Daniel Weschke
033cb92dc4
import vendor modules only once during import change text color for the method cad_wireframe in geometry_plot_pylab and add hide key
379 lines
14 KiB
Python
Executable File
379 lines
14 KiB
Python
Executable File
#!/usr/bin/env python
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# -*- coding: utf-8 -*-
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"""Example b-spline basis functions and curves.
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:Date: 2020-01-02
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.. module:: function_b_spline
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:platform: *nix, Windows
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:synopsis: Example b-spline basis functions and curves.
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.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
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"""
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from mpl_toolkits.mplot3d import Axes3D
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assert Axes3D
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import pylab
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from pylib.data import seq, unique_list
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from pylib.function import (
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sample_half_open, sample_half_open_seq,
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b_spline_basis, b_spline_knots, b_spline_curve_with_knots)
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from pylib.helper import timeit
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def b_spline_basis_functions(knots, pmax=None):
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m = len(knots) - 1 # m = 3
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if pmax is None or pmax > m:
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pmax = m
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u = seq(knots[0], knots[-1], (knots[-1]-knots[0])/50)
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Nij = [[[b_spline_basis(knots, i, j)(uj) for uj in u] for
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i in range(m-j)] for j in range(pmax+1)]
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Nj = [[sum(i) for i in zip(*Nij[:][j])] for j in range(pmax+1)]
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return u, Nij, Nj
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# @timeit('plot_matrix_seperate_single_sum')
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def plot_matrix_seperate_single_sum(u, Nij, Nj, pmax=None, figure_id=''):
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"""
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::
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i: knot span
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p: degree
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sum of all
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i=0 i=1 i=2 ... basis function
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+-----+-----+-----+-----+-----+
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p=0 | | | | | |
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+-----+-----+-----+-----+-----+
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p=1 | | | | | |
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+-----+-----+-----+-----+-----+
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... | | | | | |
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"""
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p = len(Nij[0]) - 1 # degree
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if pmax is None or pmax > p:
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pmax = p
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m = len(Nij[0]) # knot spans
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pylab.figure(figure_id)
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[([(pylab.subplot(pmax+1, m+1, i*(m+1)+j+1), pylab.plot(u, Nij[i][j])) for
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j in range(m-i)],
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pylab.subplot(pmax+1, m+1, (i+1)*(m+1)), pylab.plot(u, Nj[i])) for i in range(pmax+1)]
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# @timeit('plot_matrix_joint_single_sum')
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def plot_matrix_joint_single_sum(u, Nij, Nj, pmax=None, figure_id=''):
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"""
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::
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p: degree
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p=0 p=1 p=2 ...
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+-----+-----+-----+-----
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singe basis functions | | | |
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+-----+-----+-----+-----
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sum of all basis functions | | | |
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+-----+-----+-----+-----
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"""
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m = len(Nij[0]) # knot spans
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p = m - 1 # degree
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n = len(Nij) - 1 # degrees calculated
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if pmax is None or pmax > p:
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pmax = p
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if n < pmax:
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pmax = n
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pylab.figure(figure_id)
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[(pylab.subplot(2, pmax+1, 0*(pmax+1)+j+1),[pylab.plot(u, Nij[j][i]) for
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i in range(p+1-j)],
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pylab.subplot(2, pmax+1, 1*(pmax+1)+j+1).plot(u, Nj[j])) for j in range(pmax+1)]
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# @timeit('plot_b_spline_curve_with_knots')
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def plot_b_spline_curve_with_knots(
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Cu=None, C=None, U=None, CU=None, P=None, knots=True, figure_id='', ax=None):
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if ax is None:
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fig = pylab.figure(figure_id)
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ax = fig.add_subplot(111, projection='3d')
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# control points
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if P is not None:
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x, y, z = zip(*P)
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ax.plot(x, y, z, 'C1', linewidth=1)
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ax.plot(x, y, z, 'oC1', fillstyle='none')
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# B-spline curve
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if Cu is None and C is not None and U is not None:
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Cu = sample_half_open(C, U[0], U[-1])
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if Cu is not None:
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ax.plot(*zip(*Cu))
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if knots:
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# internal knots of clamped B-spline curve
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if CU is None and C is not None and U is not None:
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CU = sample_half_open_seq(C, unique_list(U))
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if CU is not None:
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ax.plot(*zip(*CU), '.C2')
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return ax
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def example1():
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# degree of basis functions
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# p = 0
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# knots
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u0 = 0
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u1 = 1
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u2 = 2
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u3 = 3
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# knot vector
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U = (u0, u1, u2, u3)
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# knot spans 0, 1 and 2 are [0,1), [1,2), [2,3)
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# m = len(U) - 1 = 3
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# basis functions of degree 0 are
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# N_0,0(u) = 1 on [0,1) and 0 elsewhere,
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# N_1,0(u) = 1 on [1,2) and 0 elsewhere, and
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# N_2,0(u) = 1 on [2,3) and 0 elsewhere.
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u, Nij, Nj = b_spline_basis_functions(U)
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plot_matrix_seperate_single_sum(u, Nij, Nj, figure_id='N1')
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def example2():
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U = (0, 0.25, 0.5, 0.75, 1) # m = 4
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u, Nij, Nj = b_spline_basis_functions(U)
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plot_matrix_seperate_single_sum(u, Nij, Nj, pmax=3, figure_id='N2')
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def example3():
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U = (0, 0, 0, 0.3, 0.5, 0.5, 0.6, 1, 1, 1)
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u, Nij, Nj = b_spline_basis_functions(U)
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plot_matrix_joint_single_sum(u, Nij, Nj, pmax=3, figure_id='N3')
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def example4():
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# clamped B-spline curves
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U = (0, 0, 0, 0, 0.14, 0.28, 0.42, 0.57, 0.71, 0.85, 1, 1, 1, 1)
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m = len(U) - 1 # 13
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P = [[0,1], [.1,2], [.2,2], [.3,1], [.4,1],
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[.5,0], [.6,0], [.7,1], [.6,1], [.5,2]]
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P = [[0,1,0], [.1,2,0], [.2,2,0], [.3,1,1], [.4,1,0],
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[.5,0,0], [.6,0,0], [.7,1,0], [.6,1,0], [.5,2,0]]
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n = len(P) - 1 # 9
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p = m - n - 1
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C = b_spline_curve_with_knots(p, P, U)
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# Cu = sample_half_open(C, U[0], U[-1])
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plot_b_spline_curve_with_knots(C=C, U=U, P=P, figure_id='N4')
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def example5():
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P = [(48.0888108620491, 41.3794408583987, -0.372884555563078),
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(48.2156978454883, 41.4376819952444, -0.372981234249012),
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(48.3421249992392, 41.4949853259561, -0.373021507495587),
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(48.6647993346146, 41.6362394842807, -0.372960532155267),
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(48.8631931562637, 41.7184356658063, -0.372941685915525),
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(49.2627469867943, 41.8770863299231, -0.372965702682335),
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(49.4634735626356, 41.9533782153992, -0.37296977238557),
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(49.8669592828075, 42.1000733004711, -0.372963214968813),
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(50.0698102094774, 42.1705172272789, -0.372961547924453),
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(50.4773734605376, 42.3060584254141, -0.372966255857575),
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(50.6820075976044, 42.371132473348, -0.372964768740875),
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(51.0927404446479, 42.4960106864461, -0.37295550426811),
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(51.2989587087642, 42.5558597303533, -0.37296082550931),
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(51.7131511901618, 42.6711711778783, -0.372997134411391),
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(51.9206405900576, 42.7264781422536, -0.37297347298921),
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(52.3354542080309, 42.8306222566775, -0.372830008862485),
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(52.5444045251438, 42.8799268641912, -0.372905635604393),
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(52.7547311828766, 42.9295775362814, -0.373148784408123)]
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Uu = (0.0228378692889125,
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0.0649893839528174,
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0.130414237399236,
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0.195679174703882,
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0.260898113556269,
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0.326065686455556,
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0.391167888702703,
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0.456323551413636,
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0.521155975846261)
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mult = (4, 2, 2, 2, 2, 2, 2, 2, 4)
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U = [Uu[i] for i in range(len(Uu)) for j in range(mult[i])]
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def basis():
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with timeit('b_spline_basis_functions'):
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u, Nij, Nj = b_spline_basis_functions(U, pmax=11)
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plot_matrix_joint_single_sum(u, Nij, Nj, figure_id='N5 N')
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def curve(knots_cp=True):
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n = len(P) - 1
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m = len(U) - 1
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p = m - n - 1
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with timeit('b_spline_curve_with_knots_sampled'):
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C = b_spline_curve_with_knots(p, P, U)
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Cu = sample_half_open(C, U[0], U[-1])
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plot_b_spline_curve_with_knots(
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Cu=Cu,
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CU=sample_half_open_seq(C, Uu) if knots_cp else None,
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P=P if knots_cp else None,
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figure_id='N5 C')
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pylab.gca().set_zlim3d([-1, 0])
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#basis()
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curve()
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#curve(False)
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def example6():
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#
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# given data, data to compare with own generated data
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#
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P = [(48.0888108620491, 41.3794408583987, -0.372884555563078),
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(48.2156978454883, 41.4376819952444, -0.372981234249012),
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(48.3421249992392, 41.4949853259561, -0.373021507495587),
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(48.6647993346146, 41.6362394842807, -0.372960532155267),
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(48.8631931562637, 41.7184356658063, -0.372941685915525),
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(49.2627469867943, 41.8770863299231, -0.372965702682335),
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(49.4634735626356, 41.9533782153992, -0.37296977238557),
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(49.8669592828075, 42.1000733004711, -0.372963214968813),
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(50.0698102094774, 42.1705172272789, -0.372961547924453),
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(50.4773734605376, 42.3060584254141, -0.372966255857575),
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(50.6820075976044, 42.371132473348, -0.372964768740875),
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(51.0927404446479, 42.4960106864461, -0.37295550426811),
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(51.2989587087642, 42.5558597303533, -0.37296082550931),
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(51.7131511901618, 42.6711711778783, -0.372997134411391),
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(51.9206405900576, 42.7264781422536, -0.37297347298921),
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(52.3354542080309, 42.8306222566775, -0.372830008862485),
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(52.5444045251438, 42.8799268641912, -0.372905635604393),
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(52.7547311828766, 42.9295775362814, -0.373148784408123)]
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Uu = (0.0228378692889125,
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0.0649893839528174,
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0.130414237399236,
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0.195679174703882,
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0.260898113556269,
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0.326065686455556,
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0.391167888702703,
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0.456323551413636,
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0.521155975846261)
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mult = (4, 2, 2, 2, 2, 2, 2, 2, 4)
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U = [Uu[i] for i in range(len(Uu)) for j in range(mult[i])]
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n = len(P) - 1 # number of control points - 1
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m = len(U) -1 # number of knot spans
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p = m - n - 1 # degree
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# print(p)
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C = b_spline_curve_with_knots(p, P, U)
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Cu = sample_half_open(C, U[0], U[-1])
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ax = plot_b_spline_curve_with_knots(Cu=Cu, figure_id='N6')
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#
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# now generate own knots
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#
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p = 3 # degree
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m = n + p + 1 # number of knot spans
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U = b_spline_knots(n, p)
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# U = (0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 14, 14, 14)
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# print(len(U), U)
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C = b_spline_curve_with_knots(p, P, U)
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Cu = sample_half_open(C, U[0], U[-1])
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plot_b_spline_curve_with_knots(Cu=Cu, C=C, U=U, ax=ax)
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#pylab.gca().set_zlim3d([-1, 0])
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def example7():
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P = [(-69.99999999999, 6.23746531921, 119.99999999999),
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(-69.99999999999, 5.72567326271, 120.0),
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(-70.0, 5.2192123782, 120.0),
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(-70.0, 4.718082665681, 120.0),
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(-70.0, 4.222284125153, 120.0),
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(-70.0, 3.731816756617, 120.0),
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(-70.0, 3.246680560071, 120.0),
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(-70.0, 2.766875535516, 120.0),
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(-70.0, 2.292401682953, 120.0),
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(-70.0, 1.82325900238, 120.0),
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(-70.0, 1.359447493799, 120.0),
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(-70.0, 0.900967157208, 120.0),
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(-70.0, 0.447817992609, 120.0),
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(-69.99999999999, -1.642767914458, 119.99999999999),
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(-69.95823302652, -3.284128624962, 119.96005936915),
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(-69.87482030195, -4.920567121601, 119.88028704462),
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(-69.7502001661, -6.548567099244, 119.76113869291),
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(-69.58513326705, -8.164660004507, 119.60341679526),
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(-69.38069590753, -9.765475979336, 119.40825949383),
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(-69.13826152984, -11.34779669959, 119.17711816806),
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(-68.85947036564, -12.90861011093, 118.91172378914),
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(-68.54618721656, -14.44516705927, 118.61404198996),
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(-68.20044740283, -15.95503981856, 118.28621691953),
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(-67.82439084537, -17.43618251348, 117.93050381741),
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(-67.42018430873, -18.88699343893, 117.54919035943),
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(-66.38758251206, -22.29350540161, 116.57795367665),
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(-65.73413448053, -24.21919416036, 115.96554908806),
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(-65.03556391343, -26.07956263873, 115.31370192302),
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(-64.29648522575, -27.87744521951, 114.62724902124),
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(-63.52042791056, -29.61397650413, 113.91024118834),
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(-62.71277001846, -31.2871331673, 113.16847249966),
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(-61.87901674025, -32.89613508726, 112.4077395496),
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(-61.02226890253, -34.44424317029, 111.63151855295),
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(-60.14386048877, -35.93622309031, 110.841629897),
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(-59.24623340527, -37.37387103089, 110.04091803203),
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(-58.33313678246, -38.756819007, 109.23340236149),
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(-57.40516397009, -40.08965381341, 108.42014822445),
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(-55.01642244455, -43.34968716212, 106.34685334397),
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(-53.53813210335, -45.21002358427, 105.08230356996),
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(-52.03458081272, -46.96355473328, 103.81650090025),
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(-50.50977333246, -48.61777575741, 102.55504546095),
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(-48.96692322622, -50.17949288551, 101.30260097008),
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(-47.40801072014, -51.65517742458, 100.06277532323),
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(-45.83395649691, -53.05076391735, 98.838417665337),
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(-44.24537288755, -54.37123987567, 97.632189028576),
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(-42.64319994423, -55.62048722024, 96.446976549361),
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(-41.02853017217, -56.80167054344, 95.285780596074),
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(-39.40157208613, -57.91802439479, 94.15110945761),
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(-37.76099941739, -58.97317114245, 93.044667943398),
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(-33.51657488475, -61.52870256173, 90.285109332808),
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(-30.89322834847, -62.94313830978, 88.677041723595),
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(-28.23238814008, -64.22251443102, 87.15321189152),
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(-25.55002271787, -65.36600940426, 85.732620462342),
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(-22.80465037824, -66.39367032451, 84.407541386373),
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(-20.07652968241, -67.27260606721, 83.231827543651),
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(-17.27816204332, -68.0519427367, 82.167075623263),
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(-14.44812618974, -68.69718956814, 81.25538726298),
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(-11.58521735637, -69.2186257426, 80.51004437835),
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(-8.697808521544, -69.60868640648, 79.943540692506),
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(-5.807821595725, -69.86923851767, 79.563401742733),
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(-2.906442029202, -70.00000000001, 79.372539331945),
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(0.372271370757, -69.99999999999, 79.372539331937),
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(0.762465017147, -69.99999999999, 79.372539331936),
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(1.17058093917, -69.99999999999, 79.372539331935),
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(1.596619136825, -69.99999999999, 79.372539331934),
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(2.040579610114, -69.99999999999, 79.372539331932),
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(2.502462359036, -69.99999999999, 79.372539331931),
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(2.982267383591, -69.99999999998, 79.37253933193),
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(3.479994683778, -69.99999999998, 79.372539331929),
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(3.995644259599, -69.99999999998, 79.372539331927),
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(4.529216111052, -69.99999999998, 79.372539331926),
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(5.080710238139, -69.99999999998, 79.372539331925),
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(5.650126640858, -69.99999999997, 79.372539331923),
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(6.23746531921, -69.99999999997, 79.372539331922)]
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Uu = (-3.932977778518,
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1.445001333941e-14,
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14.427668850884,
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34.626262491172,
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65.717581403178,
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114.40570375563,
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120.64191760942)
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mult = (14, 12, 12, 12, 12, 12, 14)
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U = [Uu[i] for i in range(len(Uu)) for j in range(mult[i])]
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|
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n = len(P) - 1 # number of control points - 1
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m = len(U) -1 # number of knot spans
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p = m - n - 1 # degree
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# print(p)
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|
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with timeit('b_spline_curve_with_knots'):
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C = b_spline_curve_with_knots(p, P, U)
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with timeit('sampling'):
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Cu = sample_half_open(C, U[0], U[-1])
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with timeit('plotting'):
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plot_b_spline_curve_with_knots(Cu=Cu, figure_id='N7')
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|
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# b_spline_curve_with_knots took 0.005 ms, 0.004 ms, 0.002 ms
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# sampling took 20542.242 ms, 21172.614 ms, 21136.981 ms
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# plotting took 29.950 ms, 28.201 ms, 26.364 ms
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|
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|
if __name__ == "__main__":
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|
example7()
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|
pylab.show()
|