Lap comparison math

The Analysis view compares laps of different lengths and speeds on one set of axes. This page explains the alignment, delta, consistency, and map math behind it.

Distance resampling — how laps are aligned

Laps are aligned by distance traveled, not by time. Every lap's sample series is resampled onto a uniform distance grid:

• grid points at 0, step, 2×step, … up to the lap's total distance (default step = 5 m; the API accepts 0.5–50 m);
• each channel is linearly interpolated onto the grid, with edge clamping (values before the first / after the last sample take the boundary value).

Two laps resampled this way have directly comparable values at every grid index: "what was each lap doing 850 m into the lap?" This is also a read-time downsample — a 2-minute lap goes from ~7,200 ticks to a few hundred grid points per channel.

Time delta

For each compared lap, at every grid distance d up to the shorter of the two laps:

delta_ms(d) = t_lap(d) − t_ref(d)      # both via interpolation of dist → t

Positive = slower than the reference at that point. The curve's slope is the insight: rising = losing time right here, flat = holding the gap, falling = gaining. The reference lap compared with itself is exactly zero, so it isn't drawn.

Speed deviation (consistency chart)

Across the session's best N laps (default 5), on the common distance grid (cut to the shortest lap):

• median speed at each grid point (middle value, or mean of the two middles);
• population standard deviation sqrt(Σ(v − mean)² ÷ n) at each grid point.

A spike in the deviation band marks a corner where your speed varies lap to lap — the first place to look for consistency gains.

Race line map

The map is a raw top-down plot of the recorded world coordinates (pos_x, pos_z) — no projection or rotation, GT7's coordinates are used as-is. Each reference-lap point is classified into an input zone:

Zone	Condition	Color
Braking	brake ≥ 1 %	red
Throttle	else throttle ≥ 1 %	green
Coasting	otherwise	blue

Other selected laps overlay as solid lines in their chart colors, so line differences are visible spatially. The chart cursor maps distance → grid index → coordinates, which is how hovering a chart moves the dots on the map.

Speed peaks & valleys

The ▲/▼ markers on the map are local speed extrema, found with a sliding window:

• a point is a peak if it is the maximum of the surrounding ±30 ticks (~0.5 s each side), a valley if it is the minimum;
• consecutive markers of the same kind must be at least 100 m apart.

Valleys approximate apexes (minimum corner speed) and peaks approximate the end of acceleration zones — without needing full corner detection.

Auto-numbered corners

The numbered circles on the map are corners detected from the reference lap's racing-line geometry (one canonical set, so every overlaid lap shares the same numbering). The detector was tuned empirically against real GT7 laps — 5 sessions across road courses and a banked oval — with one acceptance criterion: identical corner counts and < 30 m apex drift across laps of the same track. Pipeline:

1. Resample positions onto a uniform 2 m distance grid (strictly-increasing distances only), decoupling curvature from the 60 Hz speed-dependent spacing.
2. Signed curvature at each point: the wrapped angle between the chord headings of the 16 m windows before and after, divided by the span.
3. Hysteresis segmentation with thresholds anchored to the lap's own curvature noise floor (the p85 of frame-to-frame curvature jitter): on real GT7 telemetry (jitter ~0.0004) they land on the validated 0.0030/0.0022 rad/m enter/stay pair — sweeping lower flips the counts between laps; on smooth low-curvature data (jitter < 0.0001, e.g. the simulator's sweeping circuit) they relax to 0.0020/0.0013 so broad-radius corners still register — sweeping lower grew a phantom corner on a banked oval. A segment ends after 40 m below the stay threshold; strong opposite curvature splits immediately — an S-section is two corners even when the magnitude never dips.
4. Arcs turning less than 12° are noise and are dropped before merging — a surviving opposite blip would block a merge on some laps only, which was the dominant instability in early tuning.
5. Same-direction arcs within 90 m merge: a hairpin or double-apex complex whose curvature relaxes mid-arc stays one corner (real complexes contain 50–80 m low-curvature interludes).
6. A lap that starts mid-corner has that corner split across the start/finish line — the two edge arcs are stitched back into one (each half within 45 m of its lap edge, matching the mid-lap merge distance). The stitched corner's extent wraps the lap boundary (entry_dist > exit_dist), min speed covers both halves, and the apex comes from whichever half turns more. Stitching runs before the significance filter so a split corner is judged on its combined angle.
7. Keep arcs turning 25°–300°. Below is a kink; above is a spin, not a corner.
8. Apex = the curvature-weighted centroid of the segment, not the minimum-speed point: min speed sits at the segment edge (braking for the next corner) and wanders 60–110 m between laps, while the centroid stays within ~25 m. Minimum corner speed is still reported per corner as a stat.

The thresholds are deliberately a narrow band: raising the entry threshold above ~0.0035 loses banked/high-speed corners entirely (a 300 m-radius banked turn peaks at |κ| ≈ 0.004), and dropping the stay threshold below ~0.002 sinks into the road-noise floor and bleeds adjacent corners together.

Display rule: numbered circles while ≤ 30 corners are in view (the zoomed section or the whole lap); beyond that they collapse to small dots. The Corner Detail widget shows the current corner (T5 R) while the cursor is inside one.

Authored corners outrank detection

Detection is a fallback. It has to run per lap and it works off the racing line, so a driver who straightlines an S takes the same tarmac on a shallower arc, the arc drops below the 25° significance threshold, and every corner after it renumbers — "turn 4" then means different tarmac from one lap to the next, which is no foundation for a per-corner report card or real sectors.

Once a circuit's corners have been labelled by hand in the Tracks view, they replace detection everywhere (corners_for_lap). Authored corners are anchored to world positions, not lap distances, because distance depends on the line taken; each lap resolves its own apex_dist/entry_dist/exit_dist by finding where it passed the anchor. An anchor further than 60 m from anything the lap drove is not on this lap and is dropped — and if that leaves nothing, the lap falls back to detection, because a bundle describing a different layout should not cost the lap its corners entirely. Where a corner has no marked entry/exit, the extent is ±75 m around the apex, clipped at the midpoint to its neighbours.

angle_deg and an unset direction are still measured from the lap itself: they describe what this lap did through a corner whose identity is already settled. So a driver who straightlined turn 7 gets a small angle against turn 7, rather than turn 7 disappearing.

Cursor synchronization

All the "synced" behavior is one shared value: the cursor's grid index (round(distance ÷ step)). Every consumer — each chart panel, the race line map dots, the Corner Detail widget — reads the same index into its own resampled arrays, which is why everything stays in lockstep as you scrub.