Coverage for src/meshpy/mesh_creation_functions/beam_nurbs.py: 94%

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22"""Create a beam filament from a NURBS curve represented with splinepy.""" 

23 

24import numpy as _np 

25 

26from meshpy.core.conf import mpy as _mpy 

27from meshpy.mesh_creation_functions.beam_curve import ( 

28 create_beam_mesh_curve as _create_beam_mesh_curve, 

29) 

30 

31 

32def get_nurbs_curve_function_and_jacobian_for_integration(curve, tol=None): 

33 """Return function objects for evaluating the curve and the derivative. 

34 These functions are used in the curve integration. It can happen that the 

35 integration algorithm has to evaluate the curve outside of the defined 

36 domain. This usually leads to errors in common NURBS packages. Therefore, 

37 we check for this evaluation outside of the parameter domain here and 

38 perform a linear extrapolation. 

39 

40 Args 

41 ---- 

42 curve: splinepy object 

43 Curve that is used to describe the beam centerline. 

44 tol: float 

45 Tolerance for checking if point is close to the start or end of the 

46 interval. If None is given, use the default tolerance from mpy. 

47 

48 Return 

49 ---- 

50 (function, jacobian, curve_start, curve_end): 

51 function: 

52 Function for evaluating a position on the curve 

53 jacobian: 

54 Function for evaluating the tangent along the curve 

55 curve_start: 

56 Parameter coordinate for the start for the NURBS curve 

57 curve_end: 

58 Parameter coordinate for the end for the NURBS curve 

59 """ 

60 

61 if tol is None: 

62 tol = _mpy.eps_pos 

63 

64 knot_vector = curve.knot_vectors[0] 

65 curve_start = _np.min(knot_vector) 

66 curve_end = _np.max(knot_vector) 

67 

68 def eval_r(t): 

69 """Evaluate the position along the curve.""" 

70 return curve.evaluate([[t]])[0] 

71 

72 def eval_rp(t): 

73 """Evaluate the derivative along the curve.""" 

74 return curve.derivative([[t]], orders=[1])[0] 

75 

76 def function(t): 

77 """Convert the curve to a function that can be used for beam 

78 generation.""" 

79 

80 if curve_start <= t <= curve_end: 

81 return eval_r(t) 

82 elif t < curve_start and _np.abs(t - curve_start) < tol: 

83 diff = t - curve_start 

84 return eval_r(curve_start) + diff * eval_rp(curve_start) 

85 elif t > curve_end and _np.abs(t - curve_end) < tol: 

86 diff = t - curve_end 

87 return eval_r(curve_end) + diff * eval_rp(curve_end) 

88 raise ValueError( 

89 "Can not evaluate the curve function outside of the interval (plus tolerances).\n" 

90 f"Abs diff start: {_np.abs(curve_start - t)}\nAbs diff end: {_np.abs(t - curve_end)}" 

91 ) 

92 

93 def jacobian(t): 

94 """Convert the spline to a Jacobian function that can be used for curve 

95 generation. 

96 

97 There is no tolerance here, since the integration algorithms 

98 sometimes evaluate the derivative far outside the interval. 

99 """ 

100 

101 if curve_start <= t <= curve_end: 

102 return eval_rp(t) 

103 elif t < curve_start: 

104 return eval_rp(curve_start) 

105 elif curve_end < t: 

106 return eval_rp(curve_end) 

107 raise ValueError("Should not happen") 

108 

109 return function, jacobian, curve_start, curve_end 

110 

111 

112def create_beam_mesh_from_nurbs( 

113 mesh, beam_class, material, curve, *, tol=None, **kwargs 

114): 

115 """Generate a beam from a NURBS curve. 

116 

117 Args 

118 ---- 

119 mesh: Mesh 

120 Mesh that the curve will be added to. 

121 beam_class: Beam 

122 Class of beam that will be used for this line. 

123 material: Material 

124 Material for this line. 

125 curve: splinepy object 

126 Curve that is used to describe the beam centerline. 

127 tol: float 

128 Tolerance for checking if point is close to the start or end of the 

129 interval. If None is given, use the default tolerance from mpy. 

130 

131 **kwargs (for all of them look into create_beam_mesh_function) 

132 ---- 

133 n_el: int 

134 Number of equally spaced beam elements along the line. Defaults to 1. 

135 Mutually exclusive with l_el. 

136 l_el: float 

137 Desired length of beam elements. Mutually exclusive with n_el. 

138 Be aware, that this length might not be achieved, if the elements are 

139 warped after they are created. 

140 

141 Return: 

142 Return value from create_beam_mesh_function 

143 """ 

144 

145 ( 

146 function, 

147 jacobian, 

148 curve_start, 

149 curve_end, 

150 ) = get_nurbs_curve_function_and_jacobian_for_integration(curve, tol=tol) 

151 

152 # Create the beams 

153 return _create_beam_mesh_curve( 

154 mesh, 

155 beam_class, 

156 material, 

157 function, 

158 [curve_start, curve_end], 

159 function_derivative=jacobian, 

160 **kwargs, 

161 )