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  1. PO
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    <p>I made a <a href="http://jsfiddle.net/MadLittleMods/vqKvM/39/" rel="nofollow">jsFiddle</a> that for a given polygon, calculates an outer polygon that I hope meets your requirement. I have put the math behind it in this <a href="https://drive.google.com/viewerng/viewer?a=v&amp;pid=sites&amp;srcid=ZGVmYXVsdGRvbWFpbnxqa2dhZGdldHN0b3JlfGd4OjQ4MzI5M2Y0MjNmNzI2MjY" rel="nofollow">pdf document</a>. </p> <p><strong>Update:</strong> code has been made to deal with vertical lines.</p> <pre><code>function Vector2(x, y) { this.x = x; this.y = y; } function straight_skeleton(poly, spacing) { // http://stackoverflow.com/a/11970006/796832 // Accompanying Fiddle: http://jsfiddle.net/vqKvM/35/ var resulting_path = []; var N = poly.length; var mi, mi1, li, li1, ri, ri1, si, si1, Xi1, Yi1; for(var i = 0; i &lt; N; i++) { mi = (poly[(i+1) % N].y - poly[i].y)/(poly[(i+1) % N].x - poly[i].x); mi1 = (poly[(i+2) % N].y - poly[(i+1) % N].y)/(poly[(i+2) % N].x - poly[(i+1) % N].x); li = Math.sqrt((poly[(i+1) % N].x - poly[i].x)*(poly[(i+1) % N].x - poly[i].x)+(poly[(i+1) % N].y - poly[i].y)*(poly[(i+1) % N].y - poly[i].y)); li1 = Math.sqrt((poly[(i+2) % N].x - poly[(i+1) % N].x)*(poly[(i+2) % N].x - poly[(i+1) % N].x)+(poly[(i+2) % N].y - poly[(i+1) % N].y)*(poly[(i+2) % N].y - poly[(i+1) % N].y)); ri = poly[i].x+spacing*(poly[(i+1) % N].y - poly[i].y)/li; ri1 = poly[(i+1) % N].x+spacing*(poly[(i+2) % N].y - poly[(i+1) % N].y)/li1; si = poly[i].y-spacing*(poly[(i+1) % N].x - poly[i].x)/li; si1 = poly[(i+1) % N].y-spacing*(poly[(i+2) % N].x - poly[(i+1) % N].x)/li1; Xi1 = (mi1*ri1-mi*ri+si-si1)/(mi1-mi); Yi1 = (mi*mi1*(ri1-ri)+mi1*si-mi*si1)/(mi1-mi); // Correction for vertical lines if(poly[(i+1) % N].x - poly[i % N].x==0) { Xi1 = poly[(i+1) % N].x + spacing*(poly[(i+1) % N].y - poly[i % N].y)/Math.abs(poly[(i+1) % N].y - poly[i % N].y); Yi1 = mi1*Xi1 - mi1*ri1 + si1; } if(poly[(i+2) % N].x - poly[(i+1) % N].x==0 ) { Xi1 = poly[(i+2) % N].x + spacing*(poly[(i+2) % N].y - poly[(i+1) % N].y)/Math.abs(poly[(i+2) % N].y - poly[(i+1) % N].y); Yi1 = mi*Xi1 - mi*ri + si; } //console.log("mi:", mi, "mi1:", mi1, "li:", li, "li1:", li1); //console.log("ri:", ri, "ri1:", ri1, "si:", si, "si1:", si1, "Xi1:", Xi1, "Yi1:", Yi1); resulting_path.push({ x: Xi1, y: Yi1 }); } return resulting_path; } var canvas = document.getElementById("Canvas"); var ctx = canvas.getContext("2d"); var poly = [ new Vector2(150, 170), new Vector2(400, 120), new Vector2(200, 270), new Vector2(350, 400), new Vector2(210, 470) ]; draw(poly); draw(straight_skeleton(poly, 10)); function draw(p) { ctx.beginPath(); ctx.moveTo(p[0].x, p[0].y); for(var i = 1; i &lt; p.length; i++) { ctx.lineTo(p[i].x, p[i].y); } ctx.strokeStyle = "#000000"; ctx.closePath(); ctx.stroke(); } </code></pre> <p>A polygon is put into an array of point objects.</p> <p>The function <code>draw(p)</code> draws the polygon <code>p</code> on the canvas.</p> <p>The given polygon is in array poly, the outer in the array poly.</p> <p><code>spacing</code> is the distance between the polygons (as along the arrows in your green diagram)</p> <hr> <p>Following Angus Johnson's comment, I have produced some more fiddles to show the issues he raises. This problem is much more difficult problem than I first thought.</p> <ul> <li><a href="http://jsfiddle.net/vqKvM/5/" rel="nofollow">http://jsfiddle.net/vqKvM/5/</a></li> <li><a href="http://jsfiddle.net/vqKvM/6/" rel="nofollow">http://jsfiddle.net/vqKvM/6/</a></li> <li><a href="http://jsfiddle.net/vqKvM/7/" rel="nofollow">http://jsfiddle.net/vqKvM/7/</a></li> </ul>
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    1. POScale a polygon so the edges match up
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    1. COI've had a very quick look at your code and ISTM that it'll only properly offset the simplest polygons. For example, I can't see any code to manage very acute convex angles where vertices can move exponential distances relative to the offset distance. Also, with acute concave angles with relatively short sides, there needs to be code to remove the self-intersections that result from simple offsetting.
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    2. CO@Angus Johnson I have just tried it with the conditions you specified and I see what you mean. Thanks for pointing this out. I'll give it some more thought. Perhaps davey555 would comment on whether these conditions could arise in his application.
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