Re: Motion on interval flavors

["Corliss, George" <george.corliss@xxxxxxxxxxxxx>]

Nate,

Thank you.  That is helpful.

> Linear interpolation
>   L(U) = A + U * ( B - A )

To be sure I understand, one setting might be:

a is a point in R^3
b is a point in R^3
U is a scalar

l(U) = a + U * (b - a)

is a parametric form of a line in R^3 from point a (U = 0) to point b (U = 1).
U in (-\infty, + \infty) describes the line determined by points a and b.
This form arises in computer graphics applications ALL THE TIME.  Now,

l(U) = a + U * (b - a)

is a vector equation.  The components for x, y, and z coordinates has the scalar form

L(U) = A + U * (B - A)

you gave, where A, B, and L represent x, y, or z components of the vector equation.  Then, your example is EXACTLY how one might determine where a line of interest intersects another object of interest, say a bounding box.

Am I understanding/interpreting/applying your example correctly?  Yes, your application to Bezier and b-spline bases for polynomials is a deeper application, but am I on the right track?

That is EXACTLY the sort of example I was hoping to hear.  We may justify research interests by "Because it is interesting/beautiful," but the effort to craft a standard MUST rest on "Because it is essential (not just useful) to some task someone pays for."  

I HOPE we all accept computer graphics as a task for which people pay A LOT to get the last pixel right.

I think I hear the same sentiment in your conclusion:

> Again, I ask the question... if all the interval range enclosures are
> computed by complicated floating-point programs, why will any company waste
> the time and money to put classical interval operations into hardware. If no
> one will hardly use them?
> 
> If P1788 is a standard aimed mainly at specifying the interval operations
> that will be implemented in hardware, then IMO it should really focus on
> Kaucher/modal operations; since in so many of the above examples it is clear
> that classical interval operations will simply not be used.
> 
> Nate
> 
>

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