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Message #01514
[svn] r1871 - in trunk: lib/py pkg/dem py
Author: gladky_anton
Date: 2009-07-16 14:44:34 +0200 (Thu, 16 Jul 2009)
New Revision: 1871
Removed:
trunk/py/euclid.py
Modified:
trunk/lib/py/README
trunk/pkg/dem/RockPM.cpp
Log:
1. Deleted euclid.py
Modified: trunk/lib/py/README
===================================================================
--- trunk/lib/py/README 2009-07-16 10:16:39 UTC (rev 1870)
+++ trunk/lib/py/README 2009-07-16 12:44:34 UTC (rev 1871)
@@ -1,8 +1,3 @@
-euclid.py:
- homepage: http://partiallydisassembled.net/euclid.html
- latest SVN version: http://pyeuclid.googlecode.com/svn/trunk/euclid.py
- documentation: http://partiallydisassembled.net/euclid/
-
pygts-0.3.1:
homepage: http://pygts.sourceforge.net/
documentation: http://pygts.svn.sourceforge.net/viewvc/pygts/doc/gts.html
Modified: trunk/pkg/dem/RockPM.cpp
===================================================================
--- trunk/pkg/dem/RockPM.cpp 2009-07-16 10:16:39 UTC (rev 1870)
+++ trunk/pkg/dem/RockPM.cpp 2009-07-16 12:44:34 UTC (rev 1871)
@@ -92,7 +92,7 @@
Dem3DofGeom* contGeom=YADE_CAST<Dem3DofGeom*>(interaction->interactionGeometry.get());
assert(contGeom);
-
+ //LOG_WARN(Omega::instance().getCurrentIteration());
const shared_ptr<RpmMat>& rpm1=YADE_PTR_CAST<RpmMat>(pp1);
const shared_ptr<RpmMat>& rpm2=YADE_PTR_CAST<RpmMat>(pp2);
Deleted: trunk/py/euclid.py
===================================================================
--- trunk/py/euclid.py 2009-07-16 10:16:39 UTC (rev 1870)
+++ trunk/py/euclid.py 2009-07-16 12:44:34 UTC (rev 1871)
@@ -1,2228 +0,0 @@
-#!/usr/bin/env python
-#
-# euclid graphics maths module
-#
-# Copyright (c) 2006 Alex Holkner
-# Alex.Holkner@xxxxxxxxxxxxxxx
-#
-# This library is free software; you can redistribute it and/or modify it
-# under the terms of the GNU Lesser General Public License as published by the
-# Free Software Foundation; either version 2.1 of the License, or (at your
-# option) any later version.
-#
-# This library is distributed in the hope that it will be useful, but WITHOUT
-# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
-# FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License
-# for more details.
-#
-# You should have received a copy of the GNU Lesser General Public License
-# along with this library; if not, write to the Free Software Foundation,
-# Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
-
-'''euclid graphics maths module
-
-Documentation and tests are included in the file "euclid.txt", or online
-at http://code.google.com/p/pyeuclid
-'''
-
-__docformat__ = 'restructuredtext'
-__version__ = '$Id$'
-__revision__ = '$Revision$'
-
-import math
-import operator
-import types
-
-# Some magic here. If _use_slots is True, the classes will derive from
-# object and will define a __slots__ class variable. If _use_slots is
-# False, classes will be old-style and will not define __slots__.
-#
-# _use_slots = True: Memory efficient, probably faster in future versions
-# of Python, "better".
-# _use_slots = False: Ordinary classes, much faster than slots in current
-# versions of Python (2.4 and 2.5).
-_use_slots = True
-
-# If True, allows components of Vector2 and Vector3 to be set via swizzling;
-# e.g. v.xyz = (1, 2, 3). This is much, much slower than the more verbose
-# v.x = 1; v.y = 2; v.z = 3, and slows down ordinary element setting as
-# well. Recommended setting is False.
-_enable_swizzle_set = False
-
-# Requires class to derive from object.
-if _enable_swizzle_set:
- _use_slots = True
-
-# Implement _use_slots magic.
-class _EuclidMetaclass(type):
- def __new__(cls, name, bases, dct):
- if '__slots__' in dct:
- dct['__getstate__'] = cls._create_getstate(dct['__slots__'])
- dct['__setstate__'] = cls._create_setstate(dct['__slots__'])
- if _use_slots:
- return type.__new__(cls, name, bases + (object,), dct)
- else:
- if '__slots__' in dct:
- del dct['__slots__']
- return types.ClassType.__new__(types.ClassType, name, bases, dct)
-
- @classmethod
- def _create_getstate(cls, slots):
- def __getstate__(self):
- d = {}
- for slot in slots:
- d[slot] = getattr(self, slot)
- return d
- return __getstate__
-
- @classmethod
- def _create_setstate(cls, slots):
- def __setstate__(self, state):
- for name, value in state.items():
- setattr(self, name, value)
- return __setstate__
-
-__metaclass__ = _EuclidMetaclass
-
-class Vector2:
- __slots__ = ['x', 'y']
-
- def __init__(self, x=0, y=0):
- self.x = x
- self.y = y
-
- def __copy__(self):
- return self.__class__(self.x, self.y)
-
- copy = __copy__
-
- def __repr__(self):
- return 'Vector2(%.2f, %.2f)' % (self.x, self.y)
-
- def __eq__(self, other):
- if isinstance(other, Vector2):
- return self.x == other.x and \
- self.y == other.y
- else:
- assert hasattr(other, '__len__') and len(other) == 2
- return self.x == other[0] and \
- self.y == other[1]
-
- def __neq__(self, other):
- return not self.__eq__(other)
-
- def __nonzero__(self):
- return self.x != 0 or self.y != 0
-
- def __len__(self):
- return 2
-
- def __getitem__(self, key):
- return (self.x, self.y)[key]
-
- def __setitem__(self, key, value):
- l = [self.x, self.y]
- l[key] = value
- self.x, self.y = l
-
- def __iter__(self):
- return iter((self.x, self.y))
-
- def __getattr__(self, name):
- try:
- return tuple([(self.x, self.y)['xy'.index(c)] \
- for c in name])
- except ValueError:
- raise AttributeError, name
-
- if _enable_swizzle_set:
- # This has detrimental performance on ordinary setattr as well
- # if enabled
- def __setattr__(self, name, value):
- if len(name) == 1:
- object.__setattr__(self, name, value)
- else:
- try:
- l = [self.x, self.y]
- for c, v in map(None, name, value):
- l['xy'.index(c)] = v
- self.x, self.y = l
- except ValueError:
- raise AttributeError, name
-
- def __add__(self, other):
- if isinstance(other, Vector2):
- # Vector + Vector -> Vector
- # Vector + Point -> Point
- # Point + Point -> Vector
- if self.__class__ is other.__class__:
- _class = Vector2
- else:
- _class = Point2
- return _class(self.x + other.x,
- self.y + other.y)
- else:
- assert hasattr(other, '__len__') and len(other) == 2
- return Vector2(self.x + other[0],
- self.y + other[1])
- __radd__ = __add__
-
- def __iadd__(self, other):
- if isinstance(other, Vector2):
- self.x += other.x
- self.y += other.y
- else:
- self.x += other[0]
- self.y += other[1]
- return self
-
- def __sub__(self, other):
- if isinstance(other, Vector2):
- # Vector - Vector -> Vector
- # Vector - Point -> Point
- # Point - Point -> Vector
- if self.__class__ is other.__class__:
- _class = Vector2
- else:
- _class = Point2
- return _class(self.x - other.x,
- self.y - other.y)
- else:
- assert hasattr(other, '__len__') and len(other) == 2
- return Vector2(self.x - other[0],
- self.y - other[1])
-
-
- def __rsub__(self, other):
- if isinstance(other, Vector2):
- return Vector2(other.x - self.x,
- other.y - self.y)
- else:
- assert hasattr(other, '__len__') and len(other) == 2
- return Vector2(other.x - self[0],
- other.y - self[1])
-
- def __mul__(self, other):
- assert type(other) in (int, long, float)
- return Vector2(self.x * other,
- self.y * other)
-
- __rmul__ = __mul__
-
- def __imul__(self, other):
- assert type(other) in (int, long, float)
- self.x *= other
- self.y *= other
- return self
-
- def __div__(self, other):
- assert type(other) in (int, long, float)
- return Vector2(operator.div(self.x, other),
- operator.div(self.y, other))
-
-
- def __rdiv__(self, other):
- assert type(other) in (int, long, float)
- return Vector2(operator.div(other, self.x),
- operator.div(other, self.y))
-
- def __floordiv__(self, other):
- assert type(other) in (int, long, float)
- return Vector2(operator.floordiv(self.x, other),
- operator.floordiv(self.y, other))
-
-
- def __rfloordiv__(self, other):
- assert type(other) in (int, long, float)
- return Vector2(operator.floordiv(other, self.x),
- operator.floordiv(other, self.y))
-
- def __truediv__(self, other):
- assert type(other) in (int, long, float)
- return Vector2(operator.truediv(self.x, other),
- operator.truediv(self.y, other))
-
-
- def __rtruediv__(self, other):
- assert type(other) in (int, long, float)
- return Vector2(operator.truediv(other, self.x),
- operator.truediv(other, self.y))
-
- def __neg__(self):
- return Vector2(-self.x,
- -self.y)
-
- __pos__ = __copy__
-
- def __abs__(self):
- return math.sqrt(self.x ** 2 + \
- self.y ** 2)
-
- magnitude = __abs__
-
- def magnitude_squared(self):
- return self.x ** 2 + \
- self.y ** 2
-
- def normalize(self):
- d = self.magnitude()
- if d:
- self.x /= d
- self.y /= d
- return self
-
- def normalized(self):
- d = self.magnitude()
- if d:
- return Vector2(self.x / d,
- self.y / d)
- return self.copy()
-
- def dot(self, other):
- assert isinstance(other, Vector2)
- return self.x * other.x + \
- self.y * other.y
-
- def cross(self):
- return Vector2(self.y, -self.x)
-
- def reflect(self, normal):
- # assume normal is normalized
- assert isinstance(normal, Vector2)
- d = 2 * (self.x * normal.x + self.y * normal.y)
- return Vector2(self.x - d * normal.x,
- self.y - d * normal.y)
-
-class Vector3:
- __slots__ = ['x', 'y', 'z']
-
- def __init__(self, x=0, y=0, z=0):
- self.x = x
- self.y = y
- self.z = z
-
- def __copy__(self):
- return self.__class__(self.x, self.y, self.z)
-
- copy = __copy__
-
- def __repr__(self):
- return 'Vector3(%.2f, %.2f, %.2f)' % (self.x,
- self.y,
- self.z)
-
- def __eq__(self, other):
- if isinstance(other, Vector3):
- return self.x == other.x and \
- self.y == other.y and \
- self.z == other.z
- else:
- assert hasattr(other, '__len__') and len(other) == 3
- return self.x == other[0] and \
- self.y == other[1] and \
- self.z == other[2]
-
- def __neq__(self, other):
- return not self.__eq__(other)
-
- def __nonzero__(self):
- return self.x != 0 or self.y != 0 or self.z != 0
-
- def __len__(self):
- return 3
-
- def __getitem__(self, key):
- return (self.x, self.y, self.z)[key]
-
- def __setitem__(self, key, value):
- l = [self.x, self.y, self.z]
- l[key] = value
- self.x, self.y, self.z = l
-
- def __iter__(self):
- return iter((self.x, self.y, self.z))
-
- def __getattr__(self, name):
- try:
- return tuple([(self.x, self.y, self.z)['xyz'.index(c)] \
- for c in name])
- except ValueError:
- raise AttributeError, name
-
- if _enable_swizzle_set:
- # This has detrimental performance on ordinary setattr as well
- # if enabled
- def __setattr__(self, name, value):
- if len(name) == 1:
- object.__setattr__(self, name, value)
- else:
- try:
- l = [self.x, self.y, self.z]
- for c, v in map(None, name, value):
- l['xyz'.index(c)] = v
- self.x, self.y, self.z = l
- except ValueError:
- raise AttributeError, name
-
-
- def __add__(self, other):
- if isinstance(other, Vector3):
- # Vector + Vector -> Vector
- # Vector + Point -> Point
- # Point + Point -> Vector
- if self.__class__ is other.__class__:
- _class = Vector3
- else:
- _class = Point3
- return _class(self.x + other.x,
- self.y + other.y,
- self.z + other.z)
- else:
- assert hasattr(other, '__len__') and len(other) == 3
- return Vector3(self.x + other[0],
- self.y + other[1],
- self.z + other[2])
- __radd__ = __add__
-
- def __iadd__(self, other):
- if isinstance(other, Vector3):
- self.x += other.x
- self.y += other.y
- self.z += other.z
- else:
- self.x += other[0]
- self.y += other[1]
- self.z += other[2]
- return self
-
- def __sub__(self, other):
- if isinstance(other, Vector3):
- # Vector - Vector -> Vector
- # Vector - Point -> Point
- # Point - Point -> Vector
- if self.__class__ is other.__class__:
- _class = Vector3
- else:
- _class = Point3
- return Vector3(self.x - other.x,
- self.y - other.y,
- self.z - other.z)
- else:
- assert hasattr(other, '__len__') and len(other) == 3
- return Vector3(self.x - other[0],
- self.y - other[1],
- self.z - other[2])
-
-
- def __rsub__(self, other):
- if isinstance(other, Vector3):
- return Vector3(other.x - self.x,
- other.y - self.y,
- other.z - self.z)
- else:
- assert hasattr(other, '__len__') and len(other) == 3
- return Vector3(other.x - self[0],
- other.y - self[1],
- other.z - self[2])
-
- def __mul__(self, other):
- if isinstance(other, Vector3):
- # TODO component-wise mul/div in-place and on Vector2; docs.
- if self.__class__ is Point3 or other.__class__ is Point3:
- _class = Point3
- else:
- _class = Vector3
- return _class(self.x * other.x,
- self.y * other.y,
- self.z * other.z)
- else:
- assert type(other) in (int, long, float)
- return Vector3(self.x * other,
- self.y * other,
- self.z * other)
-
- __rmul__ = __mul__
-
- def __imul__(self, other):
- assert type(other) in (int, long, float)
- self.x *= other
- self.y *= other
- self.z *= other
- return self
-
- def __div__(self, other):
- assert type(other) in (int, long, float)
- return Vector3(operator.div(self.x, other),
- operator.div(self.y, other),
- operator.div(self.z, other))
-
-
- def __rdiv__(self, other):
- assert type(other) in (int, long, float)
- return Vector3(operator.div(other, self.x),
- operator.div(other, self.y),
- operator.div(other, self.z))
-
- def __floordiv__(self, other):
- assert type(other) in (int, long, float)
- return Vector3(operator.floordiv(self.x, other),
- operator.floordiv(self.y, other),
- operator.floordiv(self.z, other))
-
-
- def __rfloordiv__(self, other):
- assert type(other) in (int, long, float)
- return Vector3(operator.floordiv(other, self.x),
- operator.floordiv(other, self.y),
- operator.floordiv(other, self.z))
-
- def __truediv__(self, other):
- assert type(other) in (int, long, float)
- return Vector3(operator.truediv(self.x, other),
- operator.truediv(self.y, other),
- operator.truediv(self.z, other))
-
-
- def __rtruediv__(self, other):
- assert type(other) in (int, long, float)
- return Vector3(operator.truediv(other, self.x),
- operator.truediv(other, self.y),
- operator.truediv(other, self.z))
-
- def __neg__(self):
- return Vector3(-self.x,
- -self.y,
- -self.z)
-
- __pos__ = __copy__
-
- def __abs__(self):
- return math.sqrt(self.x ** 2 + \
- self.y ** 2 + \
- self.z ** 2)
-
- magnitude = __abs__
-
- def magnitude_squared(self):
- return self.x ** 2 + \
- self.y ** 2 + \
- self.z ** 2
-
- def normalize(self):
- d = self.magnitude()
- if d:
- self.x /= d
- self.y /= d
- self.z /= d
- return self
-
- def normalized(self):
- d = self.magnitude()
- if d:
- return Vector3(self.x / d,
- self.y / d,
- self.z / d)
- return self.copy()
-
- def dot(self, other):
- assert isinstance(other, Vector3)
- return self.x * other.x + \
- self.y * other.y + \
- self.z * other.z
-
- def cross(self, other):
- assert isinstance(other, Vector3)
- return Vector3(self.y * other.z - self.z * other.y,
- -self.x * other.z + self.z * other.x,
- self.x * other.y - self.y * other.x)
-
- def reflect(self, normal):
- # assume normal is normalized
- assert isinstance(normal, Vector3)
- d = 2 * (self.x * normal.x + self.y * normal.y + self.z * normal.z)
- return Vector3(self.x - d * normal.x,
- self.y - d * normal.y,
- self.z - d * normal.z)
-
-# a b c
-# e f g
-# i j k
-
-class Matrix3:
- __slots__ = list('abcefgijk')
-
- def __init__(self):
- self.identity()
-
- def __copy__(self):
- M = Matrix3()
- M.a = self.a
- M.b = self.b
- M.c = self.c
- M.e = self.e
- M.f = self.f
- M.g = self.g
- M.i = self.i
- M.j = self.j
- M.k = self.k
- return M
-
- copy = __copy__
- def __repr__(self):
- return ('Matrix3([% 8.2f % 8.2f % 8.2f\n' \
- ' % 8.2f % 8.2f % 8.2f\n' \
- ' % 8.2f % 8.2f % 8.2f])') \
- % (self.a, self.b, self.c,
- self.e, self.f, self.g,
- self.i, self.j, self.k)
-
- def __getitem__(self, key):
- return [self.a, self.e, self.i,
- self.b, self.f, self.j,
- self.c, self.g, self.k][key]
-
- def __setitem__(self, key, value):
- L = self[:]
- L[key] = value
- (self.a, self.e, self.i,
- self.b, self.f, self.j,
- self.c, self.g, self.k) = L
-
- def __mul__(self, other):
- if isinstance(other, Matrix3):
- # Caching repeatedly accessed attributes in local variables
- # apparently increases performance by 20%. Attrib: Will McGugan.
- Aa = self.a
- Ab = self.b
- Ac = self.c
- Ae = self.e
- Af = self.f
- Ag = self.g
- Ai = self.i
- Aj = self.j
- Ak = self.k
- Ba = other.a
- Bb = other.b
- Bc = other.c
- Be = other.e
- Bf = other.f
- Bg = other.g
- Bi = other.i
- Bj = other.j
- Bk = other.k
- C = Matrix3()
- C.a = Aa * Ba + Ab * Be + Ac * Bi
- C.b = Aa * Bb + Ab * Bf + Ac * Bj
- C.c = Aa * Bc + Ab * Bg + Ac * Bk
- C.e = Ae * Ba + Af * Be + Ag * Bi
- C.f = Ae * Bb + Af * Bf + Ag * Bj
- C.g = Ae * Bc + Af * Bg + Ag * Bk
- C.i = Ai * Ba + Aj * Be + Ak * Bi
- C.j = Ai * Bb + Aj * Bf + Ak * Bj
- C.k = Ai * Bc + Aj * Bg + Ak * Bk
- return C
- elif isinstance(other, Point2):
- A = self
- B = other
- P = Point2(0, 0)
- P.x = A.a * B.x + A.b * B.y + A.c
- P.y = A.e * B.x + A.f * B.y + A.g
- return P
- elif isinstance(other, Vector2):
- A = self
- B = other
- V = Vector2(0, 0)
- V.x = A.a * B.x + A.b * B.y
- V.y = A.e * B.x + A.f * B.y
- return V
- else:
- other = other.copy()
- other._apply_transform(self)
- return other
-
- def __imul__(self, other):
- assert isinstance(other, Matrix3)
- # Cache attributes in local vars (see Matrix3.__mul__).
- Aa = self.a
- Ab = self.b
- Ac = self.c
- Ae = self.e
- Af = self.f
- Ag = self.g
- Ai = self.i
- Aj = self.j
- Ak = self.k
- Ba = other.a
- Bb = other.b
- Bc = other.c
- Be = other.e
- Bf = other.f
- Bg = other.g
- Bi = other.i
- Bj = other.j
- Bk = other.k
- self.a = Aa * Ba + Ab * Be + Ac * Bi
- self.b = Aa * Bb + Ab * Bf + Ac * Bj
- self.c = Aa * Bc + Ab * Bg + Ac * Bk
- self.e = Ae * Ba + Af * Be + Ag * Bi
- self.f = Ae * Bb + Af * Bf + Ag * Bj
- self.g = Ae * Bc + Af * Bg + Ag * Bk
- self.i = Ai * Ba + Aj * Be + Ak * Bi
- self.j = Ai * Bb + Aj * Bf + Ak * Bj
- self.k = Ai * Bc + Aj * Bg + Ak * Bk
- return self
-
- def identity(self):
- self.a = self.f = self.k = 1.
- self.b = self.c = self.e = self.g = self.i = self.j = 0
- return self
-
- def scale(self, x, y):
- self *= Matrix3.new_scale(x, y)
- return self
-
- def translate(self, x, y):
- self *= Matrix3.new_translate(x, y)
- return self
-
- def rotate(self, angle):
- self *= Matrix3.new_rotate(angle)
- return self
-
- # Static constructors
- def new_identity(cls):
- self = cls()
- return self
- new_identity = classmethod(new_identity)
-
- def new_scale(cls, x, y):
- self = cls()
- self.a = x
- self.f = y
- return self
- new_scale = classmethod(new_scale)
-
- def new_translate(cls, x, y):
- self = cls()
- self.c = x
- self.g = y
- return self
- new_translate = classmethod(new_translate)
-
- def new_rotate(cls, angle):
- self = cls()
- s = math.sin(angle)
- c = math.cos(angle)
- self.a = self.f = c
- self.b = -s
- self.e = s
- return self
- new_rotate = classmethod(new_rotate)
-
-# a b c d
-# e f g h
-# i j k l
-# m n o p
-
-class Matrix4:
- __slots__ = list('abcdefghijklmnop')
-
- def __init__(self):
- self.identity()
-
- def __copy__(self):
- M = Matrix4()
- M.a = self.a
- M.b = self.b
- M.c = self.c
- M.d = self.d
- M.e = self.e
- M.f = self.f
- M.g = self.g
- M.h = self.h
- M.i = self.i
- M.j = self.j
- M.k = self.k
- M.l = self.l
- M.m = self.m
- M.n = self.n
- M.o = self.o
- M.p = self.p
- return M
-
- copy = __copy__
-
-
- def __repr__(self):
- return ('Matrix4([% 8.2f % 8.2f % 8.2f % 8.2f\n' \
- ' % 8.2f % 8.2f % 8.2f % 8.2f\n' \
- ' % 8.2f % 8.2f % 8.2f % 8.2f\n' \
- ' % 8.2f % 8.2f % 8.2f % 8.2f])') \
- % (self.a, self.b, self.c, self.d,
- self.e, self.f, self.g, self.h,
- self.i, self.j, self.k, self.l,
- self.m, self.n, self.o, self.p)
-
- def __getitem__(self, key):
- return [self.a, self.e, self.i, self.m,
- self.b, self.f, self.j, self.n,
- self.c, self.g, self.k, self.o,
- self.d, self.h, self.l, self.p][key]
-
- def __setitem__(self, key, value):
- L = self[:]
- L[key] = value
- (self.a, self.e, self.i, self.m,
- self.b, self.f, self.j, self.n,
- self.c, self.g, self.k, self.o,
- self.d, self.h, self.l, self.p) = L
-
- def __mul__(self, other):
- if isinstance(other, Matrix4):
- # Cache attributes in local vars (see Matrix3.__mul__).
- Aa = self.a
- Ab = self.b
- Ac = self.c
- Ad = self.d
- Ae = self.e
- Af = self.f
- Ag = self.g
- Ah = self.h
- Ai = self.i
- Aj = self.j
- Ak = self.k
- Al = self.l
- Am = self.m
- An = self.n
- Ao = self.o
- Ap = self.p
- Ba = other.a
- Bb = other.b
- Bc = other.c
- Bd = other.d
- Be = other.e
- Bf = other.f
- Bg = other.g
- Bh = other.h
- Bi = other.i
- Bj = other.j
- Bk = other.k
- Bl = other.l
- Bm = other.m
- Bn = other.n
- Bo = other.o
- Bp = other.p
- C = Matrix4()
- C.a = Aa * Ba + Ab * Be + Ac * Bi + Ad * Bm
- C.b = Aa * Bb + Ab * Bf + Ac * Bj + Ad * Bn
- C.c = Aa * Bc + Ab * Bg + Ac * Bk + Ad * Bo
- C.d = Aa * Bd + Ab * Bh + Ac * Bl + Ad * Bp
- C.e = Ae * Ba + Af * Be + Ag * Bi + Ah * Bm
- C.f = Ae * Bb + Af * Bf + Ag * Bj + Ah * Bn
- C.g = Ae * Bc + Af * Bg + Ag * Bk + Ah * Bo
- C.h = Ae * Bd + Af * Bh + Ag * Bl + Ah * Bp
- C.i = Ai * Ba + Aj * Be + Ak * Bi + Al * Bm
- C.j = Ai * Bb + Aj * Bf + Ak * Bj + Al * Bn
- C.k = Ai * Bc + Aj * Bg + Ak * Bk + Al * Bo
- C.l = Ai * Bd + Aj * Bh + Ak * Bl + Al * Bp
- C.m = Am * Ba + An * Be + Ao * Bi + Ap * Bm
- C.n = Am * Bb + An * Bf + Ao * Bj + Ap * Bn
- C.o = Am * Bc + An * Bg + Ao * Bk + Ap * Bo
- C.p = Am * Bd + An * Bh + Ao * Bl + Ap * Bp
- return C
- elif isinstance(other, Point3):
- A = self
- B = other
- P = Point3(0, 0, 0)
- P.x = A.a * B.x + A.b * B.y + A.c * B.z + A.d
- P.y = A.e * B.x + A.f * B.y + A.g * B.z + A.h
- P.z = A.i * B.x + A.j * B.y + A.k * B.z + A.l
- return P
- elif isinstance(other, Vector3):
- A = self
- B = other
- V = Vector3(0, 0, 0)
- V.x = A.a * B.x + A.b * B.y + A.c * B.z
- V.y = A.e * B.x + A.f * B.y + A.g * B.z
- V.z = A.i * B.x + A.j * B.y + A.k * B.z
- return V
- else:
- other = other.copy()
- other._apply_transform(self)
- return other
-
- def __imul__(self, other):
- assert isinstance(other, Matrix4)
- # Cache attributes in local vars (see Matrix3.__mul__).
- Aa = self.a
- Ab = self.b
- Ac = self.c
- Ad = self.d
- Ae = self.e
- Af = self.f
- Ag = self.g
- Ah = self.h
- Ai = self.i
- Aj = self.j
- Ak = self.k
- Al = self.l
- Am = self.m
- An = self.n
- Ao = self.o
- Ap = self.p
- Ba = other.a
- Bb = other.b
- Bc = other.c
- Bd = other.d
- Be = other.e
- Bf = other.f
- Bg = other.g
- Bh = other.h
- Bi = other.i
- Bj = other.j
- Bk = other.k
- Bl = other.l
- Bm = other.m
- Bn = other.n
- Bo = other.o
- Bp = other.p
- self.a = Aa * Ba + Ab * Be + Ac * Bi + Ad * Bm
- self.b = Aa * Bb + Ab * Bf + Ac * Bj + Ad * Bn
- self.c = Aa * Bc + Ab * Bg + Ac * Bk + Ad * Bo
- self.d = Aa * Bd + Ab * Bh + Ac * Bl + Ad * Bp
- self.e = Ae * Ba + Af * Be + Ag * Bi + Ah * Bm
- self.f = Ae * Bb + Af * Bf + Ag * Bj + Ah * Bn
- self.g = Ae * Bc + Af * Bg + Ag * Bk + Ah * Bo
- self.h = Ae * Bd + Af * Bh + Ag * Bl + Ah * Bp
- self.i = Ai * Ba + Aj * Be + Ak * Bi + Al * Bm
- self.j = Ai * Bb + Aj * Bf + Ak * Bj + Al * Bn
- self.k = Ai * Bc + Aj * Bg + Ak * Bk + Al * Bo
- self.l = Ai * Bd + Aj * Bh + Ak * Bl + Al * Bp
- self.m = Am * Ba + An * Be + Ao * Bi + Ap * Bm
- self.n = Am * Bb + An * Bf + Ao * Bj + Ap * Bn
- self.o = Am * Bc + An * Bg + Ao * Bk + Ap * Bo
- self.p = Am * Bd + An * Bh + Ao * Bl + Ap * Bp
- return self
-
- def transform(self, other):
- A = self
- B = other
- P = Point3(0, 0, 0)
- P.x = A.a * B.x + A.b * B.y + A.c * B.z + A.d
- P.y = A.e * B.x + A.f * B.y + A.g * B.z + A.h
- P.z = A.i * B.x + A.j * B.y + A.k * B.z + A.l
- w = A.m * B.x + A.n * B.y + A.o * B.z + A.p
- if w != 0:
- P.x /= w
- P.y /= w
- P.z /= w
- return P
-
- def identity(self):
- self.a = self.f = self.k = self.p = 1.
- self.b = self.c = self.d = self.e = self.g = self.h = \
- self.i = self.j = self.l = self.m = self.n = self.o = 0
- return self
-
- def scale(self, x, y, z):
- self *= Matrix4.new_scale(x, y, z)
- return self
-
- def translate(self, x, y, z):
- self *= Matrix4.new_translate(x, y, z)
- return self
-
- def rotatex(self, angle):
- self *= Matrix4.new_rotatex(angle)
- return self
-
- def rotatey(self, angle):
- self *= Matrix4.new_rotatey(angle)
- return self
-
- def rotatez(self, angle):
- self *= Matrix4.new_rotatez(angle)
- return self
-
- def rotate_axis(self, angle, axis):
- self *= Matrix4.new_rotate_axis(angle, axis)
- return self
-
- def rotate_euler(self, heading, attitude, bank):
- self *= Matrix4.new_rotate_euler(heading, attitude, bank)
- return self
-
- def rotate_triple_axis(self, x, y, z):
- self *= Matrix4.new_rotate_triple_axis(x, y, z)
- return self
-
- def transpose(self):
- (self.a, self.e, self.i, self.m,
- self.b, self.f, self.j, self.n,
- self.c, self.g, self.k, self.o,
- self.d, self.h, self.l, self.p) = \
- (self.a, self.b, self.c, self.d,
- self.e, self.f, self.g, self.h,
- self.i, self.j, self.k, self.l,
- self.m, self.n, self.o, self.p)
-
- def transposed(self):
- M = self.copy()
- M.transpose()
- return M
-
- # Static constructors
- def new(cls, *values):
- M = cls()
- M[:] = values
- return M
- new = classmethod(new)
-
- def new_identity(cls):
- self = cls()
- return self
- new_identity = classmethod(new_identity)
-
- def new_scale(cls, x, y, z):
- self = cls()
- self.a = x
- self.f = y
- self.k = z
- return self
- new_scale = classmethod(new_scale)
-
- def new_translate(cls, x, y, z):
- self = cls()
- self.d = x
- self.h = y
- self.l = z
- return self
- new_translate = classmethod(new_translate)
-
- def new_rotatex(cls, angle):
- self = cls()
- s = math.sin(angle)
- c = math.cos(angle)
- self.f = self.k = c
- self.g = -s
- self.j = s
- return self
- new_rotatex = classmethod(new_rotatex)
-
- def new_rotatey(cls, angle):
- self = cls()
- s = math.sin(angle)
- c = math.cos(angle)
- self.a = self.k = c
- self.c = s
- self.i = -s
- return self
- new_rotatey = classmethod(new_rotatey)
-
- def new_rotatez(cls, angle):
- self = cls()
- s = math.sin(angle)
- c = math.cos(angle)
- self.a = self.f = c
- self.b = -s
- self.e = s
- return self
- new_rotatez = classmethod(new_rotatez)
-
- def new_rotate_axis(cls, angle, axis):
- assert(isinstance(axis, Vector3))
- vector = axis.normalized()
- x = vector.x
- y = vector.y
- z = vector.z
-
- self = cls()
- s = math.sin(angle)
- c = math.cos(angle)
- c1 = 1. - c
-
- # from the glRotate man page
- self.a = x * x * c1 + c
- self.b = x * y * c1 - z * s
- self.c = x * z * c1 + y * s
- self.e = y * x * c1 + z * s
- self.f = y * y * c1 + c
- self.g = y * z * c1 - x * s
- self.i = x * z * c1 - y * s
- self.j = y * z * c1 + x * s
- self.k = z * z * c1 + c
- return self
- new_rotate_axis = classmethod(new_rotate_axis)
-
- def new_rotate_euler(cls, heading, attitude, bank):
- # from http://www.euclideanspace.com/
- ch = math.cos(heading)
- sh = math.sin(heading)
- ca = math.cos(attitude)
- sa = math.sin(attitude)
- cb = math.cos(bank)
- sb = math.sin(bank)
-
- self = cls()
- self.a = ch * ca
- self.b = sh * sb - ch * sa * cb
- self.c = ch * sa * sb + sh * cb
- self.e = sa
- self.f = ca * cb
- self.g = -ca * sb
- self.i = -sh * ca
- self.j = sh * sa * cb + ch * sb
- self.k = -sh * sa * sb + ch * cb
- return self
- new_rotate_euler = classmethod(new_rotate_euler)
-
- def new_rotate_triple_axis(cls, x, y, z):
- m = cls()
-
- m.a, m.b, m.c = x.x, y.x, z.x
- m.e, m.f, m.g = x.y, y.y, z.y
- m.i, m.j, m.k = x.z, y.z, z.z
-
- return m
- new_rotate_triple_axis = classmethod(new_rotate_triple_axis)
-
- def new_look_at(cls, eye, at, up):
- z = (eye - at).normalized()
- x = up.cross(z).normalized()
- y = z.cross(x)
-
- m = cls.new_rotate_triple_axis(x, y, z)
- m.d, m.h, m.l = eye.x, eye.y, eye.z
- return m
- new_look_at = classmethod(new_look_at)
-
- def new_perspective(cls, fov_y, aspect, near, far):
- # from the gluPerspective man page
- f = 1 / math.tan(fov_y / 2)
- self = cls()
- assert near != 0.0 and near != far
- self.a = f / aspect
- self.f = f
- self.k = (far + near) / (near - far)
- self.l = 2 * far * near / (near - far)
- self.o = -1
- self.p = 0
- return self
- new_perspective = classmethod(new_perspective)
-
- def determinant(self):
- return ((self.a * self.f - self.e * self.b)
- * (self.k * self.p - self.o * self.l)
- - (self.a * self.j - self.i * self.b)
- * (self.g * self.p - self.o * self.h)
- + (self.a * self.n - self.m * self.b)
- * (self.g * self.l - self.k * self.h)
- + (self.e * self.j - self.i * self.f)
- * (self.c * self.p - self.o * self.d)
- - (self.e * self.n - self.m * self.f)
- * (self.c * self.l - self.k * self.d)
- + (self.i * self.n - self.m * self.j)
- * (self.c * self.h - self.g * self.d))
-
- def inverse(self):
- tmp = Matrix4()
- d = self.determinant();
-
- if abs(d) < 0.001:
- # No inverse, return identity
- return tmp
- else:
- d = 1.0 / d;
-
- tmp.a = d * (self.f * (self.k * self.p - self.o * self.l) + self.j * (self.o * self.h - self.g * self.p) + self.n * (self.g * self.l - self.k * self.h));
- tmp.e = d * (self.g * (self.i * self.p - self.m * self.l) + self.k * (self.m * self.h - self.e * self.p) + self.o * (self.e * self.l - self.i * self.h));
- tmp.i = d * (self.h * (self.i * self.n - self.m * self.j) + self.l * (self.m * self.f - self.e * self.n) + self.p * (self.e * self.j - self.i * self.f));
- tmp.m = d * (self.e * (self.n * self.k - self.j * self.o) + self.i * (self.f * self.o - self.n * self.g) + self.m * (self.j * self.g - self.f * self.k));
-
- tmp.b = d * (self.j * (self.c * self.p - self.o * self.d) + self.n * (self.k * self.d - self.c * self.l) + self.b * (self.o * self.l - self.k * self.p));
- tmp.f = d * (self.k * (self.a * self.p - self.m * self.d) + self.o * (self.i * self.d - self.a * self.l) + self.c * (self.m * self.l - self.i * self.p));
- tmp.j = d * (self.l * (self.a * self.n - self.m * self.b) + self.p * (self.i * self.b - self.a * self.j) + self.d * (self.m * self.j - self.i * self.n));
- tmp.n = d * (self.i * (self.n * self.c - self.b * self.o) + self.m * (self.b * self.k - self.j * self.c) + self.a * (self.j * self.o - self.n * self.k));
-
- tmp.c = d * (self.n * (self.c * self.h - self.g * self.d) + self.b * (self.g * self.p - self.o * self.h) + self.f * (self.o * self.d - self.c * self.p));
- tmp.g = d * (self.o * (self.a * self.h - self.e * self.d) + self.c * (self.e * self.p - self.m * self.h) + self.g * (self.m * self.d - self.a * self.p));
- tmp.k = d * (self.p * (self.a * self.f - self.e * self.b) + self.d * (self.e * self.n - self.m * self.f) + self.h * (self.m * self.b - self.a * self.n));
- tmp.o = d * (self.m * (self.f * self.c - self.b * self.g) + self.a * (self.n * self.g - self.f * self.o) + self.e * (self.b * self.o - self.n * self.c));
-
- tmp.d = d * (self.b * (self.k * self.h - self.g * self.l) + self.f * (self.c * self.l - self.k * self.d) + self.j * (self.g * self.d - self.c * self.h));
- tmp.h = d * (self.c * (self.i * self.h - self.e * self.l) + self.g * (self.a * self.l - self.i * self.d) + self.k * (self.e * self.d - self.a * self.h));
- tmp.l = d * (self.d * (self.i * self.f - self.e * self.j) + self.h * (self.a * self.j - self.i * self.b) + self.l * (self.e * self.b - self.a * self.f));
- tmp.p = d * (self.a * (self.f * self.k - self.j * self.g) + self.e * (self.j * self.c - self.b * self.k) + self.i * (self.b * self.g - self.f * self.c));
-
- return tmp;
-
-
-class Quaternion:
- # All methods and naming conventions based off
- # http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions
-
- # w is the real part, (x, y, z) are the imaginary parts
- __slots__ = ['w', 'x', 'y', 'z']
-
- def __init__(self, w=1, x=0, y=0, z=0):
- self.w = w
- self.x = x
- self.y = y
- self.z = z
-
- def __copy__(self):
- Q = Quaternion()
- Q.w = self.w
- Q.x = self.x
- Q.y = self.y
- Q.z = self.z
- return Q
-
- copy = __copy__
-
- def __repr__(self):
- return 'Quaternion(real=%.2f, imag=<%.2f, %.2f, %.2f>)' % \
- (self.w, self.x, self.y, self.z)
-
- def __mul__(self, other):
- if isinstance(other, Quaternion):
- Ax = self.x
- Ay = self.y
- Az = self.z
- Aw = self.w
- Bx = other.x
- By = other.y
- Bz = other.z
- Bw = other.w
- Q = Quaternion()
- Q.x = Ax * Bw + Ay * Bz - Az * By + Aw * Bx
- Q.y = -Ax * Bz + Ay * Bw + Az * Bx + Aw * By
- Q.z = Ax * By - Ay * Bx + Az * Bw + Aw * Bz
- Q.w = -Ax * Bx - Ay * By - Az * Bz + Aw * Bw
- return Q
- elif isinstance(other, Vector3):
- w = self.w
- x = self.x
- y = self.y
- z = self.z
- Vx = other.x
- Vy = other.y
- Vz = other.z
- return other.__class__(\
- w * w * Vx + 2 * y * w * Vz - 2 * z * w * Vy + \
- x * x * Vx + 2 * y * x * Vy + 2 * z * x * Vz - \
- z * z * Vx - y * y * Vx,
- 2 * x * y * Vx + y * y * Vy + 2 * z * y * Vz + \
- 2 * w * z * Vx - z * z * Vy + w * w * Vy - \
- 2 * x * w * Vz - x * x * Vy,
- 2 * x * z * Vx + 2 * y * z * Vy + \
- z * z * Vz - 2 * w * y * Vx - y * y * Vz + \
- 2 * w * x * Vy - x * x * Vz + w * w * Vz)
- else:
- other = other.copy()
- other._apply_transform(self)
- return other
-
- def __imul__(self, other):
- assert isinstance(other, Quaternion)
- Ax = self.x
- Ay = self.y
- Az = self.z
- Aw = self.w
- Bx = other.x
- By = other.y
- Bz = other.z
- Bw = other.w
- self.x = Ax * Bw + Ay * Bz - Az * By + Aw * Bx
- self.y = -Ax * Bz + Ay * Bw + Az * Bx + Aw * By
- self.z = Ax * By - Ay * Bx + Az * Bw + Aw * Bz
- self.w = -Ax * Bx - Ay * By - Az * Bz + Aw * Bw
- return self
-
- def __abs__(self):
- return math.sqrt(self.w ** 2 + \
- self.x ** 2 + \
- self.y ** 2 + \
- self.z ** 2)
-
- magnitude = __abs__
-
- def magnitude_squared(self):
- return self.w ** 2 + \
- self.x ** 2 + \
- self.y ** 2 + \
- self.z ** 2
-
- def identity(self):
- self.w = 1
- self.x = 0
- self.y = 0
- self.z = 0
- return self
-
- def rotate_axis(self, angle, axis):
- self *= Quaternion.new_rotate_axis(angle, axis)
- return self
-
- def rotate_euler(self, heading, attitude, bank):
- self *= Quaternion.new_rotate_euler(heading, attitude, bank)
- return self
-
- def rotate_matrix(self, m):
- self *= Quaternion.new_rotate_matrix(m)
- return self
-
- def conjugated(self):
- Q = Quaternion()
- Q.w = self.w
- Q.x = -self.x
- Q.y = -self.y
- Q.z = -self.z
- return Q
-
- def normalize(self):
- d = self.magnitude()
- if d != 0:
- self.w /= d
- self.x /= d
- self.y /= d
- self.z /= d
- return self
-
- def normalized(self):
- d = self.magnitude()
- if d != 0:
- Q = Quaternion()
- Q.w = self.w / d
- Q.x = self.x / d
- Q.y = self.y / d
- Q.z = self.z / d
- return Q
- else:
- return self.copy()
-
- def get_angle_axis(self):
- if self.w > 1:
- self = self.normalized()
- angle = 2 * math.acos(self.w)
- s = math.sqrt(1 - self.w ** 2)
- if s < 0.001:
- return angle, Vector3(1, 0, 0)
- else:
- return angle, Vector3(self.x / s, self.y / s, self.z / s)
-
- def get_euler(self):
- t = self.x * self.y + self.z * self.w
- if t > 0.4999:
- heading = 2 * math.atan2(self.x, self.w)
- attitude = math.pi / 2
- bank = 0
- elif t < -0.4999:
- heading = -2 * math.atan2(self.x, self.w)
- attitude = -math.pi / 2
- bank = 0
- else:
- sqx = self.x ** 2
- sqy = self.y ** 2
- sqz = self.z ** 2
- heading = math.atan2(2 * self.y * self.w - 2 * self.x * self.z,
- 1 - 2 * sqy - 2 * sqz)
- attitude = math.asin(2 * t)
- bank = math.atan2(2 * self.x * self.w - 2 * self.y * self.z,
- 1 - 2 * sqx - 2 * sqz)
- return heading, attitude, bank
-
- def get_matrix(self):
- xx = self.x ** 2
- xy = self.x * self.y
- xz = self.x * self.z
- xw = self.x * self.w
- yy = self.y ** 2
- yz = self.y * self.z
- yw = self.y * self.w
- zz = self.z ** 2
- zw = self.z * self.w
- M = Matrix4()
- M.a = 1 - 2 * (yy + zz)
- M.b = 2 * (xy - zw)
- M.c = 2 * (xz + yw)
- M.e = 2 * (xy + zw)
- M.f = 1 - 2 * (xx + zz)
- M.g = 2 * (yz - xw)
- M.i = 2 * (xz - yw)
- M.j = 2 * (yz + xw)
- M.k = 1 - 2 * (xx + yy)
- return M
-
- # Static constructors
- def new_identity(cls):
- return cls()
- new_identity = classmethod(new_identity)
-
- def new_rotate_axis(cls, angle, axis):
- assert(isinstance(axis, Vector3))
- axis = axis.normalized()
- s = math.sin(angle / 2)
- Q = cls()
- Q.w = math.cos(angle / 2)
- Q.x = axis.x * s
- Q.y = axis.y * s
- Q.z = axis.z * s
- return Q
- new_rotate_axis = classmethod(new_rotate_axis)
-
- def new_rotate_euler(cls, heading, attitude, bank):
- Q = cls()
- c1 = math.cos(heading / 2)
- s1 = math.sin(heading / 2)
- c2 = math.cos(attitude / 2)
- s2 = math.sin(attitude / 2)
- c3 = math.cos(bank / 2)
- s3 = math.sin(bank / 2)
-
- Q.w = c1 * c2 * c3 - s1 * s2 * s3
- Q.x = s1 * s2 * c3 + c1 * c2 * s3
- Q.y = s1 * c2 * c3 + c1 * s2 * s3
- Q.z = c1 * s2 * c3 - s1 * c2 * s3
- return Q
- new_rotate_euler = classmethod(new_rotate_euler)
-
- def new_rotate_matrix(cls, m):
- if m[0*4 + 0] + m[1*4 + 1] + m[2*4 + 2] > 0.00000001:
- t = m[0*4 + 0] + m[1*4 + 1] + m[2*4 + 2] + 1.0
- s = 0.5/math.sqrt(t)
-
- return cls(
- s*t,
- (m[1*4 + 2] - m[2*4 + 1])*s,
- (m[2*4 + 0] - m[0*4 + 2])*s,
- (m[0*4 + 1] - m[1*4 + 0])*s
- )
-
- elif m[0*4 + 0] > m[1*4 + 1] and m[0*4 + 0] > m[2*4 + 2]:
- t = m[0*4 + 0] - m[1*4 + 1] - m[2*4 + 2] + 1.0
- s = 0.5/math.sqrt(t)
-
- return cls(
- (m[1*4 + 2] - m[2*4 + 1])*s,
- s*t,
- (m[0*4 + 1] + m[1*4 + 0])*s,
- (m[2*4 + 0] + m[0*4 + 2])*s
- )
-
- elif m[1*4 + 1] > m[2*4 + 2]:
- t = -m[0*4 + 0] + m[1*4 + 1] - m[2*4 + 2] + 1.0
- s = 0.5/math.sqrt(t)
-
- return cls(
- (m[2*4 + 0] - m[0*4 + 2])*s,
- (m[0*4 + 1] + m[1*4 + 0])*s,
- s*t,
- (m[1*4 + 2] + m[2*4 + 1])*s
- )
-
- else:
- t = -m[0*4 + 0] - m[1*4 + 1] + m[2*4 + 2] + 1.0
- s = 0.5/math.sqrt(t)
-
- return cls(
- (m[0*4 + 1] - m[1*4 + 0])*s,
- (m[2*4 + 0] + m[0*4 + 2])*s,
- (m[1*4 + 2] + m[2*4 + 1])*s,
- s*t
- )
- new_rotate_matrix = classmethod(new_rotate_matrix)
-
- def new_interpolate(cls, q1, q2, t):
- assert isinstance(q1, Quaternion) and isinstance(q2, Quaternion)
- Q = cls()
-
- costheta = q1.w * q2.w + q1.x * q2.x + q1.y * q2.y + q1.z * q2.z
- if costheta < 0.:
- costheta = -costheta
- q1 = q1.conjugated()
- elif costheta > 1:
- costheta = 1
-
- theta = math.acos(costheta)
- if abs(theta) < 0.01:
- Q.w = q2.w
- Q.x = q2.x
- Q.y = q2.y
- Q.z = q2.z
- return Q
-
- sintheta = math.sqrt(1.0 - costheta * costheta)
- if abs(sintheta) < 0.01:
- Q.w = (q1.w + q2.w) * 0.5
- Q.x = (q1.x + q2.x) * 0.5
- Q.y = (q1.y + q2.y) * 0.5
- Q.z = (q1.z + q2.z) * 0.5
- return Q
-
- ratio1 = math.sin((1 - t) * theta) / sintheta
- ratio2 = math.sin(t * theta) / sintheta
-
- Q.w = q1.w * ratio1 + q2.w * ratio2
- Q.x = q1.x * ratio1 + q2.x * ratio2
- Q.y = q1.y * ratio1 + q2.y * ratio2
- Q.z = q1.z * ratio1 + q2.z * ratio2
- return Q
- new_interpolate = classmethod(new_interpolate)
-
-# Geometry
-# Much maths thanks to Paul Bourke, http://astronomy.swin.edu.au/~pbourke
-# ---------------------------------------------------------------------------
-
-class Geometry:
- def _connect_unimplemented(self, other):
- raise AttributeError, 'Cannot connect %s to %s' % \
- (self.__class__, other.__class__)
-
- def _intersect_unimplemented(self, other):
- raise AttributeError, 'Cannot intersect %s and %s' % \
- (self.__class__, other.__class__)
-
- _intersect_point2 = _intersect_unimplemented
- _intersect_line2 = _intersect_unimplemented
- _intersect_circle = _intersect_unimplemented
- _connect_point2 = _connect_unimplemented
- _connect_line2 = _connect_unimplemented
- _connect_circle = _connect_unimplemented
-
- _intersect_point3 = _intersect_unimplemented
- _intersect_line3 = _intersect_unimplemented
- _intersect_sphere = _intersect_unimplemented
- _intersect_plane = _intersect_unimplemented
- _connect_point3 = _connect_unimplemented
- _connect_line3 = _connect_unimplemented
- _connect_sphere = _connect_unimplemented
- _connect_plane = _connect_unimplemented
-
- def intersect(self, other):
- raise NotImplementedError
-
- def connect(self, other):
- raise NotImplementedError
-
- def distance(self, other):
- c = self.connect(other)
- if c:
- return c.length
- return 0.0
-
-def _intersect_point2_circle(P, C):
- return abs(P - C.c) <= C.r
-
-def _intersect_line2_line2(A, B):
- d = B.v.y * A.v.x - B.v.x * A.v.y
- if d == 0:
- return None
-
- dy = A.p.y - B.p.y
- dx = A.p.x - B.p.x
- ua = (B.v.x * dy - B.v.y * dx) / d
- if not A._u_in(ua):
- return None
- ub = (A.v.x * dy - A.v.y * dx) / d
- if not B._u_in(ub):
- return None
-
- return Point2(A.p.x + ua * A.v.x,
- A.p.y + ua * A.v.y)
-
-def _intersect_line2_circle(L, C):
- a = L.v.magnitude_squared()
- b = 2 * (L.v.x * (L.p.x - C.c.x) + \
- L.v.y * (L.p.y - C.c.y))
- c = C.c.magnitude_squared() + \
- L.p.magnitude_squared() - \
- 2 * C.c.dot(L.p) - \
- C.r ** 2
- det = b ** 2 - 4 * a * c
- if det < 0:
- return None
- sq = math.sqrt(det)
- u1 = (-b + sq) / (2 * a)
- u2 = (-b - sq) / (2 * a)
- if not L._u_in(u1):
- u1 = max(min(u1, 1.0), 0.0)
- if not L._u_in(u2):
- u2 = max(min(u2, 1.0), 0.0)
-
- # Tangent
- if u1 == u2:
- return Point2(L.p.x + u1 * L.v.x,
- L.p.y + u1 * L.v.y)
-
- return LineSegment2(Point2(L.p.x + u1 * L.v.x,
- L.p.y + u1 * L.v.y),
- Point2(L.p.x + u2 * L.v.x,
- L.p.y + u2 * L.v.y))
-
-def _connect_point2_line2(P, L):
- d = L.v.magnitude_squared()
- assert d != 0
- u = ((P.x - L.p.x) * L.v.x + \
- (P.y - L.p.y) * L.v.y) / d
- if not L._u_in(u):
- u = max(min(u, 1.0), 0.0)
- return LineSegment2(P,
- Point2(L.p.x + u * L.v.x,
- L.p.y + u * L.v.y))
-
-def _connect_point2_circle(P, C):
- v = P - C.c
- v.normalize()
- v *= C.r
- return LineSegment2(P, Point2(C.c.x + v.x, C.c.y + v.y))
-
-def _connect_line2_line2(A, B):
- d = B.v.y * A.v.x - B.v.x * A.v.y
- if d == 0:
- # Parallel, connect an endpoint with a line
- if isinstance(B, Ray2) or isinstance(B, LineSegment2):
- p1, p2 = _connect_point2_line2(B.p, A)
- return p2, p1
- # No endpoint (or endpoint is on A), possibly choose arbitrary point
- # on line.
- return _connect_point2_line2(A.p, B)
-
- dy = A.p.y - B.p.y
- dx = A.p.x - B.p.x
- ua = (B.v.x * dy - B.v.y * dx) / d
- if not A._u_in(ua):
- ua = max(min(ua, 1.0), 0.0)
- ub = (A.v.x * dy - A.v.y * dx) / d
- if not B._u_in(ub):
- ub = max(min(ub, 1.0), 0.0)
-
- return LineSegment2(Point2(A.p.x + ua * A.v.x, A.p.y + ua * A.v.y),
- Point2(B.p.x + ub * B.v.x, B.p.y + ub * B.v.y))
-
-def _connect_circle_line2(C, L):
- d = L.v.magnitude_squared()
- assert d != 0
- u = ((C.c.x - L.p.x) * L.v.x + (C.c.y - L.p.y) * L.v.y) / d
- if not L._u_in(u):
- u = max(min(u, 1.0), 0.0)
- point = Point2(L.p.x + u * L.v.x, L.p.y + u * L.v.y)
- v = (point - C.c)
- v.normalize()
- v *= C.r
- return LineSegment2(Point2(C.c.x + v.x, C.c.y + v.y), point)
-
-def _connect_circle_circle(A, B):
- v = B.c - A.c
- v.normalize()
- return LineSegment2(Point2(A.c.x + v.x * A.r, A.c.y + v.y * A.r),
- Point2(B.c.x - v.x * B.r, B.c.y - v.y * B.r))
-
-
-class Point2(Vector2, Geometry):
- def __repr__(self):
- return 'Point2(%.2f, %.2f)' % (self.x, self.y)
-
- def intersect(self, other):
- return other._intersect_point2(self)
-
- def _intersect_circle(self, other):
- return _intersect_point2_circle(self, other)
-
- def connect(self, other):
- return other._connect_point2(self)
-
- def _connect_point2(self, other):
- return LineSegment2(other, self)
-
- def _connect_line2(self, other):
- c = _connect_point2_line2(self, other)
- if c:
- return c._swap()
-
- def _connect_circle(self, other):
- c = _connect_point2_circle(self, other)
- if c:
- return c._swap()
-
-class Line2(Geometry):
- __slots__ = ['p', 'v']
-
- def __init__(self, *args):
- if len(args) == 3:
- assert isinstance(args[0], Point2) and \
- isinstance(args[1], Vector2) and \
- type(args[2]) == float
- self.p = args[0].copy()
- self.v = args[1] * args[2] / abs(args[1])
- elif len(args) == 2:
- if isinstance(args[0], Point2) and isinstance(args[1], Point2):
- self.p = args[0].copy()
- self.v = args[1] - args[0]
- elif isinstance(args[0], Point2) and isinstance(args[1], Vector2):
- self.p = args[0].copy()
- self.v = args[1].copy()
- else:
- raise AttributeError, '%r' % (args,)
- elif len(args) == 1:
- if isinstance(args[0], Line2):
- self.p = args[0].p.copy()
- self.v = args[0].v.copy()
- else:
- raise AttributeError, '%r' % (args,)
- else:
- raise AttributeError, '%r' % (args,)
-
- if not self.v:
- raise AttributeError, 'Line has zero-length vector'
-
- def __copy__(self):
- return self.__class__(self.p, self.v)
-
- copy = __copy__
-
- def __repr__(self):
- return 'Line2(<%.2f, %.2f> + u<%.2f, %.2f>)' % \
- (self.p.x, self.p.y, self.v.x, self.v.y)
-
- p1 = property(lambda self: self.p)
- p2 = property(lambda self: Point2(self.p.x + self.v.x,
- self.p.y + self.v.y))
-
- def _apply_transform(self, t):
- self.p = t * self.p
- self.v = t * self.v
-
- def _u_in(self, u):
- return True
-
- def intersect(self, other):
- return other._intersect_line2(self)
-
- def _intersect_line2(self, other):
- return _intersect_line2_line2(self, other)
-
- def _intersect_circle(self, other):
- return _intersect_line2_circle(self, other)
-
- def connect(self, other):
- return other._connect_line2(self)
-
- def _connect_point2(self, other):
- return _connect_point2_line2(other, self)
-
- def _connect_line2(self, other):
- return _connect_line2_line2(other, self)
-
- def _connect_circle(self, other):
- return _connect_circle_line2(other, self)
-
-class Ray2(Line2):
- def __repr__(self):
- return 'Ray2(<%.2f, %.2f> + u<%.2f, %.2f>)' % \
- (self.p.x, self.p.y, self.v.x, self.v.y)
-
- def _u_in(self, u):
- return u >= 0.0
-
-class LineSegment2(Line2):
- def __repr__(self):
- return 'LineSegment2(<%.2f, %.2f> to <%.2f, %.2f>)' % \
- (self.p.x, self.p.y, self.p.x + self.v.x, self.p.y + self.v.y)
-
- def _u_in(self, u):
- return u >= 0.0 and u <= 1.0
-
- def __abs__(self):
- return abs(self.v)
-
- def magnitude_squared(self):
- return self.v.magnitude_squared()
-
- def _swap(self):
- # used by connect methods to switch order of points
- self.p = self.p2
- self.v *= -1
- return self
-
- length = property(lambda self: abs(self.v))
-
-class Circle(Geometry):
- __slots__ = ['c', 'r']
-
- def __init__(self, center, radius):
- assert isinstance(center, Vector2) and type(radius) == float
- self.c = center.copy()
- self.r = radius
-
- def __copy__(self):
- return self.__class__(self.c, self.r)
-
- copy = __copy__
-
- def __repr__(self):
- return 'Circle(<%.2f, %.2f>, radius=%.2f)' % \
- (self.c.x, self.c.y, self.r)
-
- def _apply_transform(self, t):
- self.c = t * self.c
-
- def intersect(self, other):
- return other._intersect_circle(self)
-
- def _intersect_point2(self, other):
- return _intersect_point2_circle(other, self)
-
- def _intersect_line2(self, other):
- return _intersect_line2_circle(other, self)
-
- def connect(self, other):
- return other._connect_circle(self)
-
- def _connect_point2(self, other):
- return _connect_point2_circle(other, self)
-
- def _connect_line2(self, other):
- c = _connect_circle_line2(self, other)
- if c:
- return c._swap()
-
- def _connect_circle(self, other):
- return _connect_circle_circle(other, self)
-
-# 3D Geometry
-# -------------------------------------------------------------------------
-
-def _connect_point3_line3(P, L):
- d = L.v.magnitude_squared()
- assert d != 0
- u = ((P.x - L.p.x) * L.v.x + \
- (P.y - L.p.y) * L.v.y + \
- (P.z - L.p.z) * L.v.z) / d
- if not L._u_in(u):
- u = max(min(u, 1.0), 0.0)
- return LineSegment3(P, Point3(L.p.x + u * L.v.x,
- L.p.y + u * L.v.y,
- L.p.z + u * L.v.z))
-
-def _connect_point3_sphere(P, S):
- v = P - S.c
- v.normalize()
- v *= S.r
- return LineSegment3(P, Point3(S.c.x + v.x, S.c.y + v.y, S.c.z + v.z))
-
-def _connect_point3_plane(p, plane):
- n = plane.n.normalized()
- d = p.dot(plane.n) - plane.k
- return LineSegment3(p, Point3(p.x - n.x * d, p.y - n.y * d, p.z - n.z * d))
-
-def _connect_line3_line3(A, B):
- assert A.v and B.v
- p13 = A.p - B.p
- d1343 = p13.dot(B.v)
- d4321 = B.v.dot(A.v)
- d1321 = p13.dot(A.v)
- d4343 = B.v.magnitude_squared()
- denom = A.v.magnitude_squared() * d4343 - d4321 ** 2
- if denom == 0:
- # Parallel, connect an endpoint with a line
- if isinstance(B, Ray3) or isinstance(B, LineSegment3):
- return _connect_point3_line3(B.p, A)._swap()
- # No endpoint (or endpoint is on A), possibly choose arbitrary
- # point on line.
- return _connect_point3_line3(A.p, B)
-
- ua = (d1343 * d4321 - d1321 * d4343) / denom
- if not A._u_in(ua):
- ua = max(min(ua, 1.0), 0.0)
- ub = (d1343 + d4321 * ua) / d4343
- if not B._u_in(ub):
- ub = max(min(ub, 1.0), 0.0)
- return LineSegment3(Point3(A.p.x + ua * A.v.x,
- A.p.y + ua * A.v.y,
- A.p.z + ua * A.v.z),
- Point3(B.p.x + ub * B.v.x,
- B.p.y + ub * B.v.y,
- B.p.z + ub * B.v.z))
-
-def _connect_line3_plane(L, P):
- d = P.n.dot(L.v)
- if not d:
- # Parallel, choose an endpoint
- return _connect_point3_plane(L.p, P)
- u = (P.k - P.n.dot(L.p)) / d
- if not L._u_in(u):
- # intersects out of range, choose nearest endpoint
- u = max(min(u, 1.0), 0.0)
- return _connect_point3_plane(Point3(L.p.x + u * L.v.x,
- L.p.y + u * L.v.y,
- L.p.z + u * L.v.z), P)
- # Intersection
- return None
-
-def _connect_sphere_line3(S, L):
- d = L.v.magnitude_squared()
- assert d != 0
- u = ((S.c.x - L.p.x) * L.v.x + \
- (S.c.y - L.p.y) * L.v.y + \
- (S.c.z - L.p.z) * L.v.z) / d
- if not L._u_in(u):
- u = max(min(u, 1.0), 0.0)
- point = Point3(L.p.x + u * L.v.x, L.p.y + u * L.v.y, L.p.z + u * L.v.z)
- v = (point - S.c)
- v.normalize()
- v *= S.r
- return LineSegment3(Point3(S.c.x + v.x, S.c.y + v.y, S.c.z + v.z),
- point)
-
-def _connect_sphere_sphere(A, B):
- v = B.c - A.c
- v.normalize()
- return LineSegment3(Point3(A.c.x + v.x * A.r,
- A.c.y + v.y * A.r,
- A.c.x + v.z * A.r),
- Point3(B.c.x + v.x * B.r,
- B.c.y + v.y * B.r,
- B.c.x + v.z * B.r))
-
-def _connect_sphere_plane(S, P):
- c = _connect_point3_plane(S.c, P)
- if not c:
- return None
- p2 = c.p2
- v = p2 - S.c
- v.normalize()
- v *= S.r
- return LineSegment3(Point3(S.c.x + v.x, S.c.y + v.y, S.c.z + v.z),
- p2)
-
-def _connect_plane_plane(A, B):
- if A.n.cross(B.n):
- # Planes intersect
- return None
- else:
- # Planes are parallel, connect to arbitrary point
- return _connect_point3_plane(A._get_point(), B)
-
-def _intersect_point3_sphere(P, S):
- return abs(P - S.c) <= S.r
-
-def _intersect_line3_sphere(L, S):
- a = L.v.magnitude_squared()
- b = 2 * (L.v.x * (L.p.x - S.c.x) + \
- L.v.y * (L.p.y - S.c.y) + \
- L.v.z * (L.p.z - S.c.z))
- c = S.c.magnitude_squared() + \
- L.p.magnitude_squared() - \
- 2 * S.c.dot(L.p) - \
- S.r ** 2
- det = b ** 2 - 4 * a * c
- if det < 0:
- return None
- sq = math.sqrt(det)
- u1 = (-b + sq) / (2 * a)
- u2 = (-b - sq) / (2 * a)
- if not L._u_in(u1):
- u1 = max(min(u1, 1.0), 0.0)
- if not L._u_in(u2):
- u2 = max(min(u2, 1.0), 0.0)
- return LineSegment3(Point3(L.p.x + u1 * L.v.x,
- L.p.y + u1 * L.v.y,
- L.p.z + u1 * L.v.z),
- Point3(L.p.x + u2 * L.v.x,
- L.p.y + u2 * L.v.y,
- L.p.z + u2 * L.v.z))
-
-def _intersect_line3_plane(L, P):
- d = P.n.dot(L.v)
- if not d:
- # Parallel
- return None
- u = (P.k - P.n.dot(L.p)) / d
- if not L._u_in(u):
- return None
- return Point3(L.p.x + u * L.v.x,
- L.p.y + u * L.v.y,
- L.p.z + u * L.v.z)
-
-def _intersect_plane_plane(A, B):
- n1_m = A.n.magnitude_squared()
- n2_m = B.n.magnitude_squared()
- n1d2 = A.n.dot(B.n)
- det = n1_m * n2_m - n1d2 ** 2
- if det == 0:
- # Parallel
- return None
- c1 = (A.k * n2_m - B.k * n1d2) / det
- c2 = (B.k * n1_m - A.k * n1d2) / det
- return Line3(Point3(c1 * A.n.x + c2 * B.n.x,
- c1 * A.n.y + c2 * B.n.y,
- c1 * A.n.z + c2 * B.n.z),
- A.n.cross(B.n))
-
-class Point3(Vector3, Geometry):
- def __repr__(self):
- return 'Point3(%.2f, %.2f, %.2f)' % (self.x, self.y, self.z)
-
- def intersect(self, other):
- return other._intersect_point3(self)
-
- def _intersect_sphere(self, other):
- return _intersect_point3_sphere(self, other)
-
- def connect(self, other):
- return other._connect_point3(self)
-
- def _connect_point3(self, other):
- if self != other:
- return LineSegment3(other, self)
- return None
-
- def _connect_line3(self, other):
- c = _connect_point3_line3(self, other)
- if c:
- return c._swap()
-
- def _connect_sphere(self, other):
- c = _connect_point3_sphere(self, other)
- if c:
- return c._swap()
-
- def _connect_plane(self, other):
- c = _connect_point3_plane(self, other)
- if c:
- return c._swap()
-
-class Line3:
- __slots__ = ['p', 'v']
-
- def __init__(self, *args):
- if len(args) == 3:
- assert isinstance(args[0], Point3) and \
- isinstance(args[1], Vector3) and \
- type(args[2]) == float
- self.p = args[0].copy()
- self.v = args[1] * args[2] / abs(args[1])
- elif len(args) == 2:
- if isinstance(args[0], Point3) and isinstance(args[1], Point3):
- self.p = args[0].copy()
- self.v = args[1] - args[0]
- elif isinstance(args[0], Point3) and isinstance(args[1], Vector3):
- self.p = args[0].copy()
- self.v = args[1].copy()
- else:
- raise AttributeError, '%r' % (args,)
- elif len(args) == 1:
- if isinstance(args[0], Line3):
- self.p = args[0].p.copy()
- self.v = args[0].v.copy()
- else:
- raise AttributeError, '%r' % (args,)
- else:
- raise AttributeError, '%r' % (args,)
-
- # XXX This is annoying.
- #if not self.v:
- # raise AttributeError, 'Line has zero-length vector'
-
- def __copy__(self):
- return self.__class__(self.p, self.v)
-
- copy = __copy__
-
- def __repr__(self):
- return 'Line3(<%.2f, %.2f, %.2f> + u<%.2f, %.2f, %.2f>)' % \
- (self.p.x, self.p.y, self.p.z, self.v.x, self.v.y, self.v.z)
-
- p1 = property(lambda self: self.p)
- p2 = property(lambda self: Point3(self.p.x + self.v.x,
- self.p.y + self.v.y,
- self.p.z + self.v.z))
-
- def _apply_transform(self, t):
- self.p = t * self.p
- self.v = t * self.v
-
- def _u_in(self, u):
- return True
-
- def intersect(self, other):
- return other._intersect_line3(self)
-
- def _intersect_sphere(self, other):
- return _intersect_line3_sphere(self, other)
-
- def _intersect_plane(self, other):
- return _intersect_line3_plane(self, other)
-
- def connect(self, other):
- return other._connect_line3(self)
-
- def _connect_point3(self, other):
- return _connect_point3_line3(other, self)
-
- def _connect_line3(self, other):
- return _connect_line3_line3(other, self)
-
- def _connect_sphere(self, other):
- return _connect_sphere_line3(other, self)
-
- def _connect_plane(self, other):
- c = _connect_line3_plane(self, other)
- if c:
- return c
-
-class Ray3(Line3):
- def __repr__(self):
- return 'Ray3(<%.2f, %.2f, %.2f> + u<%.2f, %.2f, %.2f>)' % \
- (self.p.x, self.p.y, self.p.z, self.v.x, self.v.y, self.v.z)
-
- def _u_in(self, u):
- return u >= 0.0
-
-class LineSegment3(Line3):
- def __repr__(self):
- return 'LineSegment3(<%.2f, %.2f, %.2f> to <%.2f, %.2f, %.2f>)' % \
- (self.p.x, self.p.y, self.p.z,
- self.p.x + self.v.x, self.p.y + self.v.y, self.p.z + self.v.z)
-
- def _u_in(self, u):
- return u >= 0.0 and u <= 1.0
-
- def __abs__(self):
- return abs(self.v)
-
- def magnitude_squared(self):
- return self.v.magnitude_squared()
-
- def _swap(self):
- # used by connect methods to switch order of points
- self.p = self.p2
- self.v *= -1
- return self
-
- length = property(lambda self: abs(self.v))
-
-class Sphere:
- __slots__ = ['c', 'r']
-
- def __init__(self, center, radius):
- assert isinstance(center, Vector3) and type(radius) == float
- self.c = center.copy()
- self.r = radius
-
- def __copy__(self):
- return self.__class__(self.c, self.r)
-
- copy = __copy__
-
- def __repr__(self):
- return 'Sphere(<%.2f, %.2f, %.2f>, radius=%.2f)' % \
- (self.c.x, self.c.y, self.c.z, self.r)
-
- def _apply_transform(self, t):
- self.c = t * self.c
-
- def intersect(self, other):
- return other._intersect_sphere(self)
-
- def _intersect_point3(self, other):
- return _intersect_point3_sphere(other, self)
-
- def _intersect_line3(self, other):
- return _intersect_line3_sphere(other, self)
-
- def connect(self, other):
- return other._connect_sphere(self)
-
- def _connect_point3(self, other):
- return _connect_point3_sphere(other, self)
-
- def _connect_line3(self, other):
- c = _connect_sphere_line3(self, other)
- if c:
- return c._swap()
-
- def _connect_sphere(self, other):
- return _connect_sphere_sphere(other, self)
-
- def _connect_plane(self, other):
- c = _connect_sphere_plane(self, other)
- if c:
- return c
-
-class Plane:
- # n.p = k, where n is normal, p is point on plane, k is constant scalar
- __slots__ = ['n', 'k']
-
- def __init__(self, *args):
- if len(args) == 3:
- assert isinstance(args[0], Point3) and \
- isinstance(args[1], Point3) and \
- isinstance(args[2], Point3)
- self.n = (args[1] - args[0]).cross(args[2] - args[0])
- self.n.normalize()
- self.k = self.n.dot(args[0])
- elif len(args) == 2:
- if isinstance(args[0], Point3) and isinstance(args[1], Vector3):
- self.n = args[1].normalized()
- self.k = self.n.dot(args[0])
- elif isinstance(args[0], Vector3) and type(args[1]) == float:
- self.n = args[0].normalized()
- self.k = args[1]
- else:
- raise AttributeError, '%r' % (args,)
-
- else:
- raise AttributeError, '%r' % (args,)
-
- if not self.n:
- raise AttributeError, 'Points on plane are colinear'
-
- def __copy__(self):
- return self.__class__(self.n, self.k)
-
- copy = __copy__
-
- def __repr__(self):
- return 'Plane(<%.2f, %.2f, %.2f>.p = %.2f)' % \
- (self.n.x, self.n.y, self.n.z, self.k)
-
- def _get_point(self):
- # Return an arbitrary point on the plane
- if self.n.z:
- return Point3(0., 0., self.k / self.n.z)
- elif self.n.y:
- return Point3(0., self.k / self.n.y, 0.)
- else:
- return Point3(self.k / self.n.x, 0., 0.)
-
- def _apply_transform(self, t):
- p = t * self._get_point()
- self.n = t * self.n
- self.k = self.n.dot(p)
-
- def intersect(self, other):
- return other._intersect_plane(self)
-
- def _intersect_line3(self, other):
- return _intersect_line3_plane(other, self)
-
- def _intersect_plane(self, other):
- return _intersect_plane_plane(self, other)
-
- def connect(self, other):
- return other._connect_plane(self)
-
- def _connect_point3(self, other):
- return _connect_point3_plane(other, self)
-
- def _connect_line3(self, other):
- return _connect_line3_plane(other, self)
-
- def _connect_sphere(self, other):
- return _connect_sphere_plane(other, self)
-
- def _connect_plane(self, other):
- return _connect_plane_plane(other, self)
-
