def __init__(self, degree=0, Knots=[], Weights=None, CPoints=None):
self.degree = degree # Spline degree
self.Knots = Knots # Knot Vector
self.CPoints = CPoints # Control points of splines [2D]
self.Weights = Weights # Weighting of the individual points
# Initializing calculated variables
self.HCPts = [] # Homogeneous points vectors [3D]
# Convert Points in Homogeneous points
self.CPts_2_HCPts()
# Creating the BSplineClass to calculate the homogeneous points
self.BSpline = BSplineClass(degree=self.degree,
Knots=self.Knots,
CPts=self.HCPts)
def __init__(self, degree=0, Knots=[], Weights=None, CPoints=None):
self.degree = degree # Spline degree
self.Knots = Knots # Knot Vector
self.CPoints = CPoints # Control points of splines [2D]
self.Weights = Weights # Weighting of the individual points
# Initializing calculated variables
self.HCPts = [] # Homogeneous points vectors [3D]
# Convert Points in Homogeneous points
self.CPts_2_HCPts()
# Creating the BSplineClass to calculate the homogeneous points
self.BSpline = BSplineClass(degree=self.degree,
Knots=self.Knots,
CPts=self.HCPts)
class NURBSClass(object):
def __init__(self, degree=0, Knots=[], Weights=None, CPoints=None):
self.degree = degree # Spline degree
self.Knots = Knots # Knot Vector
self.CPoints = CPoints # Control points of splines [2D]
self.Weights = Weights # Weighting of the individual points
# Initializing calculated variables
self.HCPts = [] # Homogeneous points vectors [3D]
# Convert Points in Homogeneous points
self.CPts_2_HCPts()
# Creating the BSplineClass to calculate the homogeneous points
self.BSpline = BSplineClass(degree=self.degree,
Knots=self.Knots,
CPts=self.HCPts)
# Calculate a number of evenly distributed points
def calc_curve_old(self, n=0, cpts_nr=20):
# Initial values for step and u
u = 0
Points = []
step = self.Knots[-1] / (cpts_nr - 1)
while u <= self.Knots[-1]:
Pt = self.NURBS_evaluate(n=n, u=u)
Points.append(Pt)
u += step
return Points
# Calculate a number points using error limiting
def calc_curve(self, n=0, tol_deg=20):
# Initial values for step and u
u = 0
Points = []
tol = radians(tol_deg)
i = 1
while self.Knots[i] == 0:
i = i + 1
step = self.Knots[i] / 3
Pt1 = self.NURBS_evaluate(n=n, u=0.0)
Points.append(Pt1)
while u < self.Knots[-1]:
if (u + step > self.Knots[-1]):
step = self.Knots[-1] - u
Pt2 = self.NURBS_evaluate(n=n, u=u + step)
Pt_test = self.NURBS_evaluate(n=n, u=u + step / 2)
dx1 = (Pt_test.x - Pt1.x)
dy1 = (Pt_test.y - Pt1.y)
L1 = sqrt(dx1 * dx1 + dy1 * dy1)
dx2 = (Pt2.x - Pt_test.x)
dy2 = (Pt2.y - Pt_test.y)
L2 = sqrt(dx2 * dx2 + dy2 * dy2)
if L1 > Zero and L2 > Zero:
cos_angle = dx1 / L1 * dx2 / L2 + dy1 / L1 * dy2 / L2
if abs(cos_angle) > 1:
cos_angle = int(cos_angle)
angle = acos(cos_angle)
else:
angle = 0.0
if angle > tol:
step = step / 2
else:
u += step
Points.append(Pt2)
step = step * 2
Pt1 = Pt2
return Points
# Calculate a point of NURBS
def NURBS_evaluate(self, n=0, u=0):
# Calculate the homogeneous points to the n th derivative
HPt = self.BSpline.bspline_ders_evaluate(n=n, u=u)
# Point back to normal coordinates transform
Point = self.HPt_2_Pt(HPt[0])
return Point
# Convert the NURBS control points and weight in a homogeneous vector
def CPts_2_HCPts(self):
for P_nr in range(len(self.CPoints)):
HCPtVec = [self.CPoints[P_nr].x * self.Weights[P_nr],
self.CPoints[P_nr].y * self.Weights[P_nr],
self.Weights[P_nr]]
self.HCPts.append(HCPtVec[:])
# Convert a homogeneous vector point in a point
def HPt_2_Pt(self, HPt):
return PointClass(x=HPt[0] / HPt[-1], y=HPt[1] / HPt[-1])
class NURBSClass(object):
def __init__(self, degree=0, Knots=[], Weights=None, CPoints=None):
self.degree = degree # Spline degree
self.Knots = Knots # Knot Vector
self.CPoints = CPoints # Control points of splines [2D]
self.Weights = Weights # Weighting of the individual points
# Initializing calculated variables
self.HCPts = [] # Homogeneous points vectors [3D]
# Convert Points in Homogeneous points
self.CPts_2_HCPts()
# Creating the BSplineClass to calculate the homogeneous points
self.BSpline = BSplineClass(degree=self.degree,
Knots=self.Knots,
CPts=self.HCPts)
# Calculate a number of evenly distributed points
def calc_curve_old(self, n=0, cpts_nr=20):
# Initial values for step and u
u = 0
Points = []
step = self.Knots[-1] / (cpts_nr - 1)
while u <= self.Knots[-1]:
Pt = self.NURBS_evaluate(n=n, u=u)
Points.append(Pt)
u += step
return Points
# Calculate a number points using error limiting
def calc_curve(self, n=0, tol_deg=20):
# Initial values for step and u
u = 0
Points = []
tol = radians(tol_deg)
i = 1
while self.Knots[i] == 0:
i = i + 1
step = self.Knots[i] / 3
Pt1 = self.NURBS_evaluate(n=n, u=0.0)
Points.append(Pt1)
while u < self.Knots[-1]:
if (u + step > self.Knots[-1]):
step = self.Knots[-1] - u
Pt2 = self.NURBS_evaluate(n=n, u=u + step)
Pt_test = self.NURBS_evaluate(n=n, u=u + step / 2)
dx1 = (Pt_test.x - Pt1.x)
dy1 = (Pt_test.y - Pt1.y)
L1 = sqrt(dx1 * dx1 + dy1 * dy1)
dx2 = (Pt2.x - Pt_test.x)
dy2 = (Pt2.y - Pt_test.y)
L2 = sqrt(dx2 * dx2 + dy2 * dy2)
if L1 > Zero and L2 > Zero:
cos_angle = dx1 / L1 * dx2 / L2 + dy1 / L1 * dy2 / L2
if abs(cos_angle) > 1:
cos_angle = int(cos_angle)
angle = acos(cos_angle)
else:
angle = 0.0
if angle > tol:
step = step / 2
else:
u += step
Points.append(Pt2)
step = step * 2
Pt1 = Pt2
return Points
# Calculate a point of NURBS
def NURBS_evaluate(self, n=0, u=0):
# Calculate the homogeneous points to the n th derivative
HPt = self.BSpline.bspline_ders_evaluate(n=n, u=u)
# Point back to normal coordinates transform
Point = self.HPt_2_Pt(HPt[0])
return Point
# Convert the NURBS control points and weight in a homogeneous vector
def CPts_2_HCPts(self):
for P_nr in range(len(self.CPoints)):
HCPtVec = [
self.CPoints[P_nr].x * self.Weights[P_nr],
self.CPoints[P_nr].y * self.Weights[P_nr], self.Weights[P_nr]
]
self.HCPts.append(HCPtVec[:])
# Convert a homogeneous vector point in a point
def HPt_2_Pt(self, HPt):
return PointClass(x=HPt[0] / HPt[-1], y=HPt[1] / HPt[-1])