Price Simplification [LuxAlgo]

The Price Simplification indicator provides a streamlined representation of price action by reducing complex market movements into essential trend segments using the Ramer-Douglas-Peucker (RDP) algorithm.

This indicator calculates its output based on a fixed window of historical data. Consequently, the line segments are displayed retrospectively and are subject to repainting as new bars develop and the calculation window shifts.

🔶 USAGE

The indicator is designed to help traders identify the core structure of price movement by filtering out "noise"—small fluctuations that do not significantly impact the overall trend. By simplifying the price into a series of connected segments, it becomes easier to visualize support/resistance levels, trend slopes, and market geometry.

Users can adjust the level of simplification to suit their needs:

• A lower ATR Multiplier will result in a line that follows price closely, capturing more minor swings.
  
• A higher ATR Multiplier will produce a more aggressive simplification, highlighting only the most significant market turns.
  

🔹 Extension Line

The script includes an "Extend Last Segment" feature. When enabled, it projects the trajectory of the final simplified segment into the future using a dashed line. This projection begins one bar after the most recent data point, providing a visual guide for the current price momentum without overlapping the historical simplification.

🔶 DETAILS

The core logic of this tool relies on the Ramer-Douglas-Peucker (RDP) algorithm, a classic algorithm used in computer graphics and cartography to reduce the number of points in a curve.

The algorithm works through an iterative process:

1. It starts with a line segment connecting the first and last points of the lookback window.
   
2. It identifies the point between these two ends that is furthest from the segment (perpendicular distance).
   
3. If this maximum distance is greater than a specified threshold, that point is kept as a "key point," and the algorithm splits the segment into two parts, repeating the process for each.
   
4. If no point is further than the threshold, all intermediate points are discarded, and the segment remains a straight line.
   

To ensure the simplification remains consistent across different assets and timeframes, the script normalizes price coordinates using the Average True Range (ATR). This means the threshold for keeping a point is relative to the current market volatility rather than a fixed price value.

🔶 SETTINGS

• Window Size: The number of recent bars used to apply the RDP algorithm to.
  
• ATR Multiplier: The sensitivity of the simplification. Higher values lead to fewer segments and a simpler line.
  
• ATR Length: The period used to calculate the ATR for price normalization.
  
• Line Color: The color of the simplified polyline.
  
• Line Width: The thickness of the polyline and extension.
  
• Extend Last Segment: When enabled, projects the slope of the final segment forward as a dashed line starting one bar after the last point.