added simulation for brownian motion

docs/examples/viz_brownian_motion.py

@@ -0,0 +1,139 @@
+"""
+======================================================================
+Brownian motion
+======================================================================
+Brownian motion, or pedesis, is the random motion of particles suspended in
+a medium. In this animation, path followed by 20 particles exhibiting brownian
+motion in 3D is plotted.
+
+Importing necessary modules
+"""
+
+from fury import window, actor, ui, utils
+import numpy as np
+from scipy.stats import norm
+
+###############################################################################
+# Variable(s) and their description-
+# total_time: time to be discretized via time_steps (default: 5)
+# num_total_steps: total number of steps each particle will take (default: 300)
+# time_step = (total_time / num_total_steps)
+#             time_step is computed and initialised in the __init__ method of
+#             the particle class
+# counter_step: to keep track of number of steps taken (initialised to 0)
+# delta: delta determines the "speed" of the Brownian motion. Increase delta
+#        to speed up the motion of the particle(s). The random variable
+#        of the position has a normal distribution whose mean is the position
+#        at counter_step = 0 and whose variance is equal to delta**2*time_step.
+#        (default: 1.8)
+# num_particles: number of particles whose path will be plotted (default: 20)
+# path_thickness: thickness of line(s) that will be used to plot the path(s)
+#                 of the particle(s) (default: 3)
+# origin: coordinate from which the the particle(s) begin the motion
+#         (default: [0, 0, 0])
+
+total_time = 5
+num_total_steps = 300
+counter_step = 0
+delta = 1.8
+num_particles = 20
+path_thickness = 3
+origin = [0, 0, 0]
+
+###############################################################################
+# class particle is used to store and update coordinates of the particles (the
+# path of the particles)
+
+
+class particle:
+    def __init__(self, colors, origin=[0, 0, 0], num_total_steps=300,
+                 total_time=5, delta=1.8, path_thickness=3):
+        origin = np.asarray(origin, dtype=float)
+        self.position = np.tile(origin, (num_total_steps, 1))
+        self.colors = colors
+        self.delta = delta
+        self.num_total_steps = num_total_steps
+        self.time_step = total_time / num_total_steps
+        self.path_actor = actor.line([self.position], colors,
+                                     linewidth=path_thickness)
+        self.vertices = utils.vertices_from_actor(self.path_actor)
+        self.vcolors = utils.colors_from_actor(self.path_actor, 'colors')
+        self.no_vertices_per_point = len(self.vertices) / num_total_steps
+        nvpp = self.no_vertices_per_point
+        self.initial_vertices = self.vertices.copy() - np.repeat(self.position,
+                                                                 nvpp, axis=0)
+
+    def update_path(self, counter_step):
+        if counter_step < self.num_total_steps:
+            x, y, z = self.position[counter_step-1]
+            x += norm.rvs(scale=self.delta**2 * self.time_step)
+            y += norm.rvs(scale=self.delta**2 * self.time_step)
+            z += norm.rvs(scale=self.delta**2 * self.time_step)
+            self.position[counter_step:] = [x, y, z]
+            self.vertices[:] = self.initial_vertices + \
+                np.repeat(self.position, self.no_vertices_per_point, axis=0)
+            utils.update_actor(self.path_actor)
+
+
+###############################################################################
+# Creating a scene object and configuring the camera's position
+
+scene = window.Scene()
+scene.background((1.0, 1.0, 1.0))
+scene.zoom(1.7)
+scene.set_camera(position=(0, 0, 40), focal_point=(0.0, 0.0, 0.0),
+                 view_up=(0.0, 0.0, 0.0))
+showm = window.ShowManager(scene,
+                           size=(600, 600), reset_camera=True,
+                           order_transparent=True)
+showm.initialize()
+
+###############################################################################
+# Creating a list of particle objects
+
+list_particles = []
+for i in range(num_particles):
+    _particle = particle(colors=np.random.rand(1, 3), origin=origin,
+                         num_total_steps=num_total_steps,
+                         total_time=total_time, path_thickness=path_thickness)
+    list_particles.append(_particle)
+    scene.add(list_particles[i].path_actor)
+
+###############################################################################
+# Creating a container (cube actor) inside which the particle(s) move around
+
+container_actor = actor.box(centers=np.array([[0, 0, 0]]),
+                            colors=(0.5, 0.9, 0.7, 0.4), scales=6)
+scene.add(container_actor)
+
+###############################################################################
+# Initializing text box to display the name of the animation
+
+tb = ui.TextBlock2D(bold=True, position=(235, 40), color=(0, 0, 0))
+tb.message = "Brownian Motion"
+scene.add(tb)
+
+
+###############################################################################
+# The path of the particles exhibiting Brownian motion is plotted here
+
+def timer_callback(_obj, _event):
+    global counter_step, list_particles
+    counter_step += 1
+    for _particle in list_particles:
+        _particle.update_path(counter_step=counter_step)
+    showm.render()
+    scene.azimuth(2)
+    if (counter_step == num_total_steps):
+        showm.exit()
+
+###############################################################################
+# Run every 30 milliseconds
+
+
+showm.add_timer_callback(True, 30, timer_callback)
+interactive = False
+if interactive:
+    showm.start()
+
+window.record(showm.scene, size=(600, 600), out_path="viz_brownian_motion.png")