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# Module `deformer`: Path deformers

The `deformer` module provides techniques to generate modulated paths. All classes in the `deformer` module can be used as attributes when drawing/stroking paths onto a canvas. Alternatively new paths can be created by deforming an existing path by means of the `deform()` method.

All classes of the `deformer` module provide the following methods:

class `deformer.``deformer`

`deformer.``__call__`((specific parameters for the class))

  Returns a deformer with modified parameters

`deformer.``deform`(path)

  Returns the deformed normpath on the basis of the path. This method allows using the deformers outside of a drawing call.

The deformer classes are the following:

class `deformer.``cycloid`(radius, halfloops=10, skipfirst=1*unit.t_cm, skiplast=1*unit.t_cm, curvesperhloop=3, sign=1, turnangle=45)

  This deformer creates a cycloid around a path. The outcome looks similar to a 3D spring stretched along the original path.

  radius: the radius of the cycloid (this is the radius of the 3D spring)

  halfloops: the number of half-loops of the cycloid

  skipfirst and skiplast: the lengths on the original path not to be bent to a cycloid

  curvesperhloop: the number of Bezier curves to approximate a half-loop

  sign: for `sign>=0` the cycloid starts to the left of the path, whereas for `sign<0` it starts to the right.

  turnangle: the angle of perspective on the 3D spring. At `turnangle=0` results in a sinusoidal curve, whereas for `turnangle=90` one essentially obtains a circle.

class `deformer.``smoothed`(radius, softness=1, obeycurv=0, relskipthres=0.01)

  This deformer creates a smoothed variant of the original path. The smoothing is done on the basis of the corners of the original path, not on a global scope! Therefore, the result might not be what one would draw by hand. At each corner (or wherever two path elements meet) a piece of twice the radius is taken out of the original path and replaced by a curve. This curve is determined by the tangent directions and the curvatures at its endpoints. Both are taken from the original path, and therefore, the new curve fits into the gap in a geometrically smooth way. Path elements that are shorter than radius \(\times\) relskipthres are ignored.

  The new curve smoothing the corner consists either of one or of two Bezier curves, depending on the surrounding path elements. If there are straight lines before and after the new curve, then two Bezier curves are used. This optimises the bending of curves in rectangular boxes or polygons. Here, the curves have an additional degree of freedom that can be set with softness \(\in(0,1]\). If one of the concerned path elements is curved, only one Bezier curve is used that is (not always uniquely) determined by its geometrical constraints. There are, nevertheless, some caveats:

  A curve that strictly obeys the sign and magnitude of the curvature might not look very smooth in some cases. Especially when connecting a curved with a straight piece, the smoothed path contains unwanted overshootings. To prevent this, the parameter default obeycurv=0 releases the curvature constraints a little: The curvature may then change its sign (still looks smooth for human eyes) or, in more extreme cases, even its magnitude (does not look so smooth). If you really need a geometrically smooth path on the basis of Bezier curves, then set obeycurv=1.

class `deformer.``parallel`(distance, relerr=0.05, sharpoutercorners=0, dointersection=1, checkdistanceparams=[0.5], lookforcurvatures=11)

  This deformer creates a parallel curve to a given path. The result is similar to what is usually referred to as the set with constant distance to the set of points on the path. It differs in one important respect, because the distance parameter in the deformer is a signed distance. The resulting parallel normpath is constructed on the level of the original pathitems. For each of them a parallel pathitem is constructed. Then, they are connected by circular arcs (or by sharp edges) around the corners of the original path. Later, everything that is nearer to the original path than distance is cut away.

  There are some caveats:

  - When the original path is too curved then the parallel path would contain points with infinte curvature. The resulting path stops at such points and leaves the too strongly curved piece out.
  - When the original path contains on or more self-intersections, then the resulting parallel path is not continuous in the parameterisation of the original path. This may result in the surprising behaviour that a piece that corresponding to a “later” parameter value is followed by an “earlier” one.

  The parameters are the following:

  distance is the minimal (signed) distance between the original and the parallel paths.

  relerr is the allowed relative error in the distance.

  sharpoutercorners connects the parallel pathitems by a wegde made of straight lines, instead of taking circular arcs. This preserves the angle of the original corners.

  dointersection is a boolean for performing the last step, the intersection step, in the path construction. Setting this to 0 gives the full parallel path, which can be favourable for self-intersecting paths.

  checkdistanceparams is a list of parameter values in the interval (0,1) where the distance is checked on each parallel pathitem.

  lookforcurvatures is the number of points per normpathitem where its curvature is checked for critical values.

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