🍷Crystal Wineglass

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Description

A sophisticated study in complex surface detailing using helical intersections. The model features a classic "diamond-cut" crystal pattern achieved by projecting and subtracting mirrored helical paths along a conical surface. This demonstrates advanced control over 3D paths in CadQuery, where the radius of the cutting tool evolves with the height of the glass.

Key Features

• Conical Helix Patterning: Procedural diamond facets generated through the intersection of left-handed and right-handed conical spirals.

• Faceted Stem: A multi-stage stem transition that enhances light refraction and provides a tactile grip.

• Optical Realism: Designed to maximize the "fire" of the crystal in PBR environments, showcasing complex internal reflections.

• Variable Geometry: Every element—from the bowl's taper to the facet depth—is controlled by parameters, allowing for instant transformation from a shot glass to a flute.

The Math of the Conical Helix

To map the lines correctly on a tapering bowl, the radius \(r\) must be a function of the height \(z\). If the cone has a half-angle \(\alpha\), the path follows:

\[x(\theta) = (R_{base} + z \cdot \tan \alpha) \cos(\theta)\]

\[y(\theta) = (R_{base} + z \cdot \tan \alpha) \sin(\theta)\]