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> NURMS CIPHER

nurms difficulty: 3–6 field: computer-aided design (CAD)

The idea in plain English: NURBS (Non-Uniform Rational B-Splines) are a way to represent smooth curves and surfaces using control points that have weights. A heavier weight pulls the curve closer to that control point. Think of it like magnets: stronger magnets (higher weights) pull the curve more. The message is encoded in these weight values. Given the control point positions and weights, you convert the normalized weights to ASCII codes to reveal the hidden message.

Why this really exists: NURBS are THE standard for 3D modeling in engineering. Every car body, airplane wing, ship hull, and consumer product is designed using NURBS surfaces in CAD software like Rhino, SolidWorks, CATIA, and Fusion 360. The name "NURMS" (Non-Uniform Rational Mesh Smooth) is a variant used in 3D game modeling. If you've ever driven a car, flown in a plane, or used a smartphone, you've touched something designed with NURBS.

▸ Concrete Example

3 control points with weights: w=[72, 101, 108]. Normalized:

Raw weights: [72, 101, 108]
Normalize to [0, 127] range: keep as-is since they're already ASCII

72 → 'H'
101 → 'e'
108 → 'l'
→ "Hel" (first part of a longer message)

The weights are the hidden data. The actual curve shape is irrelevant — the weights carry the information.

▸ How to Decode (Step by Step)

1. Get the control points and their weights from the puzzle data

2. Normalize weights to ASCII range (32-126)

3. Convert each weight to a character

4. Join → the answer word

word = ''.join(chr(int(round(w))) for w in weights)

▸ Real-World Applications

Automotive design: Every car body panel is modeled with NURBS surfaces
Aerospace: Airplane wings, fuselages, and turbine blades are NURBS-designed
Product design: iPhones, sneakers, and toothbrushes — all NURBS in CAD
Animation: Pixar uses subdivision surfaces (related to NURMS) for 3D characters

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