✏️ The Parametric Pencil

source

Description

A masterclass in "Digital Lathe" modeling. Unlike standard geometric approximations, this pencil is constructed through a multi-layered assembly (Skin, Body, Coal) and then "sharpened" using a dedicated tool object. This ensures that the transitions between the lacquer, the cedar wood, and the graphite core follow the exact laws of geometry seen in real-world objects.

Key Features

• Simulated Sharpening: The tip is generated by subtracting a conical pencil_sharpener solid from the hexagonal body, creating perfect hyperbolic intersections on each face.

• Layered Anatomy: Features three distinct internal volumes:

  1. Coal (Lead): The central core.
  2. Body (Wood): The structural layer.
  3. Skin (Lacquer): The thin outer hexagonal shell.

• Hexagonal Ergonomics: A standard hex-profile defined by the distance across flats, providing a classic drafting tool aesthetic.

Technical Insight (Geometry):

The wavy edge where the hexagonal prism meets the sharpening cone is a result of the intersection of a plane and a cone. In 3D space, this intersection creates a hyperbolic curve on each of the six faces:

\[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\]