>>
>>>> /**
>>>> * Returns vector's Euclidean Norm
>>>> */
>>>> template<class T, unsigned int TVectorDimension>
>>>> typename Vector<T, TVectorDimension>::RealValueType
>>>> Vector<T, TVectorDimension>
>>>> ::GetNorm( void ) const
>>>> {
>>>> return RealValueType( vcl_sqrt(double(this->GetSquaredNorm()) ));
>>>> }
>>>>
>>>> modification
>>>> /**
>>>> * Returns vector's Euclidean Norm
>>>> */
>>>> template<class T, unsigned int TVectorDimension>
>>>> typename Vector<T, TVectorDimension>::RealValueType
>>>> Vector<T, TVectorDimension>
>>>> ::GetNorm( void ) const
>>>> {
>>>> double sq_norm = this->GetSquaredNorm();
>>>> if( sq_norm > 0. )
>>>>   {
>>>>   return RealValueType( vcl_sqrt( sq_norm ) );
>>>>   }
>>>> else
>>>>  {
>>>>  return static_cast<RealValueType >( sq_norm );
>>>>  }
>>>> }
>>>>
>>>> or
>>>>
>>>> double sq_norm = this->GetSquaredNorm();
>>>> return ( sq_norm > 0. ) : static_cast<RealValueType
>>>>> ( vcl_sqrt( sq_norm ) ), sq_norm;
>>>>
>>>> Any objection?
>>>>
>>>> Arnaud
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>>
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>>
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>
> ========================================================
> Bradley Lowekamp
> Lockheed Martin Contractor for
> Office of High Performance Computing and Communications
> National Library of Medicine
> blowekamp at mail.nih.gov
>
>

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