Field manipulationΒΆ

The objective here is to create and manipulate a field. A field is the agregation of a mesh \mathcal{M} of a domain \mathcal{D} \in \mathbb{R}^n and a sample of values in \mathbb{R}^d associated to each vertex of the mesh.

We note (\underline{t}_0, \dots, \underline{t}_{N-1}) the vertices of \mathcal{M} and (\underline{x}_0, \dots, \underline{x}_{N-1}) the associated values in \mathbb{R}^d.

A field is stored in the Field object that stores the mesh and the values at each vertex of the mesh. It can be built from a mesh and values or as a realization of a stochastic process.

from __future__ import print_function
import openturns as ot
import math as m
# First, define a regular 2-d mesh
discretization = [10, 5]
mesher = ot.IntervalMesher(discretization)
lowerBound = [0.0, 0.0]
upperBound = [2.0, 1.0]
interval = ot.Interval(lowerBound, upperBound)
mesh =
graph = mesh.draw()
graph.setTitle('Regular 2-d mesh')
# Create a field as a realization of a process
amplitude = [1.0]
scale = [0.2]*2
myCovModel = ot.ExponentialModel(scale, amplitude)
myProcess = ot.GaussianProcess(myCovModel, mesh)
field = myProcess.getRealization()
# Create a field from a mesh and some values
values = ot.Normal([0.0]*2, [1.0]*2, ot.CorrelationMatrix(2)).getSample(len(mesh.getVertices()))
for i in range(len(values)):
    x = values[i]
    values[i] = 0.05 * x / x.norm()
field = ot.Field(mesh, values)
graph = field.draw()
graph.setTitle('Field on 2-d mesh and 2-d values')
# Compute the input mean of the field


# Draw the field without interpolation
graph = field.drawMarginal(0, False)
graph.setTitle('Marginal field (no interpolation)')
# Draw the field with interpolation
graph = field.drawMarginal(0)
graph.setTitle('Marginal field (with interpolation)')
# Deform the mesh from the field according to the values of the field
# The dimension of the mesh (ie of its vertices) must be the same as the dimension of the field (ie its values)
graph = field.asDeformedMesh().draw()
graph.setTitle('Deformed 2-d mesh')
# Export to the VTK format
with open('field.vtk') as f:
# vtk DataFile Version 3.0

POINTS 66 float
0 0 0.0
0.2 0 0.