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如何使用p5.js计算圆上直线的交点

p5.js geometry math javascript

Djave · 技术社区 · 6 年前

我正在使用

不幸的是,当我的物体通过圆时,它们不会在边缘留下点,而是离圆的边缘更远

小点是标记的位置,彩色点是物体(有起点和终点)

我这里有一个演示,有问题的部分是第42行以后: https://codepen.io/EightArmsHQ/pen/be0461014f9868e3462868776d9c8f1a你知道吗

内景

线穿过圆的地方。

p5.js 并可以访问它的所有向量函数。

// Get the vector between s and c
let scVector = p5.Vector.sub(start, circleCenter);
// Get the angle between se and sc
let escAngle = this.v.angleBetween(scVector);
// Get the distance between t (where the right angle hits the center of the circle) and c
let tcDistance = Math.sin(escAngle) * scVector.mag();
// Get the distance between t and where the line intersects the circle
let tlDistance = Math.sqrt(Math.pow(hole.r, 2) - Math.pow(tcDistance, 2));
// Get the distance between the start point and t
let stDistance = Math.sqrt(Math.pow(scVector.mag(), 2) - Math.pow(tcDistance, 2));
// Add the two distances together, giving me the distance between s and l
let totalDistance = tcDistance + stDistance;
// Create a new Vector at this angle, at the totalDistance Magnitude, then add it to the current position
let point = p5.Vector.fromAngle(this.v.heading(), totalDistance).add(start);
// Mark a point (hopefully l) on the edge of the circle.
points.push({
  x: point.x,
  y: point.y,
  fill: '#ffffff'
})

不幸的是,当我的物体通过圆时,它们不会在边缘留下点,而是离圆的边缘更远。

我这里有一个演示,有问题的部分是第42行以后: https://codepen.io/EightArmsHQ/pen/be0461014f9868e3462868776d9c8f1a

任何帮助都将不胜感激。

0 回复 | 直到 6 年前

Rabbid76 6 年前

要找到点和线的交点,我建议使用现有的算法,比如 WolframMathWorld - Circle-Line Intersection

算法简单,解释清楚,可以用一个短函数来表示。输入参数 p1 p2 ,和 cpt 属于 p5.Vector , r 第1页 到 锥体贯入度 半径呢 r . 函数返回一个区间点列表,其中可能为空:

intersectLineCircle = function(p1, p2, cpt, r) {

    let sign = function(x) { return x < 0.0 ? -1 : 1; };

    let x1 = p1.copy().sub(cpt);
    let x2 = p2.copy().sub(cpt);

    let dv = x2.copy().sub(x1)
    let dr = dv.mag();
    let D = x1.x*x2.y - x2.x*x1.y;

    // evaluate if there is an intersection
    let di = r*r*dr*dr - D*D;
    if (di < 0.0)
        return [];

    let t = sqrt(di);

    ip = [];
    ip.push( new p5.Vector(D*dv.y + sign(dv.y)*dv.x * t, -D*dv.x + p.abs(dv.y) * t).div(dr*dr).add(cpt) );
    if (di > 0.0) {
        ip.push( new p5.Vector(D*dv.y - sign(dv.y)*dv.x * t, -D*dv.x - p.abs(dv.y) * t).div(dr*dr).add(cpt) ); 
    }
    return ip;
}

Dot product
, 第2页 ,和 px 属于 . 这些点在同一条线上。函数返回 true 二甲苯 介于和和 false

inBetween = function(p1, p2, px) {

    let v = p2.copy().sub(p1);
    let d = v.mag();
    v = v.normalize();

    let vx = px.copy().sub(p1);
    let dx = v.dot(vx);

    return dx >= 0 && dx <= d;
}

var sketch = function( p ) {

p.setup = function() {
    let sketchCanvas = p.createCanvas(p.windowWidth, p.windowHeight);
    sketchCanvas.parent('p5js_canvas')
}

let points = [];
let move = []

// Circle-Line Intersection
// http://mathworld.wolfram.com/Circle-LineIntersection.html
p.intersectLineCircle = function(p1, p2, cpt, r) {

    let sign = function(x) { return x < 0.0 ? -1 : 1; };

    let x1 = p1.copy().sub(cpt);
    let x2 = p2.copy().sub(cpt);

    let dv = x2.copy().sub(x1)
    let dr = dv.mag();
    let D = x1.x*x2.y - x2.x*x1.y;

    // evaluate if there is an intersection
    let di = r*r*dr*dr - D*D;
    if (di < 0.0)
        return [];
   
    let t = p.sqrt(di);

    ip = [];
    ip.push( new p5.Vector(D*dv.y + sign(dv.y)*dv.x * t, -D*dv.x + p.abs(dv.y) * t).div(dr*dr).add(cpt) );
    if (di > 0.0) {
        ip.push( new p5.Vector(D*dv.y - sign(dv.y)*dv.x * t, -D*dv.x - p.abs(dv.y) * t).div(dr*dr).add(cpt) ); 
    }
    return ip;
}

p.inBetween = function(p1, p2, px) {

    let v = p2.copy().sub(p1);
    let d = v.mag();
    v = v.normalize();

    let vx = px.copy().sub(p1);
    let dx = v.dot(vx);
    
    return dx >= 0 && dx <= d;
}

p.endlessLine = function(x1, y1, x2, y2) {

    p1 = new p5.Vector(x1, y1);
    p2 = new p5.Vector(x2, y2);

    let dia_len = new p5.Vector(p.windowWidth, p.windowHeight).mag();
    let dir_v = p5.Vector.sub(p2, p1).setMag(dia_len);
    let lp1 = p5.Vector.add(p1, dir_v);
    let lp2 = p5.Vector.sub(p1, dir_v);

    p.line(lp1.x, lp1.y, lp2.x, lp2.y);
}

p.draw = function() {
        
    if (points.length == 0) {

        points = [];
        move = [];
        for (let i=0; i < 2; ++i ) {
            points.push( new p5.Vector(p.random(p.windowWidth-20)+10, p.random(p.windowHeight-20)+10));
            move.push( new p5.Vector(p.random(2)-1, p.random(2)-1) );
        }
        points.push( new p5.Vector(p.mouseX, p.mouseY));
    }
    else
    {
        for (let i=0; i < 2; ++i ) {
            points[i] = points[i].add(move[i]);
            if (points[i].x < 10 || points[i].x > p.windowWidth-10)
                move[i].x *= -1; 
            if (points[i].y < 10 || points[i].y > p.windowHeight-10)
                move[i].y *= -1;    
            move[i].x = Math.max(-1, Math.min(1, move[i].x+p.random(0.2)-0.1))
            move[i].y = Math.max(-1, Math.min(1, move[i].y+p.random(0.2)-0.1))
        }
        points[2].x = p.mouseX;
        points[2].y = p.mouseY;
    }
    let circle_diameter = p.min(p.windowWidth, p.windowHeight) / 2.0;

    let isectP = p.intersectLineCircle(...points, circle_diameter/2.0);

    // draw the scene

    p.background(192);
    
    p.stroke(0, 0, 255);
    p.fill(128, 128, 255);
    for (let i=0; i < points.length; ++i ) {
        p.ellipse(points[i].x, points[i].y, 10, 10);
    }

    for (let i=0; i < isectP.length; ++i ) {
        if (p.inBetween(points[0], points[1], isectP[i])) {
            p.stroke(255, 0, 0);
            p.fill(255, 128, 0);
        } else {
            p.stroke(255, 128, 0);
            p.fill(255, 255, 0);
        }

        p.ellipse(isectP[i].x, isectP[i].y, 10, 10);
    }

    p.stroke(0, 255, 0);
    p.noFill();
    p.endlessLine(points[0].x, points[0].y, points[1].x, points[1].y)
    p.ellipse(points[2].x, points[2].y, circle_diameter, circle_diameter);
}

p.windowResized = function() {
    p.resizeCanvas(p.windowWidth, p.windowHeight);
    points = [];
}

p.mouseClicked = function() {
    points = [];
}

p.keyPressed = function() {
    points = []
}

};

var circle_line = new p5(sketch);

<script src="https://cdnjs.cloudflare.com/ajax/libs/p5.js/0.9.0/p5.js"></script>
<div id="p5js_canvas"></div>