# Path: trimesh/constants.py
# class NumericalToleranceMesh(object):
# class NumericalResolutionMesh(object):
# class NumericalTolerancePath(object):
# class NumericalResolutionPath(object):
# class MeshError(Exception):
# class TransformError(Exception):
#     def __init__(self, **kwargs):
#     def __init__(self, **kwargs):
#     def __init__(self, **kwargs):
#     def __init__(self, **kwargs):
# def _log_time(method):
#     def timed(*args, **kwargs):
# 
# Path: trimesh/constants.py
# class NumericalToleranceMesh(object):
# class NumericalResolutionMesh(object):
# class NumericalTolerancePath(object):
# class NumericalResolutionPath(object):
# class MeshError(Exception):
# class TransformError(Exception):
#     def __init__(self, **kwargs):
#     def __init__(self, **kwargs):
#     def __init__(self, **kwargs):
#     def __init__(self, **kwargs):
# def _log_time(method):
#     def timed(*args, **kwargs):


import numpy as np
from ..constants import res_path as res
from ..constants import tol_path as tol
    from scipy.interpolate import splev
        from scipy.special import binom
    '''
    Arguments
    ----------
    points:  (o,d) list of points of the bezier. The first and last
             points should be the start and end of the curve.
             For a 2D cubic bezier, order o=3, dimension d=2

    Returns
    ----------
    discrete: (n,d) list of points, a polyline representation
              of the bezier curve which respects constants.RES_LENGTH
    '''
    def compute(t):
        # compute discrete points given a sampling t
        t_d = 1.0 - t
        n = len(points) - 1
        # binomial coefficents, i, and each point
        iterable = zip(binomial(n), np.arange(n + 1), points)
        stacked = [((t**i) * (t_d**(n - i))).reshape((-1, 1))
                   * p * c for c, i, p in iterable]
        discrete = np.sum(stacked, axis=0)
        return discrete

    # make sure we have a numpy array
    points = np.array(points)

    if count is None:
        # how much distance does a small percentage of the curve take
        # this is so we can figure out how finely we have to sample t
        norm = np.linalg.norm(np.diff(points, axis=0), axis=1).sum()

# Path: trimesh/constants.py
# class NumericalToleranceMesh(object):
# class NumericalResolutionMesh(object):
# class NumericalTolerancePath(object):
# class NumericalResolutionPath(object):
# class MeshError(Exception):
# class TransformError(Exception):
#     def __init__(self, **kwargs):
#     def __init__(self, **kwargs):
#     def __init__(self, **kwargs):
#     def __init__(self, **kwargs):
# def _log_time(method):
#     def timed(*args, **kwargs):
# 
# Path: trimesh/constants.py
# class NumericalToleranceMesh(object):
# class NumericalResolutionMesh(object):
# class NumericalTolerancePath(object):
# class NumericalResolutionPath(object):
# class MeshError(Exception):
# class TransformError(Exception):
#     def __init__(self, **kwargs):
#     def __init__(self, **kwargs):
#     def __init__(self, **kwargs):
#     def __init__(self, **kwargs):
# def _log_time(method):
#     def timed(*args, **kwargs):


# Path: trimesh/path/curve.py
import numpy as np
from ..constants import res_path as res
from ..constants import tol_path as tol
    from scipy.interpolate import splev
        from scipy.special import binom

    '''
    Arguments
    ----------
    points:  (o,d) list of points of the bezier. The first and last
             points should be the start and end of the curve.
             For a 2D cubic bezier, order o=3, dimension d=2

    Returns
    ----------
    discrete: (n,d) list of points, a polyline representation
              of the bezier curve which respects constants.RES_LENGTH
    '''
    def compute(t):
        # compute discrete points given a sampling t
        t_d = 1.0 - t
        n = len(points) - 1
        # binomial coefficents, i, and each point
        iterable = zip(binomial(n), np.arange(n + 1), points)
        stacked = [((t**i) * (t_d**(n - i))).reshape((-1, 1))
                   * p * c for c, i, p in iterable]
        discrete = np.sum(stacked, axis=0)
        return discrete

    # make sure we have a numpy array
    points = np.array(points)

    if count is None:
        # how much distance does a small percentage of the curve take
        # this is so we can figure out how finely we have to sample t
        norm = np.linalg.norm(np.diff(points, axis=0), axis=1).sum()

        count = np.ceil(norm / (res.seg_frac * scale))