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How to Translate from DOM to SVG Coordinates and Back Again

By Craig Buckler

HTML & CSS

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Using SVGs is relatively straight forward — until you want to mix DOM and vector interactions.

SVGs have their own coordinate system defined in a viewBox attribute. For example:

<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 800 600">

This sets a width of 800 units and a height of 600 units starting at 0,0. These units are arbitrary measurements for drawing purposes, and it’s possible to use fractions of a unit. If you position this SVG in an 800 by 600 pixel area, each SVG unit should map directly to a screen pixel.

However, vector images can be scaled to any size — especially in a responsive design. Your SVG could be scaled down to 400 by 300 or even stretched beyond recognition in a 10 by 1000 space. Adding further elements to this SVG becomes more difficult if you want to place them according to the cursor location.

Note: see Sara Soueidan’s viewport, viewBox and preserveAspectRatio article for more information about SVG coordinates.

Avoid Coordinate Translation

You may be able to avoid translating between coordinate systems entirely.

SVGs embedded in the HTML page (rather than an image or CSS background) become part of the DOM and can be manipulated in a similar way to other elements. For example, take a basic SVG with a single circle:

<svg id="mysvg" xmlns="https://www.w3.org/2000/svg" viewBox="0 0 800 600" preserveAspectRatio="xMidYMid meet">
  <circle id="mycircle" cx="400" cy="300" r="50" />
<svg>

You can apply CSS effects to this:

circle {
  stroke-width: 5;
  stroke: #f00;
  fill: #ff0;
}

circle:hover {
  stroke: #090;
  fill: #fff;
}

You can also attach event handlers to modify attributes:

const mycircle = document.getElementById('mycircle');

mycircle.addEventListener('click', (e) => {
  console.log('circle clicked - enlarging');
  mycircle.setAttribute('r', 60);
});

The following example adds thirty random circles to an SVG image, applies a hover effect in CSS, and uses JavaScript to increase the radius by ten units when a circle is clicked.

See the Pen
SVG interaction
by SitePoint (@SitePoint)
on CodePen.

SVG to DOM Coordinate Translation

It may become necessary to overlay a DOM element on top of an SVG element — for example, a menu or information box on the active country shown on a world map. Presuming the SVG is embedded into the HTML, elements become part of the DOM, so the getBoundingClientRect() method can be used to extract the position and dimensions. (Open the console in the example above to reveal the clicked circle’s new attributes following a radius increase.)

Element.getBoundingClientRect() is supported in all browsers and returns an DOMrect object with the following properties in pixel dimensions:

  • .x and .left: x-coordinate, relative to the viewport origin, of the left side of the element
  • .right: x-coordinate, relative to the viewport origin, of the right side of the element
  • .y and .top: y-coordinate, relative to the viewport origin, of the top side of the element
  • .bottom: y-coordinate, relative to the viewport origin, of the bottom side of the element
  • .width: width of the element (not supported in IE8 and below but is identical to .right minus .left)
  • .height: height of the element (not supported in IE8 and below but is identical to .bottom minus .top)

All coordinates are relative to the browser viewport and will therefore change as the page is scrolled. The absolute location on the page can be calculated by adding window.scrollX to .left and window.scrollY to .top.

DOM to SVG Coordinate Translation

This is more challenging. Presume you want to position a new SVG element on its viewBox at the position where a click event occurs. The event handler object provides the DOM .clientX and .clientY pixel coordinates, but these must be translated to SVG units.

It’s tempting to think you can calculate the coordinates of an SVG point by applying multiplication factors. For example, if a 1000-unit–width SVG is placed in a 500px width container, you can multiply any the DOM x coordinate by two to get the SVG location. It won’t work! …

  • There is no guarantee the SVG fits exactly into your container.
  • If the element dimensions change — perhaps in response to the user resizing the browser — the width and height factors must be re-calculated.
  • The SVG or one or more elements could be transformed in 2D or 3D space.
  • Even if you overcome these hurdles, it never quite works as you expect, and there’s often a margin of error.

Fortunately, SVGs provide their own matrix factoring mechanisms to translate coordinates. The first step is to create a point on the SVG using the createSVGPoint() method and pass in the screen/event x and y coordinates:

const
  svg = document.getElementById('mysvg'),
  pt = svg.createSVGPoint();

pt.x = 100;
pt.y = 200;

You can then apply a matrix transformation created from an inverse of the SVG’s .getScreenCTM() method, which maps SVG units to screen coordinates:

const svgP = pt.matrixTransform( svg.getScreenCTM().inverse() );

svgP now has .x and .y properties, which provide the coordinate on the SVG viewBox.

The following code places a circle at a point clicked on an SVG canvas:

// get SVG element and namespace
const
  svg = document.getElementById('mysvg'),
  NS = svg.getAttribute('xmlns');

// click event
svg.addEventListener('click', (e) => {

  const pt = svg.createSVGPoint();

  // pass event coordinates
  pt.x = e.clientX;
  pt.y = e.clientY;

  // transform to SVG coordinates
  const svgP = pt.matrixTransform( svg.getScreenCTM().inverse() );

  // add new SVG element
  const circle = document.createElementNS(NS, 'circle');
  circle.setAttribute('cx', svgP.x);
  circle.setAttribute('cy', svgP.y);
  circle.setAttribute('r', 10);

  svg.appendChild(circle);

});

Note: the createElementNS() methods is identical to the standard DOM createElement() method, except that it specifies an XML namespace URI. In other words, it acts on an SVG document rather than the HTML.

Translating to Transformed SVG Coordinates

There’s a further complication. The SVG or individual elements can be transformed by translating, scaling, rotating, and/or skewing, which affects the resulting SVG coordinate. For example, the following <g> layer is 4x larger than the standard SVG units, so coordinates will be one quarter those of the containing SVG:

<g id="transformed" transform="scale(4)">
  <rect x="50" y="50" width="100" height="100" />
</g>

The resulting rectangle appears to have a 400 unit width and height at position 200, 200.

Fortunately, the .getScreenCTM() method can be applied to any element as well as the SVG itself. The resulting matrix considers all transformations so you can create a simple svgPoint() translation function:

const
  svg = document.getElementById('mysvg'),
  transformed = svg.getElementById('transformed');

console.log( svgPoint(svg, 10, 10) ); // returns x, y
console.log( svgPoint(transformed, 10, 10) ); // = x/4, y/4

// translate page to SVG coordinate
function svgPoint(element, x, y) {

  const pt = svg.createSVGPoint();
  pt.x = x;
  pt.y = y;

  return pt.matrixTransform( element.getScreenCTM().inverse() );

}

The following demonstration works in all modern browsers, (and would work in IE11 if you convert the JavaScript to ES5!). A circle is added at the cursor point when the SVG is tapped/clicked.

This also occurs when a transformed <g> area is clicked, but that element rather than the SVG itself is passed to the svgPoint() function to ensure the correct coordinate is calculated:

See the Pen
DOM to SVG co-ordinate translation
by Craig Buckler (@craigbuckler)
on CodePen.

Ideally, it’s best to avoid DOM to/from SVG coordinate translation but, when that’s not possible, use the methods described above to ensure the process is robust at all page dimensions.

Craig is a freelance UK web consultant who built his first page for IE2.0 in 1995. Since that time he's been advocating standards, accessibility, and best-practice HTML5 techniques. He's created enterprise specifications, websites and online applications for companies and organisations including the UK Parliament, the European Parliament, the Department of Energy & Climate Change, Microsoft, and more. He's written more than 1,000 articles for SitePoint and you can find him @craigbuckler.

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