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Make corners straight
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@markriegler
markriegler committed Feb 7, 2025
1 parent 0785961 commit f9a7ae9
Showing 1 changed file with 287 additions and 54 deletions.
341 changes: 287 additions & 54 deletions splinepy/microstructure/tiles/smx2d_inverse.py
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Original file line number Diff line number Diff line change
Expand Up @@ -71,106 +71,339 @@ def create_tile(
v_one_half = 0.5
v_one = 1.0

# Auxiliary values
triangle_height = 0.5 * (v_one - bar_thickness - bar_thickness)
th_ne, th_se, th_sw, th_nw = parameters.ravel()
else:
raise NotImplementedError(
"Derivatives not implemented for this tile"
)

# Define crossing points of bars, analytically computed beforehand
crossing_s_x = (
-th_ne * th_se * th_sw
+ th_ne * th_sw
+ th_nw * th_se * th_sw
- th_nw * th_se
- th_nw * th_sw
+ th_nw
+ th_se
- 1
) / (
-th_ne * th_se
+ th_ne
- th_nw * th_sw
+ th_nw
+ th_se
+ th_sw
- 2
)
crossing_s_y = (
-th_ne * th_nw * th_se
- th_ne * th_nw * th_sw
+ th_ne * th_nw
+ th_ne * th_se
+ th_ne * th_sw
- th_ne
+ th_nw * th_se
+ th_nw * th_sw
- th_nw
- th_se
- th_sw
+ 1
) / (
th_ne * th_se
- th_ne
+ th_nw * th_sw
- th_nw
- th_se
- th_sw
+ 2
)
crossing_w_x = (
th_ne * th_nw * th_se
- th_ne * th_nw
+ th_ne * th_se * th_sw
- th_ne * th_se
- th_ne * th_sw
+ th_ne
- th_nw * th_se
+ th_nw
- th_se * th_sw
+ th_se
+ th_sw
- 1
) / (
-th_ne * th_nw
+ th_ne
+ th_nw
- th_se * th_sw
+ th_se
+ th_sw
- 2
)
crossing_w_y = (
th_ne * th_nw * th_sw
- th_ne * th_sw
- th_nw * th_se * th_sw
+ th_nw * th_se
- th_nw
+ th_se * th_sw
- th_se
+ 1
) / (
th_ne * th_nw
- th_ne
- th_nw
+ th_se * th_sw
- th_se
- th_sw
+ 2
)
crossing_e_x = (
-th_ne * th_nw * th_sw
+ th_ne * th_sw
- th_nw * th_se * th_sw
+ th_nw * th_se
+ th_nw * th_sw
- 1
) / (
-th_ne * th_nw
+ th_ne
+ th_nw
- th_se * th_sw
+ th_se
+ th_sw
- 2
)
crossing_e_y = (
th_ne * th_nw * th_se
- th_ne * th_se * th_sw
+ th_ne * th_sw
- th_ne
- th_nw * th_se
+ th_se * th_sw
- th_sw
+ 1
) / (
th_ne * th_nw
- th_ne
- th_nw
+ th_se * th_sw
- th_se
- th_sw
+ 2
)
crossing_n_x = (
-th_ne * th_nw * th_se
+ th_ne * th_nw * th_sw
- th_ne * th_sw
+ th_ne
+ th_nw * th_se
- th_nw * th_sw
+ th_sw
- 1
) / (
-th_ne * th_se
+ th_ne
- th_nw * th_sw
+ th_nw
+ th_se
+ th_sw
- 2
)
crossing_n_y = (
th_ne * th_se * th_sw
- th_ne * th_sw
+ th_nw * th_se * th_sw
- th_nw * th_se
- th_se * th_sw
+ 1
) / (
th_ne * th_se
- th_ne
+ th_nw * th_sw
- th_nw
- th_se
- th_sw
+ 2
)

spline_list = []

# Create triangle
triangle_sw = _np.array(
# Define control points
sw_bar_bottom = _np.array(
[
[v_zero, bar_thickness],
[v_zero, v_one_half],
[th_sw, v_zero],
[crossing_s_x, crossing_s_y],
[th_sw / 2, th_sw / 2],
[
triangle_height * 0.5,
v_one_half - triangle_height * 0.5,
(crossing_w_x + crossing_s_x) / 2,
(crossing_w_y + crossing_s_y) / 2,
],
[triangle_height / 3, v_one_half],
]
)

triangle_se = _np.array(
sw_bar_top = _np.array(
[
[v_zero, v_one_half],
[v_zero, v_one - bar_thickness],
[triangle_height / 3, v_one_half],
[th_sw / 2, th_sw / 2],
[
triangle_height * 0.5,
v_one_half + triangle_height * 0.5,
(crossing_w_x + crossing_s_x) / 2,
(crossing_w_y + crossing_s_y) / 2,
],
[v_zero, th_sw],
[crossing_w_x, crossing_w_y],
]
)
triangle_n = _np.array(

se_bar_bottom = _np.array(
[
[crossing_s_x, crossing_s_y],
[v_one - th_se, v_zero],
[
triangle_height * 0.5,
v_one_half - triangle_height * 0.5,
(crossing_s_x + crossing_e_x) / 2,
(crossing_s_y + crossing_e_y) / 2,
],
[triangle_height / 3, v_one_half],
[triangle_height, v_one_half],
[v_one - th_se / 2, th_se / 2],
]
)

se_bar_top = _np.array(
[
[
triangle_height * 0.5,
v_one_half + triangle_height * 0.5,
(crossing_s_x + crossing_e_x) / 2,
(crossing_s_y + crossing_e_y) / 2,
],
[v_one - th_se / 2, th_se / 2],
[crossing_e_x, crossing_e_y],
[v_one, th_se],
]
)

# Define bar control points
sw_bar_bottom = _np.array(
nw_bar_bottom = _np.array(
[
[v_zero, bar_thickness],
[v_zero, v_one - th_nw],
[crossing_w_x, crossing_w_y],
[th_nw / 2, v_one - th_nw / 2],
[
triangle_height * 0.5,
v_one_half - triangle_height * 0.5,
(crossing_w_x + crossing_n_x) / 2,
(crossing_w_y + crossing_n_y) / 2,
],
[bar_thickness, v_zero],
]
)

nw_bar_top = _np.array(
[
[th_nw / 2, v_one - th_nw / 2],
[
v_one_half - triangle_height * 0.5,
triangle_height * 0.5,
(crossing_w_x + crossing_n_x) / 2,
(crossing_w_y + crossing_n_y) / 2,
],
[th_nw, v_one],
[crossing_n_x, crossing_n_y],
]
)

sw_bar_top = _np.array(
ne_bar_bottom = _np.array(
[
[crossing_e_x, crossing_e_y],
[v_one, v_one - th_ne],
[
triangle_height * 0.5,
v_one_half - triangle_height * 0.5,
(crossing_e_x + crossing_n_x) / 2,
(crossing_e_y + crossing_n_y) / 2,
],
[triangle_height, v_one_half],
[v_one - th_ne / 2, v_one - th_ne / 2],
]
)

ne_bar_top = _np.array(
[
[
v_one_half - triangle_height * 0.5,
triangle_height * 0.5,
(crossing_e_x + crossing_n_x) / 2,
(crossing_e_y + crossing_n_y) / 2,
],
[v_one_half, triangle_height],
[v_one - th_ne / 2, v_one - th_ne / 2],
[crossing_n_x, crossing_n_y],
[v_one - th_ne, v_one],
]
)

# Transformation function to rotate recurrent patterns
def rotate_function(cps):
return _np.hstack(
(
cps[:, 1].reshape(-1, 1),
v_one - cps[:, 0].reshape(-1, 1),
)
)
# Define control points for middle part
middle_s = _np.array(
[
[crossing_s_x, crossing_s_y],
[
(crossing_s_x + crossing_e_x) / 2,
(crossing_s_y + crossing_e_y) / 2,
],
[
(crossing_s_x + crossing_w_x) / 2,
(crossing_s_y + crossing_w_y) / 2,
],
[v_one_half, v_one_half],
]
)

for patch_yz_cps in [
triangle_sw,
triangle_se,
triangle_n,
middle_w = _np.array(
[
[
(crossing_s_x + crossing_w_x) / 2,
(crossing_s_y + crossing_w_y) / 2,
],
[v_one_half, v_one_half],
[crossing_w_x, crossing_w_y],
[
(crossing_n_x + crossing_w_x) / 2,
(crossing_n_y + crossing_w_y) / 2,
],
]
)

middle_e = _np.array(
[
[
(crossing_s_x + crossing_e_x) / 2,
(crossing_s_y + crossing_e_y) / 2,
],
[crossing_e_x, crossing_e_y],
[v_one_half, v_one_half],
[
(crossing_n_x + crossing_e_x) / 2,
(crossing_n_y + crossing_e_y) / 2,
],
]
)

middle_n = _np.array(
[
[v_one_half, v_one_half],
[
(crossing_n_x + crossing_e_x) / 2,
(crossing_n_y + crossing_e_y) / 2,
],
[
(crossing_n_x + crossing_w_x) / 2,
(crossing_n_y + crossing_w_y) / 2,
],
[crossing_n_x, crossing_n_y],
]
)

for control_points in [
sw_bar_bottom,
sw_bar_top,
se_bar_bottom,
se_bar_top,
nw_bar_top,
nw_bar_bottom,
ne_bar_bottom,
ne_bar_top,
middle_s,
middle_w,
middle_e,
middle_n,
]:
for _ in range(4):
patch_yz_cps = rotate_function(patch_yz_cps)
spline_list.append(
_Bezier(degrees=[1, 1], control_points=patch_yz_cps)
)
spline_list.append(
_Bezier(degrees=[1, 1], control_points=control_points)
)

if i_derivative == 0:
splines = spline_list.copy()
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