# [whatwg] Canvas transform() and matrix element notation

Boris Zbarsky bzbarsky at MIT.EDU
Mon Jul 19 13:54:23 PDT 2010

```On 7/19/10 4:13 PM, David Flanagan wrote:
> The spec describes the transform() method as follows:
>
>> The transform(m11, m12, m21, m22, dx, dy) method must multiply the
>> current transformation matrix with the matrix described by:
>>
>> m11 m21 dx
>> m12 m22 dy
>> 0 0 1
>
> The first number in these argument names is the column number and the
> second is the row number.

I agree that this is somewhat weird at first glance, but it seems to be
not uncommon for graphics libraries.  For example, for cairo the call

cairo_matrix_init(m, a, b, c, d, e, f);

creates a matrix which represents the affine transformation :

x_new = a*x + c*y + e;
y_new = b*x + d*y + f;

As another example, in CoreGraphics CGAffineTransformMake(a, b, c, d, e,
f)  produces a trasformation that does :

x_new = a*x + c*y + e;
y_new = b*x + d*y + f;

I think the issue here is that these graphics libraries think in terms
of row vectors and right-multiplication by transformation matrices; see
the nice matrices written out in the CoreGraphics documentation.  In
that context the component specification order is in fact the "sensible"
one.

In practice, I assume the initial canvas implementation just called into
CoreGraphics directly, hence the treatment of the argument order.  And
now that's the argument order we have.

> 2) Java's java.awt.geom.AffineTransform class also lists the row index
> first, as in the following javadoc excerpt:
>
>> [ x']   [ m00 m01 m02 ] [ x ] [ m00x + m01y + m02 ]
>> [ y'] = [ m10 m11 m12 ] [ y ] = [ m10x + m11y + m12 ]
>> [ 1 ]   [ 0    0   1 ] [ 1 ] [ 1 ]

While true, if you look at the way one constructs an AffineTransform by
passing in the matrix entries :

AffineTransform(double m00, double m10, double m01, double m11,
double m02, double m12)

which is worse than the CoreGraphics setup, even: the convention is the
same but the example is misleading, unlike the CoreGraphics example with
a row vector.

> It would be nice if this spec was not inconsistent with other usage.

It seems that it's not, if "other usage" means "other things in the
computer world that use affine transformation matrices"...

I do think the spec could benefit from an example akin to the one in the
CoreGraphics documentation.

By the way, 100% agreed that the multiplication order needs to be
defined here.

-Boris

 http://www.cairographics.org/manual/cairo-matrix.html#cairo-matrix-init


http://developer.apple.com/mac/library/documentation/GraphicsImaging/Reference/CGAffineTransform/Reference/reference.html#//apple_ref/c/func/CGAffineTransformMake


http://developer.apple.com/mac/library/documentation/GraphicsImaging/Reference/CGAffineTransform/Reference/reference.html#//apple_ref/doc/c_ref/CGAffineTransform

```