: Create new layer by extending length of existing arc Is there a simple way of keeping the shape of the existing arc while changing its length? In other words, I would like the ends of the

@Gail6891361

A Bézier segment of a path is a polynomial. Just because we only use the curve to a parameter of range [0-1] does not mean the function does not exist outside this range, it does. Since this new curve is also a Bézier, so it can be described with a different Bézier curve accurately.



Image 1: Two Bézier curves that have been extended by 0.1 t in both directions.

I have used the following, extremely beta version, script:
#target illustrator

// extendSelectedSegment.jsx v0.0
//
// Copyright (c) 2017 Janne Ojala
// License: MIT see opensource.org/licenses/MIT
var Bezier = function(p1, p2, p3, p4) {
if (p2 === undefined){
this.paramsFromPath(p1);
} else {
this.p1 = p1;
this.p2 = p2;
this.p3 = p3;
this.p4 = p4;
}
};

Bezier.prototype.posAtParam = function(t){
var p = [undefined, undefined];
for (var i = 0; i < 2; i++){
p[i] = this.p1[i] * Math.pow(1 - t,3)
+ this.p2[i] * 3 * t * Math.pow(1 - t,2)
+ this.p3[i] * 3 * Math.pow(t,2) * (1 - t)
+ this.p4[i] * Math.pow(t,3);
}
return p;
}


Bezier.prototype.derivateAtParam = function(t){
var d = [undefined, undefined];
for (var i = 0; i < 2; i++){
d[i] = - 3 * this.p1[i] * Math.pow(1 - t,2)
+ 3 * this.p2[i] * Math.pow(1 - t,2)
- 6 * this.p2[i] * (1 - t) * t
+ 6 * this.p3[i] * (1 - t) * t
- 3 * this.p3[i] * Math.pow(t,2)
+ 3 * this.p4[i] * Math.pow(t,2);
}
return d;
}

Bezier.prototype.extendToParam = function(t, t2){
// Extend only to one direction at time.
if (t2 === undefined){
t2 = t;
t = 0;
}
var p4n = this.posAtParam(t2);
var p3n = this.derivateAtParam(t2);
for (var i = 0; i < 2; i++){
p3n[i] = p4n[i] - ((t2-t)*p3n[i])/3;
}
var p1n = this.posAtParam(t);
var p2n = this.derivateAtParam(t);
for (var i = 0; i < 2; i++){
p2n[i] = p1n[i] + ((t2-t)*p2n[i])/3;
}
return new Bezier(p1n, p2n, p3n, p4n);
}

Bezier.prototype.makePath = function(){
pth = app.activeDocument.pathItems.add();
var point1 = pth.pathPoints.add();
point1.anchor = this.p1;
point1.leftDirection = this.p1;
point1.rightDirection = this.p2;

var point2 = pth.pathPoints.add();
point2.anchor = this.p4;
point2.leftDirection = this.p3;
point2.rightDirection = this.p4;
}

Bezier.prototype.paramsFromPath = function(pth){
var point1 = pth.pathPoints[0];
this.p1 = point1.anchor;
this.p2 = point1.rightDirection;

var point2 = pth.pathPoints[1];
this.p3 = point2.leftDirection;
this.p4 = point2.anchor;
}

var sel = app.activeDocument.selection;
var bez = new Bezier(sel[0]);
bez = bez.extendToParam(0, 1.1);
bez = bez.extendToParam(-0.1, 1.0);
bez.makePath();


Now bear in mind that this works for a single selected path and has no checks. This script is posted as is and should be handled with care. But otherwise your free to do anything you like with it as long as you keep the attribution/license for my parts of the code.

Note: I am extending the Bézier function, this does not always yield a very "natural" extension as it uses the underlying function and that CAN turn on itself if you are near a situation that would make a cusp.

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@Nimeshi706

Not sure an automated solution is possible but the VectorScribe plugin by Astute Graphics has an "Extend Path" tool which can do this manually. It has a couple of different modes for calculating the path it is extending and is as easy as dragging out the path you want to extend.

You can see some examples (and how to use the keyboard shortcuts) here:

astutegraphics.com/blog/extend-path-tool-keyboard-shortcuts/

The plugin is £69 (or whatever that is in your local currency), but it does also have a 14 day free trial which may be enough for you to do what you need.

astutegraphics.com/software/vectorscribe/

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@Dunderdale640

If you only want to change the arc width without effecting the height make sure the link between width and height is unchecked.



If you want to change multiple arcs at the same time you can select the arcs and go to Object -> Transform -> Scale. Change the scale to Non-Uniform and input a larger percentage.


I would like the ends of the arc to extend further while keeping the
same shape.


There is no way to extend the arc and keep the same shape because that will distort the arc curve.

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