def combining_transforms():
X = util.test_object(1)
X_shear_reflect = reg.reflect(-1, 1).dot(reg.shear(0.5, 0.2).dot(X))
X_reflect_shear = reg.shear(0.5, 0.2).dot(reg.reflect(-1, 1).dot(X))
fig = plt.figure(figsize=(12, 5))
ax1 = fig.add_subplot(141, xlim=(-4, 4), ylim=(-4, 4))
ax2 = fig.add_subplot(142, xlim=(-4, 4), ylim=(-4, 4))
ax3 = fig.add_subplot(143, xlim=(-4, 4), ylim=(-4, 4))
ax4 = fig.add_subplot(144, xlim=(-4, 4), ylim=(-4, 4))
util.plot_object(ax1, X)
util.plot_object(ax2, X_shear_reflect)
util.plot_object(ax3, X_reflect_shear)
util.plot_object(ax4, X)
ax1.set_title('Original')
ax2.set_title('shear_reflect')
ax3.set_title('reflect_shear')
ax4.set_title('Original')
ax1.grid()
ax2.grid()
ax3.grid()
ax4.grid()
fig.show()
def combining_transforms():
X = util.test_object(1)
#------------------------------------------------------------------#
# Experiment with combining transformation matrices.
X1_1 = reg.rotate(np.pi / 4).dot(reg.reflect(-1, 1).dot(X))
X1_2 = reg.reflect(-1, 1).dot(reg.rotate(np.pi / 4).dot(X))
X2_1 = reg.shear(0.6, 0.3).dot(reg.reflect(-1, -1).dot(X))
X2_2 = reg.shear(0.6, 0.3).dot(reg.reflect(-1, 1).dot(X))
X3_1 = reg.reflect(-1, 1).dot(reg.shear(0.6, 0.3).dot(X))
X3_2 = reg.shear(0.6, 0.3).dot(reg.reflect(-1, 1).dot(X))
fig = plt.figure(figsize=(12, 5))
ax1 = fig.add_subplot(141, xlim=(-4, 4), ylim=(-4, 4))
ax2 = fig.add_subplot(142, xlim=(-4, 4), ylim=(-4, 4))
ax3 = fig.add_subplot(143, xlim=(-4, 4), ylim=(-4, 4))
ax4 = fig.add_subplot(144, xlim=(-4, 4), ylim=(-4, 4))
util.plot_object(ax1, X)
util.plot_object(ax2, X1_1)
util.plot_object(ax2, X1_2)
util.plot_object(ax3, X2_1)
util.plot_object(ax3, X2_2)
util.plot_object(ax4, X3_1)
util.plot_object(ax4, X3_2)
ax1.grid()
ax2.grid()
ax3.grid()
ax4.grid()
def arbitrary_rotation():
X = util.test_object(1)
Xh = util.c2h(X)
#------------------------------------------------------------------#
#perform rotation around the first vertex
phi = 45
c = np.cos(phi)
s = np.sin(phi)
coord_1 = X[:, 0] #rotatie om dit punt
x_r = coord_1[0]
y_r = coord_1[1]
T_1 = np.array([[1, 0, x_r], [0, 1, y_r], [0, 0, 1]])
T_2 = np.array([[c, -s, 0], [s, c, 0], [0, 0, 1]])
T_3 = np.array([[1, 0, -x_r], [0, 1, -y_r], [0, 0, 1]])
T = T_1.dot(T_2).dot(T_3)
#------------------------------------------------------------------#
X_rot = T.dot(Xh)
fig = plt.figure(figsize=(5, 5))
ax1 = fig.add_subplot(111)
util.plot_object(ax1, X)
util.plot_object(ax1, X_rot)
ax1.set_xlim(ax1.get_ylim())
ax1.grid()
def combining_transforms():
X = util.test_object(1)
X_1 = X
X_2 = reg.rotate(3 * np.pi / 4).dot(X)
X_3 = reg.reflect(-1, 1).dot(reg.rotate(3 * np.pi / 4).dot(X))
X_4 = reg.shear(0.1, 0.2).dot(
reg.reflect(-1, 1).dot(reg.rotate(3 * np.pi / 4).dot(X)))
fig = plt.figure(figsize=(12, 5))
ax1 = fig.add_subplot(141, xlim=(-4, 4), ylim=(-4, 4))
ax2 = fig.add_subplot(142, xlim=(-4, 4), ylim=(-4, 4))
ax3 = fig.add_subplot(143, xlim=(-4, 4), ylim=(-4, 4))
ax4 = fig.add_subplot(144, xlim=(-4, 4), ylim=(-4, 4))
util.plot_object(ax1, X_1)
util.plot_object(ax2, X_2)
util.plot_object(ax3, X_3)
util.plot_object(ax4, X_4)
ax1.set_title('Original')
ax2.set_title('Then rotate')
ax3.set_title('Now reflect over x')
ax4.set_title('Lastly, shear')
for ax_obj in [ax1, ax2, ax3, ax4]:
ax_obj.grid()
def arbitrary_rotation():
X = util.test_object(1)
Xh = util.c2h(X)
#Define rotation angle 45degrees
phi = np.pi / 4
#Define seperate homogenous transformation matrices
T_1 = np.array([[1, 0, -X[0, 0]], [0, 1, -X[1, 0]], [0, 0, 1]])
T_rot = np.array([[cos(phi), -sin(phi), 0], [sin(phi),
cos(phi), 0], [0, 0, 1]])
T_2 = np.array([[1, 0, X[0, 0]], [0, 1, X[1, 0]], [0, 0, 1]])
#Combine them
T = T_2.dot(T_rot.dot(T_1))
X_rot = T.dot(Xh)
fig = plt.figure(figsize=(5, 5))
ax1 = fig.add_subplot(111)
util.plot_object(ax1, X)
util.plot_object(ax1, X_rot)
ax1.set_xlim(ax1.get_ylim())
ax1.grid()
def arbitrary_rotation():
X = util.test_object(1)
Xh = util.c2h(X)
#------------------------------------------------------------------#
# TODO: Perform rotation of the test shape around the first vertex
Xt = X[:, 0]
phi = (45 / 180) * np.pi
#matrix to move the figure to new origin
translate_matrix = util.t2h(reg.identity(), -Xt)
translate_matrix[2][
2] = 1 #add the 1 in de third row and column to get 'ones'on the diagonal
rotate_matrix = np.array([[np.cos(phi), -np.sin(phi), 0],
[np.sin(phi), np.cos(phi), 0], [0, 0, 1]])
#matrix to move the figure back to original origin
translate_matrix_2 = util.t2h(reg.identity(), Xt)
translate_matrix_2[2][
2] = 1 #add the 1 in de third row and column to get 'ones'on the diagonal
T = (rotate_matrix.dot(translate_matrix)) #rotate the moved figure
T = translate_matrix_2.dot(T) #move the figure back
#------------------------------------------------------------------#
X_rot = T.dot(Xh)
fig = plt.figure(figsize=(5, 5))
ax1 = fig.add_subplot(111)
util.plot_object(ax1, X)
util.plot_object(ax1, X_rot)
ax1.set_xlim(ax1.get_ylim())
ax1.grid()
def arbitrary_rotation():
X = util.test_object(1) # The object that is rotated
Xh = util.c2h(X) # Convert the object vectors to homogeneous coords
t = X[:, 0] # First vertex to rotate around
# Define separate transformations in homogeneous coords
T_ftrans = util.t2h(reg.identity(), -1 *
t) # Translate to ensure first vertex is in the origin
T_rot = util.t2h(reg.rotate(np.pi / 4), np.array([0,
0])) # Rotate 45 degrees
T_btrans = util.t2h(reg.identity(),
t) # Translate back to the original position
# Create the final transformation matrix
T = T_btrans.dot(T_rot.dot(T_ftrans))
#------------------------------------------------------------------#
# TODO: TODO: Perform rotation of the test shape around the first vertex
#------------------------------------------------------------------#
# Transform
X_rot = T.dot(Xh)
# Plot
fig = plt.figure(figsize=(5, 5))
ax1 = fig.add_subplot(111)
util.plot_object(ax1, X)
util.plot_object(ax1, X_rot)
ax1.set_xlim(ax1.get_ylim())
ax1.grid()
def combining_transforms():
X = util.test_object(1)
#------------------------------------------------------------------#
# TODO: Experiment with combining transformation matrices.
Example_1_temp = reg.rotate(5 * np.pi / 3).dot(X)
Example_1_result = reg.reflect(-1, 1).dot(Example_1_temp)
Example2 = reg.reflect(-1, 1).dot(X)
Example2_result = reg.rotate(np.pi / 2).dot(Example2)
Example2_reversed = reg.rotate(np.pi / 2).dot(X)
Example2_reversed_result = reg.rotate(5 * np.pi / 3).dot(X)
#plotting
fig = plt.figure(figsize=(12, 5))
ax1 = fig.add_subplot(141, xlim=(-4, 4), ylim=(-4, 4))
ax2 = fig.add_subplot(142, xlim=(-4, 4), ylim=(-4, 4))
ax3 = fig.add_subplot(143, xlim=(-4, 4), ylim=(-4, 4))
util.plot_object(ax1, X)
util.plot_object(ax2, Example2_result)
util.plot_object(ax3, Example2_reversed_result)
ax1.set_title('Original')
ax2.set_title('Reflection, rotation')
ax3.set_title('Reversed')
ax1.grid()
ax2.grid()
ax3.grid()
def arbitrary_rotation():
X = util.test_object(1)
Xh = util.c2h(X) #the object in homogeneous form
#------------------------------------------------------------------#
Xt = np.array(X[:, 0])
T_rot = reg.rotate(np.pi / 4)
Xt_down = util.t2h(
reg.identity(),
-Xt) #with Xt being the translation vector set into homogeneous form
Xt_up = util.t2h(reg.identity(), Xt)
T_rot = util.t2h(T_rot, np.array(
[0, 0])) #with T being the rotational vector set into homogeneous form
T = Xt_up.dot(T_rot).dot(Xt_down)
X_fin = T.dot(Xh)
#------------------------------------------------------------------#
fig = plt.figure(figsize=(5, 5))
ax1 = fig.add_subplot(111)
util.plot_object(ax1, X)
util.plot_object(ax1, X_fin)
ax1.set_xlim(ax1.get_ylim())
ax1.grid()
def ls_affine_test():
X = util.test_object(1)
# convert to homogeneous coordinates
Xh = util.c2h(X)
T_rot = reg.rotate(np.pi / 4)
T_scale = reg.scale(1.2, 0.9)
T_shear = reg.shear(0.2, 0.1)
T = util.t2h(T_rot.dot(T_scale).dot(T_shear), [10, 20])
Xm = T.dot(Xh)
Te = reg.ls_affine(Xh, Xm)
Xmt = Te.dot(Xm)
fig = plt.figure(figsize=(12, 5))
ax1 = fig.add_subplot(131)
ax2 = fig.add_subplot(132)
ax3 = fig.add_subplot(133)
util.plot_object(ax1, Xh)
util.plot_object(ax2, Xm)
util.plot_object(ax3, Xmt)
ax1.set_title('Test shape')
ax2.set_title('Arbitrary transformation')
ax3.set_title('Retrieved test shape')
ax1.grid()
ax2.grid()
ax3.grid()
def combining_transforms():
X = util.test_object(1)
#------------------------------------------------------------------#
# TODO: Experiment with combining transformation matrices.
X_t = reg.reflect(-1, 1).dot(reg.rotate(np.pi / 2)).dot(X)
X_u = reg.shear(2, 1).dot(reg.reflect(1, -1)).dot(X)
X_v = reg.reflect(1, -1).dot(reg.shear(2, 1)).dot(X)
X_w = reg.rotate(np.pi / 2).dot(reg.shear(2, 1)).dot(X)
fig = plt.figure(figsize=(12, 5))
ax1 = fig.add_subplot(141, xlim=(-8, 8), ylim=(-8, 8))
ax2 = fig.add_subplot(142, xlim=(-8, 8), ylim=(-8, 8))
ax3 = fig.add_subplot(143, xlim=(-8, 8), ylim=(-8, 8))
ax4 = fig.add_subplot(144, xlim=(-8, 8), ylim=(-8, 8))
util.plot_object(ax1, X_t)
util.plot_object(ax2, X_u)
util.plot_object(ax3, X_v)
util.plot_object(ax4, X_w)
ax1.set_title('reflect, rotate')
ax2.set_title('shear, reflect')
ax3.set_title('reflect, shear')
ax4.set_title('rotate, shear')
ax1.grid()
ax2.grid()
ax3.grid()
ax4.grid()
def transforms_test():
X = util.test_object(1)
X_rot = reg.rotate(3*np.pi/4).dot(X)
X_shear = reg.shear(0.1, 0.2).dot(X)
X_reflect = reg.reflect(-1, -1).dot(X)
fig = plt.figure(figsize=(12,5))
ax1 = fig.add_subplot(141, xlim=(-4,4), ylim=(-4,4))
ax2 = fig.add_subplot(142, xlim=(-4,4), ylim=(-4,4))
ax3 = fig.add_subplot(143, xlim=(-4,4), ylim=(-4,4))
ax4 = fig.add_subplot(144, xlim=(-4,4), ylim=(-4,4))
util.plot_object(ax1, X)
util.plot_object(ax2, X_rot)
util.plot_object(ax3, X_shear)
util.plot_object(ax4, X_reflect)
ax1.set_title('Original')
ax2.set_title('Rotation')
ax3.set_title('Shear')
ax4.set_title('Reflection')
ax1.grid()
ax2.grid()
ax3.grid()
ax4.grid()
def combining_transforms():
X = util.test_object(1)
X_rot = reg.rotate(3 * np.pi / 7).dot(X)
X_shear = reg.shear(0.3, 0.22).dot(X)
X_rot_shear = reg.shear(0.1, 0.3).dot(X_rot)
X_shear_reflect = reg.reflect(-1, 1).dot(X_shear)
X_multicom = reg.rotate(np.pi / 3).dot(X_rot_shear)
fig = plt.figure(figsize=(12, 5))
ax1 = fig.add_subplot(141, xlim=(-4, 4), ylim=(-4, 4))
ax2 = fig.add_subplot(142, xlim=(-4, 4), ylim=(-4, 4))
ax3 = fig.add_subplot(143, xlim=(-4, 4), ylim=(-4, 4))
ax4 = fig.add_subplot(144, xlim=(-4, 4), ylim=(-4, 4))
util.plot_object(ax1, X)
util.plot_object(ax2, X_rot_shear)
util.plot_object(ax3, X_shear_reflect)
util.plot_object(ax4, X_multicom)
ax1.set_title('Original')
ax2.set_title('Combination 1')
ax3.set_title('Combination 2')
ax4.set_title('Combination 3')
ax1.grid()
ax2.grid()
ax3.grid()
ax4.grid()
def arbitrary_rotation():
X = util.test_object(1)
Xh = util.c2h(X)
#------------------------------------------------------------------#
# Perform rotation of the test shape around the first vertex
t = -X[:, 0]
Trot = reg.rotate(np.pi / 4)
Throt = util.t2h(Trot, np.zeros([1, np.size(Trot, axis=1)]))
th = util.t2h(reg.identity(), t)
thin = np.linalg.inv(th)
T = thin.dot(Throt.dot(th))
#------------------------------------------------------------------#
X_rot = T.dot(Xh)
fig = plt.figure(figsize=(5, 5))
ax1 = fig.add_subplot(111)
util.plot_object(ax1, X)
util.plot_object(ax1, X_rot)
ax1.set_xlim(ax1.get_ylim())
ax1.grid()
def combining_transforms():
X = util.test_object(1)
#------------------------------------------------------------------#
# TODO: Experiment with combining transformation matrices.
X_t = reg.rotate(np.pi/2).dot(X)*reg.reflect(-1,1).dot(X)
return X_t
def combining_transforms():
X = util.test_object(1)
X_combined = (reg.rotate(3 * np.pi / 5) * reg.shear(0.2, 0.2) * reg.shear(2, 8)).dot(X)
fig = plt.figure(figsize=(12, 5))
ax1 = fig.add_subplot(141, xlim=(-4, 4), ylim=(-4, 4))
util.plot_object(ax1, X_combined)
def combining_transforms():
X = util.test_object(1)
T = reg.reflect(-1, 1).dot(reg.rotate(np.pi / 2))
X_t = T.dot(X)
fig = plt.figure(figsize=(5, 5))
ax1 = fig.add_subplot(111)
ax1.grid()
util.plot_object(ax1, X)
util.plot_object(ax1, X_t)
def arbitrary_rotation():
X = util.test_object(1)
Xh = util.c2h(X)
#------------------------------------------------------------------#
# TODO: Perform rotation of the test shape around the first vertex
#------------------------------------------------------------------#
X_rot = T.dot(Xh)
fig = plt.figure(figsize=(5,5))
ax1 = fig.add_subplot(111)
util.plot_object(ax1, X)
util.plot_object(ax1, X_rot)
ax1.set_xlim(ax1.get_ylim())
ax1.grid()
def t2h_test():
X = util.test_object(1)
Xh = util.c2h(X)
# translation vector
t = np.array([10, 20])
# rotation matrix
T_rot = reg.rotate(np.pi / 4)
Th = util.t2h(T_rot, t)
X_rot_tran = Th.dot(Xh)
fig = plt.figure(figsize=(5, 5))
ax1 = fig.add_subplot(111)
util.plot_object(ax1, X)
util.plot_object(ax1, X_rot_tran)
ax1.grid()
def arbitrary_rotation():
X = util.test_object(1)
Xh = util.c2h(X)
#------------------------------------------------------------------#
Xt= X[:0]
T_trans = util.t2h(reg.identity(), Xt)
T_rot = reg.rotate(0.25*np.pi)
T_trans_inv = np.linalg.inv(T_trans)
T = T_trans_inv.dot(T_rot.dot(T_trans))
#------------------------------------------------------------------#
X_rot = T.dot(Xh)
fig = plt.figure(figsize=(5,5))
ax1 = fig.add_subplot(111)
util.plot_object(ax1, X)
util.plot_object(ax1, X_rot)
ax1.set_xlim(ax1.get_ylim())
ax1.grid()
def arbitrary_rotation():
X = util.test_object(1)
Xh = util.c2h(X)
p_rot = X[:, 0]
T_to_zero = util.t2h(reg.identity(), -p_rot)
T_return = util.t2h(reg.identity(), p_rot)
T_rot = util.t2h(reg.rotate(45))
T = T_return.dot(T_rot.dot(T_to_zero))
X_rot = T.dot(Xh)
fig = plt.figure(figsize=(5, 5))
ax1 = fig.add_subplot(111)
util.plot_object(ax1, X)
util.plot_object(ax1, X_rot)
ax1.set_xlim(ax1.get_ylim())
ax1.grid()
fig.show()
def arbitrary_rotation():
X = util.test_object(1)
Xh = util.c2h(X)
#------------------------------------------------------------------#
# TODO: Perform rotation of the test shape around the first vertex
Xt = X[:, 0]
T = util.t2h(reg.rotate(np.pi / 4), Xt).dot(util.t2h(reg.identity(), -Xt))
#------------------------------------------------------------------#
X_rot = T.dot(Xh)
fig = plt.figure(figsize=(5, 5))
ax1 = fig.add_subplot(111)
util.plot_object(ax1, X)
util.plot_object(ax1, X_rot)
ax1.set_xlim(ax1.get_ylim())
ax1.grid()
def arbitrary_rotation():
X = util.test_object(1)
Xh = util.c2h(X)
# ------------------------------------------------------------------#
Tlat = util.t2h(reg.identity(), np.array(X[:, 0]))
Tlat_down = util.t2h(reg.identity(), -np.array(X[:, 0]))
T_rot = reg.rotate(np.pi / 4)
T_rot_hom = util.t2h(T_rot, np.array([0, 0]))
T_tot = Tlat.dot(T_rot_hom).dot(Tlat_down)
X_fin = T_tot.dot(Xh)
# ------------------------------------------------------------------#
fig = plt.figure(figsize=(5, 5))
ax1 = fig.add_subplot(111)
util.plot_object(ax1, X)
util.plot_object(ax1, X_fin)
ax1.set_xlim(ax1.get_ylim())
ax1.grid()
def arbitrary_rotation():
X = util.test_object(1)
Xh = util.c2h(X)
#------------------------------------------------------------------#
# TODO: TODO: Perform rotation of the test shape around the first vertex
a_point = X[:,0]
ax = a_point[0]
ay = a_point[1]
trans1 = np.array([[1,0,ax],[0,1,ay],[0,0,1]]) #translatiematrix 1 (zie slides)
trans2 = np.array([[1, 0, -ax], [0, 1, -ay], [0, 0, 1]]) #translatiematrix 2
phi = (np.pi/4)
c = np.cos(phi)
s = np.sin(phi)
extra = ([[0,0]])
extra_vertical = np.transpose(extra)
extra_horizontal = ([[0,0,1]])
r = np.array([[c, -s], [s, c]])
rot1 = np.concatenate((r, extra_vertical), 1)
rot2 = np.concatenate((rot1, extra_horizontal), 0) #rotatiematrix
Transformation = trans1.dot(rot2.dot(trans2))
X_rot = Transformation.dot(Xh)
#------------------------------------------------------------------#
#X_rot = T.dot(Xh)
fig = plt.figure(figsize=(5,5))
ax1 = fig.add_subplot(111)
util.plot_object(ax1, X)
util.plot_object(ax1, X_rot)
ax1.set_xlim(ax1.get_ylim())
ax1.grid()
def arbitrary_rotation():
X = util.test_object(1)
Xh = util.c2h(X)
#------------------------------------------------------------------#
# TODO: TODO: Perform rotation of the test shape around the first vertex
#------------------------------------------------------------------#
tdown = X[:, 0] * -1
tup = X[:, 0]
tdown = util.t2h(reg.identity(), tdown)
tup = util.t2h(reg.identity(), tup)
r = util.t2h(reg.rotate(45), [0, 0])
T = tup.dot(r.dot(tdown))
X_rot = T.dot(Xh)
fig = plt.figure(figsize=(5, 5))
ax1 = fig.add_subplot(111)
util.plot_object(ax1, X)
util.plot_object(ax1, X_rot)
ax1.set_xlim(ax1.get_ylim())
ax1.grid()
plt.show()
def combining_transforms():
X = util.test_object(1)
#------------------------------------------------------------------#
X_t = reg.reflect(-1,1).dot(reg.rotate(2)).dot(X)
# -*- coding: utf-8 -*-
"""
Created on Tue Sep 10 15:36:11 2019
@author: 20161879
"""
import sys
sys.path.append("../code")
import numpy as np
import matplotlib.pyplot as plt
import registration as reg
import registration_util as util
X = util.test_object(1)
X_scaled = reg.scale(2, 3).dot(X)
fig = plt.figure(figsize=(5, 5))
ax1 = fig.add_subplot(111)
ax1.grid()
util.plot_object(ax1, X)
util.plot_object(ax1, X_scaled)
def combining_transforms():
X = util.test_object(1)
