vJSONLissajousSpline
Generate points on a 3D Lissajous-style curve from one of three formulas and four whole-number frequencies.
vJSONLissajousSpline has no input and outputs an array of XYZ points on a closed 3D curve. Formula picks the equations, Numbers A to D set the frequencies, and Points Count and Step set how finely the curve is sampled.
Parameters
| Parameter | Type | Default | Description |
|---|---|---|---|
| Formula | Dropdown | Formula A | Chooses Formula A, B or C. Default Formula A. |
| Number A | Integer | 5 | Frequency number A, used by all three formulas. Range 1 to 6, default 5. |
| Number B | Integer | 4 | Frequency number B, used by all three formulas. Range 1 to 6, default 4. |
| Number C | Integer | 1 | Frequency number C, used by all three formulas. Range 1 to 10, default 1. |
| Number D | Integer | 2 | Frequency number D, used by Formulas B and C only. Range 1 to 6, default 2. |
+3 more parameters
| Parameter | Type | Default | Description |
|---|---|---|---|
| Points Count | Integer | 1500 | Upper limit of the counter i. The loop runs while i is at most this value minus Step. Minimum 1, default 1500. |
| Step | Integer | 40 | Increment of the counter i for each point. Minimum 1, default 40. |
| Scale Factor | Float | 0.5 | Multiplier applied to X, Y and Z. Range 0 to 1, default 0.5. |
Read the full description
The node steps a counter i from 0 in increments of Step while i is at most Points Count - Step. For each i it computes the point from the formula, multiplies it by Scale Factor and writes it. With u(n) = i * n * 0.001, Formula A gives X = sin(u(A)), Y = cos(u(B)) and Z = sin(u(C)). Formula B gives X = (cos(u(A)) + cos(u(B))) / 2, Y = (sin(u(A)) + sin(u(C))) / 2 and Z = sin(u(D)). Formula C gives X = sin(u(A)) * (1 + cos(u(B))) / 2, Y = sin(u(A)) * (1 + sin(u(C))) / 2 and Z = sin(u(D)).
Number D is used only by Formulas B and C. The curve advances by Step * 0.001 * Number radians per point, so a larger Step spaces the points further apart along the curve. With the defaults (Formula A, A 5, B 4, C 1, D 2, 1500 points, Step 40, Scale Factor 0.5) the loop runs for i = 0, 40, ... 1440 and writes 37 points.
The node stops early when the curve comes back to its start. After the first 11 points, if the scaled X, Y and Z of a point are all within 0.02 of the first point, that point is written and the loop ends. Points Count is therefore a limit and not an exact count.
The output is a point list, not a smooth spline. Reduce Step to get more points on the same curve.
Example Connections
- Draw the curve
- Offset the curve before drawing
vJSONLissajousSpline.Output -> vJSONCameraProjection.ArrayA
vJSONCameraProjection.Output -> vJSONShapeRender.ArrayPoint
Background.Output -> vJSONShapeRender.Input
vJSONLissajousSpline.Output -> vJSONTranslate.ArrayA
vJSONTranslate.Output -> vJSONCameraProjection.ArrayA