Automatic Interpolation for the Animation of Unmeasured Nodes with Differential Geometric Methods

Abstract

In the field of structural dynamics, more and more demands are made on a realistic representation of mode and operating deflection shapes. This work deals specifically with the problem of interpolating sensor data for unmeasured points. This is applied to 3D geometries with large vertex sets and few measurement points. The interpolation of very complex 3D geometry objects (e.g. 3d Scans or CAD programs) is very important for the realistic visualization of vibrations in structural dynamics. The presented interpolation method respects the connectivity of the mesh and additionally adds boundary conditions and curvature of the geometry. Thereby we expect more realistic shapes for unmeasured points. The developed method is based on the mathematical framework of discrete differential geometry and provides a simple interface that requires only the 3D geometry and sensor data, resulting in a sparse linear system. The solution of this linear system then can be efficiently split into two parts; factorization and back substitution. Thus, users can interact in realtime with the animated sensor data visualization. This gives the user the ability to explore measured data in a more realistic way. For validation, we tested the interpolation method with measured data of representative 3D geometries.