Different search scopes can produce different valid counts
A uniform comparison places every rectangle in the same horizontal orientation and compares that grid with a ninety-degree grid if rotation is permitted. A mixed search can combine both orientations in one arrangement. The two methods therefore do not necessarily produce the same footprint count. Compare the inputs and the actual placements before interpreting a larger number. The mixed result is a candidate for its stated geometry, not evidence of safer or more suitable handling.
This site’s identical-rectangle engine combines strip candidates with MaxRects heuristics. Its search is finite. It labels a result optimal only when it reaches a supported upper bound or a verified fixture; otherwise a found candidate remains best-found. Preserve that status beside the count. The word optimal applies to the stated rectangle model and assumptions, not to pallet strength, restraint, cost or an operational loading sequence.
Use a small example that a uniform grid misses
Assume a 500 by 500 mm square region and identical rectangles 300 by 200 mm, with zero gap, zero clearance and horizontal rotation allowed. A uniform orientation gives floor(500 / 300) times floor(500 / 200) = 1 times 2 = 2. The rotated uniform grid also gives two. The actual mixed search finds four by placing rectangles in a pinwheel-style arrangement with a central empty square.
The four origins and oriented dimensions returned for this example are (0,0) with 200 by 300, (0,300) with 300 by 200, (200,0) with 300 by 200, and (300,200) with 200 by 300. They fit within the boundary and do not overlap. The occupied area is four times 60000, or 240000 square millimeters, leaving 10000 of the 250000 square millimeter region unused.
| Check | Numerical result | Interpretation |
|---|---|---|
| Uniform 300 × 200 orientation | 1 × 2 = 2 | Same orientation in every position |
| Uniform 200 × 300 orientation | 2 × 1 = 2 | Other uniform option |
| Mixed valid candidate | 4 rectangles | Combines the two horizontal orientations |
| Area upper bound | floor(250000 / 60000) = 4 | No valid candidate can exceed four by area |
| Returned status and proof | optimal; area-upper-bound | Found count reaches the model upper bound |
| Occupied area fraction | 240000 / 250000 = 0.96 | Geometry only, not structural performance |
A best-found result can still improve on both uniform grids
For a second assumed scenario, use a 1200 by 800 mm region and identical 401 by 300 mm cases with zero spacing and rotation allowed. Each uniform orientation fits four. The current mixed engine finds six, while its area upper bound is floor(960000 / 120300) = 7. The returned status is best-found because the candidate does not reach that bound and this scenario has no applicable verified fixture proof.
Six is therefore a valid improvement discovered by this implementation, not a statement that seven is impossible. Conversely, an upper bound of seven is not a placement drawing for seven. It is a ceiling from area that may or may not be attainable under the exact geometry. Keep the six-case coordinates, count and status together. Do not report the upper bound as an available capacity or rename best-found as a guaranteed maximum.
Align spacing and permission before comparing algorithms
A uniform result with zero gap cannot be compared fairly with a mixed result that has an entered separation requirement. Use the same usable region, gap, edge clearance and rotation permission for both scenarios. Horizontal rotation swaps footprint sides but does not change the vertical case height. If a supplier instruction forbids the required orientation, a geometrically larger candidate does not authorize using it.
The engine represents identical rectangles in one run. It does not represent two independently sized case groups, irregular outlines, handles, fork access or support faces. A mixture of oriented copies of one footprint is different from a shipment containing different footprint sizes. Identify any mismatch between the load and model before relying on the returned count. A more sophisticated search still needs the correct objects and their measured outside dimensions.
Record a uniform-versus-mixed comparison
Write region and item dimensions, units, gap, clearance and rotation permission. Save both uniform counts and the mixed count, method, status, upper bound, proof and any search-limit flag. For the square example retain two versus four with area proof. For the 401 by 300 mm example retain four versus six, best-found and upper bound seven. Preserve actual placements for the selected candidate.
Review the returned drawing and status in the tool
Use the pallet configuration calculator for the two stated footprint scenarios. Compare the uniform candidates with the mixed result and inspect its pattern rather than copying the largest visible number. The basic uniform comparison for 401 by 300 mm cases establishes the narrower uniform task; it is not a link to the mixed six-case candidate.
If a result reports that a search limit was reached, retain that warning and avoid treating the search as exhaustive. Even without that flag, a best-found status remains unproven under the model. When a future implementation discovers another valid candidate, preserve the earlier input record and compare the new placements. That is evidence of a changed search result, not a change in the physical dimensions.
Choose the operational plan using evidence beyond the count
A valid four-rectangle pinwheel or six-case mixed pattern can support a geometric review, but real packages may need a permitted facing direction, accessible labels or an accepted stacking arrangement. Obtain those conditions separately and review the candidate against them. The diagnostic conclusion should identify which search scope explains the count difference and whether the maximum is proven. It should not convert a numerical improvement into a general claim about safety or pallet performance.
Reference scope
NIST length guidance supports consistent length units for the rectangle comparisons. Every region and spacing condition here is an explicitly stated geometric example.