def _get_alpha(self):
if abs(self.dec) + self.radius > 89.9:
return 180
return math.degrees(
abs(
math.atan(
math.sin(math.radians(self.radius)) / np.sqrt(
abs(
math.cos(math.radians(self.dec - self.radius)) *
math.cos(math.radians(self.dec + self.radius)))))))
def get_alpha(radius, dec):
if abs(dec) + radius > 89.9:
return 180
return math.degrees(
abs(
math.atan(
math.sin(math.radians(radius)) / np.sqrt(
abs(
math.cos(math.radians(dec - radius)) *
math.cos(math.radians(dec + radius)))))))
def angle_between(v1, v2):
""" Returns the angle in radians between vectors 'v1' and 'v2'::
>>> angle_between((1, 0, 0), (0, 1, 0))
1.5707963267948966
>>> angle_between((1, 0, 0), (1, 0, 0))
0.0
>>> angle_between((1, 0, 0), (-1, 0, 0))
3.141592653589793
"""
v1_u = unit_vector(v1)
v2_u = unit_vector(v2)
angle = np.arccos(np.dot(v1_u, v2_u))
if math.isnan(angle):
if (v1_u == v2_u).all():
return 0.0
else:
return 180
return math.degrees(angle)
def Evolvent(self):
'''Расчет эвольвенты зуба
'''
#Расчет эвольветы зуба
# Читаем данные из полей формы
# z = Количество зубьев
z = self.doubleSpinBox_Z.value()
# m = Модуль зуба
m = self.doubleSpinBox_m.value()
# a = Угол главного профиля
a = self.doubleSpinBox_a.value()
#b = Угол наклона зубьев
b = self.doubleSpinBox_b.value()
#ha = Коэффициент высоты головки
ha = self.doubleSpinBox_ha.value()
#pf = К-т радиуса кривизны переходной кривой
pf = self.doubleSpinBox_pf.value()
#c = Коэффициент радиального зазора
c = self.doubleSpinBox_c.value()
#x = К-т смещения исходного контура
x = self.doubleSpinBox_x.value()
#y =Коэффициент уравнительного смещения
y = self.doubleSpinBox_y.value()
# n= Количество точек (точность построения)
#n=int(self.doubleSpinBox_n.value())
n=100
# заполня переменные
# Делительный диаметр
d = z * m
# Высота зуба h=
h = 2.25 * m
# Высота головки ha =
hav = m
# Высота ножки hf=
hf = 1.25 * m
#Диаметр вершин зубьев
#da = d + (2 * m)*(ha+x+y)
da = d + 2 * (ha + x - y) * m
#Диаметр впадин (справочно)
#df = d -(2 * hf)
df = d -2 * (ha + c - x) * m
#Окружной шаг зубьев или Шаг зацепления по дуге делительной окружности: Pt или p
pt = math.pi * m
#Окружная толщина зуба или Толщина зуба по дуге делительной окружности: St или S
#Суммарный коэффициент смещений: XΣ
X = 0.60 + 0.12
# St = 0.5 * pf
# St = 0.5 * pt
St = 0.5 * pt + 2 * x * m * math.tan(math.radians(a))
#inv a
inva=math.tan(math.radians(a))-math.radians(a)
#Угол зацепления invαw
invaw= (2 * X - math.tan(math.radians(a))) / (10+26) + inva
#Угол профиля
at = math.ceil(math.degrees(math.atan(math.tan(math.radians(a))
/math.cos( math.radians(b)))))
# Диаметр основной окружности
db = d * math.cos(math.radians(at))
#Диаметр начала выкружки зуба
D = 2 * m * ( ( z/( 2 * math.cos(math.radians(b)) )-(1-x)) ** 2 +
((1-x)/math.tan(math.radians(at)))**2)**0.5
#Промежуточные данные
yi = math.pi/2-math.radians(at)
hy = yi/(n-1)
x0 = math.pi/(4*math.cos(math.radians(b))
)+pf*math.cos(math.radians(at))+math.tan(math.radians(at))
y0 = 1-pf*math.sin(math.radians(at))-x
C = (math.pi/2+2*x*math.tan(math.radians(a))
)/z+math.tan(math.radians(at))-math.radians(at)
#Расчетный шаг точек эвольвенты
hdy = (da-D)/(n-1)
dyi = da
fi = 2*math.cos(math.radians(b))/z*(x0+y0*math.tan(yi))
#Заполняем текстовые поля в форме
# Делительный диаметр
# self.lineEdit_d.setText(str(d))
# Высота зуба h=
# self.lineEdit_h.setText(str(h))
# Высота головки ha =
# self.lineEdit_ha.setText(str(hav))
# Высота ножки hf=
# self.lineEdit_hf.setText(str(hf))
# Диаметр вершин зубьев
# self.lineEdit_da.setText(str(da))
# Диаметр впадин (справочно)
# self.lineEdit_df.setText(str(df))
# Окружной шаг зубьев Pt=
# self.lineEdit_Pt.setText(str(math.ceil(pt)))
# Окружная толщина зуба St=
# self.lineEdit_St.setText(str(math.ceil(St)))
# Угол профиля
# self.lineEdit_at.setText(str(at))
# Диаметр основной окружности
# self.lineEdit_db.setText(str(math.ceil(db)))
# Создаем списки
List_dyi=[]
List_Di=[]
List_Yei=[]
List_Xei=[]
List_Minus_Xei=[]
List_Xdai=[]
List_Ydai=[]
List_yi=[]
List_Ai=[]
List_Bi=[]
List_fi=[]
List_Ypki=[]
List_Xpki=[]
List_Minus_Xpki=[]
# Заполняем нуливой (первый )индекс списка значениями
List_dyi.append(dyi)
List_Di.append( math.acos( db/ List_dyi[0] ) - math.tan( math.acos( db / List_dyi[0] ) ) + C )
List_Yei.append(dyi / 2*math.cos( List_Di[0]))
List_Xei.append(List_Yei[0]*math.tan(List_Di[0]))
List_Minus_Xei.append(-List_Xei[0])
List_Xdai.append(-List_Xei[0])
List_Ydai.append(((da/2)**2-List_Xdai[0]**2)**0.5)
hda=(List_Xei[0]-List_Minus_Xei[0])/(n-1)
# Заполняем первый (второй по счету )индекс списка значениями
List_dyi.append(dyi-hdy)
List_Di.append( math.acos(db/List_dyi[1])-math.tan(math.acos(db/List_dyi[1]))+C)
List_Yei.append( List_dyi[1]/2*math.cos(List_Di[1]))
List_Xei.append( List_Yei[1]* math.tan(List_Di[1]))
List_Minus_Xei.append(-List_Xei[1])
List_Xdai.append(List_Xdai[0]+hda)
List_Ydai.append(((da/2)**2-List_Xdai[1]**2)**0.5)
Xdai=List_Xdai[1]
dyi=dyi-hdy
# Начинаем заполнять списки в цикле
i=0
while i < n-2:
i=i+1
dyi=dyi-hdy
List_Di.append(math.acos(db/dyi)-math.tan(math.acos(db/dyi))+C)
Di=math.acos(db/dyi)-math.tan(math.acos(db/dyi))+C
Yei=dyi/2*math.cos(Di)
Xei=Yei*math.tan(Di)
List_dyi.append(dyi)
List_Yei.append(dyi/2*math.cos(Di))
List_Xei.append(Yei*math.tan(Di))
List_Minus_Xei.append(-Xei)
Xdai=Xdai+hda
List_Xdai.append(Xdai)
List_Ydai.append(((da/2)**2-Xdai**2)**0.5)
#Заполняем последний индекс списка
List_dyi[n-1]=D
# Заполняем нуливой (первый )индекс списка значениями
List_yi.append(yi)
List_Ai.append(z/(2*math.cos(math.radians(b)))-y0-pf*math.cos(List_yi[0]) )
List_Bi.append(y0*math.tan(List_yi[0])+pf*math.sin(List_yi[0]))
List_fi.append(fi)
List_Ypki.append((List_Ai[0] * math.cos(fi)+List_Bi[0] * math.sin(fi)) * m)
List_Xpki.append((List_Ai[0] * math.sin(fi)-List_Bi[0] * math.cos(fi)) * m)
List_Minus_Xpki.append(-List_Xpki[0])
# Начинаем заполнять списки в цикле
i=0
while i < n-2:
i=i+1
yi=yi-hy
List_yi.append(yi)
Ai = z / (2 * math.cos(math.radians(b)))-y0-pf*math.cos(yi)
List_Ai.append( z / (2 * math.cos(math.radians(b)))-y0-pf*math.cos(yi))
Bi =y0*math.tan(yi)+pf*math.sin(yi)
List_Bi.append(y0*math.tan(yi)+pf*math.sin(yi))
fi = 2*math.cos(math.radians(b))/z*(x0+y0*math.tan(yi))
List_fi.append(2*math.cos(math.radians(b))/z*(x0+y0*math.tan(yi)))
List_Ypki.append((Ai*math.cos(fi)+Bi*math.sin(fi))*m)
Ypki=(Ai*math.cos(fi)+Bi*math.sin(fi))*m
Xpki=(Ai*math.sin(fi)-Bi*math.cos(fi))*m
List_Xpki.append((Ai*math.sin(fi)-Bi*math.cos(fi))*m)
List_Minus_Xpki.append(-Xpki)
#Заполняем последний индекс списка
List_yi.append(yi-yi)
List_Ai.append(z/(2*math.cos(math.radians(b)))-y0-pf*math.cos(List_yi[n-1]) )
List_Bi.append(y0*math.tan(List_yi[n-1])+pf*math.sin(List_yi[n-1]))
List_fi.append(2*math.cos(math.radians(b))/z*(x0+y0*math.tan(List_yi[n-1])))
List_Ypki.append((List_Ai[n-1] * math.cos(fi)+List_Bi[n-1] * math.sin(List_fi[n-1])) * m)
List_Xpki.append((List_Ai[n-1] * math.sin(fi)-List_Bi[n-1] * math.cos(List_fi[n-1])) * m)
List_Minus_Xpki.append(-List_Xpki[n-1])
# self.WiPfileZub(List_Yei,List_Xei,List_Minus_Xei,List_Ypki,List_Xpki,List_Minus_Xpki,List_Ydai,List_Xdai)
self.GragEvolvent(List_Minus_Xei+List_Minus_Xpki,List_Yei+List_Ypki,n)
DFreza = self.lineEditDFreza.text()
VisotaYAxis = self.lineEditVisota.text()
Diametr = self.lineEditDiametr.text()
if DFreza and VisotaYAxis:
E30 = (int(DFreza)/2) +float(VisotaYAxis)
else:
E30 = 0
angi_B=0
if ValkosZub:
angie_A:float = 90# угол А треугольника по высоте детали
angie_B:float = float(b) #угол B треугольника по высоте детали ( угол наклона зуба по чертежу)
angie_Y:float = 180 - (angie_A + angie_B) # трерий уго треугольника по высоте детали
side_c:float = float(E30)# высота детали первая сторона треугольника
side_a = side_c * math.sin(math.radians(angie_A)) / math.sin(math.radians(angie_Y))# вторая сторона треугольника
side_b = side_c * math.sin(math.radians(angie_B)) / math.sin(math.radians(angie_Y))# третия сторона треугольника ( ось Х)
sid_a:float = float(Diametr)/2 # радиус детали первая и вторая тророны треугольника по торцу
# sid_a:float = float(self.lineEdit_da.text())/2 # радиус детали первая и вторая тророны треугольника по торцу
sid_c:float = sid_a
if sid_c < 10 :
sid_a:float = 10
sid_c:float = 10
angi_B = float('{:.3f}'.format(math.degrees(math.acos((sid_a**2+sid_c**2-side_b**2)/(2*sid_a*sid_c)))))
QMessageBox.about (self, "Ошибка " , "Диаметр шестерни задан меньше 20 мм. \n Введите риальный диаметр шестерни " )
else:
angi_B = float('{:.3f}'.format(math.degrees(math.acos((sid_a**2+sid_c**2-side_b**2)/(2*sid_a*sid_c)))))# результат угол поворота стола
self.label_da.setText(str(round(da,1)))
self.label_d.setText(str(round(d,1)))
self.label_at.setText(str(round(at,1)))
self.label_db.setText(str(round(db,1)))
self.label_df.setText(str(round(df,1)))
self.label_St.setText(str(round(St,1)))
self.label_Pt.setText(str(round(pt,1)))
self.label_hf.setText(str(round(hf,1)))
self.label_ha.setText(str(round(ha,1)))
self.label_h.setText(str(round(h,1)))
self.lineEditDiametr.setText(str(da))
self.lineEditUgol.setText(str(angi_B))
def get_line_data(pixels, x1, y1, x2, y2, line_w=2, the_z=0, the_c=0, the_t=0):
"""
Grabs pixel data covering the specified line, and rotates it horizontally
so that x1,y1 is to the left,
Returning a numpy 2d array. Used by Kymograph.py script.
Uses PIL to handle rotating and interpolating the data. Converts to numpy
to PIL and back (may change dtype.)
@param pixels: PixelsWrapper object
@param x1, y1, x2, y2: Coordinates of line
@param line_w: Width of the line we want
@param the_z: Z index within pixels
@param the_c: Channel index
@param the_t: Time index
"""
size_x = pixels.getSizeX()
size_y = pixels.getSizeY()
line_x = x2 - x1
line_y = y2 - y1
rads = math.atan(float(line_x) / line_y)
# How much extra Height do we need, top and bottom?
extra_h = abs(math.sin(rads) * line_w)
bottom = int(max(y1, y2) + extra_h / 2)
top = int(min(y1, y2) - extra_h / 2)
# How much extra width do we need, left and right?
extra_w = abs(math.cos(rads) * line_w)
left = int(min(x1, x2) - extra_w)
right = int(max(x1, x2) + extra_w)
# What's the larger area we need? - Are we outside the image?
pad_left, pad_right, pad_top, pad_bottom = 0, 0, 0, 0
if left < 0:
pad_left = abs(left)
left = 0
x = left
if top < 0:
pad_top = abs(top)
top = 0
y = top
if right > size_x:
pad_right = right - size_x
right = size_x
w = int(right - left)
if bottom > size_y:
pad_bottom = bottom - size_y
bottom = size_y
h = int(bottom - top)
tile = (x, y, w, h)
# get the Tile
plane = pixels.getTile(the_z, the_c, the_t, tile)
# pad if we wanted a bigger region
if pad_left > 0:
data_h, data_w = plane.shape
pad_data = zeros((data_h, pad_left), dtype=plane.dtype)
plane = hstack((pad_data, plane))
if pad_right > 0:
data_h, data_w = plane.shape
pad_data = zeros((data_h, pad_right), dtype=plane.dtype)
plane = hstack((plane, pad_data))
if pad_top > 0:
data_h, data_w = plane.shape
pad_data = zeros((pad_top, data_w), dtype=plane.dtype)
plane = vstack((pad_data, plane))
if pad_bottom > 0:
data_h, data_w = plane.shape
pad_data = zeros((pad_bottom, data_w), dtype=plane.dtype)
plane = vstack((plane, pad_data))
pil = script_utils.numpy_to_image(plane, (plane.min(), plane.max()), int32)
# Now need to rotate so that x1,y1 is horizontally to the left of x2,y2
to_rotate = 90 - math.degrees(rads)
if x1 > x2:
to_rotate += 180
# filter=Image.BICUBIC see
# http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2172449/
rotated = pil.rotate(to_rotate, expand=True)
# rotated.show()
# finally we need to crop to the length of the line
length = int(math.sqrt(math.pow(line_x, 2) + math.pow(line_y, 2)))
rot_w, rot_h = rotated.size
crop_x = (rot_w - length) / 2
crop_x2 = crop_x + length
crop_y = (rot_h - line_w) / 2
crop_y2 = crop_y + line_w
cropped = rotated.crop((crop_x, crop_y, crop_x2, crop_y2))
return asarray(cropped)
def get_line_data(image, x1, y1, x2, y2, line_w=2, the_z=0, the_c=0, the_t=0):
"""
Grab pixel data covering the specified line, and rotates it horizontally.
Uses current rendering settings and returns 8-bit data.
Rotates it so that x1,y1 is to the left,
Returning a numpy 2d array. Used by Kymograph.py script.
Uses PIL to handle rotating and interpolating the data. Converts to numpy
to PIL and back (may change dtype.)
@param pixels: PixelsWrapper object
@param x1, y1, x2, y2: Coordinates of line
@param line_w: Width of the line we want
@param the_z: Z index within pixels
@param the_c: Channel index
@param the_t: Time index
"""
size_x = image.getSizeX()
size_y = image.getSizeY()
line_x = x2 - x1
line_y = y2 - y1
rads = math.atan2(line_y, line_x)
# How much extra Height do we need, top and bottom?
extra_h = abs(math.sin(rads) * line_w)
bottom = int(max(y1, y2) + extra_h / 2)
top = int(min(y1, y2) - extra_h / 2)
# How much extra width do we need, left and right?
extra_w = abs(math.cos(rads) * line_w)
left = int(min(x1, x2) - extra_w)
right = int(max(x1, x2) + extra_w)
# What's the larger area we need? - Are we outside the image?
pad_left, pad_right, pad_top, pad_bottom = 0, 0, 0, 0
if left < 0:
pad_left = abs(left)
left = 0
x = left
if top < 0:
pad_top = abs(top)
top = 0
y = top
if right > size_x:
pad_right = right - size_x
right = size_x
w = int(right - left)
if bottom > size_y:
pad_bottom = bottom - size_y
bottom = size_y
h = int(bottom - top)
# get the Tile - render single channel white
image.set_active_channels([the_c + 1], None, ['FFFFFF'])
jpeg_data = image.renderJpegRegion(the_z, the_t, x, y, w, h)
pil = Image.open(StringIO(jpeg_data))
# pad if we wanted a bigger region
if pad_left > 0 or pad_right > 0 or pad_top > 0 or pad_bottom > 0:
img_w, img_h = pil.size
new_w = img_w + pad_left + pad_right
new_h = img_h + pad_top + pad_bottom
canvas = Image.new('RGB', (new_w, new_h), '#ff0000')
canvas.paste(pil, (pad_left, pad_top))
pil = canvas
# Now need to rotate so that x1,y1 is horizontally to the left of x2,y2
to_rotate = math.degrees(rads)
# filter=Image.BICUBIC see
# http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2172449/
rotated = pil.rotate(to_rotate, expand=True)
# finally we need to crop to the length of the line
length = int(math.sqrt(math.pow(line_x, 2) + math.pow(line_y, 2)))
rot_w, rot_h = rotated.size
crop_x = (rot_w - length) / 2
crop_x2 = crop_x + length
crop_y = (rot_h - line_w) / 2
crop_y2 = crop_y + line_w
cropped = rotated.crop((crop_x, crop_y, crop_x2, crop_y2))
# return numpy array
rgb_plane = asarray(cropped)
# greyscale image. r, g, b all same. Just use first
return rgb_plane[::, ::, 0]
def getLineData(pixels, x1, y1, x2, y2, lineW=2, theZ=0, theC=0, theT=0):
"""
Grabs pixel data covering the specified line, and rotates it horizontally
so that x1,y1 is to the left,
Returning a numpy 2d array. Used by Kymograph.py script.
Uses PIL to handle rotating and interpolating the data. Converts to numpy
to PIL and back (may change dtype.)
@param pixels: PixelsWrapper object
@param x1, y1, x2, y2: Coordinates of line
@param lineW: Width of the line we want
@param theZ: Z index within pixels
@param theC: Channel index
@param theT: Time index
"""
from numpy import asarray
sizeX = pixels.getSizeX()
sizeY = pixels.getSizeY()
lineX = x2 - x1
lineY = y2 - y1
rads = math.atan(float(lineX) / lineY)
# How much extra Height do we need, top and bottom?
extraH = abs(math.sin(rads) * lineW)
bottom = int(max(y1, y2) + extraH / 2)
top = int(min(y1, y2) - extraH / 2)
# How much extra width do we need, left and right?
extraW = abs(math.cos(rads) * lineW)
left = int(min(x1, x2) - extraW)
right = int(max(x1, x2) + extraW)
# What's the larger area we need? - Are we outside the image?
pad_left, pad_right, pad_top, pad_bottom = 0, 0, 0, 0
if left < 0:
pad_left = abs(left)
left = 0
x = left
if top < 0:
pad_top = abs(top)
top = 0
y = top
if right > sizeX:
pad_right = right - sizeX
right = sizeX
w = int(right - left)
if bottom > sizeY:
pad_bottom = bottom - sizeY
bottom = sizeY
h = int(bottom - top)
tile = (x, y, w, h)
# get the Tile
plane = pixels.getTile(theZ, theC, theT, tile)
# pad if we wanted a bigger region
if pad_left > 0:
data_h, data_w = plane.shape
pad_data = zeros((data_h, pad_left), dtype=plane.dtype)
plane = hstack((pad_data, plane))
if pad_right > 0:
data_h, data_w = plane.shape
pad_data = zeros((data_h, pad_right), dtype=plane.dtype)
plane = hstack((plane, pad_data))
if pad_top > 0:
data_h, data_w = plane.shape
pad_data = zeros((pad_top, data_w), dtype=plane.dtype)
plane = vstack((pad_data, plane))
if pad_bottom > 0:
data_h, data_w = plane.shape
pad_data = zeros((pad_bottom, data_w), dtype=plane.dtype)
plane = vstack((plane, pad_data))
pil = numpyToImage(plane)
#pil.show()
# Now need to rotate so that x1,y1 is horizontally to the left of x2,y2
toRotate = 90 - math.degrees(rads)
if x1 > x2:
toRotate += 180
# filter=Image.BICUBIC see
# http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2172449/
rotated = pil.rotate(toRotate, expand=True)
#rotated.show()
# finally we need to crop to the length of the line
length = int(math.sqrt(math.pow(lineX, 2) + math.pow(lineY, 2)))
rotW, rotH = rotated.size
cropX = (rotW - length) / 2
cropX2 = cropX + length
cropY = (rotH - lineW) / 2
cropY2 = cropY + lineW
cropped = rotated.crop((cropX, cropY, cropX2, cropY2))
#cropped.show()
return asarray(cropped)
def getLineData(pixels, x1, y1, x2, y2, lineW=2, theZ=0, theC=0, theT=0):
"""
Grabs pixel data covering the specified line, and rotates it horizontally
so that x1,y1 is to the left,
Returning a numpy 2d array. Used by Kymograph.py script.
Uses PIL to handle rotating and interpolating the data. Converts to numpy
to PIL and back (may change dtype.)
@param pixels: PixelsWrapper object
@param x1, y1, x2, y2: Coordinates of line
@param lineW: Width of the line we want
@param theZ: Z index within pixels
@param theC: Channel index
@param theT: Time index
"""
from numpy import asarray
sizeX = pixels.getSizeX()
sizeY = pixels.getSizeY()
lineX = x2-x1
lineY = 1 if y2-y1 == 0 else y2-y1
rads = math.atan(float(lineX) / lineY)
# How much extra Height do we need, top and bottom?
extraH = abs(math.sin(rads) * lineW)
bottom = int(max(y1, y2) + extraH/2)
top = int(min(y1, y2) - extraH/2)
# How much extra width do we need, left and right?
extraW = abs(math.cos(rads) * lineW)
left = int(min(x1, x2) - extraW)
right = int(max(x1, x2) + extraW)
# What's the larger area we need? - Are we outside the image?
pad_left, pad_right, pad_top, pad_bottom = 0, 0, 0, 0
if left < 0:
pad_left = abs(left)
left = 0
x = left
if top < 0:
pad_top = abs(top)
top = 0
y = top
if right > sizeX:
pad_right = right - sizeX
right = sizeX
w = int(right - left)
if bottom > sizeY:
pad_bottom = bottom - sizeY
bottom = sizeY
h = int(bottom - top)
tile = (x, y, w, h)
# get the Tile
plane = pixels.getTile(theZ, theC, theT, tile)
# pad if we wanted a bigger region
if pad_left > 0:
data_h, data_w = plane.shape
pad_data = zeros((data_h, pad_left), dtype=plane.dtype)
plane = hstack((pad_data, plane))
if pad_right > 0:
data_h, data_w = plane.shape
pad_data = zeros((data_h, pad_right), dtype=plane.dtype)
plane = hstack((plane, pad_data))
if pad_top > 0:
data_h, data_w = plane.shape
pad_data = zeros((pad_top, data_w), dtype=plane.dtype)
plane = vstack((pad_data, plane))
if pad_bottom > 0:
data_h, data_w = plane.shape
pad_data = zeros((pad_bottom, data_w), dtype=plane.dtype)
plane = vstack((plane, pad_data))
pil = numpyToImage(plane)
# pil.show()
# Now need to rotate so that x1,y1 is horizontally to the left of x2,y2
toRotate = 90 - math.degrees(rads)
if x1 > x2:
toRotate += 180
# filter=Image.BICUBIC see
# http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2172449/
rotated = pil.rotate(toRotate, expand=True)
# rotated.show()
# finally we need to crop to the length of the line
length = int(math.sqrt(math.pow(lineX, 2) + math.pow(lineY, 2)))
rotW, rotH = rotated.size
cropX = (rotW - length)/2
cropX2 = cropX + length
cropY = (rotH - lineW)/2
cropY2 = cropY + lineW
cropped = rotated.crop((cropX, cropY, cropX2, cropY2))
# cropped.show()
return asarray(cropped)