Zigzag Studio - Blog1: Motion Simulation with Blender and MATLAB

Background

The motion simulation of the deployable strucuture can be done with the help of target-shoot method and the accuracy can be up to 1e-12. Thus, we get the global coordinates of the deployable structure at any time. It is enough to simulate the location of the structure bodies but not to add more rendering unluckily after all MATLAB is not for this.

So here is the problem: How to LINK the MATLAB(where we do computing) and Blender(where we do rendering)?

Something about Blender

Blender is famous of its features of open-source and how friendly it is for Python users. That is right! Any move in the Blender can be replicated with the help of Python scripts. The normal method is to refer to the Blender Document. One trick is taking the information hint on the Info window of the Scripting Tab. So keep in mind.

Blender has its body locating and rotating system with intuitive parameters while the rotation center of the body is at its origin point implicitly. The 'Location X, Y, Z' standing for the coordinate of its origin point and 'Rotation X, Y, Z' standing for the rotating angle(degree but not radian) around X, Y, Z axis respectively.

Calculate Rotation with Coordinate

Shifting and rotating are all naturally involved in the movement of an object while they should be regarded as two steps at the convenience of calculation in Blender. In this circumstance, a "shifting-rotating" pattern is adopted.

The shifting vector can be calculated easily with the distance difference of a point fixed on the body at two configurations. In other words, after conducting the shifting vector on all points of the body, it moves to a new location and the fixed referred point at the last config is right on the later one.

This point is also called the "rotation center" due to the rotation is actually at the basis of this point and its axis. Some head-up for rotation things. One point(x1,y1,z1) rotates along the X, Y, and Z-axis with alpha, beta, gamma perspectively and it turns to the point(x2,y2,z2). This rotation relationship can be described with the rotation matrix. Reversely, the rotation matrix and the rotating angle can be computed from the before and after coordinate of the point with the help of MATLAB's function pinv and rotm2eul.

One thing missing above is the order(mode) of rotation. The result at "X-Y-Z" order and at "Z-Y-X" is different. The algorithm above is at the "Z-Y-X" order but in Blender, it follows "X-Y-Z" at the default setting.

Code with Blender

Now that the shift vector and the rotation angle are computed, the next step is to make the animation in the Blender and Blender allows to manipulate the location of bodies at each frame to do so. So here I will take the Ron Resch unit to show the detail.

Build the Basic Body: Ron Resch unit is made of 12 triangle planes connected closely and it can fold or open up when tracted. I will simulate the opening-up process. Firstly, with the help of MATLAB and the basic geometry, I can get the coordinates of each points and bodies. And I draw the body in the Blender.
Reset the Rotation Center: MATLAB code would output the rotation center as well so what I have to do is to move the origin to the rotation center. It cannot be done directly but I could take advantage of the 3D Cursor in the Blender to move the cursor to the desired location and set the body's origin to the cursor.
Manipulate the Object: The basic idea here is to record the value of object's location and rotation at every frame windows. This means that there are two steps: to pick every single frames orderly and to input the location and rotation value. And with the loop based on the frame, the motion can be done automatically.

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