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

Gift Wrapping: Minimal Surface & Packing Math (3D)

A real 3D box-wrapping and bin-packing simulator: derive the provable minimum-paper formula for wrapping a box with no gaps, watch the net fold onto the box, and pack multiple boxes into a container with a genuine extreme-point heuristic.

Mathematics3DAdvanced60 FPS📱 Mobile-adapted⇄ 2D version

Details

CategoryMathematics

RenderingThree.js · WebGL

DifficultyAdvanced

Target FPS60

ControlsSliders for box length, width and height (drive the live minimal-paper formula), plus number of boxes to pack and container size (drive the live packing utilization); a Fold/Unfold button animates the paper net closing onto the 3D box; in Pack mode, click any placed box 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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Wrapping a box without waste and packing boxes into a container are both real, well-studied geometric optimization problems. This simulator derives the provable minimum-paper formula for a standard no-gap fold and animates the net closing around a real 3D box, then switches to a genuine extreme-point bin-packing heuristic that stacks multiple boxes into a container and reports live utilization — click any placed box to exclude it and see the algorithm adapt.

⚙ Under the hood

Derive the real minimum-wrapping-paper formula for a box and watch a genuine extreme-point 3D bin-packing algorithm fit multiple boxes into a container.

geometryoptimizationbin-packingsurface-areanew-year

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install