Auto Trendlines

Features

• Directional or Combinatorial pair scan — Directional only keeps falling resistance / rising support anchors; Combinatorial evaluates every pivot pair and refits the line through all inliers via OLS (optionally shifted outward to the outermost inlier in “Outer” fit mode)
• ATR-based tolerance — adapts to market volatility, no fixed pip distance
• Composite quality score — touches, span, extreme-anchor bonus, recency, fit tightness and violation penalty combined into a single score
• Violation & relevance filters — candidates with too many close/wick violations between anchors, or too far from current price, are dropped
• Greedy non-overlap — top-scoring lines are selected first; each pivot contributes to one line at most
• Retest highlighting — lines within a configurable ATR distance of price are emphasized, with optional distance label
• Touch-count labels — small label at the right end of each line shows the number of pivots it connects
• Optional convex hull — Andrew’s monotone-chain envelope (strictest descending / ascending boundary), drawn dotted in a separate color

Algorithm

For each direction (highs → resistance, lows → support):

1. Candidate generation — O(N²)

For each pair (i, j) of pivots:

1. Compute the anchor line y = slope·x + intercept from (xi, yi) and (xj, yj)

2. Find inliers — pivots with |y_actual − y_line| ≤ tolerance × ATR

3. If at least minTouches inliers, refit the line via OLS through them:

   slope     = (n·Σxy − Σx·Σy) / (n·Σx² − (Σx)²)
   intercept = (Σy − slope·Σx) / n

4. Re-evaluate inliers on the refined line — final touch count and residual sum

5. Filter: drop candidates with too many violations between anchors (unless anchored at an extreme), too far from current price, or outside the Sloped/Near-horizontal display mode

6. Score the candidate:

   score = touches · span · extreme_bonus · recency_bonus · fit_factor · violation_penalty

   • touches · span rewards multi-touch lines covering longer time ranges
   • extreme_bonus rewards lines anchored at the most extreme pivots (0.5 if none, up to 3.0)
   • recency_bonus linear decay from 1.0 (newest pivot at current bar) to 0.2 (newest pivot at lookback edge)
   • fit_factor = 1 / (1 + avg_residual / tol) rewards tight fits
   • violation_penalty = 1 / (1 + violation% / 5) punishes lines price crossed often

2. Sorting & greedy selection

Candidates are sorted by score descending (selection sort on indices). Iterating in score order:

• Compute the current candidate’s still-unused inliers
• If at least minTouches are still unused, draw the line and mark its inliers as used
• Stop after maxLines per direction

This way the strongest line wins, and weaker overlapping candidates are skipped.

3. Convex hull (optional)

For pivot highs → upper hull (resistance envelope); for pivot lows → lower hull (support envelope). Andrew’s monotone-chain algorithm:

for each pivot p in chronological order:
    while last two hull points + p form a "wrong-way" turn:
        pop last hull point
    push p onto hull

Wrong-way turn for the upper hull = cross product ≥ 0 (the second-to-last point lies below the line connecting its neighbors). The hull is drawn as a dotted polyline — every drawn segment lies above (resistance) or below (support) all original pivots in its span.

Inputs

Input	Default	Description
Left Bars / Right Bars	5 / 5	Pivot confirmation window
Line Fit	Outer	OLS or Outer (OLS shifted to outermost inlier)
Detection Method	Directional	Directional or Combinatorial pair scan
Min Touches	3	Minimum pivots a line must connect
Tolerance (× ATR)	1.0	Vertical distance threshold for “on the line”
Lookback (bars)	200	How far back pivots are considered
Max Lines per Direction	3	Cap on drawn resistance and support lines
Min Line Span (bars)	15	Minimum distance between oldest and newest touch
Max Violation %	20	Max share of bars crossing the line between anchors
Bars past last touch	30	Projection length beyond the newest touch
Show	Both	Sloped / Near-horizontal / Both
Max current distance (× ATR)	5.0	Relevance filter vs. current price
Highlight active retest	on	Emphasize lines within retest distance, optional label
Show touch-count label	on	Label at the right end with the touch count
Show convex-hull envelope	off	Draw the hull as a dotted reference
Colors / width / style	red / green / 2 / Solid	Visual settings

Notes

• Pivots are confirmed pivRight bars after the actual extreme — non-repainting once locked in. Lines update on each new confirmed pivot.
• The OLS refinement is the key reason an OLS-based line generally fits closer to the data than a naive 2-point line. The slope is the slope that minimizes the sum of squared vertical residuals across the inliers.
• The greedy non-overlap step prevents near-duplicate lines when two pivot pairs produce the same trend.
• If lines are too sparse or too dense, the main knobs to tune are: pivLeft / pivRight (more pivots), tolMult (stricter / looser fit), minTouches (clean / busy), lookback (history depth).
• Convex hull is opt-in. The hull’s segments are mathematically the strictest possible boundary lines but may fragment into many short edges in choppy markets. Useful as a “primary envelope” in clean trends.

Mathematical references

• Ordinary least squares (OLS): minimizes Σ(yᵢ − (m·xᵢ + b))² over all inlier points; closed-form solution as above.
• Convex hull (upper/lower): Andrew’s monotone-chain algorithm — O(n log n) general, O(n) when input is already sorted by x (as pivots are, by bar_index).
• RANSAC analogy: the combinatorial pair scan is a deterministic version of RANSAC where every pair (instead of random samples) is tested. Suitable for the small N typical of pivot sets (≤ 50).