# points-on-curve

This package calculate the points on a curve with a certain tolerance. It can also simplify the shape to use fewer points. 
This can really be useful when estimating lines/polygons for curves in WebGL or for Hit/Collision detections. 

## Install

From npm

```
npm install --save points-on-curve
```

The package is distributed as an ES6 module. 

## API

### pointsOnBezierCurves(points: Point[], tolerance?: number, distance?: number): Point[]

You pass in the points representing a bezier curve. Each point is an array of two numbers e.g. `[100, 123]`.

The points can also be a set of continuous curves where the last poing on the `Nth` curve acts as the first point of the next. 

```javascript
import { pointsOnBezierCurves } from 'points-on-curve';

const curve = [[70,240],[145,60],[275,90],[300,230]];
const points = pointsOnBezierCurves(curve);
// plotPoints(points);
```

![points on bezier](https://user-images.githubusercontent.com/833927/79051836-45630300-7be7-11ea-8cb6-cba2695a4807.png)

Same can be rendered with more **tolerance** (default value is 0.15):

```javascript
const points = pointsOnBezierCurves(curve, 0.7);
```
![points on bezier with 0.7 tolerance](https://user-images.githubusercontent.com/833927/79051837-45fb9980-7be7-11ea-9583-52cf882e770e.png)

Note that this method does not accept the number of points to render, but takes in a tolerance level which allows for better distribution of points. 

The value of **tolerance** can be between 0 and 1. It is used to decide how many points are needed in a section of the curve. The algorithm determined the *flatness* of a section of the curve and compares it to the *tolerance* level, if less flat, the segment gets further divided into 2 segments. 


#### Simplifying path

Based on the tolerance alone, this algorithm nicely provides enough points to represent a curve. It does not, however, efficiently get rid of unneeded points. The second *optional* argument in function, **distance** helps with that. If a `distance` value is provided, the method uses the [Ramer–Douglas–Peucker algorithm](https://en.wikipedia.org/wiki/Ramer%E2%80%93Douglas%E2%80%93Peucker_algorithm) to reduce the points. 

```javascript
const points = pointsOnBezierCurves(curve, 0.2, 0.15);
```

Following are the points generated with distance values of `0.15`, `0.75`, `1.5`, and `3.0`

![points with 0.15d](https://user-images.githubusercontent.com/833927/79051853-53b11f00-7be7-11ea-8970-7cc3f7621142.png)
![points with 0.75d](https://user-images.githubusercontent.com/833927/79051854-5449b580-7be7-11ea-9601-a1dd418b10d8.png)
![points with 1.5d](https://user-images.githubusercontent.com/833927/79051855-5449b580-7be7-11ea-9ab4-139beb0faf11.png)
![points with 3.0d](https://user-images.githubusercontent.com/833927/79051856-54e24c00-7be7-11ea-9f52-34e3ad9c81bd.png)

### curveToBezier(pointsIn: Point[]): Point[]

Sometimes it's hard to think of shape as a set of cubic bezier curves, each curve with 2 controls points. It is simple to just think of them as a curve passing through a set of points. 

This method turns those set of points to a set of points representing bezier curves.

```javascript
import { curveToBezier } from 'points-on-curve/lib/curve-to-bezier.js';

const curvePoints = [
  [20, 240],
  [95, 69],
  [225, 90],
  [250, 180],
  [290, 220],
  [380, 80],
];
const bcurve = curveToBezier(curvePoints);
// .. Plot bcurve
```
![Curve through points](https://user-images.githubusercontent.com/833927/79051797-12b90a80-7be7-11ea-92d2-5cb79adcbe30.png)

Now that we have bezier points, these could be passed to `pointsOnBezierCurves` function to get the points on the curve

![Curve through points](https://user-images.githubusercontent.com/833927/79051798-1351a100-7be7-11ea-8465-959a22b72371.png)


## License
[MIT License](https://github.com/pshihn/bezier-points/blob/master/LICENSE)