Precise deformation of rheologic object under MSD models with many voxels and calibrating parameters

The MSD (Mass-Spring-Damper) model efficiently calculates shape deformation of many kinds of materials such as elastic, visco-elastic, and rheologic objects. For this reason, dynamic animation can be made in a personal computer and its popular acceleration board within the video-frame rate. The problem of MSD model is how to maintain shape precision of each deformation. For this purpose, we have calibrated coefficients of damper and spring of Voigt part and a coefficient of damper of the other part in the basic MSD element under many surface points capturing a real rheologic object by the randomized algorithm. Nevertheless, the shape precision is not unfortunately enough. To overcome this, we improve our previous approach in the following five points: (1) The number of voxels in the MSD model increases from 75 to 600. (2) The ratio between lengths of Voigt and the other parts in the MSD element is added to three coefficients of spring and dampers of the basic element as calibrating parameters. (3) Four unknown parameters of the basic element are distinguished to calibrate in and on each voxel. In addition, the parameters are distinguished to calibrate among surface and core areas of a virtual rheologic object. (4) In order to speed up the calibration, we use GA (Genetic Algorithm) in replace of RA (Randomized Algorithm). (5) Each or both of local and global volume constant conditions are added into the previous approach. In conclusion, we investigate relations between shape deformation, volume resolution, and number of calibrated parameters in several MSD models representing a rheologic object. Also, we improve deformation precision by increasing not only volume resolution but also number of calibration parameters or by adding each or both of volume constant conditions.