# 曲线网格基础

本教程介绍如何使用 `meshkernel` 库生成曲线网格。

[返回示例目录](index.md)

以下保留原笔记本的代码和已保存输出；转换过程中未重新执行代码。

首先导入所需的库。

```python
import matplotlib.pyplot as plt
import numpy as np

from meshkernel import (
    CurvilinearParameters,
    MakeGridParameters,
    GeometryList,
    MeshKernel,
    SplinesToCurvilinearParameters,
    OrthogonalizationParameters,
)
```

定义一个函数，使用 `curvilinear_compute_transfinite_from_splines` 生成曲线网格，并创建包含该网格的 `MeshKernel` 实例：

- 首先创建用于生成曲线网格的样条曲线，各条样条曲线用 `-999.0` 分隔。
- 在新的 `CurvilinearParameters` 实例中设置 m、n 方向的划分数。
- 创建一个新的 `MeshKernel` 实例。
- 使用超限插值算法生成曲线网格。

```python
def create_mk_instance_with_curvilinear_grid_from_transfinite_method():
    r"""创建包含曲线网格的 MeshKernel 实例。"""
    mk = MeshKernel()

    separator = -999.0
    splines_x = np.array(
        [
            2.0,
            4.0,
            7.0,
            separator,
            -1.0,
            1.0,
            5.0,
            separator,
            3.0,
            -2.0,
            separator,
            7.0,
            4.0,
        ],
        dtype=np.double,
    )
    splines_y = np.array(
        [
            1.0,
            3.0,
            4.0,
            separator,
            4.0,
            6.0,
            7.0,
            separator,
            1.0,
            6.0,
            separator,
            3.0,
            8.0,
        ],
        dtype=np.double,
    )
    splines = GeometryList(splines_x, splines_y)

    curvilinear_parameters = CurvilinearParameters()
    curvilinear_parameters.n_refinement = 10
    curvilinear_parameters.m_refinement = 10

    mk.curvilinear_compute_transfinite_from_splines(splines, curvilinear_parameters)

    return mk
```

定义一个用于创建矩形曲线网格的函数。

```python
def create_mk_instance_with_a_rectangular_curvilinear_grid(num_columns=3, num_rows=3):
    r"""创建包含矩形曲线网格的 MeshKernel 实例的局部函数。"""
    mk = MeshKernel()

    # 创建 MakeGridParameters 实例并设置参数值
    make_grid_parameters = MakeGridParameters()
    make_grid_parameters.num_columns = num_columns
    make_grid_parameters.num_rows = num_rows
    make_grid_parameters.angle = 0.0
    make_grid_parameters.origin_x = 0.0
    make_grid_parameters.origin_y = 0.0
    make_grid_parameters.block_size_x = 10.0
    make_grid_parameters.block_size_y = 10.0

    mk.curvilinear_compute_rectangular_grid(make_grid_parameters)

    return mk
```

## 使用超限插值法生成曲线网格

```python
curvilinear_grid_transfinite = (
    create_mk_instance_with_curvilinear_grid_from_transfinite_method().curvilineargrid_get()
)
```

绘制结果。

```python
fig, ax = plt.subplots()
curvilinear_grid_transfinite.plot_edges(ax)
```

![单元格 10 的绘图输出](images/04_curvilineargrid_basics_10_0.png)

## 使用推进前沿法生成曲线网格

定义生成曲线网格的过程，使用 `curvilinear_compute_orthogonal_from_splines` 方法创建包含网格的 `MeshKernel` 实例：

- 首先创建用于生成曲线网格的样条曲线，各条样条曲线用 `-999.0` 分隔。
- 在新的 `CurvilinearParameters` 实例中设置 m、n 方向的划分数。
- 该算法还需要设置从样条曲线生成曲线网格所需的附加参数。
- 然后使用推进前沿算法生成曲线网格。

```python
mk = MeshKernel()

separator = -999.0
splines_x = np.array([-1.0, 2.0, 6.0, separator, 3.0, -2.0, separator], dtype=np.double)
splines_y = np.array([2.0, 5.0, 6.0, separator, 1.0, 6.0, separator], dtype=np.double)

splines_values = np.zeros_like(splines_x)
splines = GeometryList(splines_x, splines_y, splines_values)

curvilinearParameters = CurvilinearParameters()
curvilinearParameters.n_refinement = 10
curvilinearParameters.m_refinement = 10

splinesToCurvilinearParameters = SplinesToCurvilinearParameters()
splinesToCurvilinearParameters.aspect_ratio = 1.0
splinesToCurvilinearParameters.aspect_ratio_grow_factor = 1.0
splinesToCurvilinearParameters.average_width = 0.2
splinesToCurvilinearParameters.nodes_on_top_of_each_other_tolerance = 1e-4
splinesToCurvilinearParameters.min_cosine_crossing_angles = 0.95
splinesToCurvilinearParameters.check_front_collisions = 0
splinesToCurvilinearParameters.curvature_adapted_grid_spacing = 1
splinesToCurvilinearParameters.remove_skinny_triangles = 1

mk.curvilinear_compute_orthogonal_from_splines(
    splines, curvilinearParameters, splinesToCurvilinearParameters
)

curvilinear_grid_orthogonal = mk.curvilineargrid_get()
```

绘制结果。

```python
fig, ax = plt.subplots()
curvilinear_grid_orthogonal.plot_edges(ax)
```

![单元格 15 的绘图输出](images/04_curvilineargrid_basics_15_0.png)

## 曲线网格加密与粗化

加密前的网格。

```python
mk = create_mk_instance_with_curvilinear_grid_from_transfinite_method()
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 18 的绘图输出](images/04_curvilineargrid_basics_18_0.png)

在两个选定点之间，为每一行添加两条水平网格线进行加密，并绘制结果。

```python
mk.curvilinear_refine(2.299, 4.612, 3.074, 3.684, 2)
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 20 的绘图输出](images/04_curvilineargrid_basics_20_0.png)

删除相同行中的网格线，进行粗化。

```python
mk.curvilinear_refine(2.299, 4.612, 3.074, 3.684, -2)
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 22 的绘图输出](images/04_curvilineargrid_basics_22_0.png)

## 创建矩形网格

```python
mk = create_mk_instance_with_a_rectangular_curvilinear_grid()
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 24 的绘图输出](images/04_curvilineargrid_basics_24_0.png)

也可以根据多边形生成矩形网格。多边形必须闭合。

```python
node_x = np.array([2.5, 5.5, 3.5, 0.5, 2.5], dtype=np.double)
node_y = np.array([0.5, 3.0, 5.0, 2.5, 0.5], dtype=np.double)
geometry_list = GeometryList(node_x, node_y)
```

```python
make_grid_parameters = MakeGridParameters()
make_grid_parameters.num_columns = 10
make_grid_parameters.num_rows = 10
make_grid_parameters.angle = 0.0
make_grid_parameters.origin_x = 0.0
make_grid_parameters.origin_y = 0.0
make_grid_parameters.block_size_x = 0.2
make_grid_parameters.block_size_y = 0.2
```

```python
mk.curvilinear_compute_rectangular_grid_from_polygon(
    make_grid_parameters, geometry_list
)
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 28 的绘图输出](images/04_curvilineargrid_basics_28_0.png)

## 利用多边形边界上的节点生成曲线网格

定义多边形并生成曲线网格。

```python
node_x = np.array([2, 4, 6, 7, 8, 8, 8, 8, 7, 5, 3, 2, 2, 2, 2], dtype=np.double)
node_y = np.array([1, 1, 1, 1, 1, 1.2, 4, 6, 6, 6, 6, 6, 5, 3, 1], dtype=np.double)
geometry_list = GeometryList(node_x, node_y)
mk = MeshKernel()
mk.curvilinear_compute_transfinite_from_polygon(geometry_list, 0, 4, 7, False)
```

```python
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 32 的绘图输出](images/04_curvilineargrid_basics_32_0.png)

## 曲线网格正交化

移动一个节点，使网格不再正交，并绘制结果。

```python
mk = create_mk_instance_with_a_rectangular_curvilinear_grid()
mk.curvilinear_move_node(10.0, 20.0, 18.0, 12.0)
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 35 的绘图输出](images/04_curvilineargrid_basics_35_0.png)

执行正交化。

```python
# 在正交化前检查节点位置
orthogonalization_parameters = OrthogonalizationParameters()
orthogonalization_parameters.outer_iterations = 1
orthogonalization_parameters.boundary_iterations = 25
orthogonalization_parameters.inner_iterations = 25
orthogonalization_parameters.orthogonalization_to_smoothing_factor = 0.95

# 初始化曲线网格正交化算法
# 设置要正交化的网格块（本例指定网格的左下角和右上角）
mk.curvilinear_orthogonalize(orthogonalization_parameters, 0.0, 0.0, 30.0, 30.0)
```

绘制正交化后的结果。

```python
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 39 的绘图输出](images/04_curvilineargrid_basics_39_0.png)

## 固定一条网格线进行曲线网格正交化

```python
mk = create_mk_instance_with_a_rectangular_curvilinear_grid()
mk.curvilinear_move_node(10.0, 20.0, 18.0, 12.0)
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 41 的绘图输出](images/04_curvilineargrid_basics_41_0.png)

执行正交化，同时固定被移动节点所在的垂直网格线。

```python
# 在正交化前检查节点位置
orthogonalization_parameters = OrthogonalizationParameters()
orthogonalization_parameters.outer_iterations = 1
orthogonalization_parameters.boundary_iterations = 25
orthogonalization_parameters.inner_iterations = 25
orthogonalization_parameters.orthogonalization_to_smoothing_factor = 0.95

# 固定被移动节点所在的垂直网格线
mk.curvilinear_frozen_line_add(10.0, 0.0, 10.0, 30.0)

# 执行正交化
# 初始化曲线网格正交化算法
# 设置要正交化的网格块（本例指定网格的左下角和右上角）
mk.curvilinear_orthogonalize(orthogonalization_parameters, 0.0, 0.0, 30.0, 30.0)
```

绘制正交化后的结果。

```python
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 45 的绘图输出](images/04_curvilineargrid_basics_45_0.png)

## 曲线网格平滑

移动一个节点，使网格不再平滑，并绘制结果。

```python
mk = create_mk_instance_with_a_rectangular_curvilinear_grid()
mk.curvilinear_move_node(10.0, 20.0, 18.0, 12.0)
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 48 的绘图输出](images/04_curvilineargrid_basics_48_0.png)

执行平滑。

```python
mk.curvilinear_smoothing(10, 0.0, 0.0, 30.0, 30.0)
```

绘制平滑后的结果。

```python
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 52 的绘图输出](images/04_curvilineargrid_basics_52_0.png)

## 曲线网格定向平滑

移动一个节点，使网格不再平滑，并绘制结果。

```python
mk = create_mk_instance_with_a_rectangular_curvilinear_grid()
mk.curvilinear_move_node(10.0, 20.0, 18.0, 12.0)
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 55 的绘图输出](images/04_curvilineargrid_basics_55_0.png)

执行定向平滑。

```python
mk.curvilinear_smoothing_directional(
    10,  # 平滑迭代次数
    10.0,
    0.0,
    10.0,
    30.0,  # 用于定义平滑方向的网格线坐标
    0.0,
    0.0,
    30.0,
    30.0,
)  # 要平滑的网格块角点
```

绘制定向平滑后的结果。

```python
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 59 的绘图输出](images/04_curvilineargrid_basics_59_0.png)

## 曲线网格线平移

```python
mk = create_mk_instance_with_a_rectangular_curvilinear_grid(5, 5)
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 61 的绘图输出](images/04_curvilineargrid_basics_61_0.png)

初始化网格线平移操作，并设置要移动的网格线。

```python
mk.curvilinear_initialize_line_shift()
mk.curvilinear_set_line_line_shift(0.0, 0.0, 0.0, 50.0)
```

设置用于分配网格线位移的网格块。

```python
mk.curvilinear_set_block_line_shift(0.0, 0.0, 20.0, 50.0)
```

将曲线网格左侧的所有节点向左移动。

```python
mk.curvilinear_move_node_line_shift(0.0, 0.0, -50.0, 0.0)
mk.curvilinear_move_node_line_shift(0.0, 10.0, -50.0, 10.0)
mk.curvilinear_move_node_line_shift(0.0, 20.0, -50.0, 20.0)
mk.curvilinear_move_node_line_shift(0.0, 30.0, -50.0, 30.0)
mk.curvilinear_move_node_line_shift(0.0, 40.0, -50.0, 40.0)
mk.curvilinear_move_node_line_shift(0.0, 50.0, -50.0, 50.0)
```

执行网格线平移。前面指定网格块以外的节点不会移动。

```python
mk.curvilinear_line_shift()
```

```python
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 70 的绘图输出](images/04_curvilineargrid_basics_70_0.png)

## 在曲线网格中插入网格面

```python
mk = create_mk_instance_with_a_rectangular_curvilinear_grid(5, 5)
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 72 的绘图输出](images/04_curvilineargrid_basics_72_0.png)

插入两个网格面。

```python
mk.curvilinear_insert_face(-10.0, 5.0)
mk.curvilinear_insert_face(-5.0, 10.0)
```

```python
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 75 的绘图输出](images/04_curvilineargrid_basics_75_0.png)

## 删除曲线网格节点

```python
mk = create_mk_instance_with_a_rectangular_curvilinear_grid(5, 5)
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 77 的绘图输出](images/04_curvilineargrid_basics_77_0.png)

删除角点节点。

```python
mk.curvilinear_delete_node(0.0, 0.0)
```

```python
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 80 的绘图输出](images/04_curvilineargrid_basics_80_0.png)

## 曲线网格线吸引与排斥

将网格块内的节点向指定网格线吸引。

```python
mk = create_mk_instance_with_a_rectangular_curvilinear_grid(5, 5)
mk.curvilinear_line_attraction_repulsion(
    1.0,  # 正值表示排斥网格线，此处为列宽的 1 倍
    30.0,
    0.0,
    30.0,
    50.0,  # 网格线坐标
    10.0,
    0.0,
    50.0,
    50.0,
)  # 受影响的网格块
```

```python
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 84 的绘图输出](images/04_curvilineargrid_basics_84_0.png)

```python
mk = create_mk_instance_with_a_rectangular_curvilinear_grid(5, 5)
mk.curvilinear_line_attraction_repulsion(
    -1.0,  # 负值表示吸引网格线，此处为列宽的 0.5 倍
    30.0,
    0.0,
    30.0,
    50.0,  # 网格线坐标
    10.0,
    0.0,
    50.0,
    50.0,
)  # 受影响的网格块
```

```python
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 86 的绘图输出](images/04_curvilineargrid_basics_86_0.png)

## 曲线网格线镜像扩展

以两倍列宽对左侧网格线进行镜像扩展。

```python
mk = create_mk_instance_with_a_rectangular_curvilinear_grid(5, 5)
# 镜像系数、要镜像的网格线数量以及目标网格线
mk.curvilinear_line_mirror(2.0, 1, 0.0, 0.0, 0.0, 50.0)
```

```python
curvilinear_grid = mk.curvilineargrid_get()
fig, ax = plt.subplots()
curvilinear_grid.plot_edges(ax)
```

![单元格 90 的绘图输出](images/04_curvilineargrid_basics_90_0.png)