Lorenz

#!/usr/bin/env python3

"""
Create an iso-surface of the Lorenz attractor.

Here we visualize a Lorenz strange attractor by integrating the Lorenz equations in a volume.
The number of visits in each voxel is recorded as a scalar function.
The surface is extracted via a contour filter using a visit value of 50.
The number of integration steps is 10 million, in a volume of dimensions 200 x 200 x 200.
The surface roughness is caused by the discrete nature of the evaluation function.

"""
# noinspection PyUnresolvedReferences
import vtkmodules.vtkInteractionStyle
# noinspection PyUnresolvedReferences
import vtkmodules.vtkRenderingOpenGL2
from vtkmodules.vtkCommonColor import vtkNamedColors
from vtkmodules.vtkCommonCore import (
    vtkMinimalStandardRandomSequence,
    vtkShortArray
)
from vtkmodules.vtkCommonDataModel import vtkStructuredPoints
from vtkmodules.vtkFiltersCore import vtkContourFilter
from vtkmodules.vtkRenderingCore import (
    vtkActor,
    vtkPolyDataMapper,
    vtkRenderWindow,
    vtkRenderWindowInteractor,
    vtkRenderer
)


def main():
    colors = vtkNamedColors()

    Pr = 10.0  # The Lorenz parameters
    b = 2.667
    r = 28.0
    # x = 0.0
    # y = 0.0
    # z = 0.0  # starting (and current) x, y, z
    h = 0.01  # integration step size
    resolution = 200  # slice resolution
    iterations = 10000000  # number of iterations
    xmin = -30.0  # x, y, z range for voxels
    xmax = 30.0
    ymin = -30.0
    ymax = 30.0
    zmin = -10.0
    zmax = 60.0

    # Take a stab at an integration step size.
    dx = resolution / (xmax - xmin)
    dy = resolution / (ymax - ymin)
    dz = resolution / (zmax - zmin)

    s = 'The Lorenz Attractor\n'
    s += f' Pr = {Pr}\n b = {b}\n r = {r}\n'
    s += f' integration step size = {h:4.2f}\n'
    s += f' slice resolution      = {resolution}\n'
    s += f' number of iterations  = {iterations}\n'
    s += f' specified range (x, y, z):\n'
    s += f'     minimum: ({xmin:6.2f}, {ymin:6.2f}, {zmin:6.2f})\n'
    s += f'     maximum: ({xmax:6.2f}, {ymax:6.2f}, {zmax:6.2f})\n'
    print(s)

    random_sequence = vtkMinimalStandardRandomSequence(seed=8775070)
    x = random_sequence.GetRangeValue(xmin, xmax)
    random_sequence.Next()
    y = random_sequence.GetRangeValue(ymin, ymax)
    random_sequence.Next()
    z = random_sequence.GetRangeValue(zmin, zmax)
    random_sequence.Next()

    s += f' starting at: ({x:6.2f}, {y:6.2f}, {z:6.2f})'
    print(s)

    print(' generating the volume ...')

    # Allocate memory for the slices.
    slice_size = resolution * resolution
    num_pts = slice_size * resolution
    scalars = vtkShortArray()
    for i in range(0, num_pts):
        scalars.InsertTuple1(i, 0)
    for j in range(0, iterations):
        # Integrate to the next time step.
        xx = x + h * Pr * (y - x)
        yy = y + h * (x * (r - z) - y)
        zz = z + h * (x * y - (b * z))

        x = xx
        y = yy
        z = zz

        # Calculate the voxel index.
        if xmax > x > xmin and ymax > y > ymin and zmax > z > zmin:
            xxx = int(float(xx - xmin) * dx)
            yyy = int(float(yy - ymin) * dy)
            zzz = int(float(zz - zmin) * dz)
            index = xxx + yyy * resolution + zzz * slice_size
            scalars.SetTuple1(index, scalars.GetTuple1(index) + 1)

    origin = (xmin, ymin, zmin)
    spacing = ((xmax - xmin) / resolution, (ymax - ymin) / resolution, (zmax - zmin) / resolution)
    volume = vtkStructuredPoints(dimensions=(resolution, resolution, resolution),
                                 origin=origin, spacing=spacing)
    volume.point_data.SetScalars(scalars)

    print(' contouring ...')

    # Create the iso-surface.
    contour = vtkContourFilter(input_data=volume)
    contour.SetValue(0, 50)

    # Create mapper.
    mapper = vtkPolyDataMapper(scalar_visibility=False)
    contour >> mapper

    # Create actor.
    actor = vtkActor(mapper=mapper)
    actor.property.color = colors.GetColor3d('DodgerBlue')

    # Do the graphics dance.
    renderer = vtkRenderer(background=colors.GetColor3d('PaleGoldenrod'))
    ren_win = vtkRenderWindow(size=(640, 480), window_name='Lorenz')
    ren_win.AddRenderer(renderer)
    iren = vtkRenderWindowInteractor()
    iren.render_window = ren_win

    renderer.AddActor(actor)

    # Interact with the data.
    ren_win.Render()
    ren_win.SetWindowName('Lorenz')

    camera = renderer.active_camera
    camera.position = (-67.645167, -25.714343, 63.483516)
    camera.focal_point = (3.224902, -4.398594, 29.552112)
    camera.view_up = (-0.232264, 0.965078, 0.121151)
    camera.distance = 81.414176
    camera.clipping_range = (18.428905, 160.896031)

    iren.Start()


if __name__ == '__main__':
    main()