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)