VibeGeometry/docs/research/translations/shriinivas-cartesian-function-graphs.md

Translation: Shriinivas Cartesian Function Graphs

Source

• Repository: https://github.com/Shriinivas/geometrynodes
• Source file: cartesian.blend
• Source groups:
  • Geometry Nodes Line
  • Geometry Nodes Parabola
  • Geometry Nodes Circle
• Geometry Script recreation: examples/geometry_script/shriinivas_cartesian_helper.py

Graph Family

These groups are three versions of the same procedural sentence:

make a simple path
read each point's position
compute a new Y value from X
move the path into that shape
give the curve physical thickness

The source file uses this sentence to draw Cartesian function curves. The line uses y = m*x + value. The parabola uses y = a*x^2 + b*x + c. The circle uses the helper graph twice:

y = sqrt(r^2 - x^2)
y = -sqrt(r^2 - x^2)

then joins the upper and lower arcs before giving them thickness.

Translation Summary

Line

Source group: Geometry Nodes Line

Geometry Script group: VG Cartesian Line

Mechanism:

• Build a two-point Curve Line from origin to (Length, 0, 0).
• Read the current field Position.
• Split position into X/Y/Z.
• Compute y = m*x + Value.
• Recombine (x, y, z).
• Feed the vector into Set Position.
• Convert the resulting curve to mesh using a circular profile.

Metaphor: the curve is a straight rail, and the position field is a set of chalk marks along it. The math node chain tells each chalk mark how high to stand. Set Position is the hand lifting those marks into place.

Parabola

Source group: Geometry Nodes Parabola

Geometry Script group: VG Cartesian Parabola

Mechanism:

• Build a line from (Start, 0, 0) to (End, 0, 0).
• Resample it to Sample Resolution points.
• Read each point's X coordinate.
• Compute y = a*x^2 + b*x + c.
• Move the resampled curve with Set Position.
• Tube the curve with Curve to Mesh.

Metaphor: resampling makes evenly spaced beads on a string. The parabola formula is the jig that bends each bead upward or downward based on its X address.

The source group has two input sockets named Resolution; only the later one drives Resample Curve.Count. The translation keeps the unused compatibility input as Resolution and names the active control Sample Resolution. This is one place where perfect socket-name mimicry would make the generated graph less legible.

Circle

Source group: Geometry Nodes Circle

Geometry Script group: VG Cartesian Circle

Mechanism:

• Compute left and right X endpoints from -r and r.
• Build an upper arc with sqrt(r^2 - x^2).
• Build a lower arc with the same helper and Value = -1.
• Move both arcs with Set Position.
• Join the two curves.
• Tube the joined curve with Curve to Mesh.

Metaphor: the helper graph is a compass arm. Run it once above the axis and once below the axis, then clamp the two strokes together into a full circle.

The source graph reuses NodeGroup.001 as nested group nodes. The installed Geometry Script code initially failed in this path under Blender 5.1 because its @tree returned function called a missing geometrynodegroup(...) symbol. We patched the repo-local Geometry Script clone so nested @tree calls create GeometryNodeGroup nodes directly, wire inputs, and expose typed outputs.

The translation now calls vg_cartesian_helper(...) twice inside VG Cartesian Circle, preserving the repeated motif as nested graph organs instead of expanding it inline.

Control Surfaces

These graphs expose the useful joints:

• Length: extent of the line along X.
• m: line slope.
• Value: line Y offset, and helper polarity/amplitude.
• Start / End: sampled X range for the parabola.
• a, b, c: parabola coefficients.
• r: circle radius.
• Thickness: curve profile radius.
• Sample Resolution: number of samples before bending a curve.

The important pattern is that controls should match geometric intent, not node incidental detail. A user wants radius, slope, coefficient, and thickness; they do not want to manage the third socket of a math node like a cursed vending machine.

Verification

Run:

& 'C:\Program Files (x86)\Steam\steamapps\common\Blender\blender.exe' --background '.\experiments\source-blends\shriinivas-cartesian.blend' --python '.\tools\verify_cartesian_translations.py'

Verification wraps each source and translated group in the same evaluator, evaluates the resulting mesh, and compares vertices.

Results from Blender 5.1.1:

Case	Vertices	Direct max delta	Sorted max delta	Status
Helper	200	0.0	0.0	accepted
Line	64	0.0	0.0	accepted
Parabola	992	0.0	0.0	accepted
Circle	2368	1.2999999523162842	0.0	accepted

Circle has identical geometry but different vertex order. For rendered geometry and shape behavior, sorted vertex equality is the relevant check. For simulations or downstream topology-sensitive processing, direct order would matter and should be preserved deliberately.

Lessons

• A field is weather over geometry: it has a value at every point, not one value globally. Position is the weather station every point carries.
• Set Position is the hinge where an abstract formula becomes visible geometry.
• Curve to Mesh is a lathe/extruder: it turns a weightless path into a tube by dragging a profile along it.
• Named Attribute plus Switch is a graceful override hook: if a radius attribute exists, use it; otherwise fall back to scale 1.0.
• Nested Geometry Script @tree calls are now viable after the patch branch in external/geometry-script. Use them when a repeated motif deserves to remain a named, inspectable organ in the generated Blender graph.
• Python helper functions are still useful for repeated authoring idioms that do not need to survive as named node groups.
• Socket names are part of the control contract. Geometry Script title-cases one-letter parameter names, so finalization currently renames R, M, A, B, and C back to r, m, a, b, and c.