Question

I have a one dimensional gird. its spacing is a floating point. I have a point with floating point coordinate as well. I need to find its distance to the closest grid point.
For example:

            0.12
             |
             *
 |---------|---------|---------|---------|---------|
 0        0.1       0.2       0.3       0.4       0.5

The result would be -0.02 since the closest point is behind it.
However if it was

                -0.66
                  |
                  *
 |---------|---------|---------|---------|---------|
-1       -0.8      -0.6      -0.4      -0.2        0

The result will be 0.06. As you can see its in floating point and can be negative.
I tried the following:

float spacing = ...;
float point = ...;

while(point >= spacing) point -= spacing;
while(point < 0) point += spacing;

if(std::abs(point - spacing) < point) point -= spacing;

It works, but I’m sure there is a way without loops

Answer 1

Let us first compute the nearest points on the left and right as follows:

leftBorder = spacing * floor(point/spacing);
rightBorder = leftBorder + spacing;

Then the distance is straightforward:

if ((point - leftBorder) < (rightBorder - point))
    distance = leftBorder - point;
else
    distance = rightBorder - point;

Note that, we could find the nearest points alternatively by ceiling:

rightBorder = spacing * ceil(point/spacing);
leftBorder = rightBorder - spacing;