finished actions => handlers refacto, small bux fix in maestro => Test maestro1 OK

GPS/handlers/arena/worldline.js

@@ -0,0 +1,150 @@
+const PROXIMITY_EPSILON = 1e-6
+
+export function needsPrismRefresh(agent, now, prismTimeHeight, prismRefreshLeadSeconds = 0) {
+    return(now >= agent.since + prismTimeHeight - prismRefreshLeadSeconds)
+}
+
+export function advanceAgentSegment(agent, now) {
+    agent.position = positionAt(agent, now)
+    agent.since = now
+    agent.generation = (agent.generation ?? 0) + 1
+}
+
+export function positionAt(agent, t) {
+    const dt = t - agent.since
+    return({
+        x: agent.position.x + agent.vector.x * dt,
+        y: agent.position.y + agent.vector.y * dt,
+        z: agent.position.z + agent.vector.z * dt,
+    })
+}
+
+export function distanceBetween(agentA, agentB, t) {
+    const a = positionAt(agentA, t)
+    const b = positionAt(agentB, t)
+    const dx = a.x - b.x
+    const dy = a.y - b.y
+    const dz = a.z - b.z
+    return(Math.sqrt(dx * dx + dy * dy + dz * dz))
+}
+
+export function buildPrism(agent, tStart, tEnd, nearMissDistance) {
+    const p0 = positionAt(agent, tStart)
+    const p1 = positionAt(agent, tEnd)
+    const pad = nearMissDistance
+    return({
+        xMin: Math.min(p0.x, p1.x) - pad,
+        xMax: Math.max(p0.x, p1.x) + pad,
+        yMin: Math.min(p0.y, p1.y) - pad,
+        yMax: Math.max(p0.y, p1.y) + pad,
+        zMin: Math.min(p0.z, p1.z) - pad,
+        zMax: Math.max(p0.z, p1.z) + pad,
+        tMin: tStart,
+        tMax: tEnd,
+    })
+}
+
+export function prismsIntersect(a, b) {
+    return(
+        a.xMin <= b.xMax && a.xMax >= b.xMin &&
+        a.yMin <= b.yMax && a.yMax >= b.yMin &&
+        a.zMin <= b.zMax && a.zMax >= b.zMin &&
+        a.tMin <= b.tMax && a.tMax >= b.tMin
+    )
+}
+
+export function minimalDistance(agentA, agentB, tStart, tEnd) {
+    const relPos = {
+        x: positionAt(agentA, tStart).x - positionAt(agentB, tStart).x,
+        y: positionAt(agentA, tStart).y - positionAt(agentB, tStart).y,
+        z: positionAt(agentA, tStart).z - positionAt(agentB, tStart).z,
+    }
+    const relVel = {
+        x: agentA.vector.x - agentB.vector.x,
+        y: agentA.vector.y - agentB.vector.y,
+        z: agentA.vector.z - agentB.vector.z,
+    }
+
+    const relVelSq = relVel.x * relVel.x + relVel.y * relVel.y + relVel.z * relVel.z
+    let tStar = tStart
+    if(relVelSq > 0) {
+        const dot = relPos.x * relVel.x + relPos.y * relVel.y + relPos.z * relVel.z
+        tStar = tStart - dot / relVelSq
+    }
+    tStar = Math.max(tStart, Math.min(tEnd, tStar))
+
+    return({
+        distance: distanceBetween(agentA, agentB, tStar),
+        time: tStar,
+    })
+}
+
+export function firstProximityEntry(agentA, agentB, tStart, tEnd, nearMissDistance) {
+    const d0 = distanceBetween(agentA, agentB, tStart)
+    if(d0 <= nearMissDistance + PROXIMITY_EPSILON) {
+        return({ time: tStart, distance: d0 })
+    }
+
+    const relPos = {
+        x: positionAt(agentA, tStart).x - positionAt(agentB, tStart).x,
+        y: positionAt(agentA, tStart).y - positionAt(agentB, tStart).y,
+        z: positionAt(agentA, tStart).z - positionAt(agentB, tStart).z,
+    }
+    const relVel = {
+        x: agentA.vector.x - agentB.vector.x,
+        y: agentA.vector.y - agentB.vector.y,
+        z: agentA.vector.z - agentB.vector.z,
+    }
+    const relVelSq = relVel.x * relVel.x + relVel.y * relVel.y + relVel.z * relVel.z
+    if(relVelSq === 0) return(null)
+
+    const a = relVelSq
+    const b = 2 * (relPos.x * relVel.x + relPos.y * relVel.y + relPos.z * relVel.z)
+    const c = relPos.x * relPos.x + relPos.y * relPos.y + relPos.z * relPos.z - nearMissDistance * nearMissDistance
+    const D = b * b - 4 * a * c
+    if(D < 0) return(null)
+
+    const sqrtD = Math.sqrt(D)
+    const maxDt = tEnd - tStart
+    const roots = [(-b - sqrtD) / (2 * a), (-b + sqrtD) / (2 * a)]
+        .filter(dt => dt >= 0 && dt <= maxDt)
+        .sort((x, y) => x - y)
+
+    for(const dt of roots) {
+        const t = tStart + dt
+        const d = distanceBetween(agentA, agentB, t)
+        if(d > nearMissDistance + PROXIMITY_EPSILON) continue
+        if(dt < 1e-12) return({ time: tStart, distance: d0 })
+        const dBefore = distanceBetween(agentA, agentB, t - 1e-6)
+        if(dBefore > nearMissDistance + PROXIMITY_EPSILON) return({ time: t, distance: d })
+    }
+    return(null)
+}
+
+export function compareWorldlinePair(agentA, agentB, prismTimeHeight, nearMissDistance, now) {
+    const tStart = Math.max(agentA.since, agentB.since, now)
+    const tEnd = Math.min(
+        agentA.since + prismTimeHeight,
+        agentB.since + prismTimeHeight
+    )
+    if(tEnd <= tStart) return(null)
+
+    const prismA = buildPrism(agentA, tStart, tEnd, nearMissDistance)
+    const prismB = buildPrism(agentB, tStart, tEnd, nearMissDistance)
+    if(!prismsIntersect(prismA, prismB)) return(null)
+
+    const min = minimalDistance(agentA, agentB, tStart, tEnd)
+    if(min.distance > nearMissDistance + PROXIMITY_EPSILON) return(null)
+
+    const entry = firstProximityEntry(agentA, agentB, tStart, tEnd, nearMissDistance)
+    if(!entry) return(null)
+
+    return({
+        agentA: agentA.id,
+        agentB: agentB.id,
+        time: entry.time,
+        distance: entry.distance,
+        minTime: min.time,
+        minDistance: min.distance,
+    })
+}