Anisotropic Tetrahedral Mesh Adaptation with Improved Metric Alignment and Orthogonality

Abstract We propose concepts to utilize basic mathematical principles for computing the exact mass properties of objects with varying densities. For objects given as 3D triangle meshes, the method is analytically accurate and at the same time faster than any established approximation method. Our concept is based on tetrahedra as underlying primitives, which allows for the object’s actual mesh surface to be incorporated in the computation. The density within a tetrahedron is allowed to vary linearly, i.e., arbitrary density fields can be approximated by specifying the density at all vertices of a tetrahedral mesh. Involved integrals are formulated in closed form and can be evaluated by simple, easily parallelized, vector-matrix multiplications. The ability to compute exact masses and centroids for objects of varying density enables novel or more exact solutions to several interesting problems: besides the accurate analysis of objects under given density fields, this includes the synthesis of parameterized density functions for the make-it-stand challenge or manufacturing of objects with controlled rotational inertia. In addition, based on the tetrahedralization of Voronoi cells we introduce a precise method to solve $$L_{2|\infty }$$ L 2 | ∞ Lloyd relaxations by exact integration of the Chebyshev norm. In the context of additive manufacturing research, objects of varying density are a prominent topic. However, current state-of-the-art algorithms are still based on voxelizations, which produce rather crude approximations of masses and mass centers of 3D objects. Many existing frameworks will benefit by replacing approximations with fast and exact calculations. Graphic abstract

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A study of real-time simulation of liver of virtual surgical robot based on biologically position-based dynamic model

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-219024 ◽

2021 ◽

pp. 1-16

Author(s):

Dan Luo ◽

Yu Zhang ◽

Jia Li ◽

Jisheng Li

Keyword(s):

Soft Tissue ◽

Real Time ◽

Surgical Instruments ◽

Organic Polymer ◽

Tetrahedral Mesh ◽

Virtual Surgery ◽

Constraint Force ◽

Real Time Simulation ◽

Time Simulation ◽

Spring Force

Virtual surgery robot can accurately modeling of surgical instruments and human organs, and realistic simulation of various surgical phenomena such as deformation of organic tissues, surgery simulation system can provide operators with reusable virtual training and simulation environment. To meet the requirement of virtual surgery robot for the authenticity and real-time of soft tissue deformation and surgical simulation in liver surgery, a new method is proposed to simulate the deformation of soft tissue. This method combines the spring force, the external force of the system, and the constraint force produced by the constraint function of the position-based dynamics. Based on the position-based dynamics, an improved three-parameter mass-spring model is added. In the calculation of the elastic force, the nonlinearity and viscoelasticity of the soft tissue are introduced, and the joint force of the constraint projection process and the constraint force of the position-based dynamics is used to modify mass points movement. The method of position-based dynamics based on biological characteristics, not only considers the biomechanical properties of biological soft tissue as an organic polymer such as viscoelasticity, nonlinearity, and incompressibility but also retains the rapidity and stability of the position based dynamic method. Through the simulation data, the optimal side length of tetrahedral mesh in the improved three-parameter model is obtained, and the physical properties of the model are proved. The real-time simulation of the liver and other organs is completed by using the Geomagic touch force feedback device, which proves the practicability and effectiveness of this method.

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