💎 Parametric Diamond-Cut Ellipsoidal Vase¶
Description¶
A sophisticated exploration of complex surface texturing on organic forms. This model transcends basic geometric primitives by utilizing an ellipsoid of revolution as its base body. The primary challenge and achievement of this script lie in the precise mathematical mapping of a "diamond-cut" crystal pattern onto a surface with non-constant curvature.
Key Features¶
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Ellipsoidal Base Geometry: The vase profile is driven by an elliptical arc, creating a natural "swelling" form that provides more aesthetic depth than standard conical or cylindrical shapes.
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Procedural Diamond Lattice: The intricate facets are generated through the boolean subtraction of mirrored helical sweeps. The script dynamically adjusts the cutting path to account for the changing radius of the ellipsoid, ensuring perfect facet alignment from the weighted base to the polished rim.
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Optical Realism: Specifically designed for high-end PBR rendering, the geometry maximizes light refraction and internal "fire," mimicking the properties of heavy lead crystal.
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Deep Parametric Control: Every dimension—from the ellipsoid’s major/minor axes to the density and depth of the helical grooves—is fully adjustable, allowing for a wide range of silhouettes (from tall bud vases to wide decorative bowls).
Mathematical Insigh¶
To maintain a consistent cut depth on a curved surface, the tool-path radius \(r\) is calculated as a function of height \(z\) following the ellipsoidal equation:
This ensures that the "diamond" shapes remain undistorted even as the vase tapers towards the top and bottom.