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Lathe revolution with partial angles

In your harnessMesh algorithmMIT

Revolve an (r, y) profile around the Y axis, fully or through a partial angle with flat cut faces, and compute the exact volume of the polygonal solid. Use it for vases, bowls, chess pieces and turned parts.

Render of Lathe revolution with partial angles
The render its check recorded in Godot 4.7.2, 256 by 256 pixels.

What it takes and gives

Entry points
demo_profile, lathe, revolved_volume, build, main
Parameters
profile, segments, angle
Complexity
O(profile points * segments)
Axes
+Y up, metres

Limits. Profile points need r >= 0 and should go from bottom to top; a profile that crosses the axis or itself gives an invalid solid. Open profiles (not ending on the axis) give open surfaces. Points on the axis collapse to single vertices, so pole faces are triangles.

Details

Kind
Mesh algorithm
Engine
Python 3.10 or later
Files
10 files, 237.5 KB
Licence
MIT
Declared effects
reads files, runs commands, writes files
Checked with
Godot 4.7.2, gl_compatibility, OpenGL 3 driver, Mesa llvmpipe under Xvfb
Checks
generator runs system python, generator runs verifier python, gltf strict structure, interpreters agree, example matches generator, godot headless gltf load, godot compatibility render
Techniques
Polygonal surface of revolution, Exact volume by Green's theorem: n sin(angle / n) times the profile's first moment
Tags
lathe, revolve, surface of revolution, turned parts, vase, modeling
Identity
library.supply.creative_originals.0dc84a43ffc3121d06f46407.c82b812faaa72318
Version
c82b812faaa72318cfa9045e484649b7c332c5f9780e9e7aee2014ae40f0e939

The version is the SHA-256 of the item your harness downloads; every file in it names its own checksum.

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