# + tags=["hide_inp"]
import math
from chalk import *
from planar import Vec2Array
def help(f):
    import pydoc
    from IPython.display import HTML
    return HTML(pydoc.HTMLDoc().docroutine(f))
# -

# Chalk also includes a ``Trail`` primitive which allows for creating new ``Diagram``s and more complex shapes.
# ``Trail``s are specified by position-invariant offsets and can be rendered as ``Path``s.
# See the [Koch](../examples/koch/) example for a use case. 

# ### Constructors

# ``Trail``s are a sequence of vectors and can be constructed using the ``from_offsets`` method:

trail = Trail.from_offsets([V2(1, 0), V2(1, 1), V2(0, 1)])

# ### Converting to ``Diagram``

# In order to render, `Trail`s have to be turned into ``Diagram``s, which can be achieved using the `stroke` method.

# + tags=["hide_inp"]
help(Trail.stroke)
# -

trail.stroke()

# ### Transformations

# `Trail`s can be transformed using the usual geometric transformations, which are also applied to the ``Diagram`` object.
# For example, ``Trail``s can be rotated:

# + tags=["hide_inp"]
help(Trail.rotate_by)
# -

trail2 = trail.rotate_by(0.2)
trail2.stroke()

# However, since `Trail`s are translation invariant, applying the `translate` method leaves the `Trail` instance unchanged.

# ### Composition

# ``Trail``s form a monoid with addition given by list concatenation and identity given by the empty list.
# Intuitively, adding two ``Trails`` appends the two sequences of offsets.

# + tags=["hide_inp"]
help(Trail.__add__)
# -

(trail + trail2).stroke()