Animated 3D plotting with Blender
From Penguin Development
Blender is an extremely versatile 3D creation and animation suite. Since it is fully scriptable in Python, Blender may be used to generate animated 3-dimensional plots of data or mathematical functions. Below is an example of one way to generate such a plot.
Important information
The script below has been tested with Blender 2.78a for Linux. It should generally be compatible with other versions and operating systems. The script works with the pristine Blender startup file; heavily modified startup files may break certain assumptions.
To run the script, simply call blender --python blenderplot-ani.py
To create the plot in a different base file, instead use blender basefile.blend --python blenderplot-ani.py.
The order of arguments matters here.
Note that the animation data will not be saved with your .blend file! This means you must run the Python script on a pristine "background" .blend file each time you wish to examine the geometry or create a render. If the .blend file is saved, only the first frame will be captured.
The script
Code for blenderplot-ani.py follows.
#!/bin/true
# vim: se fo=tcroq tw=78 :
# Simple animated 3D plot example using Blender ( https://www.blender.org/ ).
# Given the function f(k, x, t)=exp(ikx-iωt), plots Re(f) against x and k,
# with colour given by Im(f) and t being the time.
#
# For pedagogical purposes, this just computes f at each frame (twice: once
# for the vertex positions and once for their colours). This is horribly
# inefficient; it would be much better to generate a 3D array for f(x, k, t)
# once and slice this array for each frame -- however, this is left as an
# exercise to the reader.
#
# To run, call
# blender --python blenderplot-ani.py
import os.path
import numpy as np
import bpy
### Begin user settings
omega = 1
font = '/usr/share/fonts/cm-unicode/cmunti.ttf' # Must be a unicode font!
### End user settings
### Begin generic Blender rendering code
# Global object counter.
obj_ind = 10000
plot_id = None
line_material = bpy.data.materials.new('line')
line_material.diffuse_color = (0, 0, 0)
line_material.diffuse_shader = 'LAMBERT'
line_material.specular_color = (0, 0, 0)
line_material.specular_shader = 'COOKTORR'
line_material.use_shadows = False
line_material.use_cast_shadows = False
line_material.use_raytrace = True
line_material.ambient = 0
text_material = bpy.data.materials.new('text')
text_material.diffuse_color = (.15, .05, .035)
text_material.diffuse_shader = 'OREN_NAYAR'
text_material.diffuse_intensity = .9
text_material.roughness = 2
text_material.specular_color = (.6, .2, .1)
text_material.specular_shader = 'PHONG'
text_material.specular_hardness = 80
text_material.specular_intensity = .85
text_material.use_shadows = True
text_material.use_cast_shadows = False
text_material.use_raytrace = True
text_material.raytrace_mirror.use = True
text_material.mirror_color = (.7, .3, .15)
text_material.raytrace_mirror.reflect_factor = .3
text_material.emit = 0
text_material.ambient = 0
plot_material = bpy.data.materials.new('plot')
plot_material.specular_color = (.5, .5, .5)
plot_material.specular_shader = 'COOKTORR'
plot_material.specular_intensity = .2
plot_material.use_shadows = True
plot_material.use_transparent_shadows = True
plot_material.use_raytrace = True
plot_material.use_transparency = True
plot_material.transparency_method = 'RAYTRACE'
plot_material.alpha = .95
plot_material.specular_alpha = 1
plot_material.raytrace_transparency.depth = 5
plot_material.use_vertex_color_paint = True
text_font = bpy.data.fonts.load(os.path.abspath(os.path.expanduser(font)))
def heatmap(heat):
"""Heat map: given a "heat" between 0 and 1, return a tuple of RGB
values."""
r = np.max((2*heat-1., 0))
b = np.max((1.-2*heat, 0))
return (r, 1.-r-b, b)
def zheat(z, zmin, zmax, **kwargs):
"""Colour a vertex based on its z-height compared to the minimum and
maximum z-values that occur."""
return heatmap((z-zmin)/(zmax-zmin if zmin != zmax else 1))
def plot_function(x, y, func, auto_axes = True, xmarks=None,
ymarks = None, zmarks = None, labels = None, thickness = 0.025,
text_rot = None, colourfunc=zheat, zmin = None, zmax = None):
"""Plot the function (lambda) func of x and y. The resulting surface is
smooth-shaded. Vertices may be coloured according to colourfunc: this is a
function that accepts the following parameters and returns an RGB-tuple:
x, y, z, xmin, xmax, ymin, ymax, zmin, zmax"""
global obj_ind, plot_id
ids = {
'axes': [],
'axis_labels': [],
'xmarks': [],
'ymarks': [],
'zmarks': [],
'xlabels': [],
'ylabels': [],
'zlabels': []
}
if text_rot is None:
text_rot = np.array((0, 0, 0))
if plot_id is None:
obj_id = 'plot_{}'.format(obj_ind)
obj_ind += 1
# Generate all vertices in the plot at z = 0
verts = [(i, j, 0) for i in x for j in y]
faces = []
count = 0
# Build faces from the vertices
for i in range(len(y)*(len(x)-1)):
if count < len(y)-1:
faces.append((i, i+1, i+len(y)+1, i+len(y)))
count += 1
else:
count = 0
# Create a mesh and an object at the origin
mesh = bpy.data.meshes.new(obj_id)
obj = bpy.data.objects.new(obj_id, mesh)
obj.location = (0, 0, 0)
bpy.context.scene.objects.link(obj)
mesh.from_pydata(verts, [], faces)
mesh.update(calc_edges=True)
# Create a new vertex colour map
colours = obj.data.vertex_colors.new()
# Set material
obj.data.materials.append(plot_material)
# Smooth-shade polygons
for pol in obj.data.polygons:
pol.use_smooth = True
else:
obj = bpy.data.objects[plot_id]
colours = obj.data.vertex_colors.active
verts = obj.data.vertices
# Move vertices to their correct position
for v in verts:
v.co.z = func(v.co.x, v.co.y)
obj.data.update(calc_edges=True)
sv = sorted([(v.co.x, v.co.y, v.co.z) for v in verts], key=lambda q: q[2])
# Colour vertices
for pol in obj.data.polygons:
for idx in pol.loop_indices:
co = obj.data.vertices[obj.data.loops[idx].vertex_index].co
colours.data[idx].color = colourfunc(x=co.x, y=co.y, z=co.z,
xmin=np.min(x), xmax=np.max(x),
ymin=np.min(y), ymax=np.max(y),
zmin=sv[0][2], zmax=sv[-1][2])
if auto_axes and plot_id is None:
# Axes
ids['axes'].append(add_line(np.array((min(x), min(y), 0)),
np.array((max(x), min(y), 0)), thickness, False))
ids['axes'].append(add_line(np.array((max(x), min(y), 0)),
np.array((max(x), max(y), 0)), thickness, False))
ids['axes'].append(add_line(
np.array((min(x), min(y), sv[0][2] if zmin is None else zmin)),
np.array((min(x), min(y), sv[-1][2] if zmax is None else zmax)),
thickness, False))
# Axis marks
if xmarks is not None:
for pos, label in xmarks:
p = np.array((pos, min(y), 0))
ids['xmarks'].append(add_line(p,
p-np.array((0, 1.5*thickness, 0)), thickness, False))
if label is not None and len(label) > 0:
ids['xlabels'].append(add_text(
p-np.array((0, 7*thickness, 0)), label,
thickness, text_rot))
if ymarks is not None:
for pos, label in ymarks:
p = np.array((max(x), pos, 0))
ids['ymarks'].append(add_line(p,
p+np.array((1.5*thickness, 0, 0)), thickness, False))
if label is not None and len(label) > 0:
ids[ 'ylabels'].append(add_text(
p+np.array((7*thickness, 0, 0)), label,
thickness, text_rot))
if zmarks is not None:
for pos, label in zmarks:
p = np.array((min(x), min(y), pos))
ids['zmarks'].append(add_line(p,
p-np.array((1.5*thickness/np.sqrt(2),
1.5*thickness/np.sqrt(2), 0)), thickness, False))
if label is not None and len(label) > 0:
ids['zlabels'].append(add_text(
p-np.array((7*thickness, 7*thickness, 0))/np.sqrt(2),
label, thickness, text_rot))
# Axis labels
if labels is not None:
ids['axis_labels'].append(add_text(
np.array((max(x)+8*thickness, min(y), 0)),
labels[0], 2*thickness, text_rot))
ids['axis_labels'].append(add_text(
np.array((max(x), max(y)+8*thickness, 0)),
labels[1], 2*thickness, text_rot))
ids['axis_labels'].append(add_text(
np.array((min(x), min(y),
(sv[-1][2] if zmax is None else zmax) + 8*thickness)),
labels[2], 2*thickness, text_rot))
if plot_id is None:
plot_id = obj_id
ids['plot'] = plot_id
return ids
def add_text(r, text, size=0.025, rotation=None):
"""Add text at the position r. Size is a relative parameter; use
trial-and-error here."""
global obj_ind
obj_id = 'text_{}'.format(obj_ind)
obj_ind += 1
rot = [np.pi/2, 0, 0] if rotation is None else rotation.tolist()
bpy.ops.object.text_add(location=r.tolist(), rotation=rot)
obj = bpy.context.active_object
obj.name = obj_id
obj.data.name = obj_id
obj.data.body = text
# Set the font
obj.data.font = text_font
obj.data.offset_x = -2*size
obj.data.offset_y = -2*size
obj.data.shear = 0.0
obj.data.size = 8*size
obj.data.space_character = 1
obj.data.space_word = 4*size
obj.data.extrude = size/3
obj.data.materials.append(text_material)
return obj_id
def add_line(r1, r2, w=0.01, rel_w=True):
"""Add a "line" (cylinder) between the points r1 and r2. The width is
either w (if rel_w is False) or w*|r2-r1| (if rel_w is True)."""
global obj_ind
obj_id = 'line_{}'.format(obj_ind)
obj_ind += 1
rc = (r2+r1)/2 # Centroid
rr = r2-rc # Position of r2 relative to centroid
r = np.sqrt(np.sum(rr**2))
theta = np.arccos(rr[2]/r)
phi = np.arctan2(rr[1], rr[0])
bpy.ops.mesh.primitive_cylinder_add(vertices=16,
radius=.5*w*(r if rel_w else 1), depth=2*r,
location=rc.tolist(), rotation=(0, theta, phi))
obj = bpy.context.active_object
obj.name = obj_id
for pol in obj.data.polygons:
pol.use_smooth = True
obj.data.materials.append(line_material)
return obj_id
### End generic Blender rendering code
def frame_change(scene):
"""Update the plot for a given frame."""
frame = min(max(scene.frame_current, 0), n_frames - 1)
plot_function(x, k, funcgen(t[frame]), colourfunc=colgen(t[frame]))
# Update the t-indicator
bpy.data.objects[ttext_id].data.body = 't = {: >4.3f}'.format(t[frame])
if __name__ == '__main__':
# Set up x, y and t data
n_frames = 51
nx = 101
nk = 101
xscale = 1/2
kscale = 1/3
zscale = 2
x = np.linspace(0, 10, nx)*xscale
k = np.linspace(0, 4*np.pi, nk)*kscale
t = np.linspace(0, 10, n_frames)
# Function to plot
func = lambda x, k, t: np.exp(1j*(k*x-omega*t))*zscale
# Generator for plottable function f(x, k) at time t
funcgen = lambda t: lambda x, k: np.real(func(x, k, t))
# Colour generator
colgen = lambda t: lambda x, y, **kwargs: \
heatmap((np.imag(func(x, y, t))+1)/2)
# Absolute z range for axes
azmin = -1*zscale
azmax = 1*zscale
# Axis marks
xmarks = [(i*xscale, str(i)) for i in range(1, 11)]
kmarks = [(j*np.pi/2*kscale, '{}π/2'.format(j if j != 1 else '') \
if j % 2 == 1 else '{}π'.format(j // 2 if j != 2 else '')) \
for j in range(1, 9)]
zmarks = [(z/10*zscale, str(z/10)) for z in range(-10, 12, 2)]
# Hide the 吸牛 splash screen
bpy.context.user_preferences.view.show_splash = False
# Remove existing meshes
for item in bpy.context.scene.objects:
if item.type == 'MESH':
bpy.context.scene.objects.unlink(item)
for item in bpy.data.objects:
if item.type == 'MESH':
bpy.data.objects.remove(item)
for item in bpy.data.meshes:
bpy.data.meshes.remove(item)
# Set the camera position
bpy.data.objects['Camera'].location = (11, -6, 5.5)
bpy.data.objects['Camera'].rotation_euler = (1.1, 0, 0.8)
# Let all texts face the camera
rot = np.array(bpy.data.objects['Camera'].rotation_euler)
# Initial t=0 plot; this also sets up the axes.
print(plot_function(x, k, funcgen(0),
True, labels=('x', 'k', 'z'), text_rot=rot, xmarks=xmarks,
ymarks=kmarks, zmarks=zmarks, zmin=azmin, zmax=azmax,
colourfunc=colgen(0)))
# Text label indicating current time
ttext_id = add_text(np.array((5.6, -1.2, 0)), 't = {: >4.2f}'.format(0),
size=0.05, rotation=rot)
# Set min/max/current frame
bpy.data.scenes['Scene'].frame_start = 0
bpy.data.scenes['Scene'].frame_end = n_frames - 1
bpy.data.scenes['Scene'].frame_current = 0
# Add frame change handler. This is what makes the animation happen!
bpy.app.handlers.frame_change_pre.append(frame_change)
# Add some environment lighting
wld = bpy.data.worlds['World']
wld.light_settings.use_environment_light = True
wld.light_settings.environment_energy = .5
# Add a white backdrop plane
plane_material = bpy.data.materials.new('backdrop')
plane_material.diffuse_color = (1, 1, 1)
plane_material.use_shadeless = True
bpy.ops.mesh.primitive_plane_add(location=(0, 0, -5))
bpy.context.active_object.scale = (50, 50, 0)
bpy.context.active_object.data.materials.append(plane_material)
Output video
<html5media height="270" width="480">File:Animated 3D plot.ogv</html5media>
