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# along with this program; if not, write to the Free Software
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# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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This module provides the Point and Vector classes that are used for 3D math
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computation, such as coordinates system conversion.
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In Soya 3D, a position is defined by 3 coordinates
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(x, y, z) AND the coordinates system in which the coordinates are defined
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(sometime called the "parent").
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Points and Vectors are used for math computation; my own experience in 3D
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has convinced me that ANY complicated 3D computation can be heavily
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simplified by the use of coordinates system conversions. As Soya 3D
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associates the coordinates system along with the coordinates values, it
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performs coordinates system conversion automagically !"""
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def __deepcopy__(self, memo):
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# Do not clone the parent (except if already cloned before, in the memo) !
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red = self.__reduce__()
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memo[id(self)] = clone
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if self.parent and (not id(self.parent) in memo.keys()):
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state = (None, state[1], state[2], state[3])
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s2 = copy.deepcopy(state, memo)
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clone.__setstate__(s2)
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class Point(Parentable, _soya._Point):
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class Vector(Parentable, _soya._Vector):
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__all__ = ["Point", "Vector"]
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#Vector = _soya.Vector
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#def soya_generic_reduce (obj):
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# return (soya._soya_reconstructor, (obj.__class__, ), obj.__getstate__())
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#copy_reg.constructor(Point)
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#copy_reg.constructor(Vector)
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#copy_reg.pickle(Point, soya_generic_reduce, soya._soya_reconstructor)
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#copy_reg.pickle(Vector, soya_generic_reduce, soya._soya_reconstructor)
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## class Point(_soya.Point):
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## #class Point(object):
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## "A Point is a 3D position."
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## def __init__(self, parent = None, x = 0.0, y = 0.0, z = 0.0):
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## """Point(parent = None, x = 0.0, y = 0.0, z = 0.0)
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## Creates a new Point, with coordinates X, Y and Z, defined in the coordinates
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## _soya.Point.__init__(self, parent, x, y, z)
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## # Very common error
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## #assert parent.__class__ is not float, "Parent must be a coordinate system !!!"
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## if parent.__class__ is float: raise TypeError, "Parent must be a coordinate system !!!"
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## self.parent = parent
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## def get_root(self):
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## """Point.get_root() -> World
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## Gets the root parent of a Point. The root parent is the root World of the
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## hierarchy (often called the "scene" object)."""
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## if self.parent: return self.parent.get_root()
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## def set_xyz(self, x, y, z):
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## """Point.set_xyz(x, y, z)
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## Sets the coordinates of a point to X, Y and Z."""
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## def move(self, position):
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## """Point.move(position)
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## Moves a Point to POSITION (a Point or another 3D object, such as a World,
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## Coordinates system conversion is performed if needed (=if the Point and
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## POSITION are not defined in the same coordinates system)."""
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## if (not position.parent) or (not self.parent) or (self.parent is position.parent):
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## self.x = position.x
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## self.y = position.y
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## self.z = position.z
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## self.x, self.y, self.z = self.parent.transform_point(position.x, position.y, position.z, position.parent)
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## def convert_to(self, parent):
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## """Point.convert_to(parent)
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## Converts a Point to the coordinates system PARENT in place. The x, y and z
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## coordinates are modified, and the Point's parent is set to PARENT."""
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## self.x, self.y, self.z = parent.transform_point(self.x, self.y, self.z, self.parent)
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## self.parent = parent
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## __imod__ = convert_to
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## """Point.copy() -> Point
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## Returns a copy of a Point."""
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## return Point(self.parent, self.x, self.y, self.z)
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## def clone(self, other):
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## """Point.clone(other)
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## Changes IN PLACE this Point so as it is a clone of OTHER."""
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## self.parent = other.parent
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## def __mod__(self, coordsyst):
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## """Point % coordsyst -> Point
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## Converts a Point to the coordinates system COORDSYST and returns the result.
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## The returned value may be the same Point if its coordinates system is
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## already COORDSYST, so you should be carreful if you modify it."""
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## if (not self.parent) or (not coordsyst) or (self.parent is coordsyst): return self
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## p = Point(self.parent, self.x, self.y, self.z)
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## p.convert_to(coordsyst)
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## def __add__(self, vector):
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## """Point + Vector -> Point
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## Translates a Point and returns the result (a new Point).
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## Coordinates system conversion is performed if needed (=if the Point and
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## VECTOR are not defined in the same coordinates system)."""
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## if (not vector.parent) or (not self.parent) or (self.parent is vector.parent):
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## return Point(self.parent, self.x + vector.x, self.y + vector.y, self.z + vector.z)
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## x, y, z = self.parent.transform_vector(vector.x, vector.y, vector.z, vector.parent)
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## return Point(self.parent, self.x + x, self.y + y, self.z + z)
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## def __sub__(self, vector):
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## """Point - Vector -> Point
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## Translates a Point and returns the result (a new Point).
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## Coordinates system conversion is performed if needed (=if the Point and
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## VECTOR are not defined in the same coordinates system)."""
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## if (not vector.parent) or (not self.parent) or (self.parent is vector.parent):
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## return Point(self.parent, self.x - vector.x, self.y - vector.y, self.z - vector.z)
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## x, y, z = self.parent.transform_vector(vector.x, vector.y, vector.z, vector.parent)
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## return Point(self.parent, self.x - x, self.y - y, self.z - z)
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## def add_xyz(self, x, y, z):
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## """Point.add_xyz(x, y, z)
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## Translates the coordinates of a point by X, Y and Z."""
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## def add_vector(self, vector):
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## """Point.add_vector(vector)
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## Translates a Point IN PLACE.
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## Coordinates system conversion is performed if needed (=if the Point and
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## VECTOR are not defined in the same coordinates system).
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## For Vector, add_vector means vectorial addition (translating a vector does
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## if (not vector.parent) or (not self.parent) or (self.parent is vector.parent):
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## self.x += vector.x
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## self.y += vector.y
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## self.z += vector.z
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## x, y, z = self.parent.transform_vector(vector.x, vector.y, vector.z, vector.parent)
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## __iadd__ = add_vector
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## def add_mul_vector(self, k, vector):
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## """Point.add_mul_vector(k, vector)
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## Translates a Point IN PLACE, by K * VECTOR.
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## Coordinates system conversion is performed if needed (=if the Point and
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## VECTOR are not defined in the same coordinates system).
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## For Vector, add_vector means vectorial addition (translating a vector does
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## if (not vector.parent) or (not self.parent) or (self.parent is vector.parent):
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## self.x += k * vector.x
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## self.y += k * vector.y
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## self.z += k * vector.z
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## x, y, z = self.parent.transform_vector(vector.x, vector.y, vector.z, vector.parent)
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## def distance_to(self, other):
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## """Point.distance_to(other) -> float
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## Gets the distance between a Point and anOTHER."""
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## if (not other.parent) or (not self.parent) or (self.parent is other.parent):
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## return math.sqrt((self.x - other.x) ** 2 + (self.y - other.y) ** 2 + (self.z - other.z) ** 2)
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## x, y, z = self.parent.transform_point(other.x, other.y, other.z, other.parent)
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## return math.sqrt((self.x - x) ** 2 + (self.y - y) ** 2 + (self.z - z) ** 2)
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## def vector_to(self, other):
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## """Point.vector_to(other) -> Vector
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## Gets the vector that starts at a Point and ends at OTHER."""
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## if (not other.parent) or (not self.parent) or (self.parent is other.parent):
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## return Vector(self.parent, other.x - self.x, other.y - self.y, other.z - self.z)
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## x, y, z = self.parent.transform_point(other.x, other.y, other.z, other.parent)
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## return Vector(self.parent, x - self.x, y - self.y, z - self.z)
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## __rshift__ = vector_to
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## def __eq__(self, other):
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## return hasattr(other, "x") and hasattr(other, "y") and hasattr(other, "z") and hasattr(other, "parent") and (self.parent is other.parent) and (self.x == other.x) and (self.y == other.y) and (self.z == other.z)
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## def __ne__(self, other):
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## return hasattr(other, "x") and hasattr(other, "y") and hasattr(other, "z") and hasattr(other, "parent") and (not (self.parent is other.parent) and (self.x == other.x) and (self.y == other.y) and (self.z == other.z))
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## def __repr__(self): return "<Point %s, %s, %s in %s>" % (self.x, self.y, self.z, self.parent)
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## # def __deepcopy__(self, memo):
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## # # Don't copy the parent !
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## # red = self.__reduce__()
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## # clone = _Empty()
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## # clone.__class__ = red[1][0]
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## # memo[id(self)] = clone
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## # if state is self.__dict__: state = state.copy()
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## # copy._keep_alive(state, memo)
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## # if not id(self.parent) in memo.keys():
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## # del state["parent"]
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## # state = copy.deepcopy(state, memo)
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## # state["parent"] = self.parent
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## # state = copy.deepcopy(state, memo)
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## # copy._keep_alive(state, memo)
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## # if hasattr(clone, "__setstate__"): clone.__setstate__(state)
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## # else: clone.__dict__ = state
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## def __deepcopy__(self, memo):
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## # Do not clone the parent (except if already cloned before, in the memo) !
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## red = self.__reduce__()
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## clone = red[1][0]()
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## memo[id(self)] = clone
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## if not id(self.parent) in memo.keys():
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## state = copy.copy(state)
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## state["parent"] = None
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## s2 = copy.deepcopy(state, memo)
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## if hasattr(clone, "__setstate__"): clone.__setstate__(s2)
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## else: clone.__dict__ = s2
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## class Vector(_soya.Vector):
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## #class Vector(Point):
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## """A Vector is a 3D vector (and not a kind of list or sequence ;-). Vectors are
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## usefull for 3D math computation.
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## Most of the math operator, such as +, -, *, /, abs,... work on Vectors and do
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## what they are intended to do ;-)
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## Vector inherits from Point for practical reasons, since both have x, y, z
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## coordinates and a parent."""
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## def __init__(_self, _parent = None, _x = 0.0, _y = 0.0, _z = 0.0):
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## _soya.Vector.__init__(_self, _parent, _x, _y, _z)
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## def move(self, position):
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## """Vector.move(position)
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## Moves a Vector to POSITION (a Vector).
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## Coordinates system conversion is performed if needed (=if the Vector and
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## POSITION are not defined in the same coordinates system)."""
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## if (not position.parent) or (not self.parent) or (self.parent is position.parent):
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## self.x = position.x
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## self.y = position.y
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## self.z = position.z
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## self.x, self.y, self.z = self.parent.transform_vector(position.x, position.y, position.z, position.parent)
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## def convert_to(self, parent):
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## """Vector.convert_to(parent)
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## Converts a Vector to the coordinates system PARENT in place. The x, y and z
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## coordinates are modified, and the Vector's parent is set to PARENT."""
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## if parent: self.x, self.y, self.z = parent.transform_vector(self.x, self.y, self.z, self.parent)
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## self.parent = parent
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## __imod__ = convert_to
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## """Vector.copy() -> Vector
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## Returns a copy of a Vector."""
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## return Vector(self.parent, self.x, self.y, self.z)
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## def cross_product(self, vector):
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## """Vector.cross_product(VECTOR) -> Vector
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## Returns the cross product of a Vector with VECTOR."""
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## return _soya.cross_vector(self, vector)
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## def dot_product(self, vector):
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## """Vector.dot_product(VECTOR) -> float
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## Returns the dot product of a Vector with VECTOR."""
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## if (not vector.parent) or (not self.parent) or (self.parent is vector.parent):
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## return self.x * vector.x + self.y * vector.y + self.z * vector.z
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## x, y, z = self.parent.transform_vector(vector.x, vector.y, vector.z, vector.parent)
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## return self.x * x + self.y * y + self.z * z
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## """Vector.length() -> float
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## Gets the length of a Vector."""
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## return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
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## def set_length(self, new_length):
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## """Vector.set_length(new_length)
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## Sets the length of a Vector to NEW_LENGTH. The Vector's coordinates are
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## multiplicated as needed."""
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## f = new_length / self.length()
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## def __mod__(self, coordsyst):
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## """Vector % coordsyst -> Vector
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## Converts a Vector to the coordinates system COORDSYST and returns the result.
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## The returned value may be the same Vector if its coordinates system is
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## already COORDSYST, so you should be carreful if you modify it."""
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## if (not self.parent) or (not coordsyst) or (self.parent is coordsyst): return self
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## v = Vector(self.parent, self.x, self.y, self.z)
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## v.convert_to(coordsyst)
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## def __mul__(self, number): return Vector(self.parent, self.x * number, self.y * number, self.z * number)
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## def __div__(self, number): return Vector(self.parent, self.x / number, self.y / number, self.z / number)
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## __truediv__ = __div__
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## def __imul__(self, number):
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## def __idiv__(self, number):
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## def __add__(self, vector):
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## if (not vector.parent) or (not self.parent) or (self.parent is vector.parent):
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## return Vector(self.parent, self.x + vector.x, self.y + vector.y, self.z + vector.z)
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## x, y, z = self.parent.transform_vector(vector.x, vector.y, vector.z, vector.parent)
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## return Vector(self.parent, self.x + x, self.y + y, self.z + z)
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## def __sub__(self, vector):
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## if (not vector.parent) or (not self.parent) or (self.parent is vector.parent):
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## return Vector(self.parent, self.x - vector.x, self.y - vector.y, self.z - vector.z)
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## x, y, z = self.parent.transform_vector(vector.x, vector.y, vector.z, vector.parent)
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## return Vector(self.parent, self.x - x, self.y - y, self.z - z)
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## def __neg__(self): return Vector(self.parent, -self.x, -self.y, -self.z)
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## def __abs__(self): return Vector(self.parent, abs(self.x), abs(self.y), abs(self.z))
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## def normalize(self):
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## """Vector.normalize()
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## Normalizes a Vector IN PLACE."""
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## length = self.length()
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## def __repr__(self): return "<Vector %s, %s, %s in %s>" % (self.x, self.y, self.z, self.parent)
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## def set_start_end(self, start, end):
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## """Vector.set_start_end(start, end)
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## Sets this vector IN PLACE so as it correspond to the vector start->end."""
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## self.parent = start.parent
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## if (not start.parent) or (not end.parent) or (start.parent is end.parent):
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## self.x = end.x - start.x
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## self.y = end.y - start.y
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## self.z = end.z - start.z
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## x, y, z = self.parent.transform_point(end.x, end.y, end.z, end.parent)
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## self.x = x - start.x
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## self.y = y - start.y
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## self.z = z - start.z
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## def angle_to(self, vector):
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## """Vector.angle_to(VECTOR) -> angle in degree
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## Computes the angle between this Vector and VECTOR."""
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## vector = vector % self.parent
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## s = self.length() * vector.length()
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## f = self.dot_product(vector) / s
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## if f >= 1.0: return 0.0
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## if f <= -1.0: return 180.0
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## return (math.atan(-f / math.sqrt(1.0 - f * f)) + math.pi / 2.0) * 180.0 / math.pi
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_soya.new_point = Point
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_soya.new_vector = Vector
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warnings.warn("The content of this module is now in the soya module.", DeprecationWarning)
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from soya import Point, Vector
added
removed
math3d.py
