zenno/racelib: allow accel skills to be delayed

zenno/src/lib/racelib/accel.ts

@@ -25,7 +25,7 @@ export interface Travel {
  * @param start Motion at the beginning of the segment
  * @param targetSpeed Target speed to accelerate to
  * @param totalAccel Total (positive) acceleration including skill bonuses
- * @param maxDur Max duration of the acceleration, or infinite if not given
+ * @param maxDur Max position of the acceleration, or infinite if not given
  * @param maxDist Max distance of the acceleration, or infinite if not given
  * @param decel Negative acceleration value for cases where target speed is below start speed
  * @returns Travel segment after reaching the first of the given limits
@@ -40,13 +40,13 @@ export function travelSegment(
 ): Travel {
 	const a = start.v < targetSpeed ? totalAccel : (decel ?? -1);
 	const dvt = (targetSpeed - start.v) / a;
-	const dxt = maxDist != null ? (-start.v + Math.sqrt(start.v * start.v + 4 * a * maxDist)) / (2 * a) : dvt;
+	const dxt = maxDist != null ? (-start.v + Math.sqrt(start.v * start.v + 4 * a * (maxDist - start.x))) / (2 * a) : dvt;
 	const time = maxDur != null ? Math.min(dvt, dxt, maxDur) : Math.min(dvt, dxt);
 	// To address numerical imprecision, if accel time comes from velocity or distance,
 	// set the reached values directly.
 	const v = time === dvt ? targetSpeed : start.v + time * a;
-	const dist = maxDist != null && time === dxt ? maxDist : (start.v + 0.5 * a * time) * time;
-	const end = { t: start.t + time, x: start.x + dist, v };
+	const dist = maxDist != null && time === dxt ? maxDist : start.x + (start.v + 0.5 * a * time) * time;
+	const end = { t: start.t + time, x: dist, v };
 	return { start, end, a };
 }
 
@@ -54,6 +54,10 @@ export function travelSegment(
  * Acceleration bonus from skills.
  */
 export interface Skill {
+	/**
+	 * Forward position along the course at which the skill activates.
+	 */
+	x?: number;
 	/**
 	 * Acceleration modifier in m/s².
 	 */
@@ -74,16 +78,18 @@ export interface Skill {
  */
 export function up(start: Instant, targetSpeed: number, baseAccel: number, skills: Skill[]) {
 	const segments: Travel[] = [];
-	const sk = skills.map((s) => ({ ...s })).filter((s) => s.dur > 0);
+	const sk = skills.map((s) => ({ x: 0, ...s })).filter((s) => s.dur > 0);
+	const xs = sk.map((s) => s.x).filter((x) => x > 0).sort((a, b) => a - b);
 	while (start.v < targetSpeed) {
-		const active = sk.filter((s) => s.dur > 0);
-		if (active.length === 0) {
+		const active = sk.filter((s) => s.dur > 0 && s.x <= start.x);
+		const dx = xs.find((x) => x > start.x);
+		if (active.length === 0 && dx == null) {
 			segments.push(travelSegment(start, targetSpeed, baseAccel));
 			break;
 		}
 		const boost = active.reduce((a, s) => a + s.accel, 0);
 		const time = Math.min(...active.map((s) => s.dur));
-		const seg = travelSegment(start, targetSpeed, baseAccel + boost, time);
+		const seg = travelSegment(start, targetSpeed, baseAccel + boost, time, dx);
 		segments.push(seg);
 		start = seg.end;
 		for (const s of active) {