> On Aug 20, 10:06 am, TFM gmail.com> wrote:
>
>
>

>> On Aug 17, 4:17 pm, Geoffrey Summerhayes gmail.com> wrote:

>

>>> Basically, it's a linear interpolation.

>

>>> The values of the function F and it's variants are
>>> designed to range from 0.0-4.0 in such a way
>>> that (a+bb+c+d) is a constant (4.0) for any x,y
>>> when 0.0 <= x <= 1.0 and 0.0 <= y <= 1.0
>>> So, in the corners the only color that contributes
>>> is the color of that corner and in the center they all
>>> contribute equally. (in the center a=bb=c=d=1.0)

>

>>> That's why the code had x/24 in the formula because
>>> for(x=0;x<25;++x) means x ranges from 0 to 24.

>

>>> To cover any range, you'll need to adjust the values,
>>> (1.0 - (x - xmin)/(xmax-xmin)). In my code example
>>> xmax was 24 and xmin was 0.

>

>> I was looking at Linear Interpolation on wikipedia:
>> y = y0 + (x-x0)((y1-y0)/(x1-x0))

>

>> How does your following equation fit in the wikipedia formula:
>> a = (float)(4.0 * (1.0 - realX / 2.0) * (1.0 - realY / 2.0));

>
> Follow the idea behind the math, the idea is to use linear functions
> to calculate data points.
>
> Technically, it's called bilinear interpolation. It's essentially
> an extension of linear for an extra dimension.
>

>> Also I think a couple of things are confusing me here. There are 2
>> things, one is the size of GRID which lets calls xGrid & yGrid and
>> other the the domain & range lets call it realX & realY. In my case my
>> domain & range will always be between -1 <= x <= 1 & -1 <= y <= 1 and
>> xGrid & yGrid will always be 25

>
> And you can use any coordinate set as you map the picked x and
> y domains to [0,1]. If realX = xGrid*C1+C2 where C1 and C2 are
> constants and C1!=0, it won't make any difference to the outcome
> (same for y).
>
> The equations can also be simplified, the multiplying and dividing by
> 4 were introduced just to make the logic behind the equations easier
> to follow (mainly that we are looking at an average of the colour
> contributions of each corner).
>
> In other words,
>
> xCalc = (xGrid - xGridMin)/(xGridMax - xGridMin);
>
> and
>
> xCalc = (realX - realXMin)/(realXMax - realXMin);
>
> should be equal and range from 0 to 1.
>
> Then you can use (1.0 - xCalc)*(1.0 - yCalc),
> xCalc * (1.0 - yCalc), etc.
>
> ---
> Geoff