nicematt - 8 months ago 30

Javascript Question

Firstly, I need to rotate a single line about its own axe to be rendered in HTML5 canvas.

I'm not actually rotating a line, but I'm rotating its points coordinates before I render it.

I've specific bounds which refers to the total size of what will be drawn in a path (e.g, the line), they're used to construct a point B, which is the center point of the path.

`form.bx = x + (w / 2);`

form.by = y + (h / 2);

Note:

`form`

Both of these functions rotates coordinates of a point and return them. Parameters:

- x – the x coor. of the A point.
- y – the y coor. of the A point.
- c – the angle cosine ().
`Math.cos(angle)`

- s – the angle sine ().
`Math.sin(angle)`

- Bx – the x coor. of the point on which point A will be rotated about.
- By – the y coor. of the point on which point A will be rotated about.

`function rotatePointX(x, y, c, s, Bx, By) {`

return Math.round(((Bx - x) * c) - ((By - y) * s));

}

function rotatePointY(x, y, c, s, Bx, By) {

return Math.round(((Bx - x) * s) + ((By - y) * c));

}

The problem: the rotation makes my line move to the left-top of the canvas.

Fiddle

My line should be in its specific position. What am I doing wrong? Thanks

Answer

Rotation always occurs relative to the origin, if you want to rotate relative to some other point you have to

- move all your space so that the new origin is the point the rotation will occur about
- perform the rotation
- move all your space back to its original position

1)

```
x' = x - Bx
y' = y - By
```

2)

```
x'' = x' * cos(angle) - y' * sin(angle)
y'' = x' * sin(angle) + y' * cos(angle)
```

3)

```
x''' = x'' + Bx
y''' = y'' + By
```

To find the value of `x''', y'''`

you have to replace 1 and 2 in 3

1 in 2:

```
x'' = (x - Bx) * cos(angle) - (y - By) * sin(angle)
y'' = (x - Bx) * sin(angle) + (y - By) * cos(angle)
```

2 in 3:

```
x''' = (x - Bx) * cos(angle) - (y - By) * sin(angle) + Bx
y''' = (x - Bx) * sin(angle) + (y - By) * cos(angle) + By
```

You can avoid all this mess by performing the transform doing matrix multiplication like so

```
[x'''] = [1 0 Bx] [cos(angle) -sin(angle) 0] [1 0 -Bx] [x]
[y'''] [0 1 By] [sin(angle) cos(angle) 0] [0 1 -By] [y]
[1 ] [0 0 1] [ 0 0 1] [0 0 1] [1]
```

The additional dimension is used to be able to perform translation since translation is a shearing mapping