Math node
Distance
Measures the distance between two points, 2D or 3D (2D ignores Z). Start/End take any point value — a SIMD point, [x, y, z] numbers, or a whole cloud (measured from its centroid). Split XYZ swaps the structure inputs for plain X/Y/Z float ports. Metric: Euclidean (straight line), Manhattan (grid), Chebyshev (largest axis). Also outputs Delta (End−Start), Direction (normalized, zero-safe) and Midpoint as points.
Inputs
| Port | Type | Default |
|---|---|---|
| StartThe first point — any point value works: a SIMD point from the Points pipeline, [x, y, z] numbers, or a WHOLE cloud, which measures from its centroid (a one-point cloud is just the point). Hidden when Split XYZ is on. | structure | — |
| EndThe second point — same shapes as Start. Distance, Delta, Direction and Midpoint all run Start → End. | structure | — |
| Mode2D or 3D. 2D simply ignores Z wherever it came from — a 3D point in 2D mode measures on the XY plane; the Z float ports hide too. | int | 0 |
| MetricHow the axes combine: Euclidean = straight line (the default ruler), Manhattan = |dx|+|dy|+|dz| (grid travel), Chebyshev = the largest single axis (king's moves). Direction stays geometric (Euclidean) in every metric. | int | 0 |
| Split XYZSwaps the two structure inputs for plain float ports — Start X/Y(/Z), End X/Y(/Z) — for cabling single numbers straight from Math, Mouse or LFO nodes. 2D mode shows only X and Y. | bool | false |
| Start XSplit face: the first point's X in Grafit units. | float | 0 |
| Start YSplit face: the first point's Y in Grafit units. | float | 0 |
| Start ZSplit face: the first point's Z — only in 3D mode. | float | 0 |
| End XSplit face: the second point's X in Grafit units. | float | 0 |
| End YSplit face: the second point's Y in Grafit units. | float | 0 |
| End ZSplit face: the second point's Z — only in 3D mode. | float | 0 |
Outputs
| Port | Type |
|---|---|
| Distance | float |
| Delta | structure |
| Direction | structure |
| Midpoint | structure |
How It Works
Distance is the universal ruler, and it has two faces. The structure face (Mode: Points) takes any point value on Start and End — a point, three numbers, a dictionary with x/y/z, or a whole point cloud, which is measured from its centroid (two clouds measure centre to centre). Split XYZ swaps those in for plain Start X/Y/Z and End X/Y/Z float ports, for the times when the numbers arrive separately.
Beyond the scalar distance it emits the whole vector family that patches used to rebuild by hand: Delta (End − Start), Direction (normalized, and exactly zero at zero distance — never NaN) and Midpoint, all as points that open in Break Point.
Metric picks how the distance is counted: Euclidean (the straight line), Manhattan (the sum of the axis steps — a grid walk), Chebyshev (the largest single axis — a chessboard king's move). Direction stays geometric in all three, so only the number changes.
2D mode simply ignores Z, which is what you want for screen-space work.
Use Cases
- Proximity as a control — Two tracked hands into Start and End: the distance drives a synth's filter, a particle field's strength, or a crossfade.
- Aim one thing at another — Direction into Direction to Rotation gives the degrees any Rotation port wants, and Length gives the reach in the same breath.
- Draw the connection — Midpoint places a label; Delta sizes and orients the line between the two points.
- Cloud separation — Two point clouds into the structure ports measures centroid to centroid, which is the honest "how far apart are these two groups".
- Trigger on approach — Distance into Compare (< threshold) into Do Once fires exactly when two things meet.
Tips
- Direction is zero-safe: coincident points give an exactly zero vector, not NaN, so nothing downstream explodes.
- Use Manhattan when you are working on a grid (a DMX patch, a tile layout) — it reflects the real number of steps.
- For per-point distances across a whole cloud, reach for the points family rather than measuring centroids here.
- Delta opens in Break Point, so the individual axis differences are one node away.
- Distance is the node the owner rebuilt as the canonical example of how a Grafit project should read — see the Distance example project.
Open Distance in the interactive catalog →
Distance is one of 381 nodes in Grafit Pro.
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