Trace equation of line in Photoshop

Question

Is there a direct method of using the Photoshop pen tool (or any other tool) to trace the equation of a line in 2D space and create a path from it in a given domain and/or range, provided I define a Cartesian coordinate system with an origin and two axes?

It would be cool if it could do this!

Answer 1

No, there is no native way to do this. There might be a plugin but Photoshop does not have any graphing functionality. You're best bet is to find a graphing application that can export something like .CAD, .SVG, or .EPS.

In fact if looking for plugins you'd probably be better off looking for an Illustrator plugin than a photoshop one as equations of lines are vector in nature. You'll have to look a few up and find which works best for your system.

Answer 2

One could be made. Its not terribly hard if you can make a few approximations. While I agree that mathematica and matlab are the ways to go for pro users. There are still some free alternatives that come to mind:

• Python and matplotlib can do this.
• Some javascript libraries like jsxgraph.

But if you insist on using a Photoshop as a hammer here you go (who am I to argue):

#target photoshop

var doc = app.activeDocument;

// place your function here 
//  put t in second array item if  you dont want a  2d parametric plot
function graphMeParametrically(t) {
     return new Array(
               20 * Math.sin(t) + 30,
               20 * Math.cos(t) +30
               );   
 }

// plot half arc centered on 30, 30
plotLinear(0., 3.14/10, 3.14, graphMeParametrically);

// ok so we could do better by estimating the curvature of a continnious function
plotSmooth(0., 3.14/10, 3.14, 0.01, graphMeParametrically);


function plotLinear(start, step, end, func){
    var points = new Array();
    var index = 0;
    for (var t =start;  t <= end; t+=step) {
        points.push(new PathPointInfo());
        points[index].kind = PointKind.CORNERPOINT;
        points[index].anchor = func(t);
        points[index].leftDirection = points[index].anchor;
        points[index].rightDirection = points[index].anchor;
        index+=1;
    }
    var subPath = new Array();
    subPath.push(new SubPathInfo());
    subPath[0].operation = ShapeOperation.SHAPEXOR;
    subPath[0].closed = false;
    subPath[0].entireSubPath = points;
    doc.pathItems.add("", subPath);
}

// this is a  very dirty and naive estimation 
// now updated version
function plotSmooth(start, step, end, delta, func){
    var points = new Array();
    var index = 0;

    for (var t =start;  t <= end; t+=step) {
        points.push(new PathPointInfo());
        points[index].kind = PointKind.SMOOTHPOINT;

        now =  func(t);
        next =  func(t + step);
        mag = Math.sqrt(Math.pow(next[0] - now[0], 2) + Math.pow(next[1] - now[1], 2)) /3;
        t1 = func(t + delta);
        t2 = func(t - delta);
        mag2 = Math.sqrt(Math.pow(t1[0] - t2[0], 2) + Math.pow(t1[1] - t2[1], 2)) 
        tan1 = new Array(now[0]-mag/mag2*(t2[0] - t1[0]), now[1]-mag/mag2*(t2[1] - t1[1]))
        tan2 = new Array(now[0]+mag/mag2*(t2[0] - t1[0]), now[1]+mag/mag2*(t2[1] - t1[1]))
        points[index].anchor = now;
        points[index].leftDirection = tan1;
        points[index].rightDirection = tan2;
        index+=1;
    }
    var subPath = new Array();
    subPath.push(new SubPathInfo());
    subPath[0].operation = ShapeOperation.SHAPEXOR;
    subPath[0].closed = false;
    subPath[0].entireSubPath = points;
    doc.pathItems.add("", subPath);
}

Edit the function and put this in a .jsx file the for example drag and drop on Photoshop. This will make 2 paths in your Photoshop document that can then be stroked if you like one segmented, and one that guestimates curvature. Try other curves as well.