python-scientific 2.8-4 / usr / share / pyshared / Scientific / Geometry / Objects3D.py

# This module defines some geometrical objects in 3D-space.
#
# Written by Konrad Hinsen <hinsen@cnrs-orleans.fr>
# last revision: 2007-4-27
#

"""
Geometrical objects in 3D space
"""

from Scientific.Geometry import Vector
from Scientific import N; Numeric = N

# Small number
_eps = 1.e-16

#
# The base class
#
class GeometricalObject3D:

    """
    Geometrical object in 3D space

    This is an abstract base class; to create instances, use one of
    the subclasses.
    """
 
    def intersectWith(self, other):
        """
        @param other: another geometrical object
        @type other: L{GeometricalObject3D}
        @returns: the geometrical object that results from the
        intersection with other. If there is no intersection,
        the result is C{None}.
        @rtype: L{GeometricalObject3D} or C{NoneType}
        @note: Intersection is not implemented for all possible
               pairs of objects. A 'ValueError' is raised for combinations
               that haven't been implemented yet.
        """
        if self.__class__ > other.__class__:
            self, other = other, self
        try:
            f, switch = _intersectTable[(self.__class__, other.__class__)]
            if switch:
                return f(other, self)
            else:
                return f(self, other)
        except KeyError:
            raise ValueError("Can't calculate intersection of " +
                             self.__class__.__name__ + " with " +
                             other.__class__.__name__)

    def hasPoint(self, point):
        """
        @param point: a point in space
        @type point: L{Scientific.Geometry.Vector}
        @returns: C{True} if point is in the object
        @rtype: C{bool}
        """
        return self.distanceFrom(point) < _eps

    def distanceFrom(self, point):
        """
        @param point: a point in space
        @type point: L{Scientific.Geometry.Vector}
        @returns the distance of point from the closest point of the object
        @rtype: C{float}
        """
        raise ValueError("not yet implemented")

    def volume(self):
        """
        @returns: the volume of the object. The result is C{None} for
                  unbounded objects and zero for lower-dimensional objects.
        @rtype: C{float} or C{NoneType}
        """
        raise ValueError("not yet implemented")

_intersectTable = {}

#
# Spheres
#
class Sphere(GeometricalObject3D):

    """
    Sphere
    """

    def __init__(self, center, radius):
        """
        @param center: the point that is the center of the sphere
        @type center: L{Scientific.Geometry.Vector}
        @param radius: the radius
        @type radius: C{float}
        """
        self.center = center
        self.radius = radius

    def volume(self):
        return (4.*Numeric.pi/3.) * self.radius**3

    def distanceFrom(self, point):
        d = (point-self.center).length() - self.radius
        if d < 0.:
            return 0.
        else:
            return d

#
# Planes
#
class Plane(GeometricalObject3D):

    """
    Plane
    """

    def __init__(self, *args):
        """
        There are two calling patterns:

          - Plane(point, normal), where point (a vector) is an arbitrary
            point in the plane and normal (a vector) indicated the direction
            normal to the plane.

          - Plane(p1, p2, p3), where each argument is a vector and describes
            a point in the plane. The three points may not be colinear.
        """
        if len(args) == 2:   # point, normal
            self.normal = args[1].normal()
            self.distance_from_zero = self.normal*args[0]
        else:                # three points
            v1 = args[1]-args[0]
            v2 = args[2]-args[1]
            self.normal = (v1.cross(v2)).normal()
            self.distance_from_zero = self.normal*args[1]

    def distanceFrom(self, point):
        return abs(self.normal*point-self.distance_from_zero)

    def projectionOf(self, point):
        """
        @param point: a point in space
        @type point: L{Scientific.Geometry.Vector}
        @returns: the projection of point onto the plane
        @rtype: L{Scientific.Geometry.Vector}
        """
        distance = self.normal*point-self.distance_from_zero
        return point - distance*self.normal

    def rotate(self, axis, angle):
        """
        @param axis: the rotation axis
        @type axis: L{Scientific.Geometry.Vector}
        @param angle: the rotation angle
        @type angle: C{float}
        @returns: a copy of the plane rotated around the coordinate origin
        @rtype: L{Plane}
        """
        point = rotatePoint(self.distance_from_zero*self.normal, axis, angle)
        normal = rotateDirection(self.normal, axis, angle)
        return Plane(point, normal)

    def volume(self):
        return 0.

#
# Infinite cones
#
class Cone(GeometricalObject3D):

    """
    Cone
    """

    def __init__(self, tip, axis, angle):
        """
        @param tip: the location of the tip
        @type tip: L{Scientific.Geometry.Vector}
        @param axis: direction of the symmetry axis
        @type axis: L{Scientific.Geometry.Vector}
        @param angle: the angle between the symmetry axis and the surface
        @type angle: C{float}
        """
        self.center = tip
        self.axis = axis.normal()
        self.angle = angle

    def volume(self):
        return None

#
# Circles
#
class Circle(GeometricalObject3D):

    """
    Circle
    """

    def __init__(self, center, normal, radius):
        """
        @param center: the location of the center
        @type center: L{Scientific.Geometry.Vector}
        @param normal: a direction nornal to the plane of the circle
        @type normal: L{Scientific.Geometry.Vector}
        @param radius: the radius of the circle
        @type radius: C{float}
        """
        self.center = center
        self.normal = normal
        self.radius = radius

    def volume(self):
        return 0.

#
# Lines
#
class Line(GeometricalObject3D):

    """
    Line
    """

    def __init__(self, point, direction):
        """
        @param point: any point on the line
        @type point: L{Scientific.Geometry.Vector}
        @param direction: the direction of the line
        @type direction: L{Scientific.Geometry.Vector}
        """
        self.point = point
        self.direction = direction.normal()

    def distanceFrom(self, point):
        d = self.point-point
        d = d - (d*self.direction)*self.direction
        return d.length()

    def projectionOf(self, point):
        """
        @param point: a point in space
        @type point: L{Scientific.Geometry.Vector}
        @returns: the projection of point onto the line
        @rtype: L{Scientific.Geometry.Vector}
        """
        d = self.point-point
        d = d - (d*self.direction)*self.direction
        return point+d

    def volume(self):
        return 0.

#
# Intersection calculations
#
def _addIntersectFunction(f, class1, class2):
    switch = class1 > class2
    if switch:
        class1, class2 = class2, class1
    _intersectTable[(class1, class2)] = (f, switch)

# Sphere with sphere

def _intersectSphereSphere(sphere1, sphere2):
    r1r2 = sphere2.center-sphere1.center
    d = r1r2.length()
    if d > sphere1.radius+sphere2.radius:
        return None
    if d+min(sphere1.radius, sphere2.radius) < \
                             max(sphere1.radius, sphere2.radius):
        return None
    x = 0.5*(d**2 + sphere1.radius**2 - sphere2.radius**2)/d
    h = Numeric.sqrt(sphere1.radius**2-x**2)
    normal = r1r2.normal()
    return Circle(sphere1.center + x*normal, normal, h)

_addIntersectFunction(_intersectSphereSphere, Sphere, Sphere)

# Sphere with cone

def _intersectSphereCone(sphere, cone):
    if sphere.center != cone.center:
        raise ValueError("Not yet implemented")
    from_center = sphere.radius*Numeric.cos(cone.angle)
    radius = sphere.radius*Numeric.sin(cone.angle)
    return Circle(cone.center+cone.axis*from_center, cone.axis, radius)

_addIntersectFunction(_intersectSphereCone, Sphere, Cone)

# Plane with plane

def _intersectPlanePlane(plane1, plane2):
    if abs(abs(plane1.normal*plane2.normal)-1.) < _eps:
        if abs(plane1.distance_from_zero-plane2.distance_from_zero) < _eps:
            return plane1
        else:
            return None
    else:
        direction = plane1.normal.cross(plane2.normal)
        point_in_1 = plane1.distance_from_zero*plane1.normal
        point_in_both = point_in_1 - (point_in_1*plane2.normal -
                                      plane2.distance_from_zero)*plane2.normal
        return Line(point_in_both, direction)

_addIntersectFunction(_intersectPlanePlane, Plane, Plane)

# Circle with plane

def _intersectCirclePlane(circle, plane):
    if abs(abs(circle.normal*plane.normal)-1.) < _eps:
        if plane.hasPoint(circle.center):
            return circle
        else:
            return None
    else:
        line = plane.intersectWith(Plane(circle.center, circle.normal))
        x = line.distanceFrom(circle.center)
        if x > circle.radius:
            return None
        else:
            angle = Numeric.arccos(x/circle.radius)
            along_line = Numeric.sin(angle)*circle.radius
            normal = circle.normal.cross(line.direction)
            if line.distanceFrom(circle.center+normal) > x:
                normal = -normal
            return (circle.center+x*normal-line.direction*along_line,
                    circle.center+x*normal+line.direction*along_line)
            
_addIntersectFunction(_intersectCirclePlane, Circle, Plane)

#
# Rotation
#
def rotateDirection(vector, axis, angle):
    s = Numeric.sin(angle)
    c = Numeric.cos(angle)
    c1 = 1-c
    axis = axis.direction
    return axis.cross(vector)*s + ((axis*vector)*axis)*c1 + vector*c

def rotatePoint(point, axis, angle):
    return axis.point + rotateDirection(point-axis.point, axis, angle)


#
# Lattices
#

#
# Lattice base class
#
class Lattice:

    def __init__(self, function):
        if function is not None:
            self.elements = map(function, self.elements)

    def __getitem__(self, item):
        return self.elements[item]

    def __setitem__(self, item, value):
        self.elements[item] = value

    def __len__(self):
        return len(self.elements)

#
# General rhombic lattice
#
class RhombicLattice(Lattice):

    """
    Lattice with rhombic elementary cell

    A lattice object contains values defined on a finite periodic
    structure that is created by replicating a given elementary
    cell along the three lattice vectors. The elementary cell can
    contain any number of points.
    """

    def __init__(self, elementary_cell, lattice_vectors, cells,
                 function=None, base=None):
        """
        @param elementary_cell: a list of the points in the elementary cell
        @type elementary_cell: C{list} of L{Scientific.Geometry.Vector}

        @param lattice_vectors: the edges of the elementary cell
        @type lattice_vectors: C{tuple} of three L{Scientific.Geometry.Vector}
        
        @param cells: a tuple of three integers, indicating how often the
                      elementary cell should be replicated along each
                      lattice vector
        @param cells: C{tuple} of C{int}

        @param function: the function to be applied to each point in the
                         lattice in order to obtain the value stored in the
                         lattice. If no function is specified, the point
                         itself becomes the value stored in the lattice.
        @type function: callable
        
        @param base: an offset added to all lattice points
        @type base: L{Scientific.Geometry.Vector}
        """
        if len(lattice_vectors) != len(cells):
            raise TypeError('Inconsistent dimension specification')
        if base is None:
            base = Vector(0, 0, 0)
        self.dimension = len(lattice_vectors)
        self.elements = []
        self.makeLattice(elementary_cell, lattice_vectors, cells, base)
        Lattice.__init__(self, function)

    def makeLattice(self, elementary_cell, lattice_vectors, cells, base):
        if len(cells) == 0:
            for p in elementary_cell:
                self.elements.append(p+base)
        else:
            for i in range(cells[0]):
                self.makeLattice(elementary_cell, lattice_vectors[1:],
                                 cells[1:], base+i*lattice_vectors[0])
            
#
# Bravais lattice
#
class BravaisLattice(RhombicLattice):

    """
    General Bravais lattice

    This is a subclass of RhombicLattice, describing the special case
    of an elementary cell containing one point.
    """

    def __init__(self, lattice_vectors, cells, function=None, base=None):
        """
        @param lattice_vectors: the edges of the elementary cell
        @type lattice_vectors: C{tuple} of three L{Scientific.Geometry.Vector}
        
        @param cells: a tuple of three integers, indicating how often the
                      elementary cell should be replicated along each
                      lattice vector
        @param cells: C{tuple} of C{int}

        @param function: the function to be applied to each point in the
                         lattice in order to obtain the value stored in the
                         lattice. If no function is specified, the point
                         itself becomes the value stored in the lattice.
        @type function: callable
        
        @param base: an offset added to all lattice points
        @type base: L{Scientific.Geometry.Vector}
        """
        cell = [Vector(0,0,0)]
        RhombicLattice.__init__(self, cell, lattice_vectors, cells,
                                function, base)

#
# Simple cubic lattice
#
class SCLattice(BravaisLattice):

    """Simple cubic lattice

    This is a subclass of BravaisLattice, describing the special case
    of a cubic elementary cell.
    """

    def __init__(self, cellsize, cells, function=None, base=None):
        """
        @param cellsize: the edge length of the cubic elementary cell
        @type cellsize: C{float}
        
        @param cells: a tuple of three integers, indicating how often the
                      elementary cell should be replicated along each
                      lattice vector
        @param cells: C{tuple} of C{int}

        @param function: the function to be applied to each point in the
                         lattice in order to obtain the value stored in the
                         lattice. If no function is specified, the point
                         itself becomes the value stored in the lattice.
        @type function: callable
        
        @param base: an offset added to all lattice points
        @type base: L{Scientific.Geometry.Vector}
        """
        lattice_vectors = (cellsize*Vector(1., 0., 0.),
                           cellsize*Vector(0., 1., 0.),
                           cellsize*Vector(0., 0., 1.))
        if type(cells) != type(()):
            cells = 3*(cells,)
        BravaisLattice.__init__(self, lattice_vectors, cells, function, base)