html5-canvas Navigating along a Path Finding points along an entire Path containing curves and lines

Example

This example finds an array of approximately evenly spaced points along an entire Path.

It decomposes all Path segments created with context.lineTo, context.quadraticCurveTo and/or context.bezierCurveTo into points along that Path.

Usage

// Path related variables
var A={x:50,y:100};
var B={x:125,y:25};
var BB={x:150,y:15};
var BB2={x:150,y:185};
var C={x:175,y:200};
var D={x:300,y:150};
var n=1000;
var tolerance=1.5;
var pts;

// canvas related variables
var canvas=document.createElement("canvas");
var ctx=canvas.getContext("2d");
document.body.appendChild(canvas);
canvas.width=378;
canvas.height=256;

// Tell the Context to plot waypoint in addition to 
// drawing the path
plotPathCommands(ctx,n,tolerance);

// Path drawing commands
ctx.beginPath();
ctx.moveTo(A.x,A.y);
ctx.bezierCurveTo(B.x,B.y,C.x,C.y,D.x,D.y);
ctx.quadraticCurveTo(BB.x,BB.y,A.x,A.y);
ctx.lineTo(D.x,D.y);
ctx.strokeStyle='gray';
ctx.stroke();

// Tell the Context to stop plotting waypoints
ctx.stopPlottingPathCommands();

// Demo: Incrementally draw the path using the plotted points
ptsToRects(ctx.getPathPoints());
function ptsToRects(pts){
    ctx.fillStyle='red';
    var i=0;
    requestAnimationFrame(animate);
    function animate(){
        ctx.fillRect(pts[i].x-0.50,pts[i].y-0.50,tolerance,tolerance);
        i++;
        if(i<pts.length){ requestAnimationFrame(animate); }
    }
}

An plug-in that automatically calculates points along the path

This code modifies these Canvas Context's drawing commands so the commands not only draw the line or curve, but also create an array of points along the entire path:

• beginPath,
• moveTo,
• lineTo,
• quadraticCurveTo,
• bezierCurveTo.

Important Note!

This code modifies the actual drawing functions of the Context so when you are done plotting points along the path, you should call the supplied stopPlottingPathCommands to return the Context drawing functions to their unmodified state.

The purpose of this modified Context is to allow you to "plug-in" the points-array calculation into your existing code without having to modify your existing Path drawing commands. But, you don't need to use this modified Context -- you can separately call the individual functions that decompose a line, a quadratic curve and a cubic Bezier curve and then manually concatenate those individual point-arrays into a single point-array for the entire path.

You fetch a copy of the resulting points-array using the supplied getPathPoints function.

If you draw multiple Paths with the modified Context, the points-array will contain a single concatenated set of points for all the multiple Paths drawn.

If, instead, you want to get separate points-arrays, you can fetch the current array with getPathPoints and then clear those points from the array with the supplied clearPathPoints function.

// Modify the Canvas' Context to calculate a set of approximately
//     evenly spaced waypoints as it draws path(s).
function plotPathCommands(ctx,sampleCount,pointSpacing){
    ctx.mySampleCount=sampleCount;
    ctx.myPointSpacing=pointSpacing;
    ctx.myTolerance=pointSpacing*pointSpacing;
    ctx.myBeginPath=ctx.beginPath;
    ctx.myMoveTo=ctx.moveTo;
    ctx.myLineTo=ctx.lineTo;
    ctx.myQuadraticCurveTo=ctx.quadraticCurveTo;
    ctx.myBezierCurveTo=ctx.bezierCurveTo;
    // don't use myPathPoints[] directly -- use "ctx.getPathPoints"
    ctx.myPathPoints=[];
    ctx.beginPath=function(){
        this.myLastX=0;
        this.myLastY=0;
        this.myBeginPath();
    }
    ctx.moveTo=function(x,y){
        this.myLastX=x;
        this.myLastY=y;
        this.myMoveTo(x,y);
    }
    ctx.lineTo=function(x,y){
        var pts=plotLine(this.myTolerance,this.myLastX,this.myLastY,x,y);
        Array.prototype.push.apply(this.myPathPoints,pts);
        this.myLastX=x;
        this.myLastY=y;
        this.myLineTo(x,y);
    }
    ctx.quadraticCurveTo=function(x0,y0,x1,y1){
        var pts=plotQBez(this.mySampleCount,this.myTolerance,this.myLastX,this.myLastY,x0,y0,x1,y1);
        Array.prototype.push.apply(this.myPathPoints,pts);
        this.myLastX=x1;
        this.myLastY=y1;
        this.myQuadraticCurveTo(x0,y0,x1,y1);
    }
    ctx.bezierCurveTo=function(x0,y0,x1,y1,x2,y2){
        var pts=plotCBez(this.mySampleCount,this.myTolerance,this.myLastX,this.myLastY,x0,y0,x1,y1,x2,y2);
        Array.prototype.push.apply(this.myPathPoints,pts);
        this.myLastX=x2;
        this.myLastY=y2;
        this.myBezierCurveTo(x0,y0,x1,y1,x2,y2);
    }
    ctx.getPathPoints=function(){
        return(this.myPathPoints.slice());
    }
    ctx.clearPathPoints=function(){
        this.myPathPoints.length=0;
    }
    ctx.stopPlottingPathCommands=function(){
        if(!this.myBeginPath){return;}
        this.beginPath=this.myBeginPath;
        this.moveTo=this.myMoveTo;
        this.lineTo=this.myLineTo;
        this.quadraticCurveto=this.myQuadraticCurveTo;
        this.bezierCurveTo=this.myBezierCurveTo;
        this.myBeginPath=undefined;
    }
}

A complete Demo:

// Path related variables
var A={x:50,y:100};
var B={x:125,y:25};
var BB={x:150,y:15};
var BB2={x:150,y:185};
var C={x:175,y:200};
var D={x:300,y:150};
var n=1000;
var tolerance=1.5;
var pts;

// canvas related variables
var canvas=document.createElement("canvas");
var ctx=canvas.getContext("2d");
document.body.appendChild(canvas);
canvas.width=378;
canvas.height=256;

// Tell the Context to plot waypoint in addition to 
// drawing the path
plotPathCommands(ctx,n,tolerance);

// Path drawing commands
ctx.beginPath();
ctx.moveTo(A.x,A.y);
ctx.bezierCurveTo(B.x,B.y,C.x,C.y,D.x,D.y);
ctx.quadraticCurveTo(BB.x,BB.y,A.x,A.y);
ctx.lineTo(D.x,D.y);
ctx.strokeStyle='gray';
ctx.stroke();

// Tell the Context to stop plotting waypoints
ctx.stopPlottingPathCommands();

// Incrementally draw the path using the plotted points
ptsToRects(ctx.getPathPoints());
function ptsToRects(pts){
    ctx.fillStyle='red';
    var i=0;
    requestAnimationFrame(animate);
    function animate(){
        ctx.fillRect(pts[i].x-0.50,pts[i].y-0.50,tolerance,tolerance);
        i++;
        if(i<pts.length){ requestAnimationFrame(animate); }
    }
}


////////////////////////////////////////
// A Plug-in
////////////////////////////////////////

// Modify the Canvas' Context to calculate a set of approximately
//     evenly spaced waypoints as it draws path(s).
function plotPathCommands(ctx,sampleCount,pointSpacing){
    ctx.mySampleCount=sampleCount;
    ctx.myPointSpacing=pointSpacing;
    ctx.myTolerance=pointSpacing*pointSpacing;
    ctx.myBeginPath=ctx.beginPath;
    ctx.myMoveTo=ctx.moveTo;
    ctx.myLineTo=ctx.lineTo;
    ctx.myQuadraticCurveTo=ctx.quadraticCurveTo;
    ctx.myBezierCurveTo=ctx.bezierCurveTo;
    // don't use myPathPoints[] directly -- use "ctx.getPathPoints"
    ctx.myPathPoints=[];
    ctx.beginPath=function(){
        this.myLastX=0;
        this.myLastY=0;
        this.myBeginPath();
    }
    ctx.moveTo=function(x,y){
        this.myLastX=x;
        this.myLastY=y;
        this.myMoveTo(x,y);
    }
    ctx.lineTo=function(x,y){
        var pts=plotLine(this.myTolerance,this.myLastX,this.myLastY,x,y);
        Array.prototype.push.apply(this.myPathPoints,pts);
        this.myLastX=x;
        this.myLastY=y;
        this.myLineTo(x,y);
    }
    ctx.quadraticCurveTo=function(x0,y0,x1,y1){
        var pts=plotQBez(this.mySampleCount,this.myTolerance,this.myLastX,this.myLastY,x0,y0,x1,y1);
        Array.prototype.push.apply(this.myPathPoints,pts);
        this.myLastX=x1;
        this.myLastY=y1;
        this.myQuadraticCurveTo(x0,y0,x1,y1);
    }
    ctx.bezierCurveTo=function(x0,y0,x1,y1,x2,y2){
        var pts=plotCBez(this.mySampleCount,this.myTolerance,this.myLastX,this.myLastY,x0,y0,x1,y1,x2,y2);
        Array.prototype.push.apply(this.myPathPoints,pts);
        this.myLastX=x2;
        this.myLastY=y2;
        this.myBezierCurveTo(x0,y0,x1,y1,x2,y2);
    }
    ctx.getPathPoints=function(){
        return(this.myPathPoints.slice());
    }
    ctx.clearPathPoints=function(){
        this.myPathPoints.length=0;
    }
    ctx.stopPlottingPathCommands=function(){
        if(!this.myBeginPath){return;}
        this.beginPath=this.myBeginPath;
        this.moveTo=this.myMoveTo;
        this.lineTo=this.myLineTo;
        this.quadraticCurveto=this.myQuadraticCurveTo;
        this.bezierCurveTo=this.myBezierCurveTo;
        this.myBeginPath=undefined;
    }
}


////////////////////////////////
// Helper functions
////////////////////////////////

// Return: a set of approximately evenly spaced points along a cubic Bezier curve
//
// Attribution: Stackoverflow's @Blindman67
// Cite: http://stackoverflow.com/questions/36637211/drawing-a-curved-line-in-css-or-canvas-and-moving-circle-along-it/36827074#36827074
// As modified from the above citation
// 
// ptCount: sample this many points at interval along the curve
// pxTolerance: approximate spacing allowed between points
// Ax,Ay,Bx,By,Cx,Cy,Dx,Dy: control points defining the curve
//
function plotCBez(ptCount,pxTolerance,Ax,Ay,Bx,By,Cx,Cy,Dx,Dy){
    var deltaBAx=Bx-Ax;
    var deltaCBx=Cx-Bx;
    var deltaDCx=Dx-Cx;
    var deltaBAy=By-Ay;
    var deltaCBy=Cy-By;
    var deltaDCy=Dy-Cy;
    var ax,ay,bx,by;
    var lastX=-10000;
    var lastY=-10000;
    var pts=[{x:Ax,y:Ay}];
    for(var i=1;i<ptCount;i++){
        var t=i/ptCount;
        ax=Ax+deltaBAx*t;
        bx=Bx+deltaCBx*t;
        cx=Cx+deltaDCx*t;
        ax+=(bx-ax)*t;
        bx+=(cx-bx)*t;
        //
        ay=Ay+deltaBAy*t;
        by=By+deltaCBy*t;
        cy=Cy+deltaDCy*t;
        ay+=(by-ay)*t;
        by+=(cy-by)*t;
        var x=ax+(bx-ax)*t;
        var y=ay+(by-ay)*t;
        var dx=x-lastX;
        var dy=y-lastY;
        if(dx*dx+dy*dy>pxTolerance){
            pts.push({x:x,y:y});
            lastX=x;
            lastY=y;
        }
    }
    pts.push({x:Dx,y:Dy});
    return(pts);
}

// Return: an array of approximately evenly spaced points along a Quadratic curve
//
// Attribution: Stackoverflow's @Blindman67
// Cite: http://stackoverflow.com/questions/36637211/drawing-a-curved-line-in-css-or-canvas-and-moving-circle-along-it/36827074#36827074
// As modified from the above citation
//
// ptCount: sample this many points at interval along the curve
// pxTolerance: approximate spacing allowed between points
// Ax,Ay,Bx,By,Cx,Cy: control points defining the curve
//
function plotQBez(ptCount,pxTolerance,Ax,Ay,Bx,By,Cx,Cy){
    var deltaBAx=Bx-Ax;
    var deltaCBx=Cx-Bx;
    var deltaBAy=By-Ay;
    var deltaCBy=Cy-By;
    var ax,ay;
    var lastX=-10000;
    var lastY=-10000;
    var pts=[{x:Ax,y:Ay}];
    for(var i=1;i<ptCount;i++){
        var t=i/ptCount;
        ax=Ax+deltaBAx*t;
        ay=Ay+deltaBAy*t;
        var x=ax+((Bx+deltaCBx*t)-ax)*t;
        var y=ay+((By+deltaCBy*t)-ay)*t;
        var dx=x-lastX;
        var dy=y-lastY;
        if(dx*dx+dy*dy>pxTolerance){
            pts.push({x:x,y:y});
            lastX=x;
            lastY=y;
        }
    }
    pts.push({x:Cx,y:Cy});
    return(pts);
}

// Return: an array of approximately evenly spaced points along a line
//
// pxTolerance: approximate spacing allowed between points
// Ax,Ay,Bx,By: end points defining the line
//
function plotLine(pxTolerance,Ax,Ay,Bx,By){
    var dx=Bx-Ax;
    var dy=By-Ay;
    var ptCount=parseInt(Math.sqrt(dx*dx+dy*dy))*3;
    var lastX=-10000;
    var lastY=-10000;
    var pts=[{x:Ax,y:Ay}];
    for(var i=1;i<=ptCount;i++){
        var t=i/ptCount;
        var x=Ax+dx*t;
        var y=Ay+dy*t;
        var dx1=x-lastX;
        var dy1=y-lastY;
        if(dx1*dx1+dy1*dy1>pxTolerance){
            pts.push({x:x,y:y});
            lastX=x;
            lastY=y;
        }
    }
    pts.push({x:Bx,y:By});
    return(pts);
}