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# Copyright (c) 2021 Ultimaker B.V.
# Uranium is released under the terms of the LGPLv3 or higher.
import numpy
import numpy.linalg
import math
from UM.Math.Float import Float
from typing import Optional, Any, TYPE_CHECKING, cast
if TYPE_CHECKING:
from UM.Math.Matrix import Matrix
# Disable divide-by-zero warnings so that 1.0 / (1.0, 0.0, 0.0) returns (1.0, Inf, Inf) without complaining
numpy.seterr(divide="ignore")
class Vector:
"""Simple 3D-vector class based on numpy arrays.
This class represents an immutable 3-dimensional vector.
"""
# These fields are filled in below. This is needed to help static analysis tools (read: PyCharm)
Null = None # type: Vector
Unit_X = None # type: Vector
Unit_Y = None # type: Vector
Unit_Z = None # type: Vector
def __init__(self, x: Optional[float] = None, y: Optional[float] = None, z: Optional[float] = None, data: Optional[numpy.ndarray] = None, round_digits: Optional[int] = None) -> None:
"""Initialize a new vector
:param x: X coordinate of vector.
:param y: Y coordinate of vector.
:param z: Z coordinate of vector.
"""
if x is not None and y is not None and z is not None:
self._data = numpy.array([x, y, z], dtype = numpy.float64)
elif data is not None:
self._data = data.copy()
else:
self._data = numpy.zeros(3, dtype = numpy.float64)
self.round_digits = round_digits # for comparisons
def getData(self) -> numpy.ndarray:
"""Get numpy array with the data
:returns: numpy array of length 3 holding xyz data.
"""
return self._data.astype(numpy.float64)
def setRoundDigits(self, digits: int) -> None:
self.round_digits = digits
@property
def x(self):
"""Return the x component of this vector"""
return numpy.float64(self._data[0])
@property
def y(self):
"""Return the y component of this vector"""
return numpy.float64(self._data[1])
@property
def z(self):
"""Return the z component of this vector"""
return numpy.float64(self._data[2])
def set(self, x: Optional[float] = None, y: Optional[float] = None, z: Optional[float] = None) -> "Vector":
new_x = self._data[0] if x is None else x
new_y = self._data[1] if y is None else y
new_z = self._data[2] if z is None else z
return Vector(new_x, new_y, new_z)
def angleToVector(self, vector: "Vector") -> float:
"""Get the angle from this vector to another"""
v0 = numpy.array(self._data, dtype = numpy.float64, copy = False)
v1 = numpy.array(vector.getData(), dtype = numpy.float64, copy = False)
dot = numpy.sum(v0 * v1)
dot /= self._normalizeVector(v0) * self._normalizeVector(v1)
return numpy.arccos(numpy.fabs(dot))
def normalized(self) -> "Vector":
l = self.length()
if l != 0:
new_data = self._data / l
return Vector(data=new_data)
else:
return self
def _normalizeVector(self, data: numpy.ndarray) -> numpy.ndarray:
"""Return length, i.e. Euclidean norm, of ndarray along axis."""
data = numpy.array(data, dtype = numpy.float64, copy = True)
if data.ndim == 1:
return numpy.array([math.sqrt(numpy.dot(data, data))])
data *= data
out = numpy.atleast_1d(numpy.sum(data))
numpy.sqrt(out, out)
return out
def length(self) -> float:
return numpy.linalg.norm(self._data)
def dot(self, other) -> numpy.ndarray:
return numpy.dot(self._data, other._data)
def cross(self, other) -> "Vector":
result = numpy.cross(self._data, other._data)
return Vector(result[0], result[1], result[2])
def multiply(self, matrix: "Matrix") -> "Vector":
d = numpy.empty(4, dtype = numpy.float64)
d[0] = self._data[0]
d[1] = self._data[1]
d[2] = self._data[2]
d[3] = 1.0
d = cast(numpy.ndarray, d.dot(matrix.getData()))
return Vector(d[0], d[1], d[2])
def preMultiply(self, matrix: "Matrix") -> "Vector":
d = numpy.empty(4, dtype = numpy.float64)
d[0] = self._data[0]
d[1] = self._data[1]
d[2] = self._data[2]
d[3] = 1.0
d = cast(numpy.ndarray, matrix.getData().dot(d))
return Vector(d[0], d[1], d[2])
def scale(self, other: "Vector") -> "Vector":
"""Scale a vector by another vector.
This will do a component-wise multiply of the two vectors.
"""
return Vector(self.x * other.x, self.y * other.y, self.z * other.z)
def __eq__(self, other):
if self is other:
return True
if other is None:
return False
return self.equals(other)
def equals(self, other: "Vector", epsilon: float = 1e-6) -> bool:
"""Compares this vector to another vector.
:param epsilon: optional tolerance value for the comparision.
:returns: True if the two vectors are the same.
"""
return Float.fuzzyCompare(self.x, other.x, epsilon) and \
Float.fuzzyCompare(self.y, other.y, epsilon) and \
Float.fuzzyCompare(self.z, other.z, epsilon)
def __add__(self, other):
if type(other) is Vector:
return Vector(data = self._data + other._data)
else:
return Vector(data = self._data + other)
def __iadd__(self, other):
return self + other
def __sub__(self, other):
if type(other) is Vector:
return Vector(data = self._data - other._data)
else:
return Vector(data = self._data - other)
def __isub__(self, other):
return self - other
def __mul__(self, other):
if isNumber(other):
new_data = self._data * other
elif type(other) is Vector:
new_data = self._data * other._data
else:
raise NotImplementedError()
return Vector(data=new_data)
def __imul__(self, other):
return self * other
def __rmul__(self, other):
return self * other
def __truediv__(self, other):
if isNumber(other):
new_data = self._data / other
elif type(other) is Vector:
new_data = self._data / other._data
else:
raise NotImplementedError()
return Vector(data = new_data)
def __itruediv__(self, other):
return self / other
def __rtruediv__(self, other):
if isNumber(other):
new_data = other / self._data
elif type(other) is Vector:
new_data = other._data / self._data
else:
raise NotImplementedError()
return Vector(data=new_data)
def __neg__(self):
return Vector(data = -1 * self._data)
def __repr__(self):
return "Vector({0:.3f}, {1:.3f}, {2:.3f})".format(self._data[0], self._data[1], self._data[2])
def __str__(self):
return "<{0:.3f},{1:.3f},{2:.3f}>".format(self._data[0], self._data[1], self._data[2])
def __lt__(self, other):
return self._data[0] < other._data[0] and self._data[1] < other._data[1] and self._data[2] < other._data[2]
def __gt__(self, other):
return self._data[0] > other._data[0] and self._data[1] > other._data[1] and self._data[2] > other._data[2]
def __le__(self, other):
if self.round_digits is None:
return self._data[0] <= other._data[0] and self._data[1] <= other._data[1] and self._data[2] <= other._data[2]
else:
return (
round(self._data[0], self.round_digits) <= round(other._data[0], self.round_digits) and
round(self._data[1], self.round_digits) <= round(other._data[1], self.round_digits) and
round(self._data[2], self.round_digits) <= round(other._data[2], self.round_digits))
def __ge__(self, other):
if self.round_digits is None:
return self._data[0] >= other._data[0] and self._data[1] >= other._data[1] and self._data[2] >= other._data[2]
else:
return (
round(self._data[0], self.round_digits) >= round(other._data[0], self.round_digits) and
round(self._data[1], self.round_digits) >= round(other._data[1], self.round_digits) and
round(self._data[2], self.round_digits) >= round(other._data[2], self.round_digits))
def isNumber(value: Any) -> bool:
return type(value) in [float, int, numpy.float32, numpy.float64]
Vector.Null = Vector()
Vector.Unit_X = Vector(1, 0, 0)
Vector.Unit_Y = Vector(0, 1, 0)
Vector.Unit_Z = Vector(0, 0, 1)
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