{ "meta": { "note": "True-shape nesting on rectangular and near-rectangular laser plates (synthetic, defined in the script): exact grids at zero spacing, grids with a laser gap and edge clearance, mixed rectangle orders and rounded plates with bolt holes. `lbf` (default, synchronous) and `max` (asynchronous, 15 s) through the LIVE Engine API.", "lowerBound": "ceil(total part area (outline minus holes) / sheet area) — no plan can use fewer sheets. For the zero-spacing grid jobs the parts tile the sheet exactly, so the bound is the optimum; with spacing it is weaker.", "determinism": "`lbf` is deterministic (one run). `max` is time-boxed; the page reports its worst run.", "validation": "Every layout re-placed from the response: all parts placed; every outline on its sheet and at least edgeClearance from its edges; no two outlines overlapping (triangulated, separating-axis depth) or closer than minSeparation (segment distance), each within the response's rounding tolerance.", "rotation": "Free rotation (the API default) on every job; `tilted` counts parts placed off the right angles.", "server": "https://api.cutoptim.com", "measuredAt": "2026-09-28", "engineVersion": "1.0.0+nest-d4046d5-ba8581bb", "runsPerJob": 2, "budgetMs": 15000, "script": "scripts/research/nest-rect-benchmark.ts", "reproduce": "CO_KEY= npx tsx scripts/research/nest-rect-benchmark.ts" }, "summary": { "jobs": 20, "valid": 20, "allPlaced": 20, "lbfOnBound": 14, "maxOnBound": 14, "gridJobs": 5, "gridOnBound": 5, "lbfSheets": 70, "maxSheetsWorst": 70, "boundSheets": 63, "partsPlaced": 1226, "tiltedLbf": 13, "tiltedMax": 13 }, "rows": [ { "id": "grid-500", "family": "grid", "sheet": { "w": 3000, "h": 1500 }, "gap": 0, "edge": 0, "types": 1, "parts": 36, "bound": 2, "lbf": { "sheets": 2, "placed": 36, "tilted": 0, "density": 1 }, "max": { "minSheets": 2, "maxSheets": 2, "sheets": [ 2, 2 ], "placed": 36, "tilted": 0, "wallS": [ 2.1, 2.1 ] }, "valid": true, "checks": { "maxPenetration": 0, "minEdge": 0, "minGap": null } }, { "id": "grid-250", "family": "grid", "sheet": { "w": 3000, "h": 1500 }, "gap": 0, "edge": 0, "types": 1, "parts": 144, "bound": 2, "lbf": { "sheets": 2, "placed": 144, "tilted": 0, "density": 1 }, "max": { "minSheets": 2, "maxSheets": 2, "sheets": [ 2, 2 ], "placed": 144, "tilted": 0, "wallS": [ 4.2, 3.8 ] }, "valid": true, "checks": { "maxPenetration": 0, "minEdge": 0, "minGap": null } }, { "id": "grid-1000x500", "family": "grid", "sheet": { "w": 3000, "h": 1500 }, "gap": 0, "edge": 0, "types": 1, "parts": 27, "bound": 3, "lbf": { "sheets": 3, "placed": 27, "tilted": 0, "density": 1 }, "max": { "minSheets": 3, "maxSheets": 3, "sheets": [ 3, 3 ], "placed": 27, "tilted": 0, "wallS": [ 2.1, 2.1 ] }, "valid": true, "checks": { "maxPenetration": 1.1368683772161603e-13, "minEdge": 0, "minGap": null } }, { "id": "grid-625x250", "family": "grid", "sheet": { "w": 2500, "h": 1250 }, "gap": 0, "edge": 0, "types": 1, "parts": 40, "bound": 2, "lbf": { "sheets": 2, "placed": 40, "tilted": 0, "density": 1 }, "max": { "minSheets": 2, "maxSheets": 2, "sheets": [ 2, 2 ], "placed": 40, "tilted": 0, "wallS": [ 2.1, 2.1 ] }, "valid": true, "checks": { "maxPenetration": 1.1368683772161603e-13, "minEdge": 0, "minGap": null } }, { "id": "grid-mixed", "family": "grid", "sheet": { "w": 3000, "h": 1500 }, "gap": 0, "edge": 0, "types": 2, "parts": 24, "bound": 2, "lbf": { "sheets": 2, "placed": 24, "tilted": 0, "density": 0.6667 }, "max": { "minSheets": 2, "maxSheets": 2, "sheets": [ 2, 2 ], "placed": 24, "tilted": 0, "wallS": [ 2.1, 2.2 ] }, "valid": true, "checks": { "maxPenetration": 5.684341886080802e-14, "minEdge": 0, "minGap": null } }, { "id": "spaced-490", "family": "spaced", "sheet": { "w": 3000, "h": 1500 }, "gap": 5, "edge": 10, "types": 1, "parts": 36, "bound": 2, "lbf": { "sheets": 2, "placed": 36, "tilted": 0, "density": 0.9604 }, "max": { "minSheets": 2, "maxSheets": 2, "sheets": [ 2, 2 ], "placed": 36, "tilted": 0, "wallS": [ 2.1, 2.1 ] }, "valid": true, "checks": { "maxPenetration": 0, "minEdge": 10, "minGap": 5 } }, { "id": "spaced-590", "family": "spaced", "sheet": { "w": 2500, "h": 1250 }, "gap": 5, "edge": 10, "types": 1, "parts": 24, "bound": 3, "lbf": { "sheets": 3, "placed": 24, "tilted": 0, "density": 0.8911 }, "max": { "minSheets": 3, "maxSheets": 3, "sheets": [ 3, 3 ], "placed": 24, "tilted": 0, "wallS": [ 2.2, 2.1 ] }, "valid": true, "checks": { "maxPenetration": 0, "minEdge": 10, "minGap": 5 } }, { "id": "spaced-980x480", "family": "spaced", "sheet": { "w": 3000, "h": 1500 }, "gap": 10, "edge": 5, "types": 1, "parts": 18, "bound": 2, "lbf": { "sheets": 2, "placed": 18, "tilted": 0, "density": 0.9408 }, "max": { "minSheets": 2, "maxSheets": 2, "sheets": [ 2, 2 ], "placed": 18, "tilted": 0, "wallS": [ 2.1, 2.1 ] }, "valid": true, "checks": { "maxPenetration": 0, "minEdge": 5, "minGap": 10 } }, { "id": "orders-1", "family": "orders", "sheet": { "w": 3000, "h": 1500 }, "gap": 5, "edge": 10, "types": 9, "parts": 92, "bound": 5, "lbf": { "sheets": 5, "placed": 92, "tilted": 0, "density": 0.8144 }, "max": { "minSheets": 5, "maxSheets": 5, "sheets": [ 5, 5 ], "placed": 92, "tilted": 0, "wallS": [ 2.1, 2.1 ] }, "valid": true, "checks": { "maxPenetration": 0, "minEdge": 10, "minGap": 4.999999999999943 } }, { "id": "orders-2", "family": "orders", "sheet": { "w": 2500, "h": 1250 }, "gap": 5, "edge": 10, "types": 8, "parts": 64, "bound": 4, "lbf": { "sheets": 5, "placed": 64, "tilted": 0, "density": 0.7475 }, "max": { "minSheets": 5, "maxSheets": 5, "sheets": [ 5, 5 ], "placed": 64, "tilted": 0, "wallS": [ 6.3, 6.3 ] }, "valid": true, "checks": { "maxPenetration": 0, "minEdge": 10, "minGap": 5 } }, { "id": "orders-3", "family": "orders", "sheet": { "w": 3000, "h": 1500 }, "gap": 5, "edge": 10, "types": 9, "parts": 103, "bound": 6, "lbf": { "sheets": 6, "placed": 103, "tilted": 0, "density": 0.8639 }, "max": { "minSheets": 6, "maxSheets": 6, "sheets": [ 6, 6 ], "placed": 103, "tilted": 0, "wallS": [ 4.2, 2.1 ] }, "valid": true, "checks": { "maxPenetration": 0, "minEdge": 10, "minGap": 5 } }, { "id": "orders-4", "family": "orders", "sheet": { "w": 2500, "h": 1250 }, "gap": 5, "edge": 10, "types": 9, "parts": 75, "bound": 5, "lbf": { "sheets": 5, "placed": 75, "tilted": 0, "density": 0.8817 }, "max": { "minSheets": 5, "maxSheets": 5, "sheets": [ 5, 5 ], "placed": 75, "tilted": 0, "wallS": [ 2.1, 2.1 ] }, "valid": true, "checks": { "maxPenetration": 0, "minEdge": 10, "minGap": 4.999999999999943 } }, { "id": "orders-5", "family": "orders", "sheet": { "w": 3000, "h": 1500 }, "gap": 5, "edge": 10, "types": 6, "parts": 46, "bound": 3, "lbf": { "sheets": 3, "placed": 46, "tilted": 0, "density": 0.8162 }, "max": { "minSheets": 3, "maxSheets": 3, "sheets": [ 3, 3 ], "placed": 46, "tilted": 0, "wallS": [ 2.1, 2.1 ] }, "valid": true, "checks": { "maxPenetration": 0, "minEdge": 10, "minGap": 5 } }, { "id": "orders-6", "family": "orders", "sheet": { "w": 2500, "h": 1250 }, "gap": 5, "edge": 10, "types": 9, "parts": 95, "bound": 6, "lbf": { "sheets": 7, "placed": 95, "tilted": 0, "density": 0.759 }, "max": { "minSheets": 7, "maxSheets": 7, "sheets": [ 7, 7 ], "placed": 95, "tilted": 0, "wallS": [ 6.3, 8.3 ] }, "valid": true, "checks": { "maxPenetration": 0, "minEdge": 10, "minGap": 5 } }, { "id": "orders-7", "family": "orders", "sheet": { "w": 3000, "h": 1500 }, "gap": 5, "edge": 10, "types": 6, "parts": 39, "bound": 2, "lbf": { "sheets": 3, "placed": 39, "tilted": 0, "density": 0.6266 }, "max": { "minSheets": 3, "maxSheets": 3, "sheets": [ 3, 3 ], "placed": 39, "tilted": 0, "wallS": [ 20.7, 18.7 ] }, "valid": true, "checks": { "maxPenetration": 0, "minEdge": 10, "minGap": 4.99999999999995 } }, { "id": "orders-8", "family": "orders", "sheet": { "w": 2500, "h": 1250 }, "gap": 5, "edge": 10, "types": 9, "parts": 71, "bound": 6, "lbf": { "sheets": 8, "placed": 71, "tilted": 0, "density": 0.7185 }, "max": { "minSheets": 8, "maxSheets": 8, "sheets": [ 8, 8 ], "placed": 71, "tilted": 0, "wallS": [ 6.3, 6.3 ] }, "valid": true, "checks": { "maxPenetration": 0, "minEdge": 10, "minGap": 5 } }, { "id": "plates-1", "family": "plates", "sheet": { "w": 3000, "h": 1500 }, "gap": 5, "edge": 10, "types": 2, "parts": 35, "bound": 1, "lbf": { "sheets": 1, "placed": 35, "tilted": 0, "density": 0.765 }, "max": { "minSheets": 1, "maxSheets": 1, "sheets": [ 1, 1 ], "placed": 35, "tilted": 0, "wallS": [ 2.1, 2.1 ] }, "valid": true, "checks": { "maxPenetration": 0, "minEdge": 10, "minGap": 5 } }, { "id": "plates-2", "family": "plates", "sheet": { "w": 3000, "h": 1500 }, "gap": 5, "edge": 10, "types": 4, "parts": 104, "bound": 3, "lbf": { "sheets": 4, "placed": 104, "tilted": 0, "density": 0.7215 }, "max": { "minSheets": 4, "maxSheets": 4, "sheets": [ 4, 4 ], "placed": 104, "tilted": 0, "wallS": [ 8.4, 6.3 ] }, "valid": true, "checks": { "maxPenetration": 0, "minEdge": 10, "minGap": 4.999999999999943 } }, { "id": "plates-3", "family": "plates", "sheet": { "w": 3000, "h": 1500 }, "gap": 5, "edge": 10, "types": 3, "parts": 71, "bound": 2, "lbf": { "sheets": 3, "placed": 71, "tilted": 13, "density": 0.6387 }, "max": { "minSheets": 3, "maxSheets": 3, "sheets": [ 3, 3 ], "placed": 71, "tilted": 13, "wallS": [ 12.5, 12.5 ] }, "valid": true, "checks": { "maxPenetration": 0, "minEdge": 10, "minGap": 5 } }, { "id": "plates-4", "family": "plates", "sheet": { "w": 3000, "h": 1500 }, "gap": 5, "edge": 10, "types": 4, "parts": 82, "bound": 2, "lbf": { "sheets": 2, "placed": 82, "tilted": 0, "density": 0.6886 }, "max": { "minSheets": 2, "maxSheets": 2, "sheets": [ 2, 2 ], "placed": 82, "tilted": 0, "wallS": [ 2.1, 2.2 ] }, "valid": true, "checks": { "maxPenetration": 0, "minEdge": 10, "minGap": 5 } } ] }