# Dynamic Geometry¶

Warning

The dynamic geometry interface is very new and subject to change. It is currently only available in an experimental branch of the MCell code.

## Dynamic Geometry Overview¶

The dynamic geometry additions to CellBlender support generation of MCell-compatible dynamic geometry MDL. These additions allow CellBlender users to do the following:

• Use Blender's shape keys to define dynamic geometry inside CellBlender
• Run a Python script defining geometry as a function of iteration/time step inside CellBlender

## Dynamic Geometry with Blender Shape Keys¶

Blender has a number of built-in features that support motion. The basic idea is that any object contains parameters (location, rotation, scale, vertex positions, colors, etc), and those parameters can be set to specified values at specified frames (times). Blender can then interpolate those parameters to "fill in" the frames between those that were specified. The frames where parameters are specified explicitly are called "key frames". When the key frames specify vertex positions, the keys are called "shape keys" because they modify the object's shape (as opposed to it's location, rotation, scale, color, etc).

We will build a simple model that uses shape keys to stretch a cube in the z direction as shown in the animation (above).

• Open the "Model Objects" panel and add a cube object. Click the "plus" button to add it to your model.

• Open the "Cube Object Options" panel (directly below the list of model objects) and click "Add a Material".

• Select both "Object Transparent" and "Material Transparent", and then set the "Alpha" value to 0.2. Zoom in so it nearly fills the window.

• Open the "Molecules" panel and add a volume molecule named "v" with a high diffusion constant (maybe 1e-3). Give it a nice bright color if you like (red in this example), and increase the "Scale" Factor (in "Display Options") to about 5.

• Open the "Molecule Placement" panel and add a new Release Site ("plus" button). Release 500 of your "v" molecules into the Object/Region named "Cube".

• Use the "File/Save As..." menu to save this Blender (.blend) file to a folder for this project.

• Open the "Run Simulation" panel and set the Iterations to 200 and leave the Time Step at 1e-6. Export and run the model.

• After the run completes, refresh the display with "Reload Visualization Data". You should see a cube full of molecules. You can play the simulation to see them moving around.

Now it's time to vary the size of the cube using Blender's shape keys.

• Open the "Molecules" panel and and click the "eye" icon to hide the molecules so they don't distract from the cube.

• In the bottom right corner of blender open the "Mesh" panel within Blender's "Property" panel, and close all subpanels except "Shape Keys".

• With the Cube selected, click the plus button in the Shape Keys panel to add a first key. It will be named "Basis".

• Click the plus button again in the Shape Keys panel to add a second key. It should be named "Key 1".

• With "Key 1" selected, enter "Edit mode" for the Cube object (Tab key when mouse cursor is in 3D view).

• Switch to Vertex Select mode (Ctrl-tab) and use the [a] key to unselect all vertices (black).

• Hold the shift key and use the right mouse button to select the TOP 4 vertices of the cube.

• Open the Transform panel with the [n] key (or click the + sign to open that panel). Change the "z" value of the median (of all selected points) to 4. The cube should immediately stretch vertically. Zoom out and adjust the view as needed to see the entire cube.

• Drag the "Value" field in the Shape Key panel for Key 1 to see the cube stretch and shrink.

• Set the current frame in the time line to 0 and set the Shape Key "Value" to 0.

• Right click on the "Value" field of the Shape Key and select "Insert Keyframe" from the pop up menu.

• The value field will become yellow indicating that it has a key frame set for that time.

• Set the current frame (in the time line) to 50 and change the Shape Key "Value" from 0 to 1.0.

• Again, right click on the "Value" field of the Shape Key and select "Insert Keyframe" from the pop up menu.

• Verify that dragging along the time line (from 0 to 50) will stretch the cube in the z direction.

• Set the current frame in the time line to 100 and set the Shape Key "Value" back to 0.

• Again, right click on the "Value" field of the Shape Key and select "Insert Keyframe" from the pop up menu.

• Verify that dragging the time from 0 to 50 stretches the cube, and dragging from 50 to 100 shrinks the cube.

• Change the property panel to a "Graph Editor" panel, and be sure that the Cube is selected.

• From the menu below the Graph Editor, select Key, then Add F-Curve Modifier, then Cycles to repeat the effect of these key frame assignments.

• Verify that dragging along the time line continuously varies the size of the cube from 0 to 200. It should repeat 2 full cycles.

• Return to the "Model Objects" panel in CellBlender and check the "Dynamic" box for the Cube object.

• Open the "Molecules" panel and and click the "eye" icon to show the molecules again.

• Open the "Run Simulation" panel in CellBlender and click the "Export & Run" button to start the simulation.

• After the run completes, refresh the display with "Reload Visualization Data". You can play the simulation to see the molecules diffusing within the dynamic geometry.

## Dynamic Geometry with Python Scripting¶

A dynamic geometry Python script is responsible for generating a Python description of an object's geometry given the current iteration (frame number) and time_step. CellBlender will call your script to generate the MDL required for an MCell simulation, and it will also either use that MDL for display or it may optionally call your script for the display. For these reasons, your script should be as efficient as you can make it to speed up both runs and display.

We will start with the same a simple model used in the shape key example above:

• Open the "Model Objects" panel and add a cube object. Click the "plus" button to add it to your model.

• Open the "Cube Object Options" panel (directly below the list of model objects) and click "Add a Material".

• Select both "Object Transparent" and "Material Transparent", and then set the "Alpha" value to 0.2. Zoom in so it nearly fills the window.

• Open the "Molecules" panel and add a volume molecule named "v" with a high diffusion constant (maybe 1e-3). Give it a nice bright color if you like (red in this example), and increase the "Scale" Factor (in "Display Options") to about 5.

• Open the "Molecule Placement" panel and add a new Release Site ("plus" button). Release 500 of your "v" molecules into the Object/Region named "Cube".

• Use the "File/Save As..." menu to save this Blender (.blend) file to a folder for this project.

• Open the "Run Simulation" panel and set the Iterations to 200 and leave the Time Step at 1e-6. Export and run the model.

• After the run completes, refresh the display with "Reload Visualization Data". You should see a cube full of molecules. You can play the simulation to see them moving around.

Now we'll define the dynamic geometry. But rather than using Blender's shape keys, we'll write a script that modifies the geometry of our object directly.

• Change the "Property" panel into a "Text Editor" panel.
• Create a new text file in the "Text Editor" panel (with the "+" button) and name it "dg.py".
• Copy the following script and paste it into the "Text Editor" panel for "dg.py".
# This script gets both its inputs and outputs from the environment:
#
#  frame_number is the frame number indexed from the start of the simulation
#  time_step is the amount of time between each frame (same as CellBlender's time_step)
#  points[] is a list of points where each point is a list of 3 doubles: x, y, z
#  faces[] is a list of faces where each face is a list of 3 integer indexes of points (0 based)
#
# This script must fill out the points and faces lists for the time given by frame_number and time_step.
# CellBlender will call this function repeatedly to create the dynamic MDL and possibly during display.

import math

points.clear()
faces.clear()

min_length = 0.5
max_length = 1.0
period_frames = 100

sx = min_length + ( (max_length-min_length) * ( (1 - math.cos ( 2 * math.pi * frame_number / period_frames )) / 2 ) )
sy = min_length + ( (max_length-min_length) * ( (1 - math.cos ( 2 * math.pi * frame_number / period_frames )) / 2 ) )
sz = min_length + ( (max_length-min_length) * ( (1 - math.sin ( 2 * math.pi * frame_number / period_frames )) / 2 ) )
sz = 2 * sz

# These define the coordinates of the rectangular box
points.append ( [  sx,  sy, -sz ] )
points.append ( [  sx, -sy, -sz ] )
points.append ( [ -sx, -sy, -sz ] )
points.append ( [ -sx,  sy, -sz ] )
points.append ( [  sx,  sy,  sz ] )
points.append ( [  sx, -sy,  sz ] )
points.append ( [ -sx, -sy,  sz ] )
points.append ( [ -sx,  sy,  sz ] )

# These define the faces of the rectangular box
faces.append ( [ 1, 2, 3 ] )
faces.append ( [ 7, 6, 5 ] )
faces.append ( [ 4, 5, 1 ] )
faces.append ( [ 5, 6, 2 ] )
faces.append ( [ 2, 6, 7 ] )
faces.append ( [ 0, 3, 7 ] )
faces.append ( [ 0, 1, 3 ] )
faces.append ( [ 4, 7, 5 ] )
faces.append ( [ 0, 4, 1 ] )
faces.append ( [ 1, 5, 2 ] )
faces.append ( [ 3, 2, 7 ] )
faces.append ( [ 4, 0, 7 ] )

# Taper the box to get a different shape
for i in range(len(points)):
if points[i][2] > 0:
# z coordinate is greater than 0 so shrink x and y coordinates
points[i][0] = points[i][0] * 0.2
points[i][1] = points[i][1] * 0.2
else:
# z coordinate is less than or equal to 0 so expand x and y coordinates
points[i][0] = points[i][0] * 2
points[i][1] = points[i][1] * 2


The preliminary version of CellBlender gets frame_number, time_step, points[], and faces[] from the local environment. Note that this may change in the near future.

• Return to the "Model Objects" panel in CellBlender and check the "Dynamic" box for the Cube object.

• Check the box "Show Dynamic MDL" and select the Script name given above ("dg.py").

• Open the "Run Simulation" panel in CellBlender and click the "Export & Run" button to start the simulation.

• After the run completes, refresh the display with "Reload Visualization Data". You can play the simulation to see the molecules diffusing within the dynamic geometry.

• As before, the geometry should go through 2 complete cycles over the 200 frames of the simulation. You can choose to display the object as a wire frame to get a better view of the changing geometry.

## Plotting Dynamic Geometry Volume via Clamp Concentration¶

This example uses MCell's Clamp Concentration to plot a proportional estimate of a dynamic object's volume. Follow the steps below to construct the model (this tutorial assumes some familiarity with building CellBlender models).

• Open the "Model Objects" panel and add a cube object. Click the "plus" button to add it to your model.

• Open the "Cube Object Options" panel (directly below the list of model objects) and set it's display type to "Bounds" (it is probably defaulted to "Solid"). Zoom in so it nearly fills the window.

• Open the "Molecules" panel and add a volume molecule named "v" with a high diffusion constant (maybe 1e-3). Give it a nice bright color if you like (light blue in this example), and increase the "Scale" Factor (in "Display Options") to about 5.

• Open the "Molecule Placement" panel and add a new Release Site ("plus" button). Release 5000 of your "v" molecules into the Object/Region named "Cube".

• Open the "Plot Output Settings" panel and add a new Count with the "plus" button. Select the "v" molecule and count the number in the World (default). Check the "Molecule Colors" box if you like.

• Use the "File/Save As..." menu to save this Blender (.blend) file to a folder for this project.

• Open the "Run Simulation" panel and set the Iterations to 500 and leave the Time Step at 1e-6. Export and run the model.

• After the run completes, refresh the display with "Reload Visualization Data". You should see a cube full of molecules. You can play the simulation to see them moving around.

• Open the "Plot Output Settings" panel again and plot the results with your favorite plotter.

• It should be relatively uninteresting (a straight line showing 5000 molecules).

• Open the "Surface Classes" panel to add a concentration clamp. Click the "plus" button to add a new surface class. That will open up the "Surface Class Properties" list below the class name. Click "plus" there as well to add a new Surface Class property.

• Select "Single Molecule", and choose your "v" molecule. Set the Orientation to "Bottom/Back", and change the "Type" from the default of "Transparent" to "Clamp Concentration". Set the value of the clamp to 1e-6.

• Open the "Assign Surface Classes" panel, and click the "plus" button to begin assigning your new surface class to the Cube. Set the "Surface Class Name" to be the surface class created above (most likely "Surface Class"). Set the object to get the class to "Cube", and leave the Region Selection set to "All Surfaces".

• Open the "Run Simulation" panel and again export and run the model.

• Reload the Visualization. It should look pretty much the same as before.

• Open the "Plot Output Settings" panel and plot the count again.

• It should be roughly around 5000 but varying as MCell works to keep the concentration at the requested value.

Now it's time to vary the size of the cube and watch MCell add and remove molecules to maintain the requested concentration. We will do this with a Python script that will change our Cube object for each frame of the simulation.

• Open a Blender "Text Editor" panel to copy and paste the script below as shown here (directions below animation):
• Use the "+ New" button near the bottom to create a new text file inside Blender. Change the name from "Text" to a file ending in ".py" (something like "dyn_geo.py" is fine).
• Type (or copy) the following script into the text panel:
#  time_step is the amount of time between each frame (same as CellBlender's time_step)
#  points[] is a list of points where each point is a list of 3 doubles: x, y, z
#  faces[] is a list of faces where each face is a list of 3 integer indexes of points (0 based)
#  origin[] contains the x, y, and z values for the center of the object (points are relative to this).
#
# This script must fill out the points and faces lists for the time given by frame_number and time_step.
# CellBlender will call this function repeatedly to create the dynamic MDL and possibly during display.

import math

points.clear()
faces.clear()

min_ztop = 1.0
max_ztop = 4.0
period_frames = 100

sx = sy = sz = 1.0
h = ( 1 + math.sin ( math.pi * ((2*frame_number/period_frames) - 0.5) ) ) / 2

zt = min_ztop + ( (max_ztop-min_ztop) * h )

# These define the coordinates of the rectangular box
points.append ( [  sx,  sy, -sz ] )
points.append ( [  sx, -sy, -sz ] )
points.append ( [ -sx, -sy, -sz ] )
points.append ( [ -sx,  sy, -sz ] )
points.append ( [  sx,  sy,  zt ] )
points.append ( [  sx, -sy,  zt ] )
points.append ( [ -sx, -sy,  zt ] )
points.append ( [ -sx,  sy,  zt ] )

# These define the faces of the rectangular box
faces.append ( [ 1, 2, 3 ] )
faces.append ( [ 7, 6, 5 ] )
faces.append ( [ 4, 5, 1 ] )
faces.append ( [ 5, 6, 2 ] )
faces.append ( [ 2, 6, 7 ] )
faces.append ( [ 0, 3, 7 ] )
faces.append ( [ 0, 1, 3 ] )
faces.append ( [ 4, 7, 5 ] )
faces.append ( [ 0, 4, 1 ] )
faces.append ( [ 1, 5, 2 ] )
faces.append ( [ 3, 2, 7 ] )
faces.append ( [ 4, 0, 7 ] )


This is the function that will generate your dynamic geometry as a function of frame number. It creates a cube (very much like the one you've already created) but it varies the location of the top by changing the local variable named "zt" as a function of the frame number (via the variable "h"). This code will be explained in greater detail below. Note that clicking the "Syntax highlight for scripting" button will add syntax highlighting to your Python code (as shown in the animation).

• Open the "Model Objects " panel. The "Cube" should be selected. Open the "Cube Object Options" panel (if it isn't open already) and check the "Dynamic" box. This is the check box that lets CellBlender know that it must generate dynamic geometry for this object. When you click "Dynamic", the "Script" option will appear directly to its right. If the script is left empty, then CellBlender assumes that your Dynamic Geometry will be generated using Blender's built-in keying system. But we want to use our script, so click the refresh button beside the "Script" box to reload the available scripts. Then click in the "Script" box and select "dyn_geo.py" (or whatever you named your script). This tells CellBlender to use that script to generate geometry for this object. There may also be another check box near the top of the "Model Objects" panel named "Show Dynamic MDL". That button can enable or disable the reading and displaying of dynamic data. It's there because very large models can be slow to load. This Cube model is small, so check that box to see the dynamic geometry in Blender's 3D view window.

• Open the "Run Simulation" panel and again export and run the model.

• When the simulation completes, scroll through the time line to see the dynamic geometry change (it may help to change the zoom and perspective to see the entire cube as it stretches). You'll notice that the density of the molecules remains about the same due to the Concentration Clamp applied to this object. It should resemble this animation:

• Open the "Plot Output Settings" panel again and plot the results one more time. You should see a sinusoidal plot indicating that the number of molecules is varying ... up and down. Remember that the concentration remains constant, but the volume is changing. So the total number of molecules will be proportional to the volume. That's exactly what this plot shows.

### Understanding the Script¶

This preliminary version of dynamic geometry scripting uses the following variables from the local environment:

• time_step is the amount of time between each frame (same as CellBlender's time_step)
• frame_number is an integer number representing the number of time steps that have passed to this point
• points[] is a list of points where each point is a list of 3 doubles: x, y, z (relative to the origin below)
• faces[] is a list of faces where each face is a list of 3 integer indexes of points (0 based)
• origin[] contains the x, y, and z values for the center of the object (points are relative to this).

These five variables are set to defaults before your script is called. Their values will be used to create the actual CellBlender object after your script has completed. Since points and faces are both lists, they are cleared before using them:

points.clear()
faces.clear()


Since we are trying to build a cube with a top that grows up and down, the only thing we'll vary is the z coordinate of the top of the box. So we set variables for the minimum and maximum values for the top of the box:

min_ztop = 1.0
max_ztop = 4.0


We also want to control how many frames are in a complete periodic cycle. The cube will grow from small to large and then back to small in one period:

period_frames = 100


With this setting, the box size will complete a full period in 100 frames.

We set all of the initial dimensions to 1.0:

sx = sy = sz = 1.0


Then we calculate a normalized height value based on the frame number and the number of frames in one complete period:

h = ( 1 + math.sin ( math.pi * ((2*frame_number/period_frames) - 0.5) ) ) / 2


The normalized height is then scaled and added to the minimum z-top to get the current z-top (zt):

zt = min_ztop + ( (max_ztop-min_ztop) * h )


Then we can define the 8 vertices of the cube as a function of these computed values. Note that zt is used for the 4 top corners. These vertices are appended as lists to the points list that we inherited from the local environment:

# These define the coordinates of the rectangular box
points.append ( [  sx,  sy, -sz ] )
points.append ( [  sx, -sy, -sz ] )
points.append ( [ -sx, -sy, -sz ] )
points.append ( [ -sx,  sy, -sz ] )
points.append ( [  sx,  sy,  zt ] )
points.append ( [  sx, -sy,  zt ] )
points.append ( [ -sx, -sy,  zt ] )
points.append ( [ -sx,  sy,  zt ] )


Finally, the faces of each triangle are created by appending a list of vertex indices to the faces list. Note that each face is a triangle with outward facing normals (using the "right hand rule").

# These define the faces of the rectangular box
faces.append ( [ 1, 2, 3 ] )
faces.append ( [ 7, 6, 5 ] )
faces.append ( [ 4, 5, 1 ] )
faces.append ( [ 5, 6, 2 ] )
faces.append ( [ 2, 6, 7 ] )
faces.append ( [ 0, 3, 7 ] )
faces.append ( [ 0, 1, 3 ] )
faces.append ( [ 4, 7, 5 ] )
faces.append ( [ 0, 4, 1 ] )
faces.append ( [ 1, 5, 2 ] )
faces.append ( [ 3, 2, 7 ] )
faces.append ( [ 4, 0, 7 ] )


When CellBlender is generating the dynamic geometry for each object, it will call the function associated with that object with differing values of frame_number. The function is responsible for setting the points, faces, and origin as appropriate for that frame number given the time step (also passed in).

### Conclusion¶

This example is very simple, but the power of the Python language can be used to construct almost any kind of geometry. In addition to computing geometry (as we've done here), the Python code could also read geometrical objects from files or any other data source.

Note that this preliminary version gets frame_number, time_step, points[], faces[], and origin from the local environment. This is likely to change in the near future.