Topo - VTK 4x4 transform matrix from control points¶

Kaufmann, 2021.

[1]:

from ipywidgets import TwoByTwoLayout
import bootsoff.topo.geometry as btg
import pyvista as pv
import numpy as np

Coordinates of the control points in the origin space¶

at least 4 non co-planar points are required, if more than 4 are given, a least-squares approach is used

[2]:

p0 = np.array([0., 0., 0.])
p1 = np.array([0., 4., 0.])
p2 = np.array([1., 0., 0.])
p3 = np.array([0., 0., 2.])

[3]:

origin_points = [p0, p1, p2, p3]

Corresponding coordinates of the control points in the destination space¶

[4]:

P0 = np.array([2., 0., 0.])
P1 = np.array([2., 0., 1.])
P2 = np.array([3., 0., 0.])
P3 = np.array([2., -4., 3.])

[5]:

destination_points = [P0, P1, P2, P3]

Convert control points to vtk objects¶

[6]:

origin = pv.PolyData(origin_points)
origin['Labels'] = [f'p{i}' for i in range(4)]
destination = pv.PolyData(destination_points)
destination['Labels'] = [f'P{i}' for i in range(4)]

2021-10-03 19:10:02.006 (   0.254s) [        513FF740]vtkDataSetAttributes.cx:1285  WARN| vtkPointData (0x5561511ae700): Can not set attribute Scalars. Only vtkDataArray subclasses can be set as active attributes.
2021-10-03 19:10:02.008 (   0.256s) [        513FF740]vtkDataSetAttributes.cx:1285  WARN| vtkPointData (0x55615130eca0): Can not set attribute Scalars. Only vtkDataArray subclasses can be set as active attributes.

Create plotters for the origin and destination spaces¶

[7]:

origin_plotter = pv.Plotter()
origin_plotter.add_point_labels(origin, 'Labels', point_size=12, font_size=12, point_color='green')
#origin_plotter.add_points(origin, point_size=12, color='green')
origin_plotter.add_axes_at_origin(labels_off=True)
origin_plotter.camera_position = 'iso'
# origin_plotter.show_grid()
origin_scene = origin_plotter.show(jupyter_backend='ipyvtklink', return_viewer=True)

[8]:

destination_plotter = pv.Plotter()
destination_plotter.add_point_labels(destination, 'Labels', point_size=12, font_size=12, point_color='orange')
destination_plotter.add_axes_at_origin(labels_off=True)
destination_plotter.camera_position = 'iso'
# destination_plotter.show_grid()
destination_scene = destination_plotter.show(jupyter_backend='ipyvtklink', return_viewer=True)

Compute the 4x4 transform matrix¶

[9]:

transform_matrix, _ = btg.vtk_transform_matrix_from_control_points(origin_points, destination_points)

Use the 4x4 transform to transform origin points into destination points¶

[10]:

origin_copy = origin.copy()

2021-10-03 19:10:02.577 (   0.825s) [        513FF740]vtkDataSetAttributes.cx:1285  WARN| vtkPointData (0x5561511ae700): Can not set attribute Scalars. Only vtkDataArray subclasses can be set as active attributes.

[11]:

origin_copy.clear_arrays() # must remove field before applying transform
transformed = origin_copy.transform(transform_matrix)

[12]:

transformed['Labels'] = [f'P{i}' for i in range(4)]

2021-10-03 19:10:02.591 (   0.839s) [        513FF740]vtkDataSetAttributes.cx:1285  WARN| vtkPointData (0x556152280070): Can not set attribute Scalars. Only vtkDataArray subclasses can be set as active attributes.

[13]:

transformed

2021-10-03 19:10:02.599 (   0.847s) [        513FF740]vtkDataSetAttributes.cx:1285  WARN| vtkPointData (0x556152280070): Can not set attribute Scalars. Only vtkDataArray subclasses can be set as active attributes.

[13]:

Header

Data Arrays

PolyData	Information
N Cells	4
N Points	4
X Bounds	2.000e+00, 3.000e+00
Y Bounds	-4.000e+00, 1.449e-16
Z Bounds	-3.886e-16, 3.000e+00
N Arrays	1

Name	Field	Type	N Comp	Min	Max
Labels	Points		1	nan	nan

Create a plotter for transformed points and display origin (top left), destination (top right) end transformed (bottom right) control points¶

[14]:

transformed_plotter = pv.Plotter()
transformed_plotter.add_point_labels(transformed, 'Labels', point_size=12, font_size=12, point_color='red')
#transformed_plotter.add_points(transformed, point_size=12, color='green')
transformed_plotter.add_axes_at_origin(labels_off=True)
transformed_plotter.camera_position = 'iso'
#transformed_plotter.show_grid()
transformed_scene = transformed_plotter.show(jupyter_backend='ipyvtklink', return_viewer=True)

[15]:

TwoByTwoLayout(top_left=origin_scene, top_right=destination_scene, bottom_right=transformed_scene)

[16]:

static_plotter = pv.Plotter()
static_plotter.add_point_labels(transformed, 'Labels', point_size=12, font_size=12, point_color='red')
static_plotter.add_point_labels(origin, 'Labels', point_size=12, font_size=12, point_color='green')
static_plotter.add_axes_at_origin(labels_off=True)
static_plotter.camera_position = 'iso'
static_plotter.show_grid()
static_plotter.show(jupyter_backend='static')

../../_images/examples_basic_Topo_-_VTK_4x4_transform_matrix_from_control_points_23_0.png

[17]:

[transformed.cell_points(i) for i in range(transformed.n_cells)]

[17]:

[array([[ 2.00000000e+00, -1.69891899e-16, -3.88578059e-16]]),
 array([[ 2.00000000e+00, -1.05807032e-15,  1.00000000e+00]]),
 array([[ 3.00000000e+00,  1.44942688e-16, -2.61544505e-16]]),
 array([[ 2., -4.,  3.]])]

[18]:

[destination.cell_points(i) for i in range(destination.n_cells)]

[18]:

[array([[2., 0., 0.]]),
 array([[2., 0., 1.]]),
 array([[3., 0., 0.]]),
 array([[ 2., -4.,  3.]])]