Off-by-one Error when partitioning rectangle

Question

I am trying to split a Rectangle into same-sized buckets, if there is not enough space at the border, the bucket is resized.

To determine the amount of Buckets, I use

int partitionsX = Math.Max((textureWidth / PartitionSize),1);
int partitionsY = Math.Max((textureHeight / PartitionSize), 1);
SampleBucket[] buckets = new SampleBucket[(partitionsX * partitionsY)];
for(int x=0; x < partitionsX; ++x)
{
    for(int y = 0;y < partitionsY; ++y)
    {
        int idx = x + (y * partitionsX);
        var bucketX = x * PartitionSize;
        var bucketY = y * PartitionSize;
        var bucketWidth = PartitionSize;
        var bucketHeight = PartitionSize;
        bucketWidth = Math.Min(bucketX + bucketWidth, (int)textureWidth) - bucketX;
        bucketHeight = Math.Min(bucketY + bucketHeight, (int)textureHeight) - bucketY;
        Debug.Assert(bucketWidth > 0);
        Debug.Assert(bucketHeight > 0);
        buckets[idx] = new SampleBucket()
        {
            X = bucketX,
            Y = bucketY,
            W = bucketWidth,
            H = bucketHeight,
            SampleLocations = Enumerable.Repeat(new SampleLocation() { Index = NOOP}, bucketWidth * bucketHeight).ToArray()
        };
    }
}

The problem occurs when I try to fill the buckets with my data.

foreach(var l in sampleLocations)
{
    int bucketX = (int)(l.PixelX / PartitionSize); // PixelX/PixelY is absolute within the original texture/rectangle
    int bucketY = (int)(l.PixelY / PartitionSize);
    int bucketIdx = bucketX + bucketY * partitionsX;
    Debug.Assert(bucketIdx < buckets.Length);
    var bucket = buckets[bucketIdx]; // OOB occurs here, but I don't know where my mistake is
    var locations = bucket.SampleLocations;
    var sampleX = l.PixelX - bucket.X;
    var sampleY = l.PixelY - bucket.Y;
    var sampleIdx = sampleX + sampleY * bucket.W;
    Debug.Assert(sampleIdx < locations.Length);
    locations[sampleIdx] = l;
}

with textureWidth = 416, textureHeight = 452 and a SampleLocation at PixelX = 51 and PixelY = 448 I receive an Out of Bounds Bucket, when the PartitionSize is 32.

I triple checked the math but I can't find where my mistake is.

Demo with use-case that crashes: https://dotnetfiddle.net/VKYvpP

Answer 1

The lines where you determine the partitions X and Y is using integer math. This results in less buckets than required.

To resolve the issue, take the ceiling of size / partitionSize.

int partitionsX = Math.Max((int)Math.Ceiling(textureWidth / (float)PartitionSize),1);
int partitionsY = Math.Max((int)Math.Ceiling(textureHeight / (float)PartitionSize), 1);