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# Module `metapost.path`

The `metapost` subpackage provides some of the path functionality of the MetaPost program. The `metapost.path` presents the path construction facility of MetaPost.

Similarly to the `normpath`, there is a short length epsilon (always in Postscript points pt) used as accuracy of numerical operations, such as calculating angles from short path elements, or for omitting such short path elements, etc. The default value is \(10^{-5}\) and can be changed using the module function `metapost.set()`.

## Class `path` — MetaPost-like paths

class `metapost.path.``path`(pathitems, epsilon=None)

  This class represents a MetaPost-like path which is created from the given list of knots and curves/lines. It can find an optimal way through given points.

  At points (knots), you can either specify a given tangent direction (angle in degrees) or a certain curlyness (relative to the curvature at the other end of a curve), or nothing. In the latter case, both the tangent and the mock curvature (an approximation to the real curvature, introduced by J. D. Hobby in MetaPost) will be continuous.

  The shape of the cubic Bezier curves between two points is controlled by its tension, unless you choose to set the control points manually.

  All possible path items are described below. They are either Knots or Links. Note that there is no explicit closepath class. Whether the path is open or closed depends on the type of knots used, begin endpoints or not. Note also that the number of knots and links must be equal for closed paths, and that you cannot create a path comprising closed subpaths.

  The epsilon argument governs the accuracy of the calculations implied in creating the path (see above). The value None means fallback to the default epsilon of the module.

Instances of the class `path` inherit all properties of the Postscript paths in `path`.

## Knots

class `metapost.path.``beginknot`(x, y, curl=1, angle=None)

  The first knot, starting an open path at the coordinates (x, y). The properties of the curve in that point can either be given by its curlyness (default) or the angle of its tangent vector (in degrees). The curl parameter is (as in MetaPost) the ratio of the curvatures at this point and at the other point of the curve connecting it.

class `metapost.path.``startknot`(x, y, curl=1, angle=None)

  Synonym for `beginknot`.

class `metapost.path.``endknot`(x, y, curl=1, angle=None)

  The last knot of an open path. Curlyness and angle are the same as in `beginknot`.

class `metapost.path.``smoothknot`(x, y)

  This knot is the standard knot of MetaPost. It guarantees continuous tangent vectors and mock curvatures of the two curves it connects.

  Note: If one of the links is a line, the knot is changed to a `roughknot` with either a specified angle (if the keepangles parameter is set in the line) or with curl=1.

class `metapost.path.``roughknot`(x, y, left_curl=1, right_curl=None, left_angle=None, right_angle=None)

  This knot is a possibly non-smooth knot, connecting two curves or lines. At each side of the knot (left/right) you can specify either the curlyness or the tangent angle.

  Note: If one of the links is a line with the keepangles parameter set, the angles will be set eplicitly, regardless of any curlyness set.

class `metapost.path.``knot`(x, y)

  Synonym for `smoothknot`.

## Links

class `metapost.path.``line`(keepangles=False)

  A straight line which corresponds to the MetaPost command “–”. The option keepangles will guarantee a continuous tangent. (The curvature may become discontinuous, however.) This behavior is achieved by turning adjacent knots into roughknots with specified angles. Note that a smoothknot and a roughknot with given curlyness do behave differently near a line.

class `metapost.path.``tensioncurve`(ltension=1, latleast=False, rtension=None, ratleast=None)

  The standard type of curve in MetaPost. It corresponds to the MetaPost command ”..” or to ”...” if the atleast parameters are set to True. The tension parameters indicate the tensions at the beginning (l) and the end (r) of the curve. Set the parameters (l/r)atleast to True if you want to avoid inflection points.

class `metapost.path.``controlcurve`(lcontrol, rcontrol)

  A cubic Bezier curve which has its control points explicity set, similar to the `path.curveto` class of the Postscript paths. The control points at the beginning (l) and the end (r) must be coordinate pairs (x, y).

class `metapost.path.``curve`(ltension=1, latleast=False, rtension=None, ratleast=None)

  Synonym for `tensioncurve`.

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