Rect Objects	Coordinate Systems	Curve Objects

Transformation Objects

A transformation object, a trafo object or trafo for short, represents an affine 2D transformation. Such a transformation is given by 6 numbers: m11, m21, m21, m22, v1 and v2. These coefficients are given in the same order as for a PostScript transformation matrix.

To apply a trafo to an object you can simple call the trafo with that object as argument. For details, see the section ``Operators'' below.

Trafo objects are immutable.

If such a transformation T is applied to the point (x, y) you get

            / x \   / m11 m12 \ / x \   / v1 \
        T * |   | = |         | |   | + |    |
            \ y /   \ m21 m22 / \ y /   \ v2 /

            / x \   / m11 m12 v1 \ / x \
            |   |   |            | |   |
        T * | y | = | m21 m22 v2 | | y |
            |   |   |            | |   |
            \ 1 /   \ 0   0   1  / \ 1 /

Constructors

The following functions create trafo objects:

Trafo(m11, m21, m21, m22, v1, v2)

The generic constructor: return the transformation given by the coordinates m11, m21, m21, m22, v1 and v2. These coefficients are given in the same order as for a PostScript transformation matrix.

Scale(factorx[, factory])

Return a trafo object for a scaling by the factors factorx (in x-direction) and factory (in y-direction). If omitted, factory defaults to the value of factorx.

Equivalent to Trafo(factorx, 0, 0, factory, 0, 0).

Translation(offset)

Translation(offset_x, offset_y)

Return a trafo object for a translation by offset (a PointSpec) or (offset_x, offset_y). Equivalent to Trafo(1, 0, 0, 1, offset_x, offset_y).

Rotation(angle[, center])

Rotation(angle[, center_x, center_y])

Return a trafo object for a rotation through the angle angle (counter clockwise in radians) about the center point center or (center_x, center_y). center must be a PointSpec. If center is omitted it defaults to the origin.

Equivalent to

	s = sin(angle);
	c = cos(angle);
	offx = cx - c * center_x + s * center_y;
	offy = cy - s * center_x - c * center_y;
	Trafo(c, s, -s, c, offx, offy);
	

Attributes

A trafo object has six (read only) attributes:

m11, m21, m12, m22

v1, v2

The coefficients of the trafo as python floats