def show_shape(vertex_set):
""" Demonstrate the 3D animated transformations of shapes composed of vertices and edges.
"""
cycle_period= 100
rad_one_deg = math.pi/180.0
rad_angle = 0.0
for i in range(len(faces_tk)):
for j in range(len(faces_tk[i])):
faces_tk[i][j] = faces_tk[i][j] * matrix_transforms.T_scaling(50 , 50, 50)
# Animation by rotation around 3 axes.
for i in range (500):
# Faces.
for i in range(len(faces_tk)):
faces_tk[i] = faces_tk[i] * matrix_transforms.T_roty(-rad_angle)
faces_tk[i] = faces_tk[i] * matrix_transforms.T_rotx(rad_angle*0.2)
faces_tk[i] = faces_tk[i] * matrix_transforms.T_rotz(rad_angle*1.3)
view_faces =faces_tk[i] * matrix_transforms.T_translate( 300.0, 300.0, 0.0)
fourd_shape_2_twod_line(view_faces , '#ffff00', 1)
rad_angle = rad_one_deg * 1.0
canvas_1.update() # This refreshes the drawing on the canvas.
canvas_1.after(cycle_period) # This makes execution pause for 100 milliseconds.
canvas_1.delete('lines_1')
def scale_shift_3d_object(object_vertices, scale_y, scale_z, x_shift, y_shift):
""" This places a 3D piece "object" at a convenient viewing position and at a
a convenient size.
"""
view_vertices = copy.deepcopy(object_vertices)
for h in range(len(view_vertices)):
for j in range(len(view_vertices[h])):
view_vertices[h][
j] = view_vertices[h][j] * matrix_transforms.T_scaling(
scale_x, scale_y, scale_z)
view_vertices[h][
j] = view_vertices[h][j] * matrix_transforms.T_translate(
x_shift, y_shift, 0.0)
return view_vertices
w = 0.1
h = 6.0
# Locate the shape-set (for temporary display purposes only) at x_shift, y_shift.
x_shift = 200.0
y_shift = 100.0
scale_x = 40.0
scale_y = 40.0
scale_z = 40.0
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
# Create (instantiate) objects and position them.
assemblage_A = stripface(30, x0, y0, z0, w,
h) # Make an instance of the planar object.
for h in range(
len(assemblage_A)): # Disposition and setup - Shift to a new location.
assemblage_A[h] = assemblage_A[h] * matrix_transforms.T_translate(
2.2, 2.2, 0)
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
# Dynamic (animated) rotation of the object).
def transform_display(object_vertices, rad_angle, kula):
""" Transform and then Display.
There are two very distinct and separate operations here:
A) Rotate the object around the X, Y and Z axes. This alters the position of every vertex permanently.
B) Translate and scale each vertex temporarily for viewing. These operations are performed on a separate
copy of the rotated object. After each view the copy has no worth - it will be overwritten when the
next view is created.
"""
#1: Strips: Rotate Assemblage. Any other transforms may be applied to the vertices here. Their effect will be permanent.
# For this example only rotation by a common angle is considered.
for h in range(len(object_vertices)):
new_z = 0.0
new_w = 1
new_vertex = [new_x, new_y, new_z, new_w]
homogenous_4d_array.append(new_vertex)
homogenous_4d_mat = numpy.matrix(homogenous_4d_array)
return homogenous_4d_mat
#=======================================================================
# CONVERT 2D SHAPES TO 4D MATRICES (NUMPY FORM)
fish_2d24d_mat = twod_shape_2_homogeneous_matrix(tiny_fish)
# Scale the tiny fish up into a big fish
bigfish_mat = fish_2d24d_mat * matrix_transforms.T_scaling(150.0, 200.0, 0.0)
# Dynamic rotation of fish_1 around axes within the shape
bigfish_view = bigfish_mat * matrix_transforms.T_translate(
300.0, 300.0, 0.0) # Viewing convenience.
fourd_shape_2_twod_line(bigfish_view, 'yellow', 4)
for i in range(160):
bigfish_mat = bigfish_mat * matrix_transforms.T_rotx(
rad_angle) # Rotation about X axis.
bigfish_mat = bigfish_mat * matrix_transforms.T_roty(
rad_angle) # Rotation about Y axis.
bigfish_mat = bigfish_mat * matrix_transforms.T_rotz(
rad_angle) # Rotation about Z axis.
bigfish_view = bigfish_mat * matrix_transforms.T_translate(
300.0, 300.0, 0.0) # Viewing convenience.
fourd_shape_2_twod_line(bigfish_view, 'green', 1)
rad_angle = rad_one_deg * 5.0
root.mainloop()
twod_line.append(bbb[i][1])
canvas_1.create_line(twod_line, width=line_width, fill=kula)
return twod_line
#========================================================================
# Convert 2D set SET to 4D matrices (NUMPY FORM).
fish_4d_set_mat = []
for set in range(len(fish_set)):
temp = twod_shape_2_homogeneous_matrix(fish_set[set])
fish_4d_set_mat.append(temp)
# Move origin to center-of-rotation(cor).
for set in range(len(fish_set)):
fish_4d_set_mat[
set] = fish_4d_set_mat[set] * matrix_transforms.T_translate(
-300.0, -330.0, 0.0)
# Dynamic rotation of fish_1 around axes within the shape
for i in range(100):
for set in range(len(fish_4d_set_mat)):
fish_4d_set_mat[set] = fish_4d_set_mat[set] * matrix_transforms.T_rotx(
rad_angle) # X rotation.
fish_4d_set_mat[set] = fish_4d_set_mat[set] * matrix_transforms.T_roty(
rad_angle) # Y rotation.
fish_4d_set_mat[set] = fish_4d_set_mat[set] * matrix_transforms.T_rotz(
rad_angle) # Z rotation.
view_fish_set = fish_4d_set_mat[set] * matrix_transforms.T_translate(
300.0, 280.0, 0.0)
fourd_shape_2_twod_line(view_fish_set, kulas[set], 1)
rad_angle = rad_one_deg * 10.0