yichael
/
yichael_rhythmmaster


			
				
					
						
						
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							<!DOCTYPE html>
<html>
<head>
    <meta charset="utf-8"> 
    <title>速度变化图</title>
</head>
<body>
    <canvas style="position: fixed; top: 0px; left: 0px;"></canvas>
</body>
<script>
    var canvas = document.querySelector("canvas")
    var ctx = canvas.getContext("2d");
    ctx.clearRect(0, 0, canvas.width, canvas.height);
    canvas.width = innerWidth;
    canvas.height = innerHeight;
    ctx.fillStyle = "rgb(0,0,0)";
    ctx.fillRect(0,0,canvas.width,canvas.height);
    ctx.lineWidth = 1;
    ctx.strokeStyle = "rgb(255,0,0)";
    ctx.beginPath();
    ctx.moveTo(0, innerHeight - 100);
    ctx.lineTo(innerWidth, innerHeight - 100);
    ctx.moveTo(100, 0);
    ctx.lineTo(100, innerHeight);
    ctx.closePath();
    ctx.stroke();
    ctx.fillStyle = "rgb(255,0,0)";
    ctx.textBaseline = "top";
    ctx.textAlign = "center";
    ctx.font = "40px Arial"
    ctx.fillText("v", 130, 100);
    ctx.fillText("t", 350, innerHeight - 85);

    //积分求变加速直线运动位移
    function seekDistance(acc, time, draw) {
        let dt = 0.001;
        let v0 = 0;
        let sum = 0;
        for (let t = dt; t <= time; t += dt) {
            let dv = 1 / 2 * acc * dt;
            sum += v0 * dt + dv * dt;
            v0 += dv;
            //提高加速度
            acc += dt * acc * 3;
            if (draw) {
                ctx.moveTo(100 + (t / 5 * 1000) << 0, innerHeight - 100);   
                ctx.lineTo (100 + (t / 5 * 1000) << 0, innerHeight - 100 - v0 / 5);   
                ctx.stroke();
            }
        }
        return sum;
    }
        
    //寻找最佳的加速度
    function findBestAcc(distance, time) {
        //为了后面减少运算量，先粗略找到比较接近的区间
        let accRangeMin = null;
        let accRangeMax = null;
        for (let acc = 0; acc < 10000; acc += 10) {
            let result = seekDistance(acc, time);
            let dx = result - distance;
            if (dx < 0) {
                accRangeMin = acc;
            } else if (dx > 0) {
                accRangeMax = acc;
                break;
            } else {
                return acc;
            }
        }
        if (accRangeMin == null || accRangeMax == null) {
            throw "寻找区间失败"
        }
        //在指定区间寻找最佳结果
        for (let acc = accRangeMin; acc <= accRangeMax; acc += 0.001) {
            let result = seekDistance(acc, time);
            let dx = result - distance;
            if (Math.abs(dx) < 0.1) {
                return acc;
            }
        }
        throw "找不到最佳加速度";
    }

    let acc = findBestAcc(640, 1);
    seekDistance(acc, 1, true);
</script>
</html>