WIP
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@ -1,4 +1,6 @@
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<?xml version="1.0" encoding="UTF-8"?>
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<project version="4">
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<component name="VcsDirectoryMappings" defaultProject="true" />
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<component name="VcsDirectoryMappings">
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<mapping directory="" vcs="Git" />
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</component>
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</project>
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26
main.ts
26
main.ts
@ -1,9 +1,8 @@
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// @deno-types="npm:@types/express"
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import express, { Request, Response } from 'express';
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import cors from 'cors';
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import {getCollisionPoints, ggvp, linearInterpolation, parabalInterpolatePoints} from "./physics.ts";
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import {firstPoint, getCollisionPoints, interpolation} from "./physics.ts";
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import {changeBasis} from "./math.ts";
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import IPoint from "./IPoint.ts";
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const app = express();
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const PORT = 3000;
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@ -15,10 +14,9 @@ app.get('/api/points', (req: Request, res: Response) => {
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if (g === undefined || h === undefined || l === undefined || alpha === undefined) {
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res.status(401).send("Параметры должны быть заданы");
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}
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res.json(changeBasis(
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getCollisionPoints({ g: Number(g), h: Number(h), l: Number(l), alpha: Number(alpha) }),
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-Number(alpha)
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));
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res.json(
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getCollisionPoints({ g: Number(g), h: Number(h), l: Number(l), alpha: Number(alpha) })
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);
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});
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app.get('/api/interpolation', (req: Request, res: Response) => {
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@ -26,19 +24,11 @@ app.get('/api/interpolation', (req: Request, res: Response) => {
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if (g === undefined || h === undefined || l === undefined || alpha === undefined || count === undefined) {
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res.status(401).send("Параметры должны быть заданы");
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}
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// const collisionPoints = changeBasis(getCollisionPoints({ g: Number(g), h: Number(h), l: Number(l), alpha: Number(alpha) }), -Number(alpha));
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// const points: IPoint[] = [];
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//
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// collisionPoints.forEach((point, i, array) => {
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// if (i === 0) {
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// points.push(...linearInterpolation(point, array[i+1], Number(count)));
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// return;
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// }
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// if (i >= array.length - 2) return;
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// points.push(...ggvp({ g: Number(g), h: Number(h), l: Number(l), alpha: Number(alpha) }, Number(count)));
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// });
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res.json(changeBasis(ggvp({ g: Number(g), h: Number(h), l: Number(l), alpha: Number(alpha) }, Number(count)), -Number(alpha)).map(p => ({...p, y: p.y - Number(h)})));
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const params = { g: Number(g), h: Number(h), l: Number(l), alpha: Number(alpha) };
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const fp = firstPoint(params);
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res.json([...fp, ...changeBasis(interpolation(params), -Number(alpha)).map(p => ({...p, y: p.y - Number(h), time: p.time + fp[fp.length - 1].time}))]);
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});
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app.listen(PORT, () => {
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124
physics.ts
124
physics.ts
@ -1,115 +1,75 @@
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import IParams from "./IParams.ts";
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import IVector from "./IVector.ts";
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import IPoint from "./IPoint.ts";
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function getV0(params: IParams) {
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return Math.sqrt(2 * params.g * params.h);
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}
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function getCollisionPoint(params: IParams, n: number) {
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return 4 * n * getV0(params) * Math.sin(params.alpha) / params.g;
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}
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function getVelocity(params: IParams, n: number): IVector {
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return {
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x: (2*n + 1) * getV0(params) * Math.sin(params.alpha),
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y: getV0(params) * Math.cos(params.alpha)
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}
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}
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function getAngle(params: IParams, n: number) {
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const velocity = getVelocity(params, n);
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return velocity.y / velocity.x;
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}
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function getCollisionPoints(params: IParams) {
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const points: IPoint[] = [
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{
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x: 0,
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y: 0,
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velocity: getV0(params),
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time: 0,
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angle: -Math.PI / 2 + params.alpha,
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}
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];
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let n = 0;
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while (points[points.length - 1].x < params.l) {
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n++;
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points.push({
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x: getCollisionPoint(params, n),
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y: 0,
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velocity: Math.sqrt(getVelocity(params, n).x*getVelocity(params, n).x + getVelocity(params, n).y*getVelocity(params, n).y),
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angle: getAngle(params, n),
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time: 0
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});
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}
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return points;
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}
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function linearInterpolation(p1: IPoint, p2: IPoint, count: number) {
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function getCollisionPoints(params: IParams): IPoint[] {
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const interpolationPoints = interpolation(params);
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const points: IPoint[] = [];
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const deltaX = (p2.x - p1.x) / (count - 1);
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const deltaY = (p2.y - p1.y) / (count - 1);
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const deltaV = (p2.velocity - p1.velocity) / (count - 1);
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for (let i = 0; i < count; i++) {
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const x = p1.x + i * deltaX;
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const y = p1.y + i * deltaY;
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const velocity = p1.velocity + i * deltaV;
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points.push({ x, y, velocity, angle: p1.angle, time: 2 });
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for (let i = 0; i < interpolationPoints.length - 1; i++) {
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if (interpolationPoints[i].angle - interpolationPoints[i+1].angle < 0) {
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points.push(interpolationPoints[i]);
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}
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}
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return points;
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return [{x: 0, y: 0, angle: 0, velocity: 0, time: 0}, ...points];
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}
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function parabalInterpolatePoints(params: IParams, p1: IPoint, p2: IPoint, count: number): IPoint[] {
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const points: IPoint[] = [];
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const a = (Math.tan(Math.PI - p2.angle - 2*params.alpha) - Math.tan(p1.angle))/(2*(p2.x-p1.x));
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const b = Math.tan(p1.angle) - 2*a*p1.x;
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const c = p1.y - a*p1.x*p1.x - b*p1.x;
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const y = (x: number) => a*x*x + b*x + c;
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const step = (p2.x-p1.x)/(count + 1);
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for (let i = 1; i <= count; i++) {
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const x = step*i + p1.x;
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points.push({
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x: x,
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y: y(x),
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angle: 2*a*x + b,
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time: 1,
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velocity: 0
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})
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}
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return [p1, ...points]
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}
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function ggvp(params: IParams, count: number): IPoint[] {
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function interpolation(params: IParams): IPoint[] {
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const T = (2 * getV0(params)) / params.g;
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const points: IPoint[] = [];
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let lastX = 0;
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for (let i = 0; i < count; i++) {
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let i = 0;
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while (lastX*Math.cos(params.alpha) < params.l) {
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const t = i / 100;
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const vx = getV0(params)*Math.sin(params.alpha) + params.g*Math.sin(params.alpha)*t;
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const vy = getV0(params)*Math.cos(params.alpha) - params.g*Math.cos(params.alpha)*(t % T);
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lastX = getV0(params) * Math.sin(params.alpha) * t + (params.g * Math.sin(params.alpha) * t ** 2) / 2;
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points.push({
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x: getV0(params) * Math.sin(params.alpha) * t + (params.g * Math.sin(params.alpha) * t ** 2) / 2,
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x: lastX,
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y: getV0(params) * Math.cos(params.alpha) * (t % T) - (params.g * Math.cos(params.alpha) * (t % T) ** 2) / 2,
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time: t,
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velocity: Math.sqrt(vx*vx + vy*vy),
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angle: Math.atan2(vy, vx)
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});
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i++;
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}
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return points;
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}
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export { getCollisionPoints, parabalInterpolatePoints, linearInterpolation, ggvp };
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function firstPoint(params: IParams): IPoint[] {
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const points: IPoint[] = [
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{
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x: 0,
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y: 0,
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time: 0,
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angle: -Math.PI / 2,
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velocity: 0
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}
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];
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let t = 0.01;
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while(points[points.length - 1].y >= -params.h) {
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points.push({
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x: 0,
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y: -params.g*t**2,
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time: t,
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angle: -Math.PI / 2,
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velocity: -params.g*t
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})
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t += 0.01;
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}
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return points.slice(0, points.length-1);
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}
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export { getCollisionPoints, interpolation, firstPoint };
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18
physics2.ts
18
physics2.ts
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import IPoint from "./IPoint.ts";
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import IParams from "./IParams.ts";
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function getTime(params: IParams, point: IPoint) {
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const a = params.g / 2;
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const b = -point.velocity*Math.sin(point.angle) - Math.abs(Math.tan(params.alpha)) * point.velocity * Math.cos(point.angle);
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const c = -point.y - Math.abs(Math.tan(params.alpha))*point.x;
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const discriminant = b - 4*a*c;
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const t1 = (-b - Math.sqrt(discriminant))/2/a;
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const t2 = (-b + Math.sqrt(discriminant))/2/a;
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return Math.max(t1, t2);
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}
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function getNextPoint(params: IParams, point: IPoint) {
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}
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