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Parametric Trefoil Knot (Mathematical Sculpture)

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Description

The Trefoil Knot is the simplest example of a non-trivial knot in topology. This model is a (2,3)-torus knot, meaning it winds around a torus (donut shape) twice in one direction and three times in the other. It is a continuous, self-intertwining loop that demonstrates how CadQuery can handle complex 3D paths and smooth sweeping operations.

Key Features

  • Parametric Spline Path: The knot is generated using a set of parametric equations that define a seamless, periodic curve in 3D space:
\[x = \sin(t) + 2\sin(2t)\]
\[y = \cos(t) - 2\cos(2t)\]
\[z = -\sin(3t)\]

  • Sweep Geometry: The solid volume is created by sweeping a circular profile along the calculated spline, ensuring a constant cross-section throughout the entire loop.

  • Topological Perfection: The model is a single, manifold solid with no self-intersections, making it ideal for both mathematical visualization and 3D printing.

  • Adjustable Thickness: The diameter of the "rope" and the overall scale of the knot can be easily modified through script parameters.

Dimensions (Default)

  • Major Radius: 20 mm

  • Tube Diameter: 5 mm

  • Resolution: 100+ segments for a smooth surface.