zenno/race/gate: new calculator

zenno/src/lib/race.ts

@@ -93,6 +93,20 @@ export function distance(raceLen: number): Distance {
 	return Distance.Long;
 }
 
+/**
+ * Get the distances at which each phase of a race ends.
+ * @param raceLen Length of the race in meters
+ * @returns Ends of each phase in meters
+ */
+export function phases(raceLen: number) {
+	const sixth = raceLen / 6;
+	return {
+		[Phase.EarlyRace]: sixth,
+		[Phase.MidRace]: 4 * sixth,
+		[Phase.LateRace]: raceLen,
+	}
+}
+
 /**
  * Race surfaces.
  */
@@ -372,7 +386,13 @@ export function fullSpurtHP(raceLen: number, spurtSpeed: number, hpRate: number)
 	return spurtTime * hpRate;
 }
 
-function baseSpeed(raceLen: number): number {
+/**
+ * Calculate the base speed for a race.
+ * Note that this is not the base target speed for a horse.
+ * @param raceLen Race length in meters
+ * @returns Base speed for the race
+ */
+export function baseSpeed(raceLen: number): number {
 	return 20 - (raceLen - 2000) / 1000;
 }
 
@@ -748,13 +768,22 @@ export function duelAccelMod(gutsStat: number): number {
  * Calculate the speed modifier for running uphill.
  * Contrary to the race mechanics document, this is expressed as a negative number.
  * @param powerStat Final power stat
- * @param slopePer Slope percentage, generally one of 0.5, 1.0, 1.5, or 2.0
+ * @param slopePer Slope percentage, one of 1.0, 1.5, or 2.0
  * @returns Speed modifier for running uphill, a negative value
  */
 export function uphillMod(powerStat: number, slopePer: number): number {
 	return (slopePer * -200) / powerStat;
 }
 
+/**
+ * Calculate the speed modifier while running in downhill accel mode.
+ * @param slopePer Slope percentage, one of -1.0, -1.5, or -2.0
+ * @returns Speed modifier for downhill accel mode
+ */
+export function downhillAccelMod(slopePer: number): number {
+	return 0.3 - slopePer/10;
+}
+
 /**
  * Calculate the forward speed boost given when moving lanewise while a skill
  * that grants a lane change speed boost is active.

zenno/src/lib/racelib/accel.ts

@@ -0,0 +1,90 @@
+/**
+ * Instantaneous characteristics of a horse in motion.
+ */
+export interface Instant {
+    /** Timestamp of the instant. */
+    t: number;
+    /** Forward position along the course. */
+    x: number;
+    /** Actual speed. */
+    v: number;
+}
+
+/**
+ * Forward travel characteristics under the effects of acceleration.
+ */
+export interface Travel {
+    start: Instant;
+    end: Instant;
+    /** Actual acceleration value applied between start and end. */
+    a: number;
+}
+
+/**
+ * Advance a horse according to its forward motion characteristics.
+ * @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 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
+ */
+export function travelSegment(start: Instant, targetSpeed: number, totalAccel: number, maxDur?: number, maxDist?: number, decel?: number): 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 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 };
+    return {start, end, a};
+}
+
+/**
+ * Acceleration bonus from skills.
+ */
+export interface Skill {
+    /**
+     * Acceleration modifier in m/s².
+     */
+    accel: number;
+    /**
+     * Remaining actual duration in seconds.
+     */
+    dur: number;
+}
+
+/**
+ * Accelerate up to a new target speed while under the effects of acceleration skills.
+ * @param startSpeed Speed at the start of the acceleration in m/s
+ * @param targetSpeed Speed at which the acceleration ends in m/s
+ * @param baseAccel Base acceleration value to which skills add, in m/s²
+ * @param skills Skills that are active for the acceleration period
+ * @returns Acceleration segments and remainders of skills upon reaching the target speed
+ */
+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);
+    while (start.v < targetSpeed) {
+        const active = sk.filter((s) => s.dur > 0);
+        if (active.length === 0) {
+            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);
+        segments.push(seg);
+        start = seg.end
+        for (const s of active) {
+            s.dur -= seg.end.t - seg.start.t;
+            if (s.dur < 1e-5) {
+                s.dur = 0
+            }
+        }
+    }
+    return {segments, skills: sk}
+}

zenno/src/lib/racelib/stat.ts

@@ -0,0 +1,29 @@
+/**
+ * Fundamental stats of umas.
+ */
+export enum Stat {
+	speed,
+	stamina,
+	power,
+	guts,
+	wit,
+}
+
+/**
+ * Stats as a list for easy iteration.
+ */
+export const LIST = [Stat.speed, Stat.stamina, Stat.power, Stat.guts, Stat.wit] as const;
+
+declare const __stage: unique symbol;
+
+export type Stage = 'raw' | 'base' | 'adjusted' | 'final' | 'skills';
+
+export type StatValue<T extends Stage> = number & {[__stage]: T};
+
+export interface Stats<T extends Stage> {
+	speed: StatValue<T>;
+	stamina: StatValue<T>;
+	power: StatValue<T>;
+	guts: StatValue<T>;
+	wit: StatValue<T>;
+}

zenno/src/routes/race/gate/+page.svelte

@@ -0,0 +1,267 @@
+<script lang="ts">
+    import * as race from '$lib/race';
+    import * as accel from '$lib/racelib/accel';
+
+    let rawPower = $state(1200);
+    let rawGuts = $state(1200);
+    let rawWit = $state(1200);
+    let powerBonus = $state(0);
+    let gutsBonus = $state(0);
+    let witBonus = $state(0);
+    let style = $state(race.RunningStyle.FrontRunner);
+    let surfApt = $state(race.AptitudeLevel.A);
+    let styleApt = $state(race.AptitudeLevel.A);
+    let mood = $state(race.Mood.Normal);
+    let isCareer = $state(false);
+
+    let raceLen = $state(2000);
+    let surface = $state(race.Surface.Turf);
+    let conditions = $state(race.GroundConditions.Firm);
+    let slope = $state(0);
+
+    let rawSkills: accel.Skill[] = $state([]);
+    let skillToAdd: accel.Skill = $state({accel: 0.2, dur: 1.2});
+    const quick = [
+        {name: "GW+TTL", skills: [{accel: 0.2, dur: 3}, {accel: 0.4, dur: 1.2}]},
+        {name: "GW+EL", skills: [{accel: 0.2, dur: 3}, {accel: 0.2, dur: 1.2}]},
+        {name: "Clear", skills: []},
+    ];
+    function addSkill() {
+        rawSkills.push(skillToAdd);
+        skillToAdd = {accel: 0.2, dur: 1.2};
+    }
+    function removeSkill(i: number) {
+        rawSkills.splice(i, 1);
+    }
+    function setSkillList(l: accel.Skill[]) {
+        rawSkills = l;
+    }
+
+    const phases = $derived(race.phases(raceLen));
+
+    const basePower = $derived(race.baseStat(mood, rawPower));
+    const adjPower = $derived(race.adjustedStat(race.Stat.Power, basePower, isCareer, surface, conditions));
+    const power = $derived(race.finalStat(adjPower, powerBonus));
+    const baseGuts = $derived(race.baseStat(mood, rawGuts));
+    const adjGuts = $derived(race.adjustedStat(race.Stat.Guts, baseGuts, isCareer));
+    const guts = $derived(race.finalStat(adjGuts, gutsBonus));
+    const baseWit = $derived(race.baseStat(mood, rawWit));
+    const adjWit = $derived(race.adjustedStat(race.Stat.Wit, baseWit, isCareer, styleApt));
+    const wit = $derived(race.finalStat(adjWit, witBonus));
+
+    const dashAccel = $derived(race.acceleration(power, style, surfApt, race.Phase.EarlyRace, race.AptitudeLevel.A, slope > 0, true));
+    const postAccel = $derived(race.acceleration(power, style, surfApt, race.Phase.EarlyRace, race.AptitudeLevel.A, slope > 0, false));
+    const minSpeed = $derived(race.minSpeed(raceLen, guts));
+    const baseSpeed = $derived(race.baseSpeed(raceLen));
+    const dashTarget = $derived(baseSpeed * 0.85);
+    const hillMod: [number, number] = $derived.by(() => {
+        if (slope > 0) {
+            const m = race.uphillMod(power, slope);
+            return [m, m];
+        }
+        if (slope < 0) {
+            return [0, race.downhillAccelMod(slope)];
+        }
+        return [0, 0];
+    })
+    const earlyTarget = $derived(race.sectionSpeed(raceLen, baseWit, wit, style, race.Phase.EarlyRace));
+    const speeds: [number, number] = $derived([earlyTarget[0] + hillMod[0], earlyTarget[1] + hillMod[1]]);
+    const avgEarlyTarget = $derived((earlyTarget[0] + earlyTarget[1]) * 0.5);
+
+    const startInstant: accel.Instant = {t: 0, x: 0, v: 3};
+    function doSeggsToIt(targetSpeed: number, skills: accel.Skill[]) {
+        const startDash = accel.up(startInstant, dashTarget, dashAccel, skills);
+        const postStart = {...last(startDash.segments).end, v: minSpeed};
+        const post = accel.up(postStart, targetSpeed, postAccel, startDash.skills);
+        const r = [...startDash.segments, ...post.segments];
+        return r;
+    }
+    function last<T>(l: T[]): T {
+        return l[l.length - 1];
+    }
+    const skills = $derived(rawSkills.map((s) => ({...s, dur: race.skillDuration(s.dur, raceLen)})));
+    const seggs = $derived([doSeggsToIt(speeds[0], skills), doSeggsToIt(speeds[1], skills)]);
+    const unskilledSeggs = $derived([doSeggsToIt(speeds[0], []), doSeggsToIt(speeds[1], [])]);
+    
+    const distance = $derived([
+        last(seggs[0]).end.x,
+        last(seggs[1]).end.x,
+    ]);
+    const time = $derived([
+        last(seggs[0]).end.t,
+        last(seggs[1]).end.t,
+    ]);
+    const midTime = $derived([
+        time[0] + (phases[race.Phase.EarlyRace] - distance[0])/speeds[1],
+        time[1] + (phases[race.Phase.EarlyRace] - distance[1])/speeds[0],
+    ]);
+    function gainLengths(fast: accel.Instant, slow: accel.Instant): number {
+        const m = fast.v * (slow.t - fast.t) + fast.x - slow.x;
+        return m / race.HORSE_LENGTH;
+    }
+    const gain = $derived([
+        gainLengths(last(seggs[0]).end, last(unskilledSeggs[0]).end),
+        gainLengths(last(seggs[1]).end, last(unskilledSeggs[1]).end),
+    ]);
+</script>
+
+<h1 class="text-4xl">Gate Calculator</h1>
+<form class="mx-auto my-4 p-4 grid gap-8 grid-cols-1 max-w-4xl rounded-md shadow-sm md:grid-cols-5">
+    <div class="grid rounded-md text-center shadow-md ring md:col-span-5 md:grid-cols-5">
+        <div class="m-4">
+            <label for="powerStat">Power</label>
+            <input type="number" id="powerStat" bind:value={rawPower} class="w-full" />
+        </div>
+        <div class="m-4">
+            <label for="gutsStat">Guts</label>
+            <input type="number" id="gutsStat" bind:value={rawGuts} class="w-full" />
+        </div>
+        <div class="m-4">
+            <label for="witStat">Wit</label>
+            <input type="number" id="witStat" bind:value={rawWit} class="w-full" />
+        </div>
+        <div class="m-4">
+            <label for="style">Style</label>
+            <select id="style" required bind:value={style} class="w-full">
+                {#each race.RUNNING_STYLES as [name, style]}
+                    <option value={style}>{name}</option>
+                {/each}
+            </select>
+        </div>
+        <div class="m-4">
+            <label for="mood">Mood</label>
+            <select id="mood" required bind:value={mood} class="w-full">
+                {#each race.MOODS as mood (mood)}
+                    <option value={mood}>{race.Mood[mood]}</option>
+                {/each}
+            </select>
+        </div>
+        <div class="m-4">
+            <label for="powerBonus">Power Greens</label>
+            <input type="number" id="powerBonus" bind:value={powerBonus} class="w-full" />
+        </div>
+        <div class="m-4">
+            <label for="gutsBonus">Guts Greens</label>
+            <input type="number" id="gutsBonus" bind:value={gutsBonus} class="w-full" />
+        </div>
+        <div class="m-4">
+            <label for="witBonus">Wit Greens</label>
+            <input type="number" id="witBonus" bind:value={witBonus} class="w-full" />
+        </div>
+        <div class="m-4">
+            <label for="surfaceApt">{race.Surface[surface]}</label>
+            <select id="surfaceApt" required bind:value={surfApt} class="w-full">
+                {#each race.APTITUDE_LEVELS as apt (apt)}
+                    <option value={apt}>{race.AptitudeLevel[apt]}</option>
+                {/each}
+            </select>
+        </div>
+        <div class="m-4">
+            <label for="styleApt">Style</label>
+            <select id="styleApt" required bind:value={styleApt} class="w-full">
+                {#each race.APTITUDE_LEVELS as apt (apt)}
+                    <option value={apt}>{race.AptitudeLevel[apt]}</option>
+                {/each}
+            </select>
+        </div>
+    </div>
+    <div class="mb-auto grid grid-cols-6 max-w-4xl rounded-md text-center shadow-md ring md:col-span-3">
+        <input class="m-4 w-full col-span-4 justify-self-center-safe" type="range" id="raceLen" min="1000" max="3600" step="100" bind:value={raceLen} />
+        <span class="mb-4 my-auto pl-2 col-span-2 text-sm">{raceLen}m</span>
+        <select id="surface" bind:value={surface} class="m-4 col-span-2">
+            <option value={race.Surface.Turf}>Turf</option>
+            <option value={race.Surface.Dirt}>Dirt</option>
+        </select>
+        <select id="conditions" bind:value={conditions} class="m-4 col-span-2">
+            {#each race.GROUND_CONDITONS as cond (cond)}
+                <option value={cond}>{race.GroundConditions[cond]}</option>
+            {/each}
+        </select>
+        <select id="slope" bind:value={slope} class="m-4 col-span-2">
+            {#each [2, 1.5, 1, 0, -1, -1.5, -2] as per (per)}
+                <option value={per}>{per > 0 ? `Uphill +${per}` : (per < 0 ? `Downhill ${per}` : 'Flat')}</option>
+            {/each}
+        </select>
+    </div>
+    <div class="mb-auto w-full flex flex-col max-w-4xl rounded-md text-center shadow-md ring md:col-span-2">
+        <div class="mx-4 mt-2 flex flex-row gap-2">
+            <span class="w-24 flex-1">Duration</span>
+            <span class="w-24 flex-1">Accel</span>
+            <span class="flex-none w-8"><!-- filler to align other columns --></span>
+        </div>
+        {#each rawSkills as skill, i (i)}
+            <div class="mx-4 mt-2 flex flex-row gap-2">
+                <span class="my-auto w-24 flex-1">{skill.dur}s</span>
+                <span class="my-auto w-24 flex-1">{skill.accel}</span>
+                <button type="button" class="my-auto flex-none w-8 h-8 rounded-full text-2xl hover:cursor-pointer bg-mist-300 dark:bg-mist-900" onclick={() => removeSkill(i)}>&times;</button>
+            </div>
+        {/each}
+        <div class="mx-4 mt-2 flex flex-row gap-2">
+            <input type="number" class="my-auto w-24 flex-1" min="0.9" step="0.3" bind:value={skillToAdd.dur} />
+            <input type="number" class="my-auto w-24 flex-1" min="0" step="0.05" bind:value={skillToAdd.accel} />
+            <button type="button" class="my-auto flex-none w-8 h-8 rounded-full text-2xl hover:cursor-pointer bg-mist-300 dark:bg-mist-900" onclick={addSkill}>+</button>
+        </div>
+        <div class="flex flex-row mt-1">
+            <span class="my-auto h-0 flex-1 border"></span>
+            <span class="mx-2 flex-none">Quick Setup</span>
+            <span class="my-auto h-0 flex-1 border"></span>
+        </div>
+        <div class="flex flex-row m-2 gap-2 place-content-center-safe">
+            {#each quick as q (q.name)}
+                <button type="button" class="p-2 rounded-md hover:cursor-pointer bg-mist-300 dark:bg-mist-900" onclick={() => setSkillList(q.skills)}>{q.name}</button>
+            {/each}
+        </div>
+    </div>
+</form>
+
+{#snippet info(name: string, unit: string, val: number, val2?: number)}
+    <div class="m-2 max-w-72 flex-1 flex-col rounded-md border p-2 text-center shadow-sm transition-shadow hover:shadow-md">
+        <span class="block">{name}</span>
+        {#if val2 == null}
+            <span class="block text-xl">{val.toFixed(3)} {unit}</span>
+        {:else}
+            <span class="block text-xl">{val.toFixed(3)} &ndash; {val2.toFixed(3)} {unit}</span>
+        {/if}
+    </div>
+{/snippet}
+
+<div class="mx-auto flex w-full flex-col place-items-center md:flex-row md:justify-center">
+    {@render info('Base Acceleration', 'm/s²', postAccel)}
+    {@render info('Target Speed', 'm/s', speeds[0], speeds[1])}
+</div>
+<div class="mx-auto flex w-full flex-col place-items-center md:flex-row md:justify-center">
+    {@render info('Accel Time', 's', time[0], time[1])}
+    {@render info('Accel Distance', 'm', distance[0], distance[1])}
+    {@render info('Time to Mid-Race', 's', midTime[0], midTime[1])}
+</div>
+<div class="mx-auto flex w-full flex-col place-items-center md:flex-row md:justify-center">
+    {@render info('Skill Gain', 'L', gain[0], gain[1])}
+</div>
+
+{#snippet seggsTable(name: string, s: accel.Travel[])}
+    <table class="table-fixed border">
+        <caption class="text-xl">{name}</caption>
+        <thead>
+            <tr class="py-2">
+                <th class="px-2" scope="col">Time</th>
+                <th class="px-2" scope="col">Accel</th>
+                <th class="px-2" scope="col">Distance</th>
+                <th class="px-2" scope="col">Speed</th>
+            </tr>
+        </thead>
+        <tbody>
+            {#each s as {start, end, a} (start.t)}
+                <tr class="even:bg-mist-300 dark:even:bg-mist-900">
+                    <td class="px-4 text-center">{end.t.toFixed(3)}</td>
+                    <td class="px-4 text-center">{a.toFixed(3)}</td>
+                    <td class="px-4 text-center">{end.x.toFixed(3)}</td>
+                    <td class="px-4 text-center">{end.v.toFixed(3)}</td>
+                </tr>
+            {/each}
+        </tbody>
+    </table>
+{/snippet}
+<div class="mx-auto mt-8 max-w-4xl grid grid-cols-1 md:grid-cols-2 gap-8">
+    {@render seggsTable(slope < 0 ? 'Fastest Speed (Downhill)' : 'Fastest Speed', seggs[1])}
+    {@render seggsTable('Slowest Speed', seggs[0])}
+</div>