# how to draw parametric surfaces with equations?

for example you type the equations for x,y,z and get the respective surface

The closest that exist is an example plugin called ParametricSurfaces that lets you do something like that:

Here is the plugin:
ParametricSource.xml (1.6 KB)

The rest could be done with a programmable filter though, eg see this:

https://docs.paraview.org/en/latest/ReferenceManual/pythonProgrammableFilter.html#helix-source

2 Likes

I Tried the programmable to create a supershape. but the only thing i got it was lines (1st code).
Then I tried based on mathplotlib but I couldn’t got any results either

``````# Code for 'Script'

#This script generates a helix curve.
#This is intended as the script of a 'Programmable Source'
import math
import numpy as np
from vtk.numpy_interface import algorithms as algs
from vtk.numpy_interface import dataset_adapter as dsa

numPts = 80  # Points along Helix
length = 8.0 # Length of Helix
rounds = 3.0 # Number of times around
a=1
b=1
m=4
n1=12
n2=15
n3=15

def r(fi):
return (((abs(np.cos(m*fi/4)/a))**(n2))+((abs(np.sin(m*fi/4)/b))**(n3)))**(-1/n1)

# Compute the point coordinates for the helix.

index = np.arange(-numPts/2, numPts/2, dtype=np.int32)
scalars = index * rounds * 2 * math.pi / numPts
scalars2 = index * rounds * math.pi / numPts

x = r(scalars)*np.cos(scalars)*r(scalars2)*np.cos(scalars2);
y = r(scalars)*np.sin(scalars)*r(scalars2)*np.cos(scalars2)
z = r(scalars2)*np.sin(scalars2)

# Create a (x,y,z) coordinates array and associate that with
# points to pass to the output dataset.
coordinates = algs.make_vector(x, y, z)
pts = vtk.vtkPoints()
pts.SetData(dsa.numpyTovtkDataArray(coordinates, 'Points'))
output.SetPoints(pts)

# Add scalars to the output point data.
output.PointData.append(index, 'Index')
output.PointData.append(scalars, 'Scalars')
output.PointData.append(scalars2, 'Scalars2')

# Next, we need to define the topology i.e.
# cell information. This helix will be a single
# polyline connecting all the  points in order.
ptIds = vtk.vtkIdList()
ptIds.SetNumberOfIds(numPts)
for i in range(numPts):
#Add the points to the line. The first value indicates
#the order of the point on the line. The second value
#is a reference to a point in a vtkPoints object. Depends
#on the order that Points were added to vtkPoints object.
#Note that this will not be associated with actual points
#until it is added to a vtkPolyData object which holds a
#vtkPoints object.
ptIds.SetId(i, i)

# Allocate the number of 'cells' that will be added. We are just
# adding one vtkPolyLine 'cell' to the vtkPolyData object.
output.Allocate(1, 1)

# Add the poly line 'cell' to the vtkPolyData object.
output.InsertNextCell(vtk.VTK_POLY_LINE, ptIds)
``````
``````# Code for 'Script'

#This script generates a helix curve.
#This is intended as the script of a 'Programmable Source'
import math
import numpy as np
from vtk.numpy_interface import algorithms as algs
from vtk.numpy_interface import dataset_adapter as dsa

numPts = 32  # Points along Helix
length = 8.0 # Length of Helix
rounds = 3.0 # Number of times around
a=1
b=1
m=4
n1=12
n2=15
n3=15

def r(fi):
return (((abs(np.cos(m*fi/4)/a))**(n2))+((abs(np.sin(m*fi/4)/b))**(n3)))**(-1/n1)

# Compute the point coordinates for the helix.

#index = np.arange(-numPts/2, numPts/2, dtype=np.int32)
angle = np.linspace(-np.pi, np.pi, numPts)
angle2 = np.linspace(-np.pi/2, np.pi/2, numPts)
scalars, scalars2 = np.meshgrid(angle, angle2)

x = r(scalars)*np.cos(scalars)*r(scalars2)*np.cos(scalars2);
y = r(scalars)*np.sin(scalars)*r(scalars2)*np.cos(scalars2)
z = r(scalars2)*np.sin(scalars2)
print(x)
# Create a (x,y,z) coordinates array and associate that with
# points to pass to the output dataset.
coordinates = algs.make_vector(x, y, z)
pts = vtk.vtkPoints()
pts.SetData(dsa.numpyTovtkDataArray(coordinates, 'Points'))
output.SetPoints(pts)

# Add scalars to the output point data.
output.PointData.append(angle, 'Angle')
output.PointData.append(angle2, 'Angle2')
output.PointData.append(scalars, 'Scalars')
output.PointData.append(scalars2, 'Scalars2')

# Next, we need to define the topology i.e.
# cell information. This helix will be a single
# polyline connecting all the  points in order.
ptIds = vtk.vtkIdList()
ptIds.SetNumberOfIds(numPts)
for i in range(numPts):
#Add the points to the line. The first value indicates
#the order of the point on the line. The second value
#is a reference to a point in a vtkPoints object. Depends
#on the order that Points were added to vtkPoints object.
#Note that this will not be associated with actual points
#until it is added to a vtkPolyData object which holds a
#vtkPoints object.
ptIds.SetId(i, i)

# Allocate the number of 'cells' that will be added. We are just
# adding one vtkPolyLine 'cell' to the vtkPolyData object.
output.Allocate(1, 1)

# Add the poly line 'cell' to the vtkPolyData object.
output.InsertNextCell(vtk.VTK_POLY_LINE, ptIds)
``````

You are adding lines, so you get lines I suppose.

ok how can i get a surface?

Ok it drew a shape but for the shape i want i need before the definition of x,y,z I need to add a comand like meshgrid.

``````Output mensage:
Traceback (most recent call last):
File "<string>", line 20, in <module>
File "<string>", line 43, in RequestData
File "C:\Program Files\ParaView 5.9.1-Windows-Python3.8-msvc2017-64bit\bin\Lib\site-packages\vtkmodules\numpy_interface\algorithms.py", line 861, in make_vector
return algs.make_vector(arrayx, arrayy, arrayz)
File "C:\Program Files\ParaView 5.9.1-Windows-Python3.8-msvc2017-64bit\bin\Lib\site-packages\vtkmodules\numpy_interface\internal_algorithms.py", line 559, in make_vector
raise ValueError("Can only merge 1D arrays")
ValueError: Can only merge 1D arrays
``````

When I put VTK_QUAD it drew a shape that should be closed. There is any way to use a np.meshgrid?
I found this code but it didnt drew any thing.

``````import vtk
import numpy as np
from vtk.numpy_interface import dataset_adapter as dsa
iD=vtk.vtkImageData()
dims=[31,31,31]
iD.SetSpacing(1,1,1)
iD.SetOrigin(0,0,0)
iD.SetDimensions(dims)
xaxis = np.linspace(-0.5,1,dims)
yaxis = np.linspace(-1,1,dims)
zaxis = np.linspace(-1,0.5,dims)
[xc,yc,zc] = np.meshgrid(xaxis,yaxis,zaxis)
data = np.sqrt(xc**2+yc**2+zc**2)
image=dsa.WrapDataObject(iD)
image.PointData.append(data.ravel(),"scalar")
``````