Modelling of deformation of elastic objects using perturbation functions

The paper presents a method for modelling the deformation of elastic objects using perturbation functions. It describes deformations of elastic materials capable of stretching in such a way as to return to their original shape and size when releasing force. The method uses second-order differential equations and operator functions in exponential integration. As a result, the calculation time decreases and the overall accuracy in-creases. The method is easily parallelized and allows visualizing complex realistic models. Due to parallel processing and the absence of the need to transfer a large amount of data from the shared memory to the GPU memory, the visualization speed increases compared to the option that uses CPU only. The second paragraph considers a way of defining objects that is different from the polygonal description. A basic shape and a set of perturbations are used to define an object. This approach allows reducing memory costs and improving image quality. The third paragraph lists the tasks that solved when modelling animation and deforming bodies using the elastodynamics equations. The paper describes the adaptation of the elastodynamics equations for exponential integration. Exponential methods are well suited for rigid systems when solving complex problems. For a rigid system, the authors use a time integrator on the scale of the object general movement with sufficient accuracy. There is a description of the exponential processing when sampling a time variable over a certain interval. Exponential integration is constructed using quadrature for a nonlinear integral, which leads to a rigidly accurate method necessary to save computational resources compared to classical methods. The authors propose a rigidly accurate method using an adapted scheme with a constant time step. For large systems, they use Newton's square root iteration in order to avoid explicit precomputation of the square root. The fourth paragraph gives the results of testing the method and the comparison with classical and modern approaches for rigid systems. To determine the accuracy of specifying functionally specified objects, the depth buffer of the models (functional and polygonal) is calculated and points are compared to estimate the average difference in depth. Thus, the average deviation relative to the entire model is estimated. In conclusion, the authors briefly summarize the results and describe the approaches used in the work.