def add_triedron(self,
length=10,
width=1,
arrlen=1,
xcolor=pyservoce.red,
ycolor=pyservoce.green,
zcolor=pyservoce.blue):
self.xaxis = pyservoce.draw_arrow(pyservoce.point3(0, 0, 0),
pyservoce.vector3(length, 0, 0),
clr=xcolor,
arrlen=arrlen,
width=width)
self.yaxis = pyservoce.draw_arrow(pyservoce.point3(0, 0, 0),
pyservoce.vector3(0, length, 0),
clr=ycolor,
arrlen=arrlen,
width=width)
self.zaxis = pyservoce.draw_arrow(pyservoce.point3(0, 0, 0),
pyservoce.vector3(0, 0, length),
clr=zcolor,
arrlen=arrlen,
width=width)
self.dispobjects.append(self.xaxis)
self.dispobjects.append(self.yaxis)
self.dispobjects.append(self.zaxis)
def point3(*args):
args = [evalcache.unlazy_if_need(a) for a in args]
if len(args) == 1:
if args[0] is None:
return point3(0, 0, 0)
return point3(*args[0])
return pyservoce.point3(*args)
def numpy_highmap(arr):
#result = numpy.ndarray((arr.shape[0], arr.shape[1]), dtype=pyservoce.point3)
result = numpy.ndarray(arr.shape, dtype=pyservoce.point3)
for i in range(arr.shape[0]):
for j in range(arr.shape[1]):
result[i, j] = pyservoce.point3(i, j, arr[i, j])
return result
def restore_ellipse_centers(apnt, bpnt, r1, r2, phi):
"""
Поиск центра двумерного элипса по радиусам, углу наклона главной оси и двум точкам.
"""
rot = rotateZ(phi)
irot = rot.inverse()
x1, y1, _ = irot(apnt)
x2, y2, _ = irot(bpnt)
a, b = r1**2, r2**2
if abs(a - b) < 1e-5 and abs(sqrt((x1 - x2)**2 +
(y1 - y2)**2) - r1 * 2) < 1e-5:
return point3((apnt.x + bpnt.x) / 2, (apnt.y + bpnt.y) / 2), point3(
(apnt.x + bpnt.x) / 2, (apnt.y + bpnt.y) / 2)
if abs(x1 - x2) < 1e-5:
y01 = (y1 + y2) / 2
x01 = x1 - sqrt(-a * b *
(-4 * b + y1**2 - 2 * y1 * y2 + y2**2)) / (2 * b)
y02 = (y1 + y2) / 2
x02 = x1 + sqrt(-a * b *
(-4 * b + y1**2 - 2 * y1 * y2 + y2**2)) / (2 * b)
elif abs(y1 - y2) < 1e-5:
y01 = y1 - sqrt(-a * b *
(-4 * a + x1**2 - 2 * x1 * x2 + x2**2)) / (2 * a)
x01 = (x1 + x2) / 2
y02 = y1 + sqrt(-a * b *
(-4 * a + x1**2 - 2 * x1 * x2 + x2**2)) / (2 * a)
x02 = (x1 + x2) / 2
else:
y01 = -(-a * y1**2 + a * y2**2 - b * x1**2 + b * x2**2 +
(2 * b * x1 - 2 * b * x2) *
(x1 / 2 + x2 / 2 -
sqrt(-a * b * (a * y1**2 - 2 * a * y1 * y2 + a * y2**2 +
b * x1**2 - 2 * b * x1 * x2 + b * x2**2) *
(-4 * a * b + a * y1**2 - 2 * a * y1 * y2 + a * y2**2 +
b * x1**2 - 2 * b * x1 * x2 + b * x2**2)) * (y1 - y2) /
(2 * b *
(a * y1**2 - 2 * a * y1 * y2 + a * y2**2 + b * x1**2 -
2 * b * x1 * x2 + b * x2**2)))) / (2 * a * (y1 - y2))
x01 = x1 / 2 + x2 / 2 - sqrt(
-a * b * (a * y1**2 - 2 * a * y1 * y2 + a * y2**2 + b * x1**2 -
2 * b * x1 * x2 + b * x2**2) *
(-4 * a * b + a * y1**2 - 2 * a * y1 * y2 + a * y2**2 + b * x1**2 -
2 * b * x1 * x2 + b * x2**2)) * (y1 - y2) / (
2 * b * (a * y1**2 - 2 * a * y1 * y2 + a * y2**2 + b * x1**2 -
2 * b * x1 * x2 + b * x2**2))
y02 = -(-a * y1**2 + a * y2**2 - b * x1**2 + b * x2**2 +
(2 * b * x1 - 2 * b * x2) *
(x1 / 2 + x2 / 2 +
sqrt(-a * b * (a * y1**2 - 2 * a * y1 * y2 + a * y2**2 +
b * x1**2 - 2 * b * x1 * x2 + b * x2**2) *
(-4 * a * b + a * y1**2 - 2 * a * y1 * y2 + a * y2**2 +
b * x1**2 - 2 * b * x1 * x2 + b * x2**2)) * (y1 - y2) /
(2 * b *
(a * y1**2 - 2 * a * y1 * y2 + a * y2**2 + b * x1**2 -
2 * b * x1 * x2 + b * x2**2)))) / (2 * a * (y1 - y2))
x02 = x1 / 2 + x2 / 2 + sqrt(
-a * b * (a * y1**2 - 2 * a * y1 * y2 + a * y2**2 + b * x1**2 -
2 * b * x1 * x2 + b * x2**2) *
(-4 * a * b + a * y1**2 - 2 * a * y1 * y2 + a * y2**2 + b * x1**2 -
2 * b * x1 * x2 + b * x2**2)) * (y1 - y2) / (
2 * b * (a * y1**2 - 2 * a * y1 * y2 + a * y2**2 + b * x1**2 -
2 * b * x1 * x2 + b * x2**2))
c0, c1 = point3(x01, y01), point3(x02, y02)
c0, c1 = rot(c0), rot(c1)
return c0, c1
(-4 * a * b + a * y1**2 - 2 * a * y1 * y2 + a * y2**2 +
b * x1**2 - 2 * b * x1 * x2 + b * x2**2)) * (y1 - y2) /
(2 * b *
(a * y1**2 - 2 * a * y1 * y2 + a * y2**2 + b * x1**2 -
2 * b * x1 * x2 + b * x2**2)))) / (2 * a * (y1 - y2))
x02 = x1 / 2 + x2 / 2 + sqrt(
-a * b * (a * y1**2 - 2 * a * y1 * y2 + a * y2**2 + b * x1**2 -
2 * b * x1 * x2 + b * x2**2) *
(-4 * a * b + a * y1**2 - 2 * a * y1 * y2 + a * y2**2 + b * x1**2 -
2 * b * x1 * x2 + b * x2**2)) * (y1 - y2) / (
2 * b * (a * y1**2 - 2 * a * y1 * y2 + a * y2**2 + b * x1**2 -
2 * b * x1 * x2 + b * x2**2))
c0, c1 = point3(x01, y01), point3(x02, y02)
c0, c1 = rot(c0), rot(c1)
return c0, c1
def restore_circle_centers(apnt, bpnt, r):
"""
Поиск центра двумерной окружности по радиусу, углу наклона главной оси и двум точкам.
"""
return restore_ellipse_centers(apnt, bpnt, r, r, 0)
## TEST
if __name__ == "__main__":
print(restore_ellipse_centers(point3(15, 10), point3(5, 10), 5, 5, 0))
def segment(pnt0, pnt1):
return pyservoce.segment(pyservoce.point3(pnt0), pyservoce.point3(pnt1))
def point3(*arg):
if isinstance(arg[0], pyservoce.point3):
return arg[0]
return pyservoce.point3(*arg)