【Python】将网格数据写入到VTK文件

1. vtk 文件格式

根据官网进行总结

vtk文件组成:5个部分.

第一部分,第一行:表明文件版本.写"# vtk DataFile Version 2.0"就行

第二部分,第二行:表明标题(title).随便写.

第三部分,第三行:ASCII或者 BINARY

第四部分,开始定义dataset structure.这部分用于描述数据集的几何和拓扑结构.以关键字"DATASET type"的一行开始.后续部分根据不同的dataset type,使用其他关键字/数据组合定义实际数据.

支持以下type:

STRUCTURED_POINTS

STRUCTURED_GRID

UNSTRUCTURED_GRID

POLYDATA

STRUCTURED_POINTS

RECTILINEAR_GRID

FIELD

关键字不区分大小写,可以用空格分隔.

第五部分,定义点数据或者实体数据等.称为:dataset attributes 如:

POINT_DATA type

...

CELL_DATA type

...

注意:Indices are 0-offset. Thus the first point is point id 0.;Cell types and indices are of type int; The geometry/topology description must occur prior to the data attribute description.

1.1 Dataset Format _ 定义几何/拓扑数据和关系

VTK支持5种数据集格式:structured points, structured grid, rectilinear grid, unstructured grid, and polygonal data.

这里只描述非结构化网格,其他不说,用不到.

1.2 Unstructured Grid

非结构化网格数据集由任何可用的单元类型的任意组合组成(比如四六面体混合).非结构化网格由点、单元格和单元格类型定义.

CELLS keyword 需要两个参数:

• n : the number of cells
• size : the size of the cell list. The cell list size is CELLS关键字下所有整数的个数 (i.e., sum of numPoints and connectivity indices over each cell).

例如:60代表的是从第一行以下所有整数的个数

CELLS 11 60
8 0 1 4 3 6 7 10 9
8 1 2 4 5 7 8 10 11
4 6 10 9 12
4 11 14 10 13
6 15 16 17 14 13 12
6 18 15 19 16 20 17
4 22 23 20 19
3 21 22 18
3 22 19 18
2 26 25
1 24

CELL_TYPES keyword需要一个参数: the number of cells n.这个参数值对应于CELLS的n参数.这个关键字的数据行,是指定每个单元格的单元类型的单个整数值

案例:定义非结构化网格的拓扑

DATASET UNSTRUCTURED_GRID
POINTS n dataType
p0x p0y p0z
p1x p1y p1z
…
p(n-1)x p(n-1)y p(n-1)z

CELLS n size
numPoints0, i0, j0, k0, …
numPoints1, i1, j1, k1, …
numPoints2, i2, j2, k2, …
…
numPointsn-1, in-1, jn-1, kn-1, …

CELL_TYPES n
type0
type1
type2
…
typen-1

1.3 Dataset Attribute Format --- 定义附着在节点或者单元上的数据

支持以下数据集属性:

• 标量(一到四个分量)
• 向量
• 法线
• 纹理坐标(1D, 2D和3D)
• 张量
• field data

此外,可以使用RGBA颜色规范定义lookup table,与标量数据关联.

定义dataset Attribute 要给定一个独特的dataName,不能有空格.一个文件中可以包含多个相同类型的dataset Attribute. For example, two different scalar fields defined on the dataset points, pressure and temperature, can be contained in the same file.

1.3.1 Scalars.

SCALARS dataName dataType numComp
LOOKUP_TABLE tableName
s0
s1
…
sn-1

标量定义包括lookup table的指定.lookup table 是可选的,如果不指定,vtk会使用默认表(tableName指定为default);numComp选项也是可选的,如果不给定,默认为1.参数范围:1~4

color scalars( 直接映射到颜色的无符号字符值 )的定义varies depending upon the number of values (nValues) per scalar.** If the file format is ASCII, the color scalars are defined using nValues float values between (0,1). **

COLOR_SCALARS dataName nValues
c00 c01 … c0(nValues-1)
c10 c11 … c1(nValues-1)
…
c(n-1)0 c(n-1)1 … c(n-1)(nValues-1)

1.3.2 Lookup Table.

LOOKUP_TABLE tableName size
r0 g0 b0 a0
r1 g1 b1 a1
…
rsize-1 gsize-1 bsize-1 asize-1

tableName 是表的标识,不能有空格.每一行表示rgba数组.a表示透明度,a=0时颜色透明.如果文件是ASCII格式,每个值范围为(0-1的浮点数;

1.3.3 Vectors.

VECTORS dataName dataType
v0x v0y v0z
v1x v1y v1z
…
v(n-1)x v(n-1)y v(n-1)z

1.3.4 Normals.

Normals are assumed normalized |n| = 1.

NORMALS dataName dataType
n0x n0y n0z
n1x n1y n1z
…
n(n-1)x n(n-1)y n(n-1)z

1.3.5 Tensors.

Currently only real-valued, symmetric tensors are supported.

TENSORS dataName dataType

t000 t001 t002

t010 t011 t012

t020 t021 t022

t100 t101 t102

t110 t111 t112

t120 t121 t122

…

tn - 100 tn - 101 tn - 102

tn - 110 tn - 111 tn - 112

tn - 120 tn - 121 tn - 122

1.4 example

# vtk DataFile Version 2.0
Unstructured Grid Example
ASCII
DATASET UNSTRUCTURED_GRID

POINTS 27 float
0 0 0  1 0 0  2 0 0  0 1 0  1 1 0  2 1 0
0 0 1  1 0 1  2 0 1  0 1 1  1 1 1  2 1 1
0 1 2  1 1 2  2 1 2  0 1 3  1 1 3  2 1 3
0 1 4  1 1 4  2 1 4  0 1 5  1 1 5  2 1 5
0 1 6  1 1 6  2 1 6

CELLS 11 60
8 0 1 4 3 6 7 10 9
8 1 2 4 5 7 8 10 11
4 6 10 9 12
4 11 14 10 13
6 15 16 17 14 13 12
6 18 15 19 16 20 17
4 22 23 20 19
3 21 22 18
3 22 19 18
2 26 25
1 24

CELL_TYPES 11
12
11
10
8
7
6
9
5
4
3
1

POINT_DATA 27
SCALARS scalars float 1
LOOKUP_TABLE default
0.0 1.0 2.0 3.0 4.0 5.0
6.0 7.0 8.0 9.0 10.0 11.0
12.0 13.0 14.0 15.0 16.0 17.0
18.0 19.0 20.0 21.0 22.0 23.0
24.0 25.0 26.0

VECTORS vectors float
1 0 0  1 1 0  0 2 0  1 0 0  1 1 0  0 2 0
1 0 0  1 1 0  0 2 0  1 0 0  1 1 0  0 2 0
0 0 1  0 0 1  0 0 1  0 0 1  0 0 1  0 0 1
0 0 1  0 0 1  0 0 1  0 0 1  0 0 1  0 0 1
0 0 1  0 0 1  0 0 1

CELL_DATA 11
SCALARS scalars float 1
LOOKUP_TABLE CellColors
0.0 1.0 2.0 3.0 4.0 5.0
6.0 7.0 8.0 9.0 10.0

LOOKUP_TABLE CellColors 11
.4 .4 1 1
.4 1 .4 1
.4 1 1 1
1 .4 .4 1
1 .4 1 1
1 1 .4 1
1 1 1 1
1 .5 .5 1
.5 1 .5 1
.5 .5 .5 1
1 .5 .4 1

2.使用python将网格和数据写入vtk文件

def export_vtk(output_file:str,
                nodes:np.ndarray,
                element_Blocks:List[np.ndarray],
                element_types:List[str],
                point_data: Dict[str:Dict[str:np.ndarray]] = {},
                cell_data:  Dict[str:Dict[str:np.ndarray]] = {},
                **kwargs)->bool:
    """导出vtk格式的网格数据文件
    inputs:
    output_file: 输出文件名
    nodes: 节点坐标矩阵,shape=(n,3)
    element_Blocks: 单元列表,
    element_types: 单元类型列表,
    point_data: 节点数据字典.e.g. {'SCALARS':{'disp':disp_array,'stress':stress_array},'VECTORS':{'velocity':velocity_array}}
    cell_data: 单元数据字典.e.g. {'SCALARS':{'disp':disp_array,'stress':stress_array},'VECTORS':{'velocity':velocity_array}}
    """
    def cal_cell_num(element_Blocks:List[np.ndarray])->tuple:
        cell_num,cell_piont_num=0,0
        for _,block in enumerate(element_Blocks):
            cell_num+=block.shape[0]
            cell_piont_num+=block.shape[0]*(block.shape[1]+1)
        return cell_num,cell_piont_num

    SEP="  " if 'sep'not in kwargs.keys()  else kwargs['sep']

    type_dict={"beam": 3, # vtk_line, 梁单元
                "tri": 5, # vtk_triangle, 三角形单元
                "quad":9, # vtk_quad, 四边形单元
                "tet":10, # vtk_tetra, 四面体单元
                "hex":12, # vtk_hexahedron, 六面体单元
                "wedge":13, # vtk_wedge, 三棱柱单元
                "pyramid":14, # vtk_pyramid, 四棱锥单元
                }

    f=open(output_file,'w')

    # 写入文件头
    f.write('# vtk DataFile Version 3.0\n')
    f.write(f'{kwargs["title"]}\n') if 'title' in kwargs.keys() else f.write('Finite Element Results\n')
    f.write('ASCII\n')
    f.write('DATASET UNSTRUCTURED_GRID\n')

    # 写入点坐标
    f.write(f'\nPOINTS {nodes.shape[0]} float\n')
    for i in range(nodes.shape[0]):
        f.write(SEP.join(map(str,nodes[i,:]))+'\n')

    # 写入单元数据
    n,size=cal_cell_num(element_Blocks)

    # 构造单元数据
    f.write(f'\nCELLS {n} {size}\n')
    cells_lines,cell_type_lines="",""
    for block ,typeStr in zip(element_Blocks,element_types):
        for i in range(block.shape[0]):
            cells_lines+=f"{block.shape[1]} "+SEP.join(map(str,block[i,:]))+'\n'
            cell_type_lines+=f"{type_dict[typeStr]}\n"
    f.write(cells_lines)

    # 写入单元类型数据
    f.write(f'\nCELL_TYPES {n}\n')
    f.write(cell_type_lines)

    # 写入节点数据,节点字典数据为空则跳过
    if point_data:
        f.write(f'\nPOINT_DATA {nodes.shape[0]}\n')
        if 'SCALARS' in point_data.keys():
            for var_name,array in point_data['SCALARS'].items():
                if array.ndim==1:
                    # 如果是一维数组,则扩展成二维数组
                    array=array.reshape((-1,1))
                # 标量的Ncomp=1~4
                f.write(f'SCALARS {var_name} float {array.shape[1]}\n')
                f.write(f'LOOKUP_TABLE default\n')
                for i in range(array.shape[0]):
                    f.write(SEP.join(map(str,array[i,:]))+'\n')

        # VECTORS dataName dataType
        # v0x v0y v0z
        # v1x v1y v1z
        # …
        # v(n-1)x v(n-1)y v(n-1)z
        if 'VECTORS' in point_data.keys():
            for var_name,array in point_data['VECTORS'].items():
                if array.ndim==1:
                    # 如果是一维数组,则扩展成二维数组,向量必须是(-1,3)
                    array=array.reshape((-1,3))
                assert array.shape[1]==3, "VECTORS data must be (-1,3) shape"

                f.write(f'VECTORS {var_name} float\n')
                for i in range(array.shape[0]):
                    f.write(SEP.join(map(str,array[i,:]))+'\n')
    else:
        pass

    # 写入单元数据,单元字典数据为空则跳过
    if cell_data:
        f.write(f'\nCELL_DATA {n}\n')
        if 'SCALARS' in cell_data.keys():
            for var_name,array in cell_data['SCALARS'].items():
                if array.ndim==1:
                    # 如果是一维数组,则扩展成二维数组
                    array=array.reshape((-1,1))
                # 标量的Ncomp=1~4
                f.write(f'SCALARS {var_name} float {array.shape[1]}\n')
                f.write(f'LOOKUP_TABLE default\n')
                for i in range(array.shape[0]):
                    f.write(SEP.join(map(str,array[i,:]))+'\n')

        if 'VECTORS' in cell_data.keys():
            for var_name,array in cell_data['VECTORS'].items():
                if array.ndim==1:
                    # 如果是一维数组,则扩展成二维数组,向量必须是(-1,3)
                    array=array.reshape((-1,3))
                assert array.shape[1]==3, "VECTORS data must be (-1,3) shape"

                f.write(f'VECTORS {var_name} float\n')
                for i in range(array.shape[0]):
                    f.write(SEP.join(map(str,array[i,:]))+'\n')
    else:
        pass