# Coverage for pygeodesy/vector3d.py : 95%

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Pure Python implementation of vector-based functions by I{(C) Chris Veness 2011-2015} published under the same MIT Licence**, see U{Vector-based geodesy <https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}. @newfield example: Example, Examples ''' from pygeodesy.basics import EPS, EPS1, isscalar, len2, map1, \ property_doc_, property_RO, _xkwds from pygeodesy.errors import CrossError, IntersectionError, _IsnotError, \ _TypeError, _ValueError from pygeodesy.fmath import fdot, fsum, fsum_, hypot_ from pygeodesy.formy import n_xyz2latlon, n_xyz2philam, _radical2 from pygeodesy.interns import _coincident_, _colinear_, _COMMA_, _COMMA_SPACE_, \ _datum_, _h_, _height_, _invalid_, _Missing, \ _name_, _near_concentric_, NN, _other_, _PARENTH_, \ _radius1_, _radius2_, _scalar_, _too_distant_fmt_, \ _y_, _z_ from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY from pygeodesy.named import _NamedBase, Vector3Tuple, _xnamed from pygeodesy.streprs import strs from pygeodesy.units import Radius, Radius_ from math import atan2, cos, sin, sqrt __all__ = _ALL_LAZY.vector3d __version__ = '20.08.12' def _xyzn4(xyz, y, z, Error=_TypeError): # imported by .ecef '''(INTERNAL) Get an C{(x, y, z, name)} 4-tuple. ''' try: t = xyz.x, xyz.y, xyz.z except AttributeError: t = xyz, y, z try: x, y, z = map1(float, *t) except (TypeError, ValueError) as x: d = dict(zip(('xyz', _y_, _z_), t)) raise Error(txt=str(x), **d) return x, y, z, getattr(xyz, _name_, NN) def _xyzhdn6(xyz, y, z, height, datum, ll, Error=_TypeError): # by .cartesianBase, .nvectorBase '''(INTERNAL) Get an C{(x, y, z, h, d, name)} 6-tuple. ''' x, y, z, n = _xyzn4(xyz, y, z, Error=Error) h = height or getattr(xyz, _height_, None) \ or getattr(xyz, _h_, None) \ or getattr(ll, _height_, None) d = datum or getattr(xyz, _datum_, None) \ or getattr(ll, _datum_, None) return x, y, z, h, d, n class VectorError(_ValueError): '''L{Vector3d} or C{*Nvector} issue. ''' pass class Vector3d(_NamedBase): # XXX or _NamedTuple or Vector3Tuple? '''Generic 3-D vector manipulation. In a geodesy context, these may be used to represent: - n-vector representing a normal to point on earth's surface - earth-centered, earth-fixed vector (= n-vector for spherical model) - great circle normal to vector - motion vector on earth's surface - etc. ''' _crosserrors = True # un/set by .errors.crosserrors _fromll = None #: (INTERNAL) original ll. _length = None #: (INTERNAL) cached length. _united = None #: (INTERNAL) cached norm, unit (L{Vector3d}). _xyz = None #: (INTERNAL) cached xyz (L{Vector3Tuple}). _x = 0 #: (INTERNAL) X component. _y = 0 #: (INTERNAL) Y component. _z = 0 #: (INTERNAL) Z component. def __init__(self, x, y, z, ll=None, name=NN): '''New 3-D L{Vector3d}. The vector may be normalised or use x/y/z values for height relative to the surface of the sphere or ellipsoid, distance from earth centre, etc. @arg x: X component of vector (C{scalar}). @arg y: Y component of vector (C{scalar}). @arg z: Z component of vector (C{scalar}). @kwarg ll: Optional latlon reference (C{LatLon}). @kwarg name: Optional name (C{str}). ''' self._x = x self._y = y self._z = z if ll: self._fromll = ll if name: self.name = name def __add__(self, other): '''Add this to an other vector (L{Vector3d}). @return: Vectorial sum (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.plus(other) # __iadd__ = __add__ __radd__ = __add__ def __abs__(self): '''Return the norm of this vector. @return: Norm, unit length (C{float}); ''' return self.length def __cmp__(self, other): # Python 2- '''Compare this and an other vector @arg other: The other vector (L{Vector3d}). @return: -1, 0 or +1 (C{int}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return -1 if self.length < other.length else ( +1 if self.length > other.length else 0) cmp = __cmp__ def __div__(self, scalar): '''Divide this vector by a scalar. @arg scalar: The divisor (C{scalar}). @return: Quotient (L{Vector3d}). @raise TypeError: Non-scalar B{C{scalar}}. ''' return self.dividedBy(scalar) # __itruediv__ = __div__ __truediv__ = __div__ def __eq__(self, other): '''Is this vector equal to an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if equal, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.isequalTo(other) def __ge__(self, other): '''Is this vector longer than or equal to an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.length >= other.length def __gt__(self, other): '''Is this vector longer than an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.length > other.length def __le__(self, other): # Python 3+ '''Is this vector shorter than or equal to an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.length <= other.length def __lt__(self, other): # Python 3+ '''Is this vector shorter than an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.length < other.length # Luciano Ramalho, "Fluent Python", page 397, O'Reilly 2016 def __matmul__(self, other): # PYCHOK Python 3.5+ ... c = a @ b '''Compute the cross product of this and an other vector. @arg other: The other vector (L{Vector3d}). @return: Cross product (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.cross(other) # __imatmul__ = __matmul__ def __mul__(self, scalar): '''Multiply this vector by a scalar @arg scalar: Factor (C{scalar}). @return: Product (L{Vector3d}). ''' return self.times(scalar) # __imul__ = __mul__ # __rmul__ = __mul__ def __ne__(self, other): '''Is this vector not equal to an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return not self.isequalTo(other) def __neg__(self): '''Negate this vector. @return: Negative (L{Vector3d}) ''' return self.negate() def __pos__(self): '''Copy this vector. @return: Positive (L{Vector3d}) ''' return self.copy() # Luciano Ramalho, "Fluent Python", page 397, O'Reilly 2016 def __rmatmul__(self, other): # PYCHOK Python 3.5+ ... c = a @ b '''Compute the cross product of an other and this vector. @arg other: The other vector (L{Vector3d}). @return: Cross product (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return other.cross(self) def __rsub__(self, other): '''Subtract this vector from an other vector. @arg other: The other vector (L{Vector3d}). @return: Difference (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return other.minus(self) def __sub__(self, other): '''Subtract an other vector from this vector. @arg other: The other vector (L{Vector3d}). @return: Difference (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.minus(other) # __isub__ = __sub__ def _update(self, updated, *attrs): '''(INTERNAL) Zap cached attributes if updated. ''' if updated: _NamedBase._update(self, updated, '_length', # '_fromll' '_united', '_xyz', *attrs) def angleTo(self, other, vSign=None): '''Compute the angle between this and an other vector. @arg other: The other vector (L{Vector3d}). @kwarg vSign: Optional vector, if supplied (and out of the plane of this and the other), angle is signed positive if this->other is clockwise looking along vSign or negative in opposite direction, otherwise angle is unsigned. @return: Angle (C{radians}). @raise TypeError: If B{C{other}} or B{C{vSign}} not a L{Vector3d}. ''' x = self.cross(other) s = x.length if s < EPS: return 0.0 # use vSign as reference to get sign of s if vSign and x.dot(vSign) < 0: s = -s return atan2(s, self.dot(other)) def cross(self, other, raiser=None): '''Compute the cross product of this and an other vector. @arg other: The other vector (L{Vector3d}). @kwarg raiser: Optional, L{CrossError} label if raised (C{str}). @return: Cross product (L{Vector3d}). @raise CrossError: Zero or near-zero cross product and both B{C{raiser}} and L{crosserrors} set. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) x = self.y * other.z - self.z * other.y y = self.z * other.x - self.x * other.z z = self.x * other.y - self.y * other.x if raiser and self.crosserrors and max(map1(abs, x, y, z)) < EPS: t = _coincident_ if self.isequalTo(other) else _colinear_ r = getattr(other, '_fromll', None) or other raise CrossError(raiser, r, txt=t) return self.classof(x, y, z) @property_doc_('''raise or ignore L{CrossError} exceptions (C{bool}).''') def crosserrors(self): '''Get L{CrossError} exceptions (C{bool}). ''' return self._crosserrors @crosserrors.setter # PYCHOK setter! def crosserrors(self, raiser): '''Raise L{CrossError} exceptions (C{bool}). ''' self._crosserrors = bool(raiser) def dividedBy(self, factor): '''Divide this vector by a scalar. @arg factor: The divisor (C{scalar}). @return: New, scaled vector (L{Vector3d}). @raise TypeError: Non-scalar B{C{factor}}. @raise VectorError: Invalid or zero B{C{factor}}. ''' if not isscalar(factor): raise _IsnotError(_scalar_, factor=factor) try: return self.times(1.0 / factor) except (ValueError, ZeroDivisionError) as x: raise VectorError(factor=factor, txt=str(x)) def dot(self, other): '''Compute the dot (scalar) product of this and an other vector. @arg other: The other vector (L{Vector3d}). @return: Dot product (C{float}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return fdot(self.xyz, *other.xyz) def equals(self, other, units=False): # PYCHOK no cover '''DEPRECATED, use method C{isequalTo}. ''' return self.isequalTo(other, units=units) def isequalTo(self, other, units=False, eps=EPS): '''Check if this and an other vector are equal or equivalent. @arg other: The other vector (L{Vector3d}). @kwarg units: Optionally, compare the normalized, unit version of both vectors. @kwarg eps: Tolerance for equality (C{scalar}). @return: C{True} if vectors are identical, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. @example: >>> v1 = Vector3d(52.205, 0.119) >>> v2 = Vector3d(52.205, 0.119) >>> e = v1.isequalTo(v2) # True ''' self.others(other) if units: d = self.unit().minus(other.unit()) else: d = self.minus(other) return max(map(abs, d.xyz)) < eps @property_RO def length(self): '''Get the length (norm, magnitude) of this vector (C{float}). ''' if self._length is None: self._length = hypot_(self.x, self.y, self.z) return self._length def minus(self, other): '''Subtract an other vector from this vector. @arg other: The other vector (L{Vector3d}). @return: New vector difference (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.classof(self.x - other.x, self.y - other.y, self.z - other.z) def negate(self): '''Return this vector in opposite direction. @return: New, opposite vector (L{Vector3d}). ''' return self.classof(-self.x, -self.y, -self.z) @property_RO def _N_vector(self): '''(INTERNAL) Get the (C{nvectorBase._N_vector_}) ''' from pygeodesy.nvectorBase import _N_vector_ return _N_vector_(*(self._xyz or self.xyz)) def others(self, other, name=_other_, up=1): '''Refined class comparison. @arg other: The other vector (L{Vector3d}). @kwarg name: Optional, other's name (C{str}). @kwarg up: Number of call stack frames up (C{int}). @return: The B{C{other}} if compatible. @raise TypeError: Incompatible B{C{other}} C{type}. ''' try: _NamedBase.others(self, other, name=name, up=up + 1) except TypeError: if not isinstance(other, Vector3d): raise return other def parse(self, str3d, sep=_COMMA_, name=NN): '''Parse an C{"x, y, z"} string to a similar L{Vector3d} instance. @arg str3d: X, y and z string (C{str}), see function L{parse3d}. @kwarg sep: Optional separator (C{str}). @kwarg name: Optional instance name (C{str}), overriding this name. @return: The similar instance (L{Vector3d}). @raise VectorError: Invalid B{C{str3d}}. ''' return parse3d(str3d, sep=sep, Vector=self.classof, name=name or self.name) def plus(self, other): '''Add this vector and an other vector. @arg other: The other vector (L{Vector3d}). @return: Vectorial sum (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.classof(self.x + other.x, self.y + other.y, self.z + other.z) sum = plus # alternate name def rotate(self, axis, theta): '''Rotate this vector around an axis by a specified angle. See U{Rotation matrix from axis and angle <https://WikiPedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle>} and U{Quaternion-derived rotation matrix <https://WikiPedia.org/wiki/Quaternions_and_spatial_rotation#Quaternion-derived_rotation_matrix>}. @arg axis: The axis being rotated around (L{Vector3d}). @arg theta: The angle of rotation (C{radians}). @return: New, rotated vector (L{Vector3d}). @JSname: I{rotateAround}. ''' a = self.others(axis, name='axis').unit() # axis being rotated around c = cos(theta) b = a.times(1 - c) s = a.times(sin(theta)) p = self.unit().xyz # point being rotated # multiply p by a quaternion-derived rotation matrix return self.classof(fdot(p, a.x * b.x + c, a.x * b.y - s.z, a.x * b.z + s.y), fdot(p, a.y * b.x + s.z, a.y * b.y + c, a.y * b.z - s.x), fdot(p, a.z * b.x - s.y, a.z * b.y + s.x, a.z * b.z + c)) def rotateAround(self, axis, theta): # PYCHOK no cover '''DEPRECATED, use method C{rotate}. ''' return self.rotate(axis, theta) def times(self, factor): '''Multiply this vector by a scalar. @arg factor: Scale factor (C{scalar}). @return: New, scaled vector (L{Vector3d}). @raise TypeError: Non-scalar B{C{factor}}. ''' if not isscalar(factor): raise _IsnotError(_scalar_, factor=factor) return self.classof(self.x * factor, self.y * factor, self.z * factor) def to2ab(self): # PYCHOK no cover '''DEPRECATED, use property C{Nvector.philam}. @return: A L{PhiLam2Tuple}C{(phi, lam)}. ''' return n_xyz2philam(self.x, self.y, self.z) def to2ll(self): # PYCHOK no cover '''DEPRECATED, use property C{Nvector.latlon}. @return: A L{LatLon2Tuple}C{(lat, lon)}. ''' return n_xyz2latlon(self.x, self.y, self.z) def to3xyz(self): # PYCHOK no cover '''DEPRECATED, use property C{xyz}. @return: A L{Vector3Tuple}C{(x, y, z)}. ''' return self.xyz def toStr(self, prec=5, fmt=_PARENTH_, sep=_COMMA_SPACE_): # PYCHOK expected '''Return a string representation of this vector. @kwarg prec: Optional number of decimal places (C{int}). @kwarg fmt: Optional, enclosing format to use (C{str}). @kwarg sep: Optional separator between components (C{str}). @return: Vector as "(x, y, z)" (C{str}). ''' t = sep.join(strs(self.xyz, prec=prec)) if fmt: t = fmt % (t,) return t def unit(self, ll=None): '''Normalize this vector to unit length. @kwarg ll: Optional, original location (C{LatLon}). @return: Normalized vector (L{Vector3d}). ''' if self._united is None: n = self.length if n > EPS and abs(n - 1) > EPS: u = self._xnamed(self.dividedBy(n)) u._length = 1 else: u = self.copy() u._fromll = ll or self._fromll self._united = u._united = u return self._united @property_RO def x(self): '''Get the X component (C{float}). ''' return self._x @property_RO def xyz(self): '''Get the X, Y and Z components (L{Vector3Tuple}C{(x, y, z)}). ''' if self._xyz is None: self._xyz = Vector3Tuple(self.x, self.y, self.z) return self._xnamed(self._xyz) @property_RO def y(self): '''Get the Y component (C{float}). ''' return self._y @property_RO def z(self): '''Get the Z component (C{float}). ''' return self._z def intersections2(center1, radius1, center2, radius2, sphere=True, # MCCABE 14 Vector=None, **Vector_kwds): '''Compute the intersection of two spheres or circles, each defined by a center point and a radius. @arg center1: Center of the first sphere or circle (L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg radius1: Radius of the first sphere or circle (same units as the B{C{center1}} coordinates). @arg center2: Center of the second sphere or circle (L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg radius2: Radius of the second sphere or circle (same units as the B{C{center1}} and B{C{center2}} coordinates). @kwarg sphere: If C{True} compute the center and radius of the intersection of two spheres. If C{False}, ignore the C{z}-component and compute the intersection of two circles (C{bool}). @kwarg Vector: Class to return intersections (L{Vector3d} or C{Vector3Tuple}) or C{None} for L{Vector3d}. @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword arguments, ignored if B{C{Vector=None}}. @return: 2-Tuple of the C{center} and C{radius} of the intersection of the spheres if B{C{sphere}} is C{True}. The C{radius} is C{0.0} for abutting spheres. Otherwise, a 2-tuple of the intersection points of two circles. For abutting circles, both intersection points are the same B{C{Vector}} instance. @raise IntersectionError: Concentric, invalid or non-intersecting spheres or circles. @raise UnitError: Invalid B{C{radius1}} or B{C{radius2}}. @see: U{Sphere-Sphere<https://MathWorld.Wolfram.com/Sphere- SphereIntersection.html>} and U{circle-circle <https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} intersections. ''' r1 = Radius_(radius1, name=_radius1_) r2 = Radius_(radius2, name=_radius2_) try: return _intersects2(center1, r1, center2, r2, sphere=sphere, Vector=Vector, **Vector_kwds) except (TypeError, ValueError) as x: raise IntersectionError(center1=center1, radius1=radius1, center2=center2, radius2=radius2, txt=str(x)) def _intersects2(center1, r1, center2, r2, sphere=True, too_d=None, # in .ellipsoidalBase._intersections2 Vector=None, **Vector_kwds): # (INTERNAL) Intersect two spheres or circles, see L{intersections2} # above, separated to allow callers to embellish any exceptions def _Vector(x, y, z): n = intersections2.__name__ if Vector is None: v = Vector3d(x, y, z, name=n) else: kwds = _xkwds(Vector_kwds, name=n) v = Vector(x, y, z, **kwds) return v def _xVector(c1, u, x, y): xy1 = x, y, 1 # transform to original space return _Vector(fdot(xy1, u.x, -u.y, c1.x), fdot(xy1, u.y, u.x, c1.y), 0) c1 = Vector3d(center1.x, center1.y, center1.z if sphere else 0) c2 = Vector3d(center2.x, center2.y, center2.z if sphere else 0) if r1 < r2: # r1, r2 == R, r c1, c2 = c2, c1 r1, r2 = r2, r1 m = c2.minus(c1) d = m.length if d < max(r2 - r1, EPS): raise ValueError(_near_concentric_) o = fsum_(-d, r1, r2) # overlap == -(d - (r1 + r2)) # compute intersections with c1 at (0, 0) and c2 at (d, 0), like # <https://MathWorld.Wolfram.com/Circle-CircleIntersection.html> if o > EPS: # overlapping, r1, r2 == R, r x = _radical2(d, r1, r2).xline y = 1 - (x / r1)**2 if y > EPS: y = r1 * sqrt(y) # y == a / 2 elif y < 0: raise ValueError(_invalid_) else: # abutting y = 0 elif o < 0: t = d if too_d is None else too_d raise ValueError(_too_distant_fmt_ % (t,)) else: # abutting x, y = r1, 0 u = m.unit() if sphere: # sphere radius and center c = c1 if x < EPS else ( c2 if x > EPS1 else c1.plus(u.times(x))) t = _Vector(c.x, c.y, c.z), Radius(y) elif y > 0: # intersecting circles t = _xVector(c1, u, x, y), _xVector(c1, u, x, -y) else: # abutting circles t = _xVector(c1, u, x, 0) t = t, t return t def parse3d(str3d, sep=_COMMA_, name=NN, Vector=Vector3d, **Vector_kwds): '''Parse an C{"x, y, z"} string. @arg str3d: X, y and z values (C{str}). @kwarg sep: Optional separator (C{str}). @kwarg name: Optional instance name (C{str}). @kwarg Vector: Optional class (L{Vector3d}). @kwarg Vector_kwds: Optional B{C{Vector}} keyword arguments, ignored if B{C{Vector=None}}. @return: New B{C{Vector}} or if B{C{Vector}} is C{None}, a L{Vector3Tuple}C{(x, y, z)}. @raise VectorError: Invalid B{C{str3d}}. ''' try: v = [float(v.strip()) for v in str3d.split(sep)] if len(v) != 3: raise ValueError except (TypeError, ValueError) as x: raise VectorError(str3d=str3d, txt=str(x)) r = Vector3Tuple(*v) if Vector is None else \ Vector(*v, **Vector_kwds) return _xnamed(r, name, force=True) def sumOf(vectors, Vector=Vector3d, **Vector_kwds): '''Compute the vectorial sum of several vectors. @arg vectors: Vectors to be added (L{Vector3d}[]). @kwarg Vector: Optional class for the vectorial sum (L{Vector3d}). @kwarg Vector_kwds: Optional B{C{Vector}} keyword arguments, ignored if B{C{Vector=None}}. @return: Vectorial sum as B{C{Vector}} or if B{C{Vector}} is C{None}, a L{Vector3Tuple}C{(x, y, z)}. @raise VectorError: No B{C{vectors}}. ''' n, vectors = len2(vectors) if n < 1: raise VectorError(vectors=n, txt=_Missing) r = Vector3Tuple(fsum(v.x for v in vectors), fsum(v.y for v in vectors), fsum(v.z for v in vectors)) if Vector is not None: r = Vector(r.x, r.y, r.z, **Vector_kwds) # PYCHOK x, y, z return r __all__ += _ALL_DOCS(intersections2, sumOf) # **) MIT License # # Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.