计算表面上的曲率导数

Question

我想使用vtk和python计算曲面上的曲率导数。我首先使用以下方法计算曲率：

curvatures = vtk.vtkCurvatures()
curvatures.SetInputConnection(reader.GetOutputPort())
curvatures.SetCurvatureTypeToGaussian()

并使用以下公式计算曲率导数：

Derivativers = vtk.vtkCellDerivatives()
Derivativers.SetInputConnection(curvatures.GetOutputPort())

似乎vtkCurvatures和vtkCellDerivatives的结果相同。

我该怎么做才能获得曲面的曲率导数。非常感谢！

Answer 1

我认为您的代码是正确的。但是我们需要确保曲率点数据数组是当前活动的标量数组。我已经附上了一个输入数据文件，您可以将其保存为名称'Test.vtk'。它有两个点数据数组-PointIds（一个标量数组）和PointNormals（一个矢量数组）。然后，我们将计算高斯曲率，该曲率将成为点数据的标量的第三个数组。我们将打印所有点数据数组的名称，而不管它们是标量还是向量。然后，我们将'Gauss_Curvature'标量数组显式设置为Active Scalar。我们将计算单元导数，这将创建一个称为'ScalarGradient'的单元数据向量数组，该数组将是曲率的梯度。这将保存在文件'Output.vtk'

中

import vtk

rd = vtk.vtkPolyDataReader()
rd.SetFileName('Test.vtk')
curv = vtk.vtkCurvatures()
curv.SetInputConnection(rd.GetOutputPort())
curv.SetCurvatureTypeToGaussian()
curv.Update()
pd = curv.GetOutput()

for i in range(pd.GetPointData().GetNumberOfArrays()):
    print(pd.GetPointData().GetArrayName(i))
# This will print the following:
# PointIds
# PointNormals
# Gauss_Curvature

# To set the active scalar to Gauss_Curvature
pd.GetPointData().SetActiveScalars('Gauss_Curvature')

curvdiff = vtk.vtkCellDerivatives()
curvdiff.SetInputData(pd)
curvdiff.SetVectorModeToComputeGradient()
curvdiff.Update()

writer = vtk.vtkPolyDataWriter()
writer.SetFileName('Output.vtk')
writer.SetInputConnection(curvdiff.GetOutputPort())
writer.Write()

给我以下输出-首先是曲率，然后是梯度。请注意，两个图中的色阶不同。因此，尽管颜色方案使曲率和导数值看起来很相似，但它们却是不同的。

如果要重现结果，则输入的vtk文件如下所示

# vtk DataFile Version 4.2
vtk output
ASCII
DATASET POLYDATA
POINTS 72 double
2.0927648978 0.33091989273 -0.39812666792 1.6450815105 0.64303293033 -1.236079764 1.7000810807 1.2495041516 -0.44287861593 
1.0622264471 1.4540269048 -1.1853937884 0.8533187462 0.72833963362 -1.8409362444 0.161573121 1.415272931 -1.6182009866 
-0.4682233113 2.0970647997 -0.17539653223 0.30090053169 1.9778473 -0.80327873468 -0.62604403311 1.746197318 -1.0984268611 
0.62604948422 1.746195345 1.0984268742 0.4682298575 2.0970633231 0.17539654742 -0.30089435724 1.9778482191 0.80327874624 
1.3794219731 1.1031586743 1.2360880686 1.9321437012 0.84755424016 0.44288858377 1.3329709879 1.6469225081 0.39813606858 
-1.3329658439 1.6469266769 -0.39813605266 -1.3794185207 1.1031629885 -1.2360880529 -1.9321410548 0.84756028031 -0.44288857482 
-0.16156870247 1.4152734137 1.6182009959 -1.0622219128 1.4540302146 1.1853938087 -0.85331647216 0.72834227646 1.8409362479 
-1.7000771766 1.2495094572 0.44287862867 -2.0927638628 0.33092642637 0.39812667143 -1.6450795106 0.64303805991 1.2360797754 
0.10502897512 0.5677157381 2.0771002606 -0.54417928828 -0.19289519204 2.0770984773 0.43913323132 -0.37482057542 2.077101172 
1.0574135878 0.37481822068 1.8409414841 1.3064404335 -0.56771795917 1.6182050108 1.7903331906 0.19289323113 1.1854016225 
-0.72812102639 -1.6469234624 1.18539471 -0.20411225533 -1.1031605232 1.8409380189 -1.1448850389 -0.84755547744 1.6181982897 
0.26564737208 -1.7461967516 1.236085002 -0.23207016686 -2.0970637037 0.44288263714 0.75978960067 -1.9778489401 0.39813448025 
1.1992202745 -1.4152750453 1.0984284306 1.5819944619 -1.4540310306 0.17539958384 1.8633106814 -0.72834386503 0.80328466622 
-1.825278792 -0.33092031521 1.0984201446 -2.0502257619 -0.64303229501 0.17538963068 -1.5624229303 -1.2495043655 0.80327527281 
-0.26565282447 -1.7461959014 -1.2360850131 0.23206361633 -2.0970644256 -0.44288265596 -0.7597957797 -1.977846564 -0.39813449851 
-1.1992246997 -1.4152712955 -1.0984284473 -1.5819990123 -1.4540260972 -0.17539960215 -1.8633129661 -0.72833804688 -0.80328468018 
0.20410881451 -1.1031611451 -1.8409380327 1.1448823984 -0.84755903977 -1.6181983017 0.72811588321 -1.6469257176 -1.1853947189 
2.0502237661 -0.64303869999 -0.17538964133 1.5624190405 -1.2495092418 -0.80327529169 1.8252777661 -0.33092600698 -1.0984201511 
-0.43913440065 -0.37481918558 -2.0771011678 -0.10502720377 0.56771608521 -2.0771002475 0.54417868626 -0.19289687027 -2.0770984714 
-1.3064422115 -0.56771386838 -1.6182050202 -1.7903325818 0.19289882961 -1.185401614 -1.057412421 0.3748215375 -1.8409414839 
-0.76083174443 1.3178134523 -1.9919051229 -0.7608358562 -1.3178110596 -1.9919051353 -2.4621262785 3.8465962003e-06 -0.47023127203 
1.5216839818 -2.3645462409e-06 -1.991898872 2.4621262803 -3.846902628e-06 0.47023127288 1.2310617434 -2.1322669408 -0.47022115796 
-1.2310684033 -2.1322631023 0.47022113869 -1.5216839821 2.3661982943e-06 1.9918988726 0.76083174316 -1.3178134534 1.9919051234 
0.76083585779 1.317811059 1.9919051359 -1.2310617441 2.1322669425 0.47022115881 1.2310684021 2.1322631008 -0.47022113785 

POLYGONS 140 560
3 12 14 9 
3 27 69 24 
3 70 21 19 
3 1 53 63 
3 2 14 13 
3 38 36 37 
3 28 68 36 
3 39 67 23 
3 64 38 51 
3 13 14 12 
3 20 24 18 
3 34 35 33 
3 40 41 39 
3 16 58 17 
3 20 18 19 
3 26 27 24 
3 11 6 70 
3 10 14 71 
3 22 39 23 
3 6 10 7 
3 3 5 7 
3 29 64 13 
3 41 30 32 
3 57 45 47 
3 54 61 57 
3 66 30 41 
3 50 43 42 
3 30 33 31 
3 33 35 36 
3 65 37 35 
3 37 36 35 
3 26 68 28 
3 68 33 36 
3 27 28 29 
3 28 36 38 
3 29 28 38 
3 38 37 51 
3 61 48 42 
3 37 65 52 
3 66 34 30 
3 43 65 35 
3 32 30 31 
3 30 34 33 
3 40 39 22 
3 41 32 39 
3 66 41 46 
3 32 67 39 
3 67 32 25 
3 33 68 31 
3 32 31 25 
3 31 26 25 
3 27 26 28 
3 26 31 68 
3 64 29 38 
3 12 69 27 
3 18 9 11 
3 69 12 9 
3 18 24 69 
3 20 67 25 
3 26 24 25 
3 24 20 25 
3 13 12 29 
3 12 27 29 
3 18 11 19 
3 11 9 10 
3 69 9 18 
3 9 14 10 
3 70 6 15 
3 11 10 6 
3 10 71 7 
3 71 14 2 
3 70 15 21 
3 6 8 15 
3 21 17 22 
3 15 8 16 
3 20 23 67 
3 19 11 70 
3 21 23 19 
3 23 20 19 
3 22 17 62 
3 22 23 21 
3 15 17 21 
3 62 40 22 
3 58 57 47 
3 62 17 58 
3 62 47 40 
3 58 16 59 
3 15 16 17 
3 6 7 8 
3 16 60 59 
3 48 54 56 
3 8 5 60 
3 2 1 3 
3 7 5 8 
3 3 1 4 
3 2 3 71 
3 71 3 7 
3 3 4 5 
3 5 55 60 
3 49 50 48 
3 8 60 16 
3 60 55 59 
3 4 55 5 
3 54 57 59 
3 1 63 4 
3 56 55 4 
3 49 48 56 
3 44 45 42 
3 63 56 4 
3 48 61 54 
3 56 54 55 
3 54 59 55 
3 59 57 58 
3 47 62 58 
3 40 46 41 
3 57 61 45 
3 47 45 46 
3 43 34 44 
3 47 46 40 
3 46 44 66 
3 37 52 51 
3 42 48 50 
3 42 43 44 
3 43 35 34 
3 45 44 46 
3 44 34 66 
3 61 42 45 
3 50 65 43 
3 65 50 52 
3 56 63 49 
3 51 52 53 
3 49 63 53 
3 50 49 52 
3 49 53 52 
3 2 0 1 
3 1 0 53 
3 0 51 53 
3 0 64 51 
3 13 64 0 
3 2 13 0 

POINT_DATA 72
SCALARS PointIds vtkIdType
LOOKUP_TABLE default
0 1 2 3 4 5 6 7 8 
9 10 11 12 13 14 15 16 17 
18 19 20 21 22 23 24 25 26 
27 28 29 30 31 32 33 34 35 
36 37 38 39 40 41 42 43 44 
45 46 47 48 49 50 51 52 53 
54 55 56 57 58 59 60 61 62 
63 64 65 66 67 68 69 70 71 

NORMALS PointNormals double
0.94738623196 0.18727650058 -0.25958975291 0.78313719053 0.35367076216 -0.51148131227 0.83545291047 0.50824408436 -0.20906072109 
0.47898857295 0.62402000487 -0.61738884061 0.34465195337 0.40584589543 -0.84646567573 0.15649087604 0.66776200195 -0.72773931766 
-0.15609353126 0.97764567412 -0.14086782943 0.059136449433 0.91410106494 -0.40115099829 -0.27742338135 0.85504231805 -0.43810832201 
0.27739675558 0.85505949665 0.43809165386 0.1561128187 0.97764027026 0.14088395868 -0.05910174957 0.91410169764 0.40115467037 
0.6978536347 0.50139725414 0.51146954756 0.85786633279 0.46941626794 0.20907826874 0.63588503517 0.72681646701 0.25959207486 
-0.63587825439 0.72682167945 -0.25959409059 -0.69785435483 0.50138010962 -0.51148537136 -0.85787788306 0.46940090711 -0.20906536337 
-0.15651072102 0.66775823558 0.72773850593 -0.47897825964 0.62400201859 0.61741502054 -0.34463970914 0.40587327082 0.84645753521 
-0.8354604399 0.50822639825 0.20907362693 -0.94738511041 0.18728497536 0.25958773195 -0.78315168201 0.35366155935 0.51146548701 
-0.0042059530133 0.19834561529 0.98012311821 -0.16967339936 -0.10281294988 0.98012266318 0.17387129188 -0.095532679284 0.98012360499 
0.52381294065 0.095528092331 0.84645991446 0.65654796659 -0.19833859028 0.72774073074 0.77988819356 0.10280486141 0.61741846913 
-0.30091501143 -0.72680688867 0.6174155023 -0.17918019275 -0.50140137515 0.8464579845 -0.50004323045 -0.46941965564 0.72773755886 
0.085293841035 -0.8550588207 0.51146786196 -0.022407612419 -0.97764266904 0.20907584885 0.31149794024 -0.91410144601 0.25959117785 
0.60180306843 -0.66776342878 0.4380925359 0.76860432156 -0.62401813766 0.14088563004 0.82118451863 -0.40586818759 0.40115707731 
-0.87920342686 -0.18729607405 0.43808847833 -0.92471829912 -0.35362213463 0.14088098936 -0.76208606823 -0.50823351579 0.40115273655 
-0.08527862936 -0.85505086473 -0.51148369876 0.022426691996 -0.97764498848 -0.20906295701 -0.31150584284 -0.91409817614 -0.25959320919 
-0.60177487516 -0.6677778914 -0.43810921854 -0.76861864432 -0.62400413386 -0.14086951598 -0.82120131764 -0.40583781416 -0.40115341765 
0.17915035572 -0.50139827931 -0.84646613373 0.5000564084 -0.4694043424 -0.72773838139 0.30092542605 -0.72682480482 -0.61738933507 
0.92471333385 -0.3536415386 -0.14086487277 0.7620681671 -0.50826324483 -0.40114907784 0.8792018588 -0.18726442077 -0.43810515655 
-0.17386795802 -0.09554490851 -0.98012300434 0.0041936861197 0.19834885542 -0.98012251507 0.16968233044 -0.10280393451 -0.9801220627 
-0.65654129971 -0.19835764899 -0.72774155087 -0.77990892195 0.10280480888 -0.61739229403 -0.52379534825 0.095552395563 -0.84646805779 
-0.3035934934 0.52568869256 -0.79465866212 -0.30345974591 -0.52576590314 -0.79465866742 -0.98224561547 8.0181630296e-06 -0.18759944248 
0.60705977261 7.7220189155e-05 -0.79465616874 0.98224726985 9.1023794904e-07 0.18759078032 0.49111663606 -0.85065410882 -0.18759540755 
-0.49112361722 -0.85065199031 0.18758673723 -0.60706560357 -2.8418937296e-07 0.79465171803 0.30352977695 -0.52573221141 0.79465421184 
0.30352929122 0.52573248433 0.79465421681 -0.49112519531 0.85065107744 0.18758674521 0.49113052171 0.85064609373 -0.18759539936