Home▸Mathematics▸Gift Wrapping: Minimal Surface & Packing Math

Gift Wrapping: Minimal Surface & Packing Math

Interactive 2D blueprint of the real minimum-wrapping-paper formula for a box, plus a genuine 2D shelf bin-packing visualization — adjust box dimensions, box count and container size to watch paper area and packing utilization recompute live.

Mathematics2DModerate60 FPS📱 Mobile-adapted⇄ 3D version

Details

CategoryMathematics

RenderingCanvas 2D

DifficultyModerate

Target FPS60

ControlsSliders for box length, width and height (drive the live minimal-paper formula and blueprint), plus number of boxes to pack and container size (drive a live 2D shelf-packing utilization readout); drag to pan and scroll to zoom the canvas; in Pack mode, click a placed rectangle to exclude it and see the algorithm repack the rest, with New Boxes and Repack All buttons.

geometryoptimizationbin-packingsurface-areanew-year

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The minimum rectangle of paper needed to wrap a box with no gaps has a provable formula, and fitting boxes into a container is the real, NP-hard bin-packing problem solved in practice with heuristics. This 2D view draws a technical blueprint of the box's unrolled net with live dimension readouts, and a genuine shelf-packing (NFDH) algorithm laying rectangles into a container — drag to pan, scroll to zoom, and click a placed rectangle to exclude it and watch the packing adapt.

⚙ Under the hood

A 2D blueprint of the real minimum-wrapping-paper formula for a box, plus a genuine 2D shelf bin-packing algorithm fitting rectangles into a container.

geometryoptimizationbin-packingsurface-areanew-year

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install