[boost] Re: [interval] Re: suggestions and minor doc error

From: Mark Gilbert (markgilbert_at_[hidden])
Date: 2005-06-09 18:02:09

"Guillaume Melquiond" <guillaume.melquiond_at_[hidden]> wrote in message 
news:1118349671.6045.19.camel_at_saline...
>Le jeudi 09 juin 2005 à 14:23 -0500, Mark Gilbert a écrit :

>> T evaluate(T t) const { return low + t * extent(); }
>> T normalize(T t) const { return (t - low) / extent(); }
>> evaluate and normalize map the interval to a normalized interval with 
>> values
>> in the range [0,1].

>Concerning 'evaluate' and 'normalize' though, they don't strike me as
>necessary. First, the names are not really indicative of their semantic.
>Second, the interval [0,1] seems a bit arbitrary: [-1,1] would make as
>much sense to me.

Hi Guillaume,

Let me argue for evaluate and normalize a little.  Here is code that 
generates 21 points on a line from (x0,y0) to (x1,y1):
for (int i = 0; i <= 20; i++)
{
    double p = i / 20.0;
    dopoint(interval(x0,x1).evaluate(p), interval(y0,y1).evaluate(p));
}

Here is a linear interpolator for a function that is known only at integer 
values:
double interpolate(double values[], double x)
{
    int x0 = ifloor(x);
    int x1 = iceil(x);
    double xfrac = x - x0;
    return interval(values[x0],values[x1]).evaluate(xfrac));
}

Mapping to and from the range [0,1] lets you get at the ideas "where does 
this value fall in my interval?" and "what value is at this position in my 
interval?"  Your median function is similar to evaluate, but 0.5 is just one 
position in the interval that might be interesting.  Perhaps evaluate(0.25) 
or evaluate(x) are more interesting for some applications.

Regarding the names.  I work a lot with parameterized curves in space, which 
are "normally" parameterized on [0,1].  I "evaluate" a value in that range 
to get a point on the curve (or a value in an interval).  Perhaps without 
that context, other names would be better, though normalize might still be 
analogous to normalizing a vector to a unit vector.

Instead of evaluate and normalize:
scale and normalize?
at_position and position (or get_position)?
map_from_01 and map_to_01?

I'm not sure I like any of those, but we can probably think of something 
better if you decide the functions themselves might be handy.

Cheers,
Mark Gilbert