feat(frontend): add DeltaTimeGraph cumulative delta chart (#17)

Introduce a reusable SVG chart primitive for lap-by-lap cumulative time
delta vs a reference driver, with pure math in lib/delta.ts, dedicated
styles, null-lap gap handling, and Vitest coverage for math and rendering.

Co-authored-by: Cursor <cursoragent@cursor.com>

frontend/src/lib/delta.ts

@@ -0,0 +1,112 @@
+// Cumulative lap-time delta math for driver comparison charts.
+// Pure functions only — no React — so everything is unit-testable.
+
+export interface DeltaSeries {
+  label: string
+  color: string
+  /** Lap duration in seconds; null = no time (pit/out lap). */
+  lapTimes: (number | null)[]
+}
+
+export interface DriverDeltaResult {
+  label: string
+  color: string
+  /** Cumulative delta vs reference (seconds); null when that lap has no time. */
+  deltas: (number | null)[]
+}
+
+/** Format a delta value for axis labels and tooltips (e.g. "+2.5s", "-1.2s"). */
+export function formatDeltaSeconds(delta: number): string {
+  const sign = delta >= 0 ? '+' : ''
+  return `${sign}${delta.toFixed(1)}s`
+}
+
+function buildCumulative(lapTimes: ReadonlyArray<number | null>): number[] {
+  const cumulative: number[] = []
+  let running = 0
+  for (const lap of lapTimes) {
+    if (lap !== null) {
+      running += lap
+    }
+    cumulative.push(running)
+  }
+  return cumulative
+}
+
+function resolveReference(
+  series: ReadonlyArray<DeltaSeries>,
+  referenceLabel?: string,
+): DeltaSeries | null {
+  if (series.length === 0) return null
+  if (referenceLabel) {
+    return series.find((s) => s.label === referenceLabel) ?? series[0]
+  }
+  return series[0]
+}
+
+/**
+ * Compute per-lap cumulative time delta for each non-reference driver.
+ * Positive = behind reference; negative = ahead.
+ * Null laps carry cumulative forward but emit null in deltas (skip when plotting).
+ */
+export function computeCumulativeDeltas(
+  series: ReadonlyArray<DeltaSeries>,
+  referenceLabel?: string,
+): DriverDeltaResult[] {
+  const reference = resolveReference(series, referenceLabel)
+  if (!reference) return []
+
+  const refCumulative = buildCumulative(reference.lapTimes)
+
+  return series
+    .filter((s) => s.label !== reference.label)
+    .map((driver) => {
+      const driverCumulative = buildCumulative(driver.lapTimes)
+      const lapCount = Math.max(driver.lapTimes.length, refCumulative.length)
+      const deltas: (number | null)[] = []
+
+      for (let i = 0; i < lapCount; i++) {
+        if (driver.lapTimes[i] === null) {
+          deltas.push(null)
+          continue
+        }
+        const refValue = refCumulative[i] ?? refCumulative[refCumulative.length - 1] ?? 0
+        const driverValue =
+          driverCumulative[i] ?? driverCumulative[driverCumulative.length - 1] ?? 0
+        deltas.push(driverValue - refValue)
+      }
+
+      return {
+        label: driver.label,
+        color: driver.color,
+        deltas,
+      }
+    })
+}
+
+/** Split delta samples into contiguous SVG polyline point strings (gaps at null laps). */
+export function deltaPolylineSegments(
+  deltas: ReadonlyArray<number | null>,
+  toPoint: (lapIndex: number, delta: number) => string,
+): string[] {
+  const segments: string[] = []
+  let current: string[] = []
+
+  for (let i = 0; i < deltas.length; i++) {
+    const value = deltas[i]
+    if (value === null) {
+      if (current.length > 0) {
+        segments.push(current.join(' '))
+        current = []
+      }
+      continue
+    }
+    current.push(toPoint(i, value))
+  }
+
+  if (current.length > 0) {
+    segments.push(current.join(' '))
+  }
+
+  return segments
+}