> ## Documentation Index
> Fetch the complete documentation index at: https://docs.ntop.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Points or Frames based on Curvature

> AI context for Points or Frames based on Curvature. Not linked in navigation.

> This page is for AI assistant context only. To use this package, visit [community.ntop.com](https://community.ntop.com/packages/ajayprasad97/points-or-frames-based-on-curvature).

> **Community submission — not verified by nTop.** This package was submitted by an outside community member and has not been reviewed or verified by nTop. Treat its accuracy, safety, and compatibility claims with appropriate caution.

## Summary

Distribute points and frames non-uniformly along a spline, packing more into high-curvature regions and fewer into flat sections.

## Package Details

| Field            | Value                                                            |
| ---------------- | ---------------------------------------------------------------- |
| **ID**           | `points-or-frames-based-on-curvature`                            |
| **Type**         | Block                                                            |
| **Author**       | ajayprasad97                                                     |
| **Version**      | 0.1.0                                                            |
| **nTop Version** | 5.47                                                             |
| **Domain**       | Geometry                                                         |
| **Application**  | Curve                                                            |
| **Complexity**   | Intermediate                                                     |
| **Tags**         | `curvature`, `spline`, `points`, `frames`, `arc length`, `sweep` |
| **License**      | MIT                                                              |
| **Verified**     | No                                                               |

***

Generates a set of points (and matching reference frames) distributed non-uniformly along a spline, packing more points into high-curvature regions and fewer into flat/straight regions.

## Why not just space points evenly?

Evenly-spaced points either waste density on straight sections or under-resolve sharp bends. This block instead builds a curvature-weighted arc-length reparameterization, so point density tracks local geometric complexity.

## How it works

1. Sample curvature densely along the curve (step size = `Increment`).
2. Convert curvature into a weight list (higher curvature → higher weight, with a floor so flat regions still get some density).
3. Build a running total of the weights — a discrete integral.
4. Normalize that into a monotonic 0→1 curve — effectively a CDF (cumulative distribution function) over arc length, weighted by curvature.
5. Pick `Target Points` evenly-spaced levels in that 0→1 range.
6. For each level, invert the CDF to find the actual arc-length distance it corresponds to.
7. Evaluate the curve at each resulting distance to get the final point/frame outputs.

## Installation

Clone this repo or copy the package folder into your nTop workspace:

```bash theme={null}
git clone https://github.com/nTopology/Utilities-community.git
```

The package lives at `packages/ajayprasad97/points-or-frames-based-on-curvature/`.

## Usage

1. Open the provided `.ntop` file in nTop 5.47+.
2. Input a spline.
3. Set `Target Points` to the total number of points/frames to generate.

## Inputs & outputs

| Name            | Type       | Notes                                                                                                         |
| --------------- | ---------- | ------------------------------------------------------------------------------------------------------------- |
| `Spline`        | Spline     | The curve to distribute points along. Any degree, open or closed.                                             |
| `Target Points` | Integer    | Total number of output points/frames. Distributed non-uniformly by curvature, not spread evenly. Default: 50. |
| `Point`         | Point List | Output points, dense at high curvature.                                                                       |
| `Frame`         | Frame List | Local coordinate frames at those same points, useful for sweeps, cross-sections, or lattice orientation.      |

## Tuning

* `Increment`: controls sampling resolution of the underlying curvature scan. Smaller = more accurate but slower. Should scale with curve length rather than staying a fixed absolute value.
* The internal weight ramp (currently 0.2 → 1.0) controls how aggressively curvature pulls in extra points vs. how much minimum density flat sections retain. Raise the floor for more even coverage; lower it for more aggressive clustering at bends.

## Known limitations

* Very short or near-straight curves may need a smaller `Increment` to resolve curvature accurately.
* Cumulative sum is computed with an O(n²) custom block, fine at the \~400-500 sample counts used by default; revisit if curvature sampling resolution grows much finer.

## License

MIT.

***

## Source

[https://community.ntop.com/packages/ajayprasad97/points-or-frames-based-on-curvature](https://community.ntop.com/packages/ajayprasad97/points-or-frames-based-on-curvature)