# Copyright (C) 2021-2025 Université Gustave Eiffel.
# This file is part of the EasyFEA project.
# EasyFEA is distributed under the terms of the GNU General Public License v3, see LICENSE.txt and CREDITS.md for more information.
"""Tri element module."""
import numpy as np
from .._group_elems import _GroupElem
from ...utilities import _types
[docs]
class TRI3(_GroupElem):
# v
# ^
# |
# 2
# |`\
# | `\
# | `\
# | `\
# | `\
# 0----------1 --> u
def __init__(
self,
gmshId: int,
connect: _types.IntArray,
coordGlob: _types.FloatArray,
nodes: _types.IntArray,
):
super().__init__(gmshId, connect, coordGlob, nodes)
@property
def origin(self) -> list[int]:
return super().origin
@property
def triangles(self) -> list[int]:
return [0, 1, 2]
@property
def surfaces(self) -> _types.IntArray:
return np.array([[0, 1, 2, 0]], dtype=int)
@property
def faces(self) -> _types.IntArray:
return np.arange(self.nPe, dtype=int)
[docs]
def Get_Local_Coords(self):
list_x = [0, 1, 0]
list_y = [0, 0, 1]
local_coords = np.array([list_x, list_y]).T
return local_coords
[docs]
def _N(self) -> _types.FloatArray:
N1 = lambda r, s: -r - s + 1
N2 = lambda r, s: r
N3 = lambda r, s: s
N = np.array([N1, N2, N3]).reshape(-1, 1)
return N
[docs]
def _dN(self) -> _types.FloatArray:
dN1 = [lambda r, s: -1, lambda r, s: -1]
dN2 = [lambda r, s: 1, lambda r, s: 0]
dN3 = [lambda r, s: 0, lambda r, s: 1]
dN = np.array([dN1, dN2, dN3])
return dN
[docs]
def _ddN(self) -> _types.FloatArray:
return super()._ddN()
[docs]
def _dddN(self) -> _types.FloatArray:
return super()._dddN()
[docs]
def _ddddN(self) -> _types.FloatArray:
return super()._ddddN()
[docs]
class TRI6(_GroupElem):
# v
# ^
# |
# 2
# |`\
# | `\
# 5 `4
# | `\
# | `\
# 0----3-----1 --> u
def __init__(
self,
gmshId: int,
connect: _types.IntArray,
coordGlob: _types.FloatArray,
nodes: _types.IntArray,
):
super().__init__(gmshId, connect, coordGlob, nodes)
@property
def origin(self) -> list[int]:
return super().origin
@property
def triangles(self) -> list[int]:
# fmt: off
return [0,3,5,
3,1,4,
5,4,2,
3,4,5]
# fmt: on
@property
def surfaces(self) -> _types.IntArray:
return np.array([[0, 3, 1, 4, 2, 5, 0]], dtype=int)
@property
def faces(self) -> _types.IntArray:
return np.arange(self.nPe, dtype=int)
[docs]
def Get_Local_Coords(self):
list_x = [0, 1, 0, 0.5, 0.5, 0]
list_y = [0, 0, 1, 0, 0.5, 0.5]
local_coords = np.array([list_x, list_y]).T
return local_coords
[docs]
def _N(self) -> _types.FloatArray:
N1 = lambda r, s: (r + s - 1) * (2 * r + 2 * s - 1)
N2 = lambda r, s: r * (2 * r - 1)
N3 = lambda r, s: s * (2 * s - 1)
N4 = lambda r, s: -4 * r * (r + s - 1)
N5 = lambda r, s: 4 * r * s
N6 = lambda r, s: -4 * s * (r + s - 1)
N = np.array([N1, N2, N3, N4, N5, N6]).reshape(-1, 1)
return N
[docs]
def _dN(self) -> _types.FloatArray:
dN1 = [lambda r, s: 4 * r + 4 * s - 3, lambda r, s: 4 * r + 4 * s - 3]
dN2 = [lambda r, s: 4 * r - 1, lambda r, s: 0]
dN3 = [lambda r, s: 0, lambda r, s: 4 * s - 1]
dN4 = [lambda r, s: -8 * r - 4 * s + 4, lambda r, s: -4 * r]
dN5 = [lambda r, s: 4 * s, lambda r, s: 4 * r]
dN6 = [lambda r, s: -4 * s, lambda r, s: -4 * r - 8 * s + 4]
dN = np.array([dN1, dN2, dN3, dN4, dN5, dN6])
return dN
[docs]
def _ddN(self) -> _types.FloatArray:
ddN1 = [lambda r, s: 4, lambda r, s: 4]
ddN2 = [lambda r, s: 4, lambda r, s: 0]
ddN3 = [lambda r, s: 0, lambda r, s: 4]
ddN4 = [lambda r, s: -8, lambda r, s: 0]
ddN5 = [lambda r, s: 0, lambda r, s: 0]
ddN6 = [lambda r, s: 0, lambda r, s: -8]
ddNtild = np.array([ddN1, ddN2, ddN3, ddN4, ddN5, ddN6])
return ddNtild
[docs]
def _dddN(self) -> _types.FloatArray:
return super()._dddN()
[docs]
def _ddddN(self) -> _types.FloatArray:
return super()._ddddN()
[docs]
class TRI10(_GroupElem):
# v
# ^
# |
# 2
# | \
# 7 6
# | \
# 8 (9) 5
# | \
# 0---3---4---1 --> u
def __init__(
self,
gmshId: int,
connect: _types.IntArray,
coordGlob: _types.FloatArray,
nodes: _types.IntArray,
):
super().__init__(gmshId, connect, coordGlob, nodes)
@property
def origin(self) -> list[int]:
return super().origin
@property
def triangles(self) -> list[int]:
# fmt: off
return [0,3,8,
3,4,9,
4,1,5,
4,5,9,
3,9,8,
8,9,7,
9,5,6,
9,6,7,
7,6,2]
# fmt: on
@property
def surfaces(self) -> _types.IntArray:
return np.array([[0, 3, 4, 1, 5, 6, 2, 7, 8, 0]], dtype=int)
@property
def faces(self) -> _types.IntArray:
return np.arange(self.nPe, dtype=int)
[docs]
def Get_Local_Coords(self):
# fmt: off
list_x = [
0,1,0,
1/3,2/3,
2/3, 1/3,
0,0,
1/3
]
list_y = [
0,0,1,
0,0,
1/3, 2/3,
2/3,1/3,
1/3
]
# fmt: off
local_coords = np.array([list_x, list_y]).T
return local_coords
[docs]
def _N(self) -> _types.FloatArray:
N1 = (
lambda r, s: -9 * r**3 / 2
- 27 * r**2 * s / 2
+ 9 * r**2
- 27 * r * s**2 / 2
+ 18 * r * s
- 11 * r / 2
- 9 * s**3 / 2
+ 9 * s**2
- 11 * s / 2
+ 1
)
N2 = lambda r, s: 9 * r**3 / 2 - 9 * r**2 / 2 + r
N3 = lambda r, s: 9 * s**3 / 2 - 9 * s**2 / 2 + s
N4 = (
lambda r, s: 27 * r**3 / 2
+ 27 * r**2 * s
- 45 * r**2 / 2
+ 27 * r * s**2 / 2
- 45 * r * s / 2
+ 9 * r
)
N5 = (
lambda r, s: -27 * r**3 / 2
- 27 * r**2 * s / 2
+ 18 * r**2
+ 9 * r * s / 2
- 9 * r / 2
)
N6 = lambda r, s: 27 * r**2 * s / 2 - 9 * r * s / 2
N7 = lambda r, s: 27 * r * s**2 / 2 - 9 * r * s / 2
N8 = (
lambda r, s: -27 * r * s**2 / 2
+ 9 * r * s / 2
- 27 * s**3 / 2
+ 18 * s**2
- 9 * s / 2
)
N9 = (
lambda r, s: 27 * r**2 * s / 2
+ 27 * r * s**2
- 45 * r * s / 2
+ 27 * s**3 / 2
- 45 * s**2 / 2
+ 9 * s
)
N10 = lambda r, s: -27 * r**2 * s - 27 * r * s**2 + 27 * r * s
N = np.array([N1, N2, N3, N4, N5, N6, N7, N8, N9, N10]).reshape(-1, 1)
return N
[docs]
def _dN(self) -> _types.FloatArray:
dN1 = [
lambda r, s: -27 * r**2 / 2
- 27 * r * s
+ 18 * r
- 27 * s**2 / 2
+ 18 * s
- 11 / 2,
lambda r, s: -27 * r**2 / 2
- 27 * r * s
+ 18 * r
- 27 * s**2 / 2
+ 18 * s
- 11 / 2,
]
dN2 = [lambda r, s: 27 * r**2 / 2 - 9 * r + 1, lambda r, s: 0]
dN3 = [lambda r, s: 0, lambda r, s: 27 * s**2 / 2 - 9 * s + 1]
dN4 = [
lambda r, s: 81 * r**2 / 2
+ 54 * r * s
- 45 * r
+ 27 * s**2 / 2
- 45 * s / 2
+ 9,
lambda r, s: 27 * r**2 + 27 * r * s - 45 * r / 2,
]
dN5 = [
lambda r, s: -81 * r**2 / 2 - 27 * r * s + 36 * r + 9 * s / 2 - 9 / 2,
lambda r, s: -27 * r**2 / 2 + 9 * r / 2,
]
dN6 = [
lambda r, s: 27 * r * s - 9 * s / 2,
lambda r, s: 27 * r**2 / 2 - 9 * r / 2,
]
dN7 = [
lambda r, s: 27 * s**2 / 2 - 9 * s / 2,
lambda r, s: 27 * r * s - 9 * r / 2,
]
dN8 = [
lambda r, s: -27 * s**2 / 2 + 9 * s / 2,
lambda r, s: -27 * r * s + 9 * r / 2 - 81 * s**2 / 2 + 36 * s - 9 / 2,
]
dN9 = [
lambda r, s: 27 * r * s + 27 * s**2 - 45 * s / 2,
lambda r, s: 27 * r**2 / 2
+ 54 * r * s
- 45 * r / 2
+ 81 * s**2 / 2
- 45 * s
+ 9,
]
dN10 = [
lambda r, s: -54 * r * s - 27 * s**2 + 27 * s,
lambda r, s: -27 * r**2 - 54 * r * s + 27 * r,
]
dN = np.array([dN1, dN2, dN3, dN4, dN5, dN6, dN7, dN8, dN9, dN10])
return dN
[docs]
def _ddN(self) -> _types.FloatArray:
ddN1 = [lambda r, s: -27 * r - 27 * s + 18, lambda r, s: -27 * r - 27 * s + 18]
ddN2 = [lambda r, s: 27 * r - 9, lambda r, s: 0]
ddN3 = [lambda r, s: 0, lambda r, s: 27 * s - 9]
ddN4 = [lambda r, s: 81 * r + 54 * s - 45, lambda r, s: 27 * r]
ddN5 = [lambda r, s: -81 * r - 27 * s + 36, lambda r, s: 0]
ddN6 = [lambda r, s: 27 * s, lambda r, s: 0]
ddN7 = [lambda r, s: 0, lambda r, s: 27 * r]
ddN8 = [lambda r, s: 0, lambda r, s: -27 * r - 81 * s + 36]
ddN9 = [lambda r, s: 27 * s, lambda r, s: 54 * r + 81 * s - 45]
ddN10 = [lambda r, s: -54 * s, lambda r, s: -54 * r]
ddN = np.array([ddN1, ddN2, ddN3, ddN4, ddN5, ddN6, ddN7, ddN8, ddN9, ddN10])
return ddN
[docs]
def _dddN(self) -> _types.FloatArray:
dddN1 = [lambda r, s: -27, lambda r, s: -27]
dddN2 = [lambda r, s: 27, lambda r, s: 0]
dddN3 = [lambda r, s: 0, lambda r, s: 27]
dddN4 = [lambda r, s: 81, lambda r, s: 0]
dddN5 = [lambda r, s: -81, lambda r, s: 0]
dddN6 = [lambda r, s: 0, lambda r, s: 0]
dddN7 = [lambda r, s: 0, lambda r, s: 0]
dddN8 = [lambda r, s: 0, lambda r, s: -81]
dddN9 = [lambda r, s: 0, lambda r, s: 81]
dddN10 = [lambda r, s: 0, lambda r, s: 0]
dddN = np.array(
[dddN1, dddN2, dddN3, dddN4, dddN5, dddN6, dddN7, dddN8, dddN9, dddN10]
)
return dddN
[docs]
def _ddddN(self) -> _types.FloatArray:
return super()._ddddN()
[docs]
class TRI15(_GroupElem):
# v
# 2
# | \
# 9 8
# | \
# 10 (14) 7
# | \
# 11 (12) (13) 6
# | \
# 0---3---4---5---1
def __init__(
self,
gmshId: int,
connect: _types.IntArray,
coordGlob: _types.FloatArray,
nodes: _types.IntArray,
):
super().__init__(gmshId, connect, coordGlob, nodes)
@property
def origin(self) -> list[int]:
return super().origin
@property
def triangles(self) -> list[int]:
# fmt: off
return [0,3,11,
3,4,12,
4,5,13,
5,1,6,
5,6,13,
4,13,12,
3,12,11,
11,12,10,
12,13,14,
13,6,7,
13,7,14,
12,14,10,
10,14,9,
14,7,8,
14,8,9,
10,14,9,
9,8,2]
# fmt: on
@property
def surfaces(self) -> _types.IntArray:
return np.array([[0, 3, 4, 5, 1, 6, 7, 8, 2, 9, 10, 11, 0]], dtype=int)
@property
def faces(self) -> _types.IntArray:
return np.arange(self.nPe, dtype=int)
[docs]
def Get_Local_Coords(self):
# fmt: off
list_x = [
0,1,0,
1/4,1/2,3/4,
3/4,1/2,1/4,
0,0,0,
1/4,1/2,1/4
]
list_y = [
0,0,1,
0,0,0,
1/4,1/2,3/4,
3/4,1/2,1/4,
1/4,1/4,1/2
]
# fmt: on
local_coords = np.array([list_x, list_y]).T
return local_coords
[docs]
def _N(self) -> _types.FloatArray:
N1 = (
lambda r, s: (r + s - 1)
* (2 * r + 2 * s - 1)
* (4 * r + 4 * s - 3)
* (4 * r + 4 * s - 1)
/ 3
)
N2 = lambda r, s: r * (2 * r - 1) * (4 * r - 3) * (4 * r - 1) / 3
N3 = lambda r, s: s * (2 * s - 1) * (4 * s - 3) * (4 * s - 1) / 3
N4 = (
lambda r, s: -16
* r
* (r + s - 1)
* (2 * r + 2 * s - 1)
* (4 * r + 4 * s - 3)
/ 3
)
N5 = lambda r, s: 4 * r * (4 * r - 1) * (r + s - 1) * (4 * r + 4 * s - 3)
N6 = lambda r, s: -16 * r * (2 * r - 1) * (4 * r - 1) * (r + s - 1) / 3
N7 = lambda r, s: 16 * r * s * (2 * r - 1) * (4 * r - 1) / 3
N8 = lambda r, s: 4 * r * s * (4 * r - 1) * (4 * s - 1)
N9 = lambda r, s: 16 * r * s * (2 * s - 1) * (4 * s - 1) / 3
N10 = lambda r, s: -16 * s * (2 * s - 1) * (4 * s - 1) * (r + s - 1) / 3
N11 = lambda r, s: 4 * s * (4 * s - 1) * (r + s - 1) * (4 * r + 4 * s - 3)
N12 = (
lambda r, s: -16
* s
* (r + s - 1)
* (2 * r + 2 * s - 1)
* (4 * r + 4 * s - 3)
/ 3
)
N13 = lambda r, s: 32 * r * s * (r + s - 1) * (4 * r + 4 * s - 3)
N14 = lambda r, s: -32 * r * s * (4 * r - 1) * (r + s - 1)
N15 = lambda r, s: -32 * r * s * (4 * s - 1) * (r + s - 1)
N = np.array(
[N1, N2, N3, N4, N5, N6, N7, N8, N9, N10, N11, N12, N13, N14, N15]
).reshape(-1, 1)
return N
[docs]
def _dN(self) -> _types.FloatArray:
dN1 = [
lambda r, s: 128 * r**3 / 3
+ 128 * r**2 * s
- 80 * r**2
+ 128 * r * s**2
- 160 * r * s
+ 140 * r / 3
+ 128 * s**3 / 3
- 80 * s**2
+ 140 * s / 3
- 25 / 3,
lambda r, s: 128 * r**3 / 3
+ 128 * r**2 * s
- 80 * r**2
+ 128 * r * s**2
- 160 * r * s
+ 140 * r / 3
+ 128 * s**3 / 3
- 80 * s**2
+ 140 * s / 3
- 25 / 3,
]
dN2 = [lambda r, s: 128 * r**3 / 3 - 48 * r**2 + 44 * r / 3 - 1, lambda r, s: 0]
dN3 = [lambda r, s: 0, lambda r, s: 128 * s**3 / 3 - 48 * s**2 + 44 * s / 3 - 1]
dN4 = [
lambda r, s: -512 * r**3 / 3
- 384 * r**2 * s
+ 288 * r**2
- 256 * r * s**2
+ 384 * r * s
- 416 * r / 3
- 128 * s**3 / 3
+ 96 * s**2
- 208 * s / 3
+ 16,
lambda r, s: -128 * r**3
- 256 * r**2 * s
+ 192 * r**2
- 128 * r * s**2
+ 192 * r * s
- 208 * r / 3,
]
dN5 = [
lambda r, s: 256 * r**3
+ 384 * r**2 * s
- 384 * r**2
+ 128 * r * s**2
- 288 * r * s
+ 152 * r
- 16 * s**2
+ 28 * s
- 12,
lambda r, s: 128 * r**3 + 128 * r**2 * s - 144 * r**2 - 32 * r * s + 28 * r,
]
dN6 = [
lambda r, s: -512 * r**3 / 3
- 128 * r**2 * s
+ 224 * r**2
+ 64 * r * s
- 224 * r / 3
- 16 * s / 3
+ 16 / 3,
lambda r, s: -128 * r**3 / 3 + 32 * r**2 - 16 * r / 3,
]
dN7 = [
lambda r, s: 128 * r**2 * s - 64 * r * s + 16 * s / 3,
lambda r, s: 128 * r**3 / 3 - 32 * r**2 + 16 * r / 3,
]
dN8 = [
lambda r, s: 128 * r * s**2 - 32 * r * s - 16 * s**2 + 4 * s,
lambda r, s: 128 * r**2 * s - 16 * r**2 - 32 * r * s + 4 * r,
]
dN9 = [
lambda r, s: 128 * s**3 / 3 - 32 * s**2 + 16 * s / 3,
lambda r, s: 128 * r * s**2 - 64 * r * s + 16 * r / 3,
]
dN10 = [
lambda r, s: -128 * s**3 / 3 + 32 * s**2 - 16 * s / 3,
lambda r, s: -128 * r * s**2
+ 64 * r * s
- 16 * r / 3
- 512 * s**3 / 3
+ 224 * s**2
- 224 * s / 3
+ 16 / 3,
]
dN11 = [
lambda r, s: 128 * r * s**2 - 32 * r * s + 128 * s**3 - 144 * s**2 + 28 * s,
lambda r, s: 128 * r**2 * s
- 16 * r**2
+ 384 * r * s**2
- 288 * r * s
+ 28 * r
+ 256 * s**3
- 384 * s**2
+ 152 * s
- 12,
]
dN12 = [
lambda r, s: -128 * r**2 * s
- 256 * r * s**2
+ 192 * r * s
- 128 * s**3
+ 192 * s**2
- 208 * s / 3,
lambda r, s: -128 * r**3 / 3
- 256 * r**2 * s
+ 96 * r**2
- 384 * r * s**2
+ 384 * r * s
- 208 * r / 3
- 512 * s**3 / 3
+ 288 * s**2
- 416 * s / 3
+ 16,
]
dN13 = [
lambda r, s: 384 * r**2 * s
+ 512 * r * s**2
- 448 * r * s
+ 128 * s**3
- 224 * s**2
+ 96 * s,
lambda r, s: 128 * r**3
+ 512 * r**2 * s
- 224 * r**2
+ 384 * r * s**2
- 448 * r * s
+ 96 * r,
]
dN14 = [
lambda r, s: -384 * r**2 * s
- 256 * r * s**2
+ 320 * r * s
+ 32 * s**2
- 32 * s,
lambda r, s: -128 * r**3
- 256 * r**2 * s
+ 160 * r**2
+ 64 * r * s
- 32 * r,
]
dN15 = [
lambda r, s: -256 * r * s**2
+ 64 * r * s
- 128 * s**3
+ 160 * s**2
- 32 * s,
lambda r, s: -256 * r**2 * s
+ 32 * r**2
- 384 * r * s**2
+ 320 * r * s
- 32 * r,
]
dN = np.array(
[
dN1,
dN2,
dN3,
dN4,
dN5,
dN6,
dN7,
dN8,
dN9,
dN10,
dN11,
dN12,
dN13,
dN14,
dN15,
]
)
return dN
[docs]
def _ddN(self) -> _types.FloatArray:
ddN1 = [
lambda r, s: 128 * r**2
+ 256 * r * s
- 160 * r
+ 128 * s**2
- 160 * s
+ 140 / 3,
lambda r, s: 128 * r**2
+ 256 * r * s
- 160 * r
+ 128 * s**2
- 160 * s
+ 140 / 3,
]
ddN2 = [lambda r, s: 128 * r**2 - 96 * r + 44 / 3, lambda r, s: 0]
ddN3 = [lambda r, s: 0, lambda r, s: 128 * s**2 - 96 * s + 44 / 3]
ddN4 = [
lambda r, s: -512 * r**2
- 768 * r * s
+ 576 * r
- 256 * s**2
+ 384 * s
- 416 / 3,
lambda r, s: -256 * r**2 - 256 * r * s + 192 * r,
]
ddN5 = [
lambda r, s: 768 * r**2
+ 768 * r * s
- 768 * r
+ 128 * s**2
- 288 * s
+ 152,
lambda r, s: 128 * r**2 - 32 * r,
]
ddN6 = [
lambda r, s: -512 * r**2 - 256 * r * s + 448 * r + 64 * s - 224 / 3,
lambda r, s: 0,
]
ddN7 = [lambda r, s: 256 * r * s - 64 * s, lambda r, s: 0]
ddN8 = [lambda r, s: 128 * s**2 - 32 * s, lambda r, s: 128 * r**2 - 32 * r]
ddN9 = [lambda r, s: 0, lambda r, s: 256 * r * s - 64 * r]
ddN10 = [
lambda r, s: 0,
lambda r, s: -256 * r * s + 64 * r - 512 * s**2 + 448 * s - 224 / 3,
]
ddN11 = [
lambda r, s: 128 * s**2 - 32 * s,
lambda r, s: 128 * r**2
+ 768 * r * s
- 288 * r
+ 768 * s**2
- 768 * s
+ 152,
]
ddN12 = [
lambda r, s: -256 * r * s - 256 * s**2 + 192 * s,
lambda r, s: -256 * r**2
- 768 * r * s
+ 384 * r
- 512 * s**2
+ 576 * s
- 416 / 3,
]
ddN13 = [
lambda r, s: 768 * r * s + 512 * s**2 - 448 * s,
lambda r, s: 512 * r**2 + 768 * r * s - 448 * r,
]
ddN14 = [
lambda r, s: -768 * r * s - 256 * s**2 + 320 * s,
lambda r, s: -256 * r**2 + 64 * r,
]
ddN15 = [
lambda r, s: -256 * s**2 + 64 * s,
lambda r, s: -256 * r**2 - 768 * r * s + 320 * r,
]
ddN = np.array(
[
ddN1,
ddN2,
ddN3,
ddN4,
ddN5,
ddN6,
ddN7,
ddN8,
ddN9,
ddN10,
ddN11,
ddN12,
ddN13,
ddN14,
ddN15,
]
)
return ddN
[docs]
def _dddN(self) -> _types.FloatArray:
dddN1 = [
lambda r, s: 256 * r + 256 * s - 160,
lambda r, s: 256 * r + 256 * s - 160,
]
dddN2 = [lambda r, s: 256 * r - 96, lambda r, s: 0]
dddN3 = [lambda r, s: 0, lambda r, s: 256 * s - 96]
dddN4 = [lambda r, s: -1024 * r - 768 * s + 576, lambda r, s: -256 * r]
dddN5 = [lambda r, s: 1536 * r + 768 * s - 768, lambda r, s: 0]
dddN6 = [lambda r, s: -1024 * r - 256 * s + 448, lambda r, s: 0]
dddN7 = [lambda r, s: 256 * s, lambda r, s: 0]
dddN8 = [lambda r, s: 0, lambda r, s: 0]
dddN9 = [lambda r, s: 0, lambda r, s: 256 * r]
dddN10 = [lambda r, s: 0, lambda r, s: -256 * r - 1024 * s + 448]
dddN11 = [lambda r, s: 0, lambda r, s: 768 * r + 1536 * s - 768]
dddN12 = [lambda r, s: -256 * s, lambda r, s: -768 * r - 1024 * s + 576]
dddN13 = [lambda r, s: 768 * s, lambda r, s: 768 * r]
dddN14 = [lambda r, s: -768 * s, lambda r, s: 0]
dddN15 = [lambda r, s: 0, lambda r, s: -768 * r]
dddN = np.array(
[
dddN1,
dddN2,
dddN3,
dddN4,
dddN5,
dddN6,
dddN7,
dddN8,
dddN9,
dddN10,
dddN11,
dddN12,
dddN13,
dddN14,
dddN15,
]
)
return dddN
[docs]
def _ddddN(self) -> _types.FloatArray:
ddddN1 = [lambda r, s: 256, lambda r, s: 256]
ddddN2 = [lambda r, s: 256, lambda r, s: 0]
ddddN3 = [lambda r, s: 0, lambda r, s: 256]
ddddN4 = [lambda r, s: -1024, lambda r, s: 0]
ddddN5 = [lambda r, s: 1536, lambda r, s: 0]
ddddN6 = [lambda r, s: -1024, lambda r, s: 0]
ddddN7 = [lambda r, s: 0, lambda r, s: 0]
ddddN8 = [lambda r, s: 0, lambda r, s: 0]
ddddN9 = [lambda r, s: 0, lambda r, s: 0]
ddddN10 = [lambda r, s: 0, lambda r, s: -1024]
ddddN11 = [lambda r, s: 0, lambda r, s: 1536]
ddddN12 = [lambda r, s: 0, lambda r, s: -1024]
ddddN13 = [lambda r, s: 0, lambda r, s: 0]
ddddN14 = [lambda r, s: 0, lambda r, s: 0]
ddddN15 = [lambda r, s: 0, lambda r, s: 0]
ddddN = np.array(
[
ddddN1,
ddddN2,
ddddN3,
ddddN4,
ddddN5,
ddddN6,
ddddN7,
ddddN8,
ddddN9,
ddddN10,
ddddN11,
ddddN12,
ddddN13,
ddddN14,
ddddN15,
]
)
return ddddN