* Bug fixes by Stéphane Grabli with respect to pyZDependingThicknessShader,

pyMaterialColorShader, pyBluePrintEllipsesShader and pyBluePrintSquaresShader.

* Fixes for Vector instantiation that now takes only a sequence object of
2, 3, or 4 elements -- an API change in revision 28417.

* Deleted vector.py that is no longer used.
This commit is contained in:
Tamito Kajiyama 2010-07-06 20:07:07 +00:00
parent ae9b9b43e6
commit d347a27a97
3 changed files with 53 additions and 288 deletions

@ -62,7 +62,7 @@ class pyViewMapGradientVectorF0D(UnaryFunction0DVec2f):
p = iter.getObject().getPoint2D() p = iter.getObject().getPoint2D()
gx = ReadCompleteViewMapPixelCF(self._l, int(p.x()+self._step), int(p.y()))- ReadCompleteViewMapPixelCF(self._l, int(p.x()), int(p.y())) gx = ReadCompleteViewMapPixelCF(self._l, int(p.x()+self._step), int(p.y()))- ReadCompleteViewMapPixelCF(self._l, int(p.x()), int(p.y()))
gy = ReadCompleteViewMapPixelCF(self._l, int(p.x()), int(p.y()+self._step))- ReadCompleteViewMapPixelCF(self._l, int(p.x()), int(p.y())) gy = ReadCompleteViewMapPixelCF(self._l, int(p.x()), int(p.y()+self._step))- ReadCompleteViewMapPixelCF(self._l, int(p.x()), int(p.y()))
return Vector(gx, gy) return Vector([gx, gy])
class pyViewMapGradientNormF0D(UnaryFunction0DDouble): class pyViewMapGradientNormF0D(UnaryFunction0DDouble):
def __init__(self, l): def __init__(self, l):
@ -75,7 +75,7 @@ class pyViewMapGradientNormF0D(UnaryFunction0DDouble):
p = iter.getObject().getPoint2D() p = iter.getObject().getPoint2D()
gx = ReadCompleteViewMapPixelCF(self._l, int(p.x()+self._step), int(p.y()))- ReadCompleteViewMapPixelCF(self._l, int(p.x()), int(p.y())) gx = ReadCompleteViewMapPixelCF(self._l, int(p.x()+self._step), int(p.y()))- ReadCompleteViewMapPixelCF(self._l, int(p.x()), int(p.y()))
gy = ReadCompleteViewMapPixelCF(self._l, int(p.x()), int(p.y()+self._step))- ReadCompleteViewMapPixelCF(self._l, int(p.x()), int(p.y())) gy = ReadCompleteViewMapPixelCF(self._l, int(p.x()), int(p.y()+self._step))- ReadCompleteViewMapPixelCF(self._l, int(p.x()), int(p.y()))
grad = Vector(gx, gy) grad = Vector([gx, gy])
return grad.length return grad.length

@ -307,11 +307,11 @@ class pyImportance2DThicknessShader(StrokeShader):
def getName(self): def getName(self):
return "pyImportanceThicknessShader" return "pyImportanceThicknessShader"
def shade(self, stroke): def shade(self, stroke):
origin = Vector(self._x, self._y) origin = Vector([self._x, self._y])
it = stroke.strokeVerticesBegin() it = stroke.strokeVerticesBegin()
while it.isEnd() == 0: while it.isEnd() == 0:
v = it.getObject() v = it.getObject()
p = Vector(v.getProjectedX(), v.getProjectedY()) p = Vector([v.getProjectedX(), v.getProjectedY()])
d = (p-origin).length d = (p-origin).length
if(d>self._w): if(d>self._w):
k = self._kmin k = self._kmin
@ -336,11 +336,11 @@ class pyImportance3DThicknessShader(StrokeShader):
def getName(self): def getName(self):
return "pyImportance3DThicknessShader" return "pyImportance3DThicknessShader"
def shade(self, stroke): def shade(self, stroke):
origin = Vector(self._x, self._y, self._z) origin = Vector([self._x, self._y, self._z])
it = stroke.strokeVerticesBegin() it = stroke.strokeVerticesBegin()
while it.isEnd() == 0: while it.isEnd() == 0:
v = it.getObject() v = it.getObject()
p = Vector(v.getX(), v.getY(), v.getZ()) p = Vector([v.getX(), v.getY(), v.getZ()])
d = (p-origin).length d = (p-origin).length
if(d>self._w): if(d>self._w):
k = self._kmin k = self._kmin
@ -368,7 +368,7 @@ class pyZDependingThicknessShader(StrokeShader):
z = self.__func(it.castToInterface0DIterator()) z = self.__func(it.castToInterface0DIterator())
if z < z_min: if z < z_min:
z_min = z z_min = z
elif z > z_max: if z > z_max:
z_max = z z_max = z
it.increment() it.increment()
z_diff = 1 / (z_max - z_min) z_diff = 1 / (z_max - z_min)
@ -507,6 +507,10 @@ class pyMaterialColorShader(StrokeShader):
g = -0.969256 * X + 1.875991 * Y + 0.041556 * Z g = -0.969256 * X + 1.875991 * Y + 0.041556 * Z
b = 0.055648 * X - 0.204043 * Y + 1.057311 * Z b = 0.055648 * X - 0.204043 * Y + 1.057311 * Z
r = max(0,r)
g = max(0,g)
b = max(0,b)
att = it.getObject().attribute() att = it.getObject().attribute()
att.setColor(r, g, b) att.setColor(r, g, b)
it.increment() it.increment()
@ -592,10 +596,10 @@ class pyBackboneStretcherShader(StrokeShader):
v1 = it1.getObject() v1 = it1.getObject()
vn_1 = itn_1.getObject() vn_1 = itn_1.getObject()
vn = itn.getObject() vn = itn.getObject()
p0 = Vector(v0.getProjectedX(), v0.getProjectedY()) p0 = Vector([v0.getProjectedX(), v0.getProjectedY()])
pn = Vector(vn.getProjectedX(), vn.getProjectedY()) pn = Vector([vn.getProjectedX(), vn.getProjectedY()])
p1 = Vector(v1.getProjectedX(), v1.getProjectedY()) p1 = Vector([v1.getProjectedX(), v1.getProjectedY()])
pn_1 = Vector(vn_1.getProjectedX(), vn_1.getProjectedY()) pn_1 = Vector([vn_1.getProjectedX(), vn_1.getProjectedY()])
d1 = p0-p1 d1 = p0-p1
d1.normalize() d1.normalize()
dn = pn-pn_1 dn = pn-pn_1
@ -625,10 +629,10 @@ class pyLengthDependingBackboneStretcherShader(StrokeShader):
v1 = it1.getObject() v1 = it1.getObject()
vn_1 = itn_1.getObject() vn_1 = itn_1.getObject()
vn = itn.getObject() vn = itn.getObject()
p0 = Vector(v0.getProjectedX(), v0.getProjectedY()) p0 = Vector([v0.getProjectedX(), v0.getProjectedY()])
pn = Vector(vn.getProjectedX(), vn.getProjectedY()) pn = Vector([vn.getProjectedX(), vn.getProjectedY()])
p1 = Vector(v1.getProjectedX(), v1.getProjectedY()) p1 = Vector([v1.getProjectedX(), v1.getProjectedY()])
pn_1 = Vector(vn_1.getProjectedX(), vn_1.getProjectedY()) pn_1 = Vector([vn_1.getProjectedX(), vn_1.getProjectedY()])
d1 = p0-p1 d1 = p0-p1
d1.normalize() d1.normalize()
dn = pn-pn_1 dn = pn-pn_1
@ -777,8 +781,8 @@ class pyTVertexRemoverShader(StrokeShader):
class pyExtremitiesOrientationShader(StrokeShader): class pyExtremitiesOrientationShader(StrokeShader):
def __init__(self, x1,y1,x2=0,y2=0): def __init__(self, x1,y1,x2=0,y2=0):
StrokeShader.__init__(self) StrokeShader.__init__(self)
self._v1 = Vector(x1,y1) self._v1 = Vector([x1,y1])
self._v2 = Vector(x2,y2) self._v2 = Vector([x2,y2])
def getName(self): def getName(self):
return "pyExtremitiesOrientationShader" return "pyExtremitiesOrientationShader"
def shade(self, stroke): def shade(self, stroke):
@ -940,7 +944,7 @@ class pyPerlinNoise2DShader(StrokeShader):
it = stroke.strokeVerticesBegin() it = stroke.strokeVerticesBegin()
while it.isEnd() == 0: while it.isEnd() == 0:
v = it.getObject() v = it.getObject()
vec = Vector(v.getProjectedX(), v.getProjectedY()) vec = Vector([v.getProjectedX(), v.getProjectedY()])
nres = self.__noise.turbulence2(vec, self.__freq, self.__amp, self.__oct) nres = self.__noise.turbulence2(vec, self.__freq, self.__amp, self.__oct)
v.setPoint(v.getProjectedX() + nres, v.getProjectedY() + nres) v.setPoint(v.getProjectedX() + nres, v.getProjectedY() + nres)
it.increment() it.increment()
@ -952,8 +956,8 @@ class pyBluePrintCirclesShader(StrokeShader):
def getName(self): def getName(self):
return "pyBluePrintCirclesShader" return "pyBluePrintCirclesShader"
def shade(self, stroke): def shade(self, stroke):
p_min = Vector(10000, 10000) p_min = Vector([10000, 10000])
p_max = Vector(0, 0) p_max = Vector([0, 0])
it = stroke.strokeVerticesBegin() it = stroke.strokeVerticesBegin()
while it.isEnd() == 0: while it.isEnd() == 0:
p = it.getObject().getPoint() p = it.getObject().getPoint()
@ -976,7 +980,7 @@ class pyBluePrintCirclesShader(StrokeShader):
sv_nb = sv_nb / self.__turns sv_nb = sv_nb / self.__turns
center = (p_min + p_max) / 2 center = (p_min + p_max) / 2
radius = (center.x - p_min.x + center.y - p_min.y) / 2 radius = (center.x - p_min.x + center.y - p_min.y) / 2
p_new = Vector(0, 0) p_new = Vector([0, 0])
####################################################### #######################################################
it = stroke.strokeVerticesBegin() it = stroke.strokeVerticesBegin()
for j in range(self.__turns): for j in range(self.__turns):
@ -994,7 +998,6 @@ class pyBluePrintCirclesShader(StrokeShader):
stroke.RemoveVertex(it.getObject()) stroke.RemoveVertex(it.getObject())
it.increment() it.increment()
class pyBluePrintEllipsesShader(StrokeShader): class pyBluePrintEllipsesShader(StrokeShader):
def __init__(self, turns = 1): def __init__(self, turns = 1):
StrokeShader.__init__(self) StrokeShader.__init__(self)
@ -1002,8 +1005,8 @@ class pyBluePrintEllipsesShader(StrokeShader):
def getName(self): def getName(self):
return "pyBluePrintEllipsesShader" return "pyBluePrintEllipsesShader"
def shade(self, stroke): def shade(self, stroke):
p_min = Vector(10000, 10000) p_min = Vector([10000, 10000])
p_max = Vector(0, 0) p_max = Vector([0, 0])
it = stroke.strokeVerticesBegin() it = stroke.strokeVerticesBegin()
while it.isEnd() == 0: while it.isEnd() == 0:
p = it.getObject().getPoint() p = it.getObject().getPoint()
@ -1018,16 +1021,11 @@ class pyBluePrintEllipsesShader(StrokeShader):
it.increment() it.increment()
stroke.Resample(32 * self.__turns) stroke.Resample(32 * self.__turns)
sv_nb = stroke.strokeVerticesSize() sv_nb = stroke.strokeVerticesSize()
# print("min :", p_min.x, p_min.y) # DEBUG
# print("mean :", p_sum.x, p_sum.y) # DEBUG
# print("max :", p_max.x, p_max.y) # DEBUG
# print("----------------------") # DEBUG
#######################################################
sv_nb = sv_nb / self.__turns sv_nb = sv_nb / self.__turns
center = (p_min + p_max) / 2 center = (p_min + p_max) / 2
radius_x = center.x - p_min.x radius_x = center.x - p_min.x
radius_y = center.y - p_min.y radius_y = center.y - p_min.y
p_new = Vector(0, 0) p_new = Vector([0, 0])
####################################################### #######################################################
it = stroke.strokeVerticesBegin() it = stroke.strokeVerticesBegin()
for j in range(self.__turns): for j in range(self.__turns):
@ -1036,7 +1034,7 @@ class pyBluePrintEllipsesShader(StrokeShader):
center.x = center.x + randint(-5, 5) center.x = center.x + randint(-5, 5)
center.y = center.y + randint(-5, 5) center.y = center.y + randint(-5, 5)
i = 0 i = 0
while i < sv_nb: while i < sv_nb and it.isEnd() == 0:
p_new.x = center.x + radius_x * cos(2 * pi * float(i) / float(sv_nb - 1)) p_new.x = center.x + radius_x * cos(2 * pi * float(i) / float(sv_nb - 1))
p_new.y = center.y + radius_y * sin(2 * pi * float(i) / float(sv_nb - 1)) p_new.y = center.y + radius_y * sin(2 * pi * float(i) / float(sv_nb - 1))
it.getObject().setPoint(p_new) it.getObject().setPoint(p_new)
@ -1052,11 +1050,13 @@ class pyBluePrintSquaresShader(StrokeShader):
StrokeShader.__init__(self) StrokeShader.__init__(self)
self.__turns = turns self.__turns = turns
self.__bb_len = bb_len self.__bb_len = bb_len
def getName(self): def getName(self):
return "pyBluePrintSquaresShader" return "pyBluePrintSquaresShader"
def shade(self, stroke): def shade(self, stroke):
p_min = Vector(10000, 10000) p_min = Vector([10000, 10000])
p_max = Vector(0, 0) p_max = Vector([0, 0])
it = stroke.strokeVerticesBegin() it = stroke.strokeVerticesBegin()
while it.isEnd() == 0: while it.isEnd() == 0:
p = it.getObject().getPoint() p = it.getObject().getPoint()
@ -1077,20 +1077,20 @@ class pyBluePrintSquaresShader(StrokeShader):
second = 2 * first second = 2 * first
third = 3 * first third = 3 * first
fourth = sv_nb fourth = sv_nb
vec_first = Vector(p_max.x - p_min.x + 2 * self.__bb_len, 0) vec_first = Vector([p_max.x - p_min.x + 2 * self.__bb_len, 0])
vec_second = Vector(0, p_max.y - p_min.y + 2 * self.__bb_len) vec_second = Vector([0, p_max.y - p_min.y + 2 * self.__bb_len])
vec_third = vec_first * -1 vec_third = vec_first * -1
vec_fourth = vec_second * -1 vec_fourth = vec_second * -1
p_first = Vector(p_min.x - self.__bb_len, p_min.y) p_first = Vector([p_min.x - self.__bb_len, p_min.y])
p_second = Vector(p_max.x, p_min.y - self.__bb_len) p_second = Vector([p_max.x, p_min.y - self.__bb_len])
p_third = Vector(p_max.x + self.__bb_len, p_max.y) p_third = Vector([p_max.x + self.__bb_len, p_max.y])
p_fourth = Vector(p_min.x, p_max.y + self.__bb_len) p_fourth = Vector([p_min.x, p_max.y + self.__bb_len])
####################################################### #######################################################
it = stroke.strokeVerticesBegin() it = stroke.strokeVerticesBegin()
visible = 1 visible = 1
for j in range(self.__turns): for j in range(self.__turns):
i = 0 i = 0
while i < sv_nb: while i < sv_nb and it.isEnd() == 0:
if i < first: if i < first:
p_new = p_first + vec_first * float(i)/float(first - 1) p_new = p_first + vec_first * float(i)/float(first - 1)
if i == first - 1: if i == first - 1:
@ -1107,6 +1107,12 @@ class pyBluePrintSquaresShader(StrokeShader):
p_new = p_fourth + vec_fourth * float(i - third)/float(fourth - third - 1) p_new = p_fourth + vec_fourth * float(i - third)/float(fourth - third - 1)
if i == fourth - 1: if i == fourth - 1:
visible = 0 visible = 0
if it.getObject() == None:
i = i + 1
it.increment()
if visible == 0:
visible = 1
continue
it.getObject().setPoint(p_new) it.getObject().setPoint(p_new)
it.getObject().attribute().setVisible(visible) it.getObject().attribute().setVisible(visible)
if visible == 0: if visible == 0:
@ -1128,9 +1134,9 @@ class pyBluePrintDirectedSquaresShader(StrokeShader):
return "pyBluePrintDirectedSquaresShader" return "pyBluePrintDirectedSquaresShader"
def shade(self, stroke): def shade(self, stroke):
stroke.Resample(32 * self.__turns) stroke.Resample(32 * self.__turns)
p_mean = Vector(0, 0) p_mean = Vector([0, 0])
p_min = Vector(10000, 10000) p_min = Vector([10000, 10000])
p_max = Vector(0, 0) p_max = Vector([0, 0])
it = stroke.strokeVerticesBegin() it = stroke.strokeVerticesBegin()
while it.isEnd() == 0: while it.isEnd() == 0:
p = it.getObject().getPoint() p = it.getObject().getPoint()
@ -1169,11 +1175,11 @@ class pyBluePrintDirectedSquaresShader(StrokeShader):
theta = atan(2 * p_var_xy / (p_var_xx - p_var_yy)) / 2 theta = atan(2 * p_var_xy / (p_var_xx - p_var_yy)) / 2
## print(theta) ## print(theta)
if p_var_yy > p_var_xx: if p_var_yy > p_var_xx:
e1 = Vector(cos(theta + pi / 2), sin(theta + pi / 2)) * sqrt(lambda1) * self.__mult e1 = Vector([cos(theta + pi / 2), sin(theta + pi / 2)]) * sqrt(lambda1) * self.__mult
e2 = Vector(cos(theta + pi), sin(theta + pi)) * sqrt(lambda2) * self.__mult e2 = Vector([cos(theta + pi), sin(theta + pi)]) * sqrt(lambda2) * self.__mult
else: else:
e1 = Vector(cos(theta), sin(theta)) * sqrt(lambda1) * self.__mult e1 = Vector([cos(theta), sin(theta)]) * sqrt(lambda1) * self.__mult
e2 = Vector(cos(theta + pi / 2), sin(theta + pi / 2)) * sqrt(lambda2) * self.__mult e2 = Vector([cos(theta + pi / 2), sin(theta + pi / 2)]) * sqrt(lambda2) * self.__mult
####################################################### #######################################################
sv_nb = sv_nb / self.__turns sv_nb = sv_nb / self.__turns
first = sv_nb / 4 first = sv_nb / 4

@ -1,241 +0,0 @@
# This module defines 3d geometrical vectors with the standard
# operations on them.
#
# Written by: Konrad Hinsen
# Last revision: 1996-1-26
#
"""This module defines three-dimensional geometrical vectors. Vectors support
the usual mathematical operations (v1, v2: vectors, s: scalar):
v1+v2 addition
v1-v2 subtraction
v1*v2 scalar product
s*v1 multiplication with a scalar
v1/s division by a scalar
v1.cross(v2) cross product
v1.length() length
v1.normal() normal vector in direction of v1
v1.angle(v2) angle between two vectors
v1.x(), v1[0] first element
v1.y(), v1[1] second element
v1.z(), v1[2] third element
The module offers the following items for export:
Vec3D(x,y,z) the constructor for vectors
isVector(x) a type check function
ex, ey, ez unit vectors along the x-, y-, and z-axes (predefined constants)
Note: vector elements can be any kind of numbers on which the operations
addition, subtraction, multiplication, division, comparison, sqrt, and acos
are defined. Integer elements are treated as floating point elements.
"""
import math, types
class Vec3:
isVec3 = 1
def __init__(self, x=0., y=0., z=0.):
self.data = [x,y,z]
def __repr__(self):
return 'Vec3(%s,%s,%s)' % (`self.data[0]`,\
`self.data[1]`,`self.data[2]`)
def __str__(self):
return `self.data`
def __add__(self, other):
return Vec3(self.data[0]+other.data[0],\
self.data[1]+other.data[1],self.data[2]+other.data[2])
__radd__ = __add__
def __neg__(self):
return Vec3(-self.data[0], -self.data[1], -self.data[2])
def __sub__(self, other):
return Vec3(self.data[0]-other.data[0],\
self.data[1]-other.data[1],self.data[2]-other.data[2])
def __rsub__(self, other):
return Vec3(other.data[0]-self.data[0],\
other.data[1]-self.data[1],other.data[2]-self.data[2])
def __mul__(self, other):
if isVec3(other):
return reduce(lambda a,b: a+b,
map(lambda a,b: a*b, self.data, other.data))
else:
return Vec3(self.data[0]*other, self.data[1]*other,
self.data[2]*other)
def __rmul__(self, other):
if isVec3(other):
return reduce(lambda a,b: a+b,
map(lambda a,b: a*b, self.data, other.data))
else:
return Vec3(other*self.data[0], other*self.data[1],
other*self.data[2])
def __div__(self, other):
if isVec3(other):
raise TypeError, "Can't divide by a vector"
else:
return Vec3(_div(self.data[0],other), _div(self.data[1],other),
_div(self.data[2],other))
def __rdiv__(self, other):
raise TypeError, "Can't divide by a vector"
def __cmp__(self, other):
return cmp(self.data[0],other.data[0]) \
or cmp(self.data[1],other.data[1]) \
or cmp(self.data[2],other.data[2])
def __getitem__(self, index):
return self.data[index]
def x(self):
return self.data[0]
def y(self):
return self.data[1]
def z(self):
return self.data[2]
def length(self):
return math.sqrt(self*self)
def normal(self):
len = self.length()
if len == 0:
raise ZeroDivisionError, "Can't normalize a zero-length vector"
return self/len
def cross(self, other):
if not isVec3(other):
raise TypeError, "Cross product with non-vector"
return Vec3(self.data[1]*other.data[2]-self.data[2]*other.data[1],
self.data[2]*other.data[0]-self.data[0]*other.data[2],
self.data[0]*other.data[1]-self.data[1]*other.data[0])
def angle(self, other):
if not isVec3(other):
raise TypeError, "Angle between vector and non-vector"
cosa = (self*other)/(self.length()*other.length())
cosa = max(-1.,min(1.,cosa))
return math.acos(cosa)
class Vec2:
isVec2 = 1
def __init__(self, x=0., y=0.):
self.data = [x,y]
def __repr__(self):
return 'Vec2(%s,%s,%s)' % (`self.data[0]`,\
`self.data[1]`)
def __str__(self):
return `self.data`
def __add__(self, other):
return Vec2(self.data[0]+other.data[0],\
self.data[1]+other.data[1])
__radd__ = __add__
def __neg__(self):
return Vec2(-self.data[0], -self.data[1])
def __sub__(self, other):
return Vec2(self.data[0]-other.data[0],\
self.data[1]-other.data[1])
def __rsub__(self, other):
return Vec2(other.data[0]-self.data[0],\
other.data[1]-self.data[1])
def __mul__(self, other):
if isVec2(other):
return reduce(lambda a,b: a+b,
map(lambda a,b: a*b, self.data, other.data))
else:
return Vec2(self.data[0]*other, self.data[1]*other)
def __rmul__(self, other):
if isVec2(other):
return reduce(lambda a,b: a+b,
map(lambda a,b: a*b, self.data, other.data))
else:
return Vec2(other*self.data[0], other*self.data[1])
def __div__(self, other):
if isVec2(other):
raise TypeError, "Can't divide by a vector"
else:
return Vec2(_div(self.data[0],other), _div(self.data[1],other))
def __rdiv__(self, other):
raise TypeError, "Can't divide by a vector"
def __cmp__(self, other):
return cmp(self.data[0],other.data[0]) \
or cmp(self.data[1],other.data[1])
def __getitem__(self, index):
return self.data[index]
def x(self):
return self.data[0]
def y(self):
return self.data[1]
def length(self):
return math.sqrt(self*self)
def normal(self):
len = self.length()
if len == 0:
raise ZeroDivisionError, "Can't normalize a zero-length vector"
return self/len
#def cross(self, other):
# if not isVec2(other):
# raise TypeError, "Cross product with non-vector"
# return Vec2(self.data[1]*other.data[2]-self.data[2]*other.data[1],
# self.data[2]*other.data[0]-self.data[0]*other.data[2],
# self.data[0]*other.data[1]-self.data[1]*other.data[0])
def angle(self, other):
if not isVec2(other):
raise TypeError, "Angle between vector and non-vector"
cosa = (self*other)/(self.length()*other.length())
cosa = max(-1.,min(1.,cosa))
return math.acos(cosa)
# Type check
def isVec3(x):
return hasattr(x,'isVec3')
def isVec2(x):
return hasattr(x,'isVec2')
# "Correct" division for arbitrary number types
def _div(a,b):
if type(a) == types.IntType and type(b) == types.IntType:
return float(a)/float(b)
else:
return a/b
# Some useful constants
ex = Vec3(1.,0.,0.)
ey = Vec3(0.,1.,0.)
ez = Vec3(0.,0.,1.)