rpg-mcp

import { CalculationResult } from './schemas.js'; export class PhysicsEngine { // Projectile motion // Returns array of points {x, y, t} projectile(v0: number, angleDeg: number, gravity: number = 9.81, steps: number = 10, initialHeight: number = 0): CalculationResult { const angleRad = angleDeg * (Math.PI / 180); const vx = v0 * Math.cos(angleRad); const vy = v0 * Math.sin(angleRad); // Time of flight: solve 0 = h + vy*t - 0.5*g*t^2 // 0.5*g*t^2 - vy*t - h = 0 // t = (vy + sqrt(vy^2 - 4(0.5g)(-h))) / (2*0.5g) // t = (vy + sqrt(vy^2 + 2gh)) / g const totalTime = (vy + Math.sqrt(vy * vy + 2 * gravity * initialHeight)) / gravity; const points: { t: number, x: number, y: number }[] = []; const dt = totalTime / steps; for (let i = 0; i <= steps; i++) { const t = i * dt; const x = vx * t; const y = initialHeight + vy * t - 0.5 * gravity * t * t; points.push({ t: Number(t.toFixed(2)), x: Number(x.toFixed(2)), y: Number(y.toFixed(2)) }); } const maxHeight = initialHeight + (vy * vy) / (2 * gravity); const range = vx * totalTime; return { input: `projectile(v0=${v0}, angle=${angleDeg}, g=${gravity}, h=${initialHeight})`, result: JSON.stringify(points), steps: [ `Initial Velocity: ${v0} m/s`, `Angle: ${angleDeg} deg`, `Initial Height: ${initialHeight} m`, `Total Time: ${totalTime.toFixed(2)} s`, `Max Height: ${maxHeight.toFixed(2)} m`, `Range: ${range.toFixed(2)} m` ], timestamp: new Date().toISOString(), metadata: { points, maxHeight, range, flightTime: totalTime } }; } // Kinematics (SUVAT) // s = ut + 0.5at^2 // v = u + at // v^2 = u^2 + 2as // s = 0.5(u+v)t // s = vt - 0.5at^2 // Params: u (initial velocity), v (final velocity), a (acceleration), t (time), s (displacement) // Pass object with knowns, solves for unknowns if possible. kinematics(params: { u?: number, v?: number, a?: number, t?: number, s?: number }): CalculationResult { const { u, v, a, t, s } = params; const results: any = { ...params }; const steps: string[] = []; // Iterative solving (simple pass) // We need at least 3 knowns to solve for the other 2. // 1. v = u + at if (v === undefined && u !== undefined && a !== undefined && t !== undefined) { results.v = u + a * t; steps.push(`v = u + at => ${u} + ${a}*${t} = ${results.v}`); } if (u === undefined && v !== undefined && a !== undefined && t !== undefined) { results.u = v - a * t; steps.push(`u = v - at => ${v} - ${a}*${t} = ${results.u}`); } if (t === undefined && v !== undefined && u !== undefined && a !== undefined && a !== 0) { results.t = (v - u) / a; steps.push(`t = (v - u) / a => (${v} - ${u}) / ${a} = ${results.t}`); } if (a === undefined && v !== undefined && u !== undefined && t !== undefined && t !== 0) { results.a = (v - u) / t; steps.push(`a = (v - u) / t => (${v} - ${u}) / ${t} = ${results.a}`); } // 2. s = ut + 0.5at^2 if (s === undefined && u !== undefined && t !== undefined && a !== undefined) { results.s = u * t + 0.5 * a * t * t; steps.push(`s = ut + 0.5at^2 => ${u}*${t} + 0.5*${a}*${t}^2 = ${results.s}`); } // 3. v^2 = u^2 + 2as if (v === undefined && u !== undefined && a !== undefined && s !== undefined) { const v2 = u * u + 2 * a * s; results.v = Math.sqrt(v2); steps.push(`v^2 = u^2 + 2as => ${u}^2 + 2*${a}*${s} = ${v2} => v = ${results.v}`); } return { input: `kinematics(${JSON.stringify(params)})`, result: JSON.stringify(results), steps, timestamp: new Date().toISOString() }; } }