Merging two bezier-based shapes into one to create a new outline

Question

Lets say I have the data to render two overlaying bezier-based shapes, that are overlapping, displayed in a svg or on the canvas (doesn't really matter where). I would like to calculate the outline of the shape resulting from the merge of the two shapes, so that I have a clean (new) outline and as few nodes and handles as possible. I would like to achieve the effect that vector programs like adobe illustrator offers with Pathfinder > Add or the font program glyphs with Remove Overlap. Example: https://helpx.adobe.com/illustrator/using/combining-objects.html

Is there possible a library or a concept for that task? I am working with javascript in the browser, but any other source for how to make such a calculation would help as well.

It is also important, that this calculation happens before the rendering an agnostic to the rendered result (be it svg/canvas).

In the illustration bellow, on the left side is the input shape. and on the right side the expected result. I have the data, meaning all the nodes and handles (from the bezier curve) and I would like to calculate the coordinates of the red (nodes) and green dots (handles) on the right side.

Answer 1

Paper.js might be the perfect library for this task:
In particular it's Boolean operations – like unite() to merge path elements. The syntax looks something like this:

let unitedPath = items[0].unite(items[1]);  

The following example also employs Jarek Foksa's pathData polyfill.

Example: unite paths:

const svg = document.querySelector("#svgunite");
const btnDownload = document.querySelector("#btnDownload");
const decimals = 1;
// set auto ids for processing
function setAutoIDs(svg) {
  let svgtEls = svg.querySelectorAll(
    "path, polygon, rect, circle, line, text, g"
  );
  svgtEls.forEach(function(el, i) {
    if (!el.getAttribute("id")) {
      el.id = el.nodeName + "-" + i;
    }
  });
}
setAutoIDs(svg);

function shapesToPathMerged(svg) {
  let els = svg.querySelectorAll('path, rect, circle, polygon, ellipse ');
  let pathsCombinedData = '';
  let className = els[1].getAttribute('class');
  let id = els[1].id;
  let d = els[1].getAttribute('d');
  let fill = els[1].getAttribute('fill');

  els.forEach(function(el, i) {
    let pathData = el.getPathData({
      normalize: true
    });
    if (i == 0 && el.nodeName.toLowerCase() != 'path') {
      let firstTmp = document.createElementNS("http://www.w3.org/2000/svg", 'path');
      let firstClassName = els[1].getAttribute('class');
      let firstId = el.id;
      let firstFill = el.getAttribute('fill');
      firstTmp.setPathData(pathData);
      firstTmp.id = firstId;
      firstTmp.setAttribute('class', firstClassName);
      firstTmp.setAttribute('fill', firstFill);
      svg.insertBefore(firstTmp, el);
      el.remove();
    }
    if (i > 0) {
      pathData.forEach(function(command, c) {
        pathsCombinedData += ' ' + command['type'] + '' + command['values'].join(' ');
      });
      el.remove();
    }
  })
  let pathTmp = document.createElementNS("http://www.w3.org/2000/svg", 'path');
  pathTmp.id = id;
  pathTmp.setAttribute('class', className);
  pathTmp.setAttribute('fill', fill);
  pathTmp.setAttribute('d', pathsCombinedData);
  svg.insertBefore(pathTmp, els[0].nextElementSibling);
};

shapesToPathMerged(svg);


function unite(svg) {
  // init paper.js and add mandatory canvas
  canvas = document.createElement('canvas');
  canvas.id = "canvasPaper";
  canvas.setAttribute('style', 'display:none')
  document.body.appendChild(canvas);
  paper.setup("canvasPaper");

  let all = paper.project.importSVG(svg, function(item, i) {
    let items = item.getItems();
    // remove first item not containing path data
    items.shift();
    // get id names for selecting svg elements after processing
    let ids = Object.keys(item._namedChildren);

    if (items.length) {
      let lastEl = items[items.length - 1];
      // unite paper.js objects
      let united = items[0].unite(lastEl);
      // convert united paper.js object to svg pathData
      let unitedData = united
        .exportSVG({
          precision: decimals
        })
        .getAttribute("d");
      let svgElFirst = svg.querySelector('#' + ids[0]);
      let svgElLast = svg.querySelector('#' + ids[ids.length - 1]);
      // overwrite original svg path
      svgElFirst.setAttribute("d", unitedData);
      // delete united svg path
      svgElLast.remove();
    }
  });
  // get data URL
  getdataURL(svg)

}

function getdataURL(svg) {
  let markup = svg.outerHTML;
  markupOpt = 'data:image/svg+xml;utf8,' + markup.replaceAll('"', '\'').
  replaceAll('\t', '').
  replaceAll('\n', '').
  replaceAll('\r', '').
  replaceAll('></path>', '/>').
  replaceAll('<', '%3C').
  replaceAll('>', '%3E').
  replaceAll('#', '%23').
  replaceAll(',', ' ').
  replaceAll(' -', '-').
  replace(/ +(?= )/g, '');

  let btn = document.createElement('a');
  btn.href = markupOpt;
  btn.innerText = 'Download Svg';
  btn.setAttribute('download', 'united.svg');
  document.body.insertAdjacentElement('afterbegin', btn);
  return markupOpt;
}

svg{
  display:inline-block;
  width:10em
}

<script src="https://cdnjs.cloudflare.com/ajax/libs/paper.js/0.12.0/paper-full.min.js"></script>
<script src="https://cdn.jsdelivr.net/npm/path-data-polyfill@1.0.3/path-data-polyfill.min.js"></script>


<p>
  <button type="button" onclick="unite(svg)">Subtract Path </button>
</p>
<svg class="svgunite" id="svgunite" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" stroke-width="1" stroke="#000">
<path fill="none" d="M50.05 23.21l-19.83 61.51h-9.27l23.6-69.44h10.82l23.7 69.44h-9.58l-20.44-61.51h1z"/>
<rect fill="none" x="35.49" y="52.75" width="28.5" height="6.17">
</rect>
</svg>

Optional: Path normalization (using getPathData() polyfill)

You might also need to convert svg primitives (<rect>, <circle>, <polygon>) like the horizontal stroke in the capital A .

The pathData polyfill provides a method of normalizing svg elements.
This normalization will output a d attribute (for every selected svg child element) containing only a reduced set of cubic path commands (M, C, L, Z) – all based on absolute coordinates.

Little downer:
I won't say paper.js can boast of a plethora of tutorials or detailed examples. But you might check the reference for pathItem to see all options.

See also: Subtracting SVG paths programmatically