gistfile1.txt

"""
in curve_in C
out curve_out C
"""

from math import sqrt, exp
import numpy as np

from sverchok.data_structure import zip_long_repeat, ensure_nesting_level, repeat_last_for_length
from sverchok.utils.curve.core import SvCurve, UnsupportedCurveTypeException
from sverchok.utils.curve.nurbs import SvNurbsCurve
from sverchok.utils.curve.bezier import SvCubicBezierCurve
from sverchok.utils.curve.nurbs_algorithms import concatenate_nurbs_curves
from sverchok.dependencies import scipy
from scipy.optimize import fsolve

def process_segment(segment, c1, c2):
    #print(f"Fit to {c1}, {c2}")
    A, B, C, D = segment.get_control_points()
    v1 = B - A
    v13 = np.linalg.norm(v1)**3
    v2 = D - C
    v23 = np.linalg.norm(v2)**3
    
    def equations(p):
        X, Y = p
        x, y = exp(X), exp(Y)
        #x, y = p
        C_star = D - y*v2
        B_star = A + x*v1
        eq1 = 2 * np.linalg.norm(np.cross(v1, C_star - A)) / (x*x * v13) - 3*c1
        eq2 = 2 * np.linalg.norm(np.cross(v2, B_star - D)) / (y*y * v23) - 3*c2
        return (eq1, eq2)
    
    initial_guess = [0, 0]
    ps = fsolve(equations, initial_guess)
    #print(solution)
    #ps, info, ier, mesg = solution
    X, Y = ps
    x, y = exp(X), exp(Y)
    #x,y = ps
    #print(f"Sol: {x}, {y}")
    B_star = A + x*v1
    C_star = D - y*v2
    result = SvCubicBezierCurve(A, B_star, C_star, D)
    #k1 = result.curvature(0)
    #k2 = result.curvature(1)
    #print("Res", k1, k2)
    return result

def process(curve):
    p = curve.get_degree()
    if p != 3:
        raise UnsupportedCurveTypeException("Only degree 3 curves are supported for now")
    segments = curve.to_bezier_segments()
    start_curvatures = []
    end_curvatures = []
    for segment in segments:
        c1 = segment.curvature(0)
        c2 = segment.curvature(1)
        #print("Src", c1, c2)
        start_curvatures.append(c1)
        end_curvatures.append(c2)
    target_curvatures = [start_curvatures[0]]
    for c1, c2 in zip(end_curvatures[:-1], start_curvatures[1:]):
        c = sqrt(c1*c2)
        target_curvatures.append(c)
    target_curvatures.append(end_curvatures[-1])
    #print("Target", target_curvatures)
    result = []
    for segment, c1, c2 in zip(segments, target_curvatures[:-1], target_curvatures[1:]):
        segment = process_segment(segment, c1, c2)
        result.append(segment)
    return concatenate_nurbs_curves(result)

curve_in = ensure_nesting_level(curve_in, 1, data_types=(SvCurve,))
curve_out = []
for curve in curve_in:
    curve = SvNurbsCurve.to_nurbs(curve)
    if curve is None:
        raise UnsupportedCurveTypeException("One of curve is not NURBS")
    curve = process(curve)
    curve_out.append(curve)