# Cubic Bézier Curve Extrapolation

Cubic Bézier Curve Extrapolation is an indicator on [Vela](https://vela.luxalgo.com/chart), our next-generation charting platform, written in Pine Script®.

A drawing-style tool that builds a cubic Bézier curve from four user-positioned control points (starting at the first, ending at the last, bent by the two in between) and extrapolates it forward to project the path of price. The curve colors itself by direction and needs almost no configuration: just reposition the points like any drawing object. For traders who want smooth, hand-shaped trend projection.

- Indicator in the LuxAlgo Library, by LuxAlgo, published Mar 7, 2022.
- Access: free.
- Concepts: [Polynomial Regression](https://www.luxalgo.com/library/concept/polynomial-regression/) (primary)
- Open on Vela: https://vela.luxalgo.com/chart?pineScriptCodeId=cmpwn13fy001fvhsghbkfkl12
- Page: https://www.luxalgo.com/library/indicator/cubic-b-zier-curve-extrapolation/

**Cubic Bézier Curve Extrapolation** fits a smooth Bézier curve through four control points placed on the chart, then extends it forward to sketch where the current dynamic could lead. Where [polynomial curve fitting](https://www.luxalgo.com/library/concept/polynomial-regression/) solves for a shape from price data alone, a Bézier construction hands the shape to the trader: the curve always begins at the first control point and ends at the last, while the middle points bend its path. This build evaluates the curve polynomially: the degree is one less than the number of control points, hence cubic from four.

## How to Trade the Cubic Bézier Curve Extrapolation?

- **Place the control points**: drag the four points like a standard drawing object: onto swing highs and lows, or positioned to capture the nuance of the recent trend.
- **Read the projection**: the extrapolated segment estimates how the fitted dynamic extends forward, a visual hypothesis for continuation or a rounding turn.
- **Watch the color**: the curve shifts hue with direction (one shade for the rising phase, a second once it rolls lower), separating phases at a glance.

Bézier fitting favors smoothness over exact data fit, so treat projections as scenario guides rather than forecasts. Traders who need the curve to hug the data more tightly may find rational Bézier curves a better match.

## Cubic Bézier Curve Extrapolation Settings

- **Extrapolation Length**: how many observations the curve is projected forward.
- **Source**: listed in the settings but not used; the curve is built only from the four control points' prices.
- **Width**: line thickness, alongside the two direction-based colors.

## Frequently Asked Questions

### How is this different from regression-based extrapolation?

[Polynomial Regression Extrapolation](https://www.luxalgo.com/library/indicator/polynomial-regression-extrapolation/) derives its curve from price by least squares with no manual input, while the Bézier version gives you four control points to shape the fit yourself. Regression for objectivity, Bézier for control.

### Is there much to configure?

Very little. Beyond the extrapolation length, usage amounts to positioning the control points. Repositioning them as structure evolves is the intended workflow, exactly like managing any drawing on the chart.

### How can I start using the Cubic Bézier Curve Extrapolation?

Free on the LuxAlgo Library. Quant, our coding agent, will load it straight from this page whenever you want to experiment with control-point placement. You can also copy the source code from this page and run it anywhere Pine Script® runs.

## Related indicators

- [Polynomial Regression Extrapolation](https://www.luxalgo.com/library/indicator/polynomial-regression-extrapolation/) (Polynomial Regression): markdown at https://www.luxalgo.com/library/indicator/polynomial-regression-extrapolation.md
- [Daily Polynomial Regressions](https://www.luxalgo.com/library/indicator/daily-polynomial-regressions/) (Polynomial Regression): markdown at https://www.luxalgo.com/library/indicator/daily-polynomial-regressions.md
- [Spline Quantile Regression Channel](https://www.luxalgo.com/library/indicator/spline-quantile-regression-channel/) (Polynomial Regression): markdown at https://www.luxalgo.com/library/indicator/spline-quantile-regression-channel.md
- [Bitcoin Power Law](https://www.luxalgo.com/library/indicator/bitcoin-power-law/) (Linear Regression): markdown at https://www.luxalgo.com/library/indicator/bitcoin-power-law.md
- [Recursive Least Squares Forecast](https://www.luxalgo.com/library/indicator/recursive-least-squares-forecast/) (Linear Regression): markdown at https://www.luxalgo.com/library/indicator/recursive-least-squares-forecast.md
- [Adaptive Harmonic Forecast](https://www.luxalgo.com/library/indicator/adaptive-harmonic-forecast/) (FFT/spectral Analysis): markdown at https://www.luxalgo.com/library/indicator/adaptive-harmonic-forecast.md
- [Kalman Filter](https://www.luxalgo.com/library/indicator/kalman-filter/) (Statistics): markdown at https://www.luxalgo.com/library/indicator/kalman-filter.md
- [Bitcoin Expectile Model](https://www.luxalgo.com/library/indicator/bitcoin-expectile-model/) (Quantile Regression): markdown at https://www.luxalgo.com/library/indicator/bitcoin-expectile-model.md

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Source: https://www.luxalgo.com/library/indicator/cubic-b-zier-curve-extrapolation/ (LuxAlgo Library). Free to use with attribution: https://www.luxalgo.com/library/license/