Plotting A Graph

Now let's try a change in the co-ordinate system to make plotting a graph easy.

In principle you could plot a sin function using:

ctx.beginPath();
ctx.moveTo(0,0);

for(var i=0;i<4*Math.PI;i+=0.1){
 ctx.lineTo(i,Math.sin(i));
}
ctx.stroke();

However, if you try it you will just see a small splodge at the top of the canvas. The reason is, of course that the x value varies from 0 to about 12 and the y value varies between +1 and -1, which in pixel co-ordinates gives you the small splodge!

You can use constants to scale and shift the graph to make it fit in with the current co-ordinate system if you want to.

For example:

ctx.beginPath();
ctx.moveTo(0,50);
for(var i=0;i<4*Math.PI;i+=0.1){
 ctx.lineTo(i*10,10*Math.sin(i)+50);
}
ctx.stroke();

This produces a reasonable sine wave, but a much cleaner method of plotting graphs is to make use of the transformation to provide the co-ordinates that we would really like to use.

We would like a co-ordinate system that varies between 0 and 12 in the x direction and +1 and -1 in the y direction. If we assume that the canvas is 400x400 then the change in the co-ordinate system can be created using:

ctx.scale(400/12,400/2)
ctx.translate(0,1);
ctx.beginPath();
ctx.moveTo(0,0);
for(var i=0;i<4*Math.PI;i+=0.1){
 ctx.lineTo(i,Math.sin(i));
}
ctx.lineWidth=2/400;  
ctx.stroke();

First we scale so that the x axis runs from 0 to 12 and the y axis from 0 to 2. Then we translate so the y axis runs from -1 to 1.

The only complication is that that the transformation affects every measured aspect of the drawing, including line width. So we have to reduce the line width back to roughly one pixel expressed in the new co-ordinate system.

[画像:sine]

In Chapter But Not In This Extract

• Stack of States
• Active Transformations and State

Summary

• Transformations include rotation, scaling and translation.

• You can write all three as a simple matrix if you use homogeneous co-ordinates (x,y,1)

• You can set the transform matrix directly or use one of the utility methods to set scaling, rotation and translation.

• The order in which you apply transformations makes a difference.

• You can think of transformations as actively moving something or just changing the co-ordinates. Canvas transforms change the co-ordinate system.

• If you want to think "actively" then think of the transformations you want to perform on a shape and then apply them in the reverse order before drawing the shape.

• One approach to organizing graphics is to draw everything centered on the origin and at unit scale and then use transformations to size, rotation and position where you really want to draw the shape.

• You can change the co-ordinate system in use to anything that suits the current drawing task.

• You can save the drawing state before changing the co-ordinate system so that it can be restored.

• The drawing state includes the current transformation matrix, clipping region and all drawing attributes.

Now available as a paperback or ebook from Amazon.

JavaScript Bitmap Graphics
With Canvas

[画像:largecover360]

Contents

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

<ASIN:B07XJQDS4Z>

<ASIN:1871962579>

<ASIN:1871962560>

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