JavaScript Canvas Custom Coordinates
Written by Ian Elliot   
Monday, 19 July 2021
Article Index
JavaScript Canvas Custom Coordinates
Plotting A Graph

Canvas provides a full transformation facility that allows you to use any co-ordinate system you want to.  In this extract from  Ian Elliot's book on JavaScript Graphics we look at how to use custom coordinates.

Now available as a paperback or ebook from Amazon.

JavaScript Bitmap Graphics
With Canvas




  1. JavaScript Graphics
  2. Getting Started With Canvas
  3. Drawing Paths
      Extract: Basic Paths
      Extract: SVG Paths
      Extract: Bezier Curves
  4. Stroke and Fill
      Extract: Stroke Properties 
      Extract: Fill and Holes
      Extract: Gradient & Pattern Fills
  5. Transformations
      Extract: Transformations
      Extract: Custom Coordinates 
      Extract  Graphics State
  6. Text
      Extract: Text, Typography & SVG 
      Extract: Unicode
  7. Clipping, Compositing and Effects
      Extract: Clipping & Basic Compositing
  8. Generating Bitmaps
      Extract:  Introduction To Bitmaps
      Extract :  Animation 
  9. WebWorkers & OffscreenCanvas
      Extract: Web Workers
      Extract: OffscreenCanvas
  10. Bit Manipulation In JavaScript
      Extract: Bit Manipulation
  11. Typed Arrays
      Extract: Typed Arrays 
  12. Files, blobs, URLs & Fetch
      Extract: Blobs & Files
      Extract: Read/Writing Local Files
      Extract: Fetch API **NEW!
  13. Image Processing
      Extract: ImageData
      Extract:The Filter API
  14. 3D WebGL
      Extract: WebGL 3D
  15. 2D WebGL
    Extract: WebGL Convolutions




So far we have been working with the default co-ordinate system that, apart from antialiasing concerns, is a pixel co-ordinate system. Canvas provides a full transformation facility that allows you to use any co-ordinate system you want to. Alternatively you can view it as a way of drawing paths at the location and scale that you require.

In Chapter But Not In This Extract

  • Transformations
  • Transformation Functions
  • A Logical Approach to Transforms

Setting Your Own Co-ordinates

When you first use a canvas the co-ordinate system is in terms of the number of pixels in the Bitmap. Often, however, you want to work with a different co‑ordinate system. For example, you might want to work with the origin in the middle and the x and y co-ordinate ranging from -1 to +1.

You can set any co-ordinate system you care to work with using suitable transformations. If your co-ordinate system runs from xmin to xmax and from ymin to ymax you can apply it to the canvas using:


where width and height are the size in pixels of the canvas. 

Using this formulation the y co-ordinate increases down the screen, as did the original pixel co-ordinates. If you want the y co-ordinate to increase up the screen then use the transformation:


and notice the change to ymax in the second line.

So, for example, if you wanted to draw a graph using co-ordinates between 0,0 in the bottom left corner and 10,10 in the top right, i.e. y increasing up the screen, you would use:

var ctx = document.body.appendChild(
              createCanvas(500, 500)).getContext("2d");
var xmax = 10;
var xmin = 0;
var ymax = 10;
var ymin = 0;
var width = 500;
var height = 500;
ctx.scale(width / (xmax - xmin), 
-height / (ymax - ymin)); ctx.translate(-xmin, -ymax); ctx.moveTo(0, 0); ctx.lineTo(0, 10); ctx.moveTo(0, 0); ctx.lineTo(10, 0); ctx.moveTo(0, 0); ctx.lineTo(10, 10); ctx.lineWidth = 0.1; ctx.stroke();

This draws axes and a 45 degree line:


Notice the need to set the lineWidth to take account of the scaling. Also notice that the vertical axis is centered on x=0 and hence half of its thickness is “off” the Canvas. To see this more clearly remove the lineWidth setting.

Last Updated ( Monday, 19 July 2021 )