Points node
Superformula
Gielis’ superformula: six numbers (m, n1, n2, n3, a, b) draw a circle, a star, a flower, a shell — every one a port, so a Spectrum band, a PCA score or a Timeline curve can shape it. 2D gives a closed curve of Points; 3D applies the formula twice (profile × section) into a Rows × Points cloud. Morph blends toward a second parameter set with no blend shapes. Feed Points Visualize, Lines Visualize, Plexus, particles or Plot 3D; Radii is the shape as an array.
Inputs
| Port | Type | Default |
|---|---|---|
| Mode2D curve: one closed polyline of Points. 3D cloud: the formula applied twice, a Rows × Points latitude/longitude cloud. | int | 0 |
| MSymmetry: the number of lobes (6 = a hexagonal flower, 3 a triangle, 0 a circle). Non-integers open the curve — that is the morph look. | float | 6 |
| N1Overall roundness: small values pinch the lobes to spikes, large values round everything toward a circle. | float | 1 |
| N2Exponent on the cosine term — sharpens or softens one family of lobes. | float | 7 |
| N3Exponent on the sine term — the other family of lobes. | float | 18 |
| AHorizontal stretch of the base shape (1 = round). | float | 1 |
| BVertical stretch of the base shape (1 = round). | float | 1 |
| Morph0 = the first parameter set, 1 = the second (M2, N1 2, N2 2, N3 2); in between the shape morphs with no blend shapes — cable a Timeline. | float | 0 |
| M2Second set: symmetry. | float | 3 |
| N1 2Second set: roundness. | float | 0.5 |
| N2 2Second set: cosine exponent. | float | 0.5 |
| N3 2Second set: sine exponent. | float | 16 |
| PointsPoints around the curve (3…4096). | int | 256 |
| RowsLatitude rows of the 3D cloud (3…256). | int | 32 |
| ScaleSize in Grafit units (with Normalize on, the largest radius becomes exactly Scale). | float | 0.5 |
| RotationTurns the shape, degrees clockwise. | float | 0 |
| NormalizeDivide by the largest radius so the shape never blows up when the exponents change; off = the raw formula values. | bool | true |
Outputs
| Port | Type |
|---|---|
| PointsPoints around the curve (3…4096). | structure |
| Count | int |
| Radii | float |
| Max Radius | float |
How It Works
Superformula brings Gielis' shape DNA to the points family. Six numbers — m, n1, n2, n3, a, b — draw a circle, a star, a flower or a shell, and every one of them is a port, so a Spectrum band, a PCA score or a Timeline curve can shape the form directly.
In 2D the formula produces a closed curve of Points. In 3D it is applied twice — once for the profile, once for the section — into a Rows × Points cloud, which is how the superformula makes shells, seed pods and radiolaria.
Morph slides toward a second parameter set (M2, N1 2, N2 2, N3 2) with no blend shapes involved — the formula is simply evaluated with interpolated numbers, so every intermediate is a real superformula shape. Cable a Timeline into Morph and the form breathes between two identities.
Normalize keeps the largest radius at the same size while the parameters change, so a morph does not pulse in scale. Radii hands the shape out as a plain array and Max Radius reports its extent.
Use Cases
- Audio-reactive form — Band levels from Spectrum into m and n1: the shape grows petals with the music.
- Oscilloscope music — A 2D superformula into Scope Voice is the canonical "hear a shape" patch; the drawing is the timbre.
- Generative 3D — 3D mode into Plot 3D or Points Visualize gives shells and pods that no modeller was needed for.
- Data as shape — Six analysis outputs into the six parameters makes a form that is the measurement, a shape signature you can recognise.
- Morph loops — A Timeline curve on Morph gives an endless transformation between two shapes, with no blend targets to author.
Tips
- m controls the symmetry (how many lobes); n1 controls how pinched or inflated they are. Start there and leave a and b at 1.
- Small n1 values make sharp spikes; large ones round the form out. Negative territory is where the strange shapes live.
- In 3D, Rows is the profile resolution and Points is the section resolution — raise the one that looks faceted.
- Turn Normalize off when you want the shape to grow and shrink as the parameters change.
- Radii is useful on its own: it is a one-dimensional signature of the shape that Plot can draw.
Open Superformula in the interactive catalog →
Superformula is one of 381 nodes in Grafit Pro.
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