html5 canvas貝塞爾曲線獲得所有要點

Question

我喜歡從貝塞爾曲線得到一些點。

在JavaScript中找到三次貝塞爾曲線的所有點

位置很容易。 首先，計算混合函數。 這些控制曲線上控制點的“效果”。

B0_t = (1-t)^3

B1_t = 3 * t * (1-t)^2

B2_t = 3 * t^2 * (1-t)

B3_t = t^3

請注意，當t為0（其他均為零）時，B0_t如何為1。 同樣，當t為1時B3_t為1（其他所有值均為零）。 因此曲線開始於（ax，ay），結束於（dx，dy）。 任何中間點（px_t，py_t）都將由以下給出（從0到1變化t，在循環內以較小的增量）：

px_t = (B0_t * ax) + (B1_t * bx) + (B2_t * cx) + (B3_t * dx)

py_t = (B0_t * ay) + (B1_t * by) + (B2_t * cy) + (B3_t * dy)

我的密碼

            var ax = 100, ay = 250;
            var bx = 150, by = 100;
            var cx = 350, cy = 100;
            var dx = 400, dy = 250;


            ctx.lineWidth = 1;
            ctx.strokeStyle = "#333";
            ctx.beginPath();
            ctx.moveTo(ax, ay);
            ctx.bezierCurveTo(bx, by, cx, cy, dx, dy);
            ctx.stroke();

            var t = 0 
            var B0_t = (1 - t) ^ 3
            var B1_t = 3 * t * (1 - t) ^ 2
            var B2_t = 3 * t ^ 2 * (1 - t)
            var B3_t = t ^ 3


              // override manually *Notice* above
             //This is work first and laste point in curve
            //  B0_t = 1; B1_t = 0; B2_t = 0; B3_t = 0; t = 0;
           // B0_t = 0; B1_t = 0; B2_t = 0; B3_t = 1; t = 1;  

            var px_t = (B0_t * ax) + (B1_t * bx) + (B2_t * cx) + (B3_t * dx)
            var py_t = (B0_t * ay) + (B1_t * by) + (B2_t * cy) + (B3_t * dy)


// doesnt work

var t = 0

var B0_t = (1 - t) ^ 3   //*Notice* above should be 1 
//Debug    (1 - t) ^ 3 = 2 ?? 

var B1_t = 3 * t * (1 - t) ^ 2 //*Notice* above should be 0 
//Debug    3 * t * (1 - t) ^ 2 = 2 ??

var B2_t = 3 * t ^ 2 * (1 - t)//*Notice* above should be 0 
//Debug    3 * t ^ 2 * (1 - t) =2 ??

var B3_t = t ^ 3//*Notice* above should be 0 but its 2
//Debug    t ^ 3 = 3 ??

var px_t = (B0_t * ax) + (B1_t * bx) + (B2_t * cx) + (B3_t * dx)

var py_t = (B0_t * ay) + (B1_t * by) + (B2_t * cy) + (B3_t * dy)

感謝任何幫助謝謝

Answer 1

如何沿着貝塞爾曲線找到像素

這組函數將沿着三次貝塞爾曲線在間隔T處找到一個[x,y]點，其中0<=T<=1 。

簡而言之：它從起點到終點沿着三次貝塞爾曲線繪制點。

// Given the 4 control points on a Bezier curve 
// get x,y at interval T along the curve (0<=T<=1)
// The curve starts when T==0 and ends when T==1
function getCubicBezierXYatPercent(startPt, controlPt1, controlPt2, endPt, percent) {
    var x = CubicN(percent, startPt.x, controlPt1.x, controlPt2.x, endPt.x);
    var y = CubicN(percent, startPt.y, controlPt1.y, controlPt2.y, endPt.y);
    return ({
        x: x,
        y: y
    });
}

// cubic helper formula
function CubicN(T, a, b, c, d) {
    var t2 = T * T;
    var t3 = t2 * T;
    return a + (-a * 3 + T * (3 * a - a * T)) * T + (3 * b + T * (-6 * b + b * 3 * T)) * T + (c * 3 - c * 3 * T) * t2 + d * t3;
}

您可以通過向繪圖函數發送0.00至1.00之間的大量T值來獲取沿曲線的點。

示例代碼和演示：

 var canvas=document.getElementById("canvas"); var ctx=canvas.getContext("2d"); var cw=canvas.width; var ch=canvas.height; var cBez1=[{x:250,y: 120},{x:290,y:-40},{x:300,y:200},{x:400,y:150}] drawBez(cBez1); var cPoints=findCBezPoints(cBez1); drawPlots(cPoints); function findCBezPoints(b){ var startPt=b[0]; var controlPt1=b[1]; var controlPt2=b[2]; var endPt=b[3]; var pts=[b[0]]; var lastPt=b[0]; var tests=5000; for(var t=0;t<=tests;t++){ // calc another point along the curve var pt=getCubicBezierXYatT(b[0],b[1],b[2],b[3], t/tests); // add the pt if it's not already in the pts[] array var dx=pt.x-lastPt.x; var dy=pt.y-lastPt.y; var d=Math.sqrt(dx*dx+dy*dy); var dInt=parseInt(d); if(dInt>0 || t==tests){ lastPt=pt; pts.push(pt); } } return(pts); } // Given the 4 control points on a Bezier curve // Get x,y at interval T along the curve (0<=T<=1) // The curve starts when T==0 and ends when T==1 function getCubicBezierXYatT(startPt, controlPt1, controlPt2, endPt, T) { var x = CubicN(T, startPt.x, controlPt1.x, controlPt2.x, endPt.x); var y = CubicN(T, startPt.y, controlPt1.y, controlPt2.y, endPt.y); return ({ x: x, y: y }); } // cubic helper formula function CubicN(T, a, b, c, d) { var t2 = T * T; var t3 = t2 * T; return a + (-a * 3 + T * (3 * a - a * T)) * T + (3 * b + T * (-6 * b + b * 3 * T)) * T + (c * 3 - c * 3 * T) * t2 + d * t3; } function drawPlots(pts){ ctx.fillStyle='red'; // don't draw the last dot b/ its radius will display past the curve for(var i=0;i<pts.length-1;i++){ ctx.beginPath(); ctx.arc(pts[i].x,pts[i].y,1,0,Math.PI*2); ctx.fill(); } } function drawBez(b){ ctx.lineWidth=7; ctx.beginPath(); ctx.moveTo(b[0].x,b[0].y); ctx.bezierCurveTo(b[1].x,b[1].y, b[2].x,b[2].y, b[3].x,b[3].y); ctx.stroke(); } 

 body{ background-color: ivory; } #canvas{border:1px solid red; margin:0 auto; } 

 <h4>Black line is context.bezierCurveTo<br>Red "line" is really dot-points plotted along the curve</h4> <canvas id="canvas" width=500 height=300></canvas>