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9.1.2.b.py
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9.1.2.b.py
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import numpy as np
import matplotlib.pyplot as plt
from matplotlib.widgets import Slider
from mpl_toolkits.mplot3d import Axes3D
%matplotlib notebook
class plot3dCube(object):
def __init__(self, origin, length, color):
# origin[x,y,z], length[Lx,Ly,Lz],
self.g = 1
self.origin = origin
self.length = length
#initial plot
self.updateCube(origin,length)
self.height = length[2]
# create plot figure
self.fig = plt.figure(figsize=(6,7))
self.ax = self.fig.add_subplot(111, projection='3d')
self.ax.set_xlim3d(-1, 0)
self.ax.set_ylim3d(-1, 0)
self.ax.set_zlim3d(-5, 10)
self.ax.set_xlabel('X')
self.ax.set_ylabel('Y')
self.ax.set_zlabel('Z')
# set color
self.color = color
# dictionary of surfaces and edges
self.dFrm = {}
# surface variable name
surface = "self.surface"
# edge variable name
edge = "self.edge"
# generate frame and edge plots
for i in range(len(self.sqrP)):
# number
n = str(i)
self.dFrm[surface+n], self.dFrm[edge+n] = self.initFrame(self.sqrP[i][:])
# slider plot
# adjust plot
plt.subplots_adjust(left = 0.1, bottom = 0.45)
# input the position of sliders
xSlider = plt.axes([0.2,0.2,0.5,0.03])
ySlider = plt.axes([0.2,0.15,0.5,0.03])
zSlider = plt.axes([0.2,0.1,0.5,0.03])
xSlider.set_xticks(np.array([90,180,270]), minor = True)
ySlider.set_xticks(np.array([1,2,3,4]), minor = True)
zSlider.set_xticks(np.array([1,2,3,4]), minor = True)
# input values and update graph
self.slider1 = Slider(xSlider, 't', 0, 4*np.pi*np.sqrt(5), valinit = 0, valstep = 0.1)
self.slider2 = Slider(ySlider, 'm', 1, 5, valinit = 1, valstep = 0.1)
self.slider3 = Slider(zSlider, 'k', 1, 5, valinit = 1, valstep = 0.1)
# updates the graph when input is changes
self.slider1.on_changed(self.updateGraph)
self.slider2.on_changed(self.updateGraph)
self.slider3.on_changed(self.updateGraph)
def updateCube(self,origin, length):
Lx,Ly,Lz = length
x1,y1,z1 = origin
x2,y2,z2 = [length[i]+origin[i] for i in range(3)]
# for A as X,Y,Z
# A_1212 uses [[x1, x2][x1,x2]]
# A_1122 is just X_1.T
# A_1111 all x1
# A_2222 all x2
r = [x1, x2]
X_1212 = np.array([r,r])
X_1111 = np.ones(4).reshape(2, 2)*x1
X_2222 = np.ones(4).reshape(2, 2)*x2
r = [y1, y2]
Y_1212, Y_1122 = np.meshgrid(r, r)
Y_1111 = np.ones(4).reshape(2, 2)*y1
Y_2222 = np.ones(4).reshape(2, 2)*y2
r = [z1, z2]
Z_1122 = np.array([r,r]).transpose()
Z_1111 = np.ones(4).reshape(2, 2)*z1
Z_2222 = np.ones(4).reshape(2, 2)*z2
# points of the cube
self.points = np.array([[x1, y1, z1],
[x2, y1, z1],
[x2, y2, z1],
[x1, y2, z1],
[x1, y1, z2],
[x2, y1, z2],
[x2, y2, z2],
[x1, y2, z2]])
# square points for surface, edges
self.sqrP = [[X_1212,Y_1122,Z_1111],[X_1212,Y_1122,Z_2222],
[X_1212,Y_1111,Z_1122],[X_1212,Y_2222,Z_1122],
[X_1111,Y_1212,Z_1122],[X_2222,Y_1212,Z_1122]]
def initFrame(self, sqrP):
surface = self.ax.plot_surface(sqrP[0],sqrP[1],sqrP[2],alpha=0.5,color=self.color[0])
edge = self.ax.plot_wireframe(sqrP[0],sqrP[1],sqrP[2],alpha=0.5,color=self.color[1])
return surface, edge
def updateGraph(self, event):
t, m, k = self.slider1.val, self.slider2.val, self.slider3.val
g = self.g
z = (g*m-g*m*np.cos(np.sqrt(k/m)*t))/k
self.origin[2] = z
self.length[2] = self.height - z
self.updateCube(self.origin, self.length)
self.updateFrames()
def updateFrame(self, surface, edge, X, Y, Z):
#destory previous surfaces and edges
surface.remove()
edge.remove()
# plot surfaces and edges
surface = self.ax.plot_surface(X,Y,Z, alpha = 0.5, color = self.color[0])
edge = self.ax.plot_wireframe(X,Y,Z, alpha = 0.5, color = self.color[1])
return surface, edge
def updateFrames(self):
surface = "self.surface"
edge = "self.edge"
# destroy current surface and edge, new surface and edge
for j in range(6):
n = str(j)
self.dFrm[surface+n], self.dFrm[edge+n]= self.updateFrame(self.dFrm[surface+n],self.dFrm[edge+n],
self.sqrP[j][0],self.sqrP[j][1],self.sqrP[j][2])
plt.draw()
plt.pause(.01)
# main function
p = plot3dCube([0,0,0], [-1,-1,-5],["grey","black"])