# Three-Dimensional Modeling of Heart Soft Tissue Motion
## 1 Introduction  
Traditional medical surgery carries out preoperative simulation and determines the operation plan based on historical data and experience, but the process is seriously affected by subjective factors. With the appearance of virtual surgery simulation, a more objective preoperative simulation becomes possible. As the specific application of virtual reality technology in the medical field, virtual surgery simulation is gradually becoming the research object of scientific researchers in various countries [1]. In the research of biological tissue modeling, modeling can be simply divided into two categories according to whether force calculation is included, namely, physical modeling and geometric modeling [2]. Geometric modeling is mainly used to describe and express the shape of an object. In the modeling process, the influence of force is not considered, and the accuracy of the shape is emphasized. Meanwhile, physical modeling is based on physical principles, and the process of model change is determined through internal force calculations. Therefore, the structure is more complex. The earliest geometric modeling was realized as a wireframe, which only described the shape of the object through basic points, lines, and surfaces. This method could not be applied to more complex situations [3]. In 1963, [PERSON] [4] of the United States introduced a cubic Hermite interpolation curve and expressed the curve and surface with a parameter vector function. Since then, the parametric form has become the main form of curve and surface shape descriptions. The most classical method used in geometric modeling is the Bezier method [5] proposed by [PERSON], a French engineer. He defined curves and surfaces by controllingpolygons and converted complex surface control into relatively simple polygon control. This method greatly reduces the complexity of modeling and has good overall shape control ability. In the following years, the Bezier method was continuously improved by adjusting the basis function of the Bezier method. [PERSON] and [PERSON] gave the standard algorithm of a B-spline based on the Bezier method [6]. Later, [PERSON] and [PERSON] respectively studied a non-uniform B-spline [7] and a rational B-spline [8]. The B-spline method can solve the problem of insufficient local control in the Bezier method, and the surface order is independent of the number of vertices. However, the B-spline method has a big problem that it cannot describe the surface in a unified curve and surface expression form [9]. In the early 1990s, [PERSON] and [PERSON] proposed a non-uniform rational B-spline (NURBS) method based on rational B-spline [10]. This method can represent many surfaces by adjusting the weight factors and node vectors. Although it has the problem of high complexity and improper parameter selection that may lead to distortion, it has become the most widely used geometric modeling method because it has a common mathematical form for arbitrary curves and surfaces and has good local control ability. Geometric modeling methods include the chain mail model [11], but the curve and surface model based on the Bezier method has always been the mainstream of geometric modeling. The pure Bezier method is mostly used in industrial design, and its modeling accuracy is improved in terms of two aspects: one is to improve the order of the Bezier method [12] and the other is to optimize the basis function [13; 14], such as the NURBS method. In the field of soft tissue modeling, simple geometric modeling is no longer competent, and physical modeling is added on this basis. Current mainstream physical modeling methods include the finite element method and particle spring model [15], which have their advantages and disadvantages and should be selected according to the relevant characteristics of soft tissue [16]. The finite element method and particle spring model are often used for the physical modeling of biological tissue [17].