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Applying transformations on a path or canvas: Drawing an ellipse
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PyX does not directly provide a path corresponding to an ellipse. This example
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shows two ways how to draw an ellipse using affine transformations. ...
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In order to create an ellipse, we best start from a unit circle centered around
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the point of origin of the coordinate system (here: `circ`). In variant 1, we
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tell PyX to apply a couple of affine transformations before stroking this
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circle on the canvas `c`. These affine transformations are contained in the
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`trafo` module. We first use `trafo.scale` to apply a non-uniform scaling,
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namely by a factor of 2 in x-direction and a factor of 0.9 in y-direction.
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Doing so, we define the two principle axes of the ellipse. In a next step, we
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rotate with `trafo.rotate` the ellipse by an angle of 45 degrees in the
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mathematical positive direction, i.e. counter-clockwise. Last, we shift the
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origin of the ellipse to the desired point by applying a `trafo.translate`
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! Note that the order of the transformations matters. If you, for instance, would
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first translate the ellipse, the later scaling would also affect the distance
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by which you have shifted the ellipse. PyX applies the transformations one after
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the other, from left to right, so the example shown above does the correct thing.
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! You can also treat transformations as mathematical objects (they are
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represented by two-dimensional matrices together with an offset vector) and
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multiply them using the `*` operator. Note, however, that mathematically,
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transformations are applied from right to left, such that variant 1
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would need to be written as
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c.stroke(circ, [trafo.translate(1,0) * trafo.rotate(45) * trafo.scale(sx=2, sy=1.5)])
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! PyX also provides some convenience methods for applying certain
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transformations with a given point as the origin. These allow one to write variant 1
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c.stroke(circ, [trafo.scale(sx=2, sy=1.5, x=1, y=0), trafo.rotate(45, x=1, y=0)])
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where we have started already from a circle centered around the desired point 1,0.
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When telling the stroke method to apply a number of transformations, we use
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that a transformation is a so-called deformer. Deformers take an original path,
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do some operation on it and return the modified version. PyX thus internally
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converts the circle into a path representing the ellipse. Alternatively, we can
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also let the PostScript or PDF interpreter do the same transformation. This is what
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is shown in variant 2. There, we first stroke the circle on a new canvas `sc`.
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When inserting this canvas in the original canvas `c`, we again pass a set of
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transformations as arguments. Since PyX cannot deform an entire canvas, it just
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writes these transformations into the output file. If you compare the resulting
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output (the right ellipse) with the one of variant 1, you will notice a
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difference, though: when transforming a whole canvas, the lineshape is
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transformed as well. Often, this is not the intended result, so you better
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transform individual objects when stroking or filling them.
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!! When you look at the EPS or PDF output generated by the example, you will
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notice that the bounding box is too large. The reason for this artefact lies in
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the way PyX calculates the bounding box for a transformed canvas: It simply
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applies the transformation to the bounding box of the canvas and takes the
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bounding box of this new object. While this certainly yields a bounding box of
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the canvas, it does not necessarily yield a minimal one. To see this, you just
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have to consider the two extreme cases of a circle, which is rotationally
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invariant, and a square, which only posseses a discrete rotational symmetry.
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Whereas the minimal bounding box of the circle does not change under rotations
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around its center, the same is not true for the square. When you rotate a
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circle by applying a deformer (as in variant 1), PyX will thus calculate the
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correct bounding box. On the other hand, when you insert the circle into a
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canvas and afterwards transform this canvas (as in variant 2), PyX cannot
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distinguish between a circle and a square anymore and calculates a too large
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examples/drawing2/ellipse.txt
