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常用数学公式

2022-06-27 21

简介： 牙叔教程简单易懂

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牙叔教程简单易懂

直线两点式转一般式

function getLineGeneralEquationFromTwoPoint(point1, point2) {
  let x1 = point1.x;
  let y1 = point1.y;
  let x2 = point2.x;
  let y2 = point2.y;
  let a = y2 - y1;
  let b = x1 - x2;
  let c = x2 * y1 - x1 * y2;
  return {
    a: a,
    b: b,
    c: c,
  };
}

两条直线的交点

function getFocusCoordinatesOfTwoLines(line1, line2) {
  var x1 = line1.x1;
  var y1 = line1.y1;
  var x2 = line1.x2;
  var y2 = line1.y2;
  var x3 = line2.x1;
  var y3 = line2.y1;
  var x4 = line2.x2;
  var y4 = line2.y2;
  var x =
    ((x1 * y2 - y1 * x2) * (x3 - x4) - (x1 - x2) * (x3 * y4 - y3 * x4)) /
    ((x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4));
  var y =
    ((x1 * y2 - y1 * x2) * (y3 - y4) - (y1 - y2) * (x3 * y4 - y3 * x4)) /
    ((x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4));
  return { x: x, y: y };
}

线段延长后的坐标计算

function extendEndPoint(startPoint, endPoint, distance) {
  var A = [startPoint.x, startPoint.y];
  var B = [endPoint.x, endPoint.y];
  // 横坐标差, 纵坐标差
  var aToB = [B[0] - A[0], B[1] - A[1]];

  // A点到B点的线段长度
  var aToBDistance = Math.sqrt(aToB[0] * aToB[0] + aToB[1] * aToB[1]);

  // 一份有多长
  // 横坐标一份有多长
  // 纵坐标一份有多长
  var atoBNormalization = [aToB[0] / aToBDistance, aToB[1] / aToBDistance];

  // 延长 distance 个像素就乘以 distance, 加上终点
  var newEndPoint = {
    x: atoBNormalization[0] * distance + B[0],
    y: atoBNormalization[1] * distance + B[1],
  };
  return newEndPoint;
}

已知三个点, 求夹角

下面是求角A, 返回值是角度

function getAngle(pointA, pointB, pointC) {
  var lengthAB = Math.sqrt(Math.pow(pointA.x - pointB.x, 2) + Math.pow(pointA.y - pointB.y, 2)),
    lengthAC = Math.sqrt(Math.pow(pointA.x - pointC.x, 2) + Math.pow(pointA.y - pointC.y, 2)),
    lengthBC = Math.sqrt(Math.pow(pointB.x - pointC.x, 2) + Math.pow(pointB.y - pointC.y, 2));
  var cosA = (Math.pow(lengthAB, 2) + Math.pow(lengthAC, 2) - Math.pow(lengthBC, 2)) / (2 * lengthAB * lengthAC);
  var angleA = Math.round((Math.acos(cosA) * 180) / Math.PI);
  return angleA;
}

let arr = [
  { x: 1, y: 0 },
  { x: 0.5, y: 1 },
  { x: 0, y: 0 },
];
let r = getAngle(arr[0], arr[1], arr[2]);
console.log(r);

已知点和直线, 求对称点坐标

// 求: 点P(x0,y0)关于直线 Ax + By + C = 0 对称的点P'(x,y)

// 计算公式

// x=x0-2Ad, y=y0-2Bd

// d=(Ax0+By0+C)/(A^2+B^2)

function calculateSymmetryPoint(P, A, B, C) {
  let d = (A * P.x + B * P.y + C) / (Math.pow(A, 2) + Math.pow(B, 2));
  let x = P.x - 2 * A * d;
  let y = P.y - 2 * B * d;
  return { x: x, y: y };
}

let P = {
  x: 1,
  y: 3,
};

let A = 2;
let B = 1;
let C = 5;

let r = calculateSymmetryPoint(P, A, B, C);
console.log(r);

已知两点, 求直线点斜式公式

let A = {
  x: 1,
  y: 3,
};
let B = {
  x: 2,
  y: 4,
};
// 点斜式直线
// 斜率
let k = (B.y - A.y) / (B.x - A.x);
// 偏移量
let b = A.y - k * A.x;

console.log("k = " + k + " b = " + b);

两点距离

function getDistance(pointA, pointB) {
  return Math.sqrt(Math.pow(pointA.x - pointB.x, 2) + Math.pow(pointA.y - pointB.y, 2));
}

已知两点, 求直线角度

顺时针,角度为正;

逆时针, 角度为负

function calcAngle(x1, y1, x2, y2) {
  var angle = Math.atan2(y1 - y2, x2 - x1); //弧度
  var theta = angle * (180 / Math.PI); // 角度
  theta < 0 && (theta = 360 + theta);
  return theta;
}

let x1 = 0;
let y1 = 0;
let x2 = 1;
let y2 = -1;
log(calcAngle(x1, y1, x2, y2));

名人名言

思路是最重要的, 其他的百度, bing, stackoverflow, github, 安卓文档, autojs文档, 最后才是群里问问
--- 牙叔教程

声明

部分内容来自网络
本教程仅用于学习, 禁止用于其他用途