Cluster Centroids

Cluster Span Bounds the Centroid

Use the strip endpoints as a quick reasonableness check before trusting the centroid arithmetic. In this toy cluster the hits span 1 to 2 meters, so the 5/4 meter centroid must stay between them; real reconstruction also has finite strip pitch, alignment offsets, thresholds, and resolution limits.

The centroid must remain inside the checked cluster span. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The span comes from the endpoint positions

The cluster endpoints are 1 meter and 2 meters.

1 m≤x≤2 m1\ \text{m}\le x\le2\ \text{m}
Cluster centroidWeighted hits place a centroid inside the span.w=3w=1centroidspan=1..2 mnumerator=5 mtotalWeight=4 countcentroid=5/4 mspan=1..2 m

The centroid must lie inside that span

The centroid 5 over 4 meters is between the endpoints.

1≤54≤21\le\frac{5}{4}\le2
Cluster centroidWeighted hits place a centroid inside the span.w=3w=1centroidspan=1..2 mnumerator=5 mtotalWeight=4 countcentroid=5/4 mspan=1..2 m