Interactive deformable models with quadratic bases in Bernstein–Bézier-form

Weber, Daniel; Kalbe, Thomas; Sourander, André; Fellner, Dieter W.; Goesele, Michael

doi:10.1007/s00371-011-0579-6

Cited by 15 publications

(14 citation statements)

References 6 publications

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“…A general advantage of modeling the field of displacements with this type of shape functions is that the computation of integrals reduces to a sum of coefficients with binomial weights that are computed from the indices i; j; k and l [18]. For finite element simulations, typically integrals of products of basis functions need to be computed.…”

Section: Higher-order Finite Element Discretization Of Elasticitymentioning

confidence: 99%

“…For a degree-p discretization the initial element stiffness matrices 0 K p T must be computed for each element T. A total of p þ 3 3 À Á 3 Â 3 block matrices are computed, one for each of the elements p þ 3 3 À Á node pairs. As described in our previous work [18] one block of the stiffness matrix for a pair of nodes I; J is computed by…”

Section: Corotational Elasticity With Higher Order Femmentioning

confidence: 99%

“…In the computer graphics community quadratic finite elements were used for deformation simulation [3] and interactive shape editing [17]. In a previous work [18] we used quadratic finite elements in B-form for the simulation of volumetric deformation. Later we developed a GPU implementation for linear and quadratic finite elements [19].…”

Section: Related Workmentioning

confidence: 99%

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Deformation simulation using cubic finite elements and efficient p-multigrid methods

Weber

Mueller-Roemer

Altenhofen

et al. 2015

Computers & Graphics

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Section: Higher-order Finite Element Discretization Of Elasticitymentioning

confidence: 99%

Section: Corotational Elasticity With Higher Order Femmentioning

confidence: 99%

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Deformation simulation using cubic finite elements and efficient p-multigrid methods

Weber

Mueller-Roemer

Altenhofen

et al. 2015

Computers & Graphics

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“…Scalar fields are no longer just defined through values at nodes: more degrees of freedom per elements are now available, depending on the choice of basis functions and their polynomial orders. The accuracy gains brought by higher order basis in tetrahedral finite-element simulation were demonstrated in graphics by, e.g., [Roth et al 1998] and [Weber et al 2011]. However, the accuracy of finite element solutions is often strongly influenced by how well the geometry of the domain is approximated, which limits the applicability of straight-edge meshes in practice.…”

Section: Previous Workmentioning

confidence: 99%

“…While meshes made out of Bézier simplices (sometimes referred to as Bernstein-Bézier meshes) have often been used in the graphics literature (see, e.g., [Bargteil and Cohen 2014;DeRose 1988;Roth et al 1998;Weber et al 2011]), we briefly review their construction here for completeness.…”

Section: Primer On Bézier Meshesmentioning

confidence: 99%

Curved optimal delaunay triangulation

et al. 2018

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Meshes with curvilinear elements hold the appealing promise of enhanced geometric flexibility and higher-order numerical accuracy compared to their commonly-used straight-edge counterparts. However, the generation of curved meshes remains a computationally expensive endeavor with current meshing approaches: high-order parametric elements are notoriously difficult to conform to a given boundary geometry, and enforcing a smooth and non-degenerate Jacobian everywhere brings additional numerical difficulties to the meshing of complex domains. In this paper, we propose an extension of Optimal Delaunay Triangulations (ODT) to curved and graded isotropic meshes. By exploiting a continuum mechanics interpretation of ODT instead of the usual approximation theoretical foundations, we formulate a very robust geometry and topology optimization of Bézier meshes based on a new simple functional promoting isotropic and uniform Jacobians throughout the domain. We demonstrate that our resulting curved meshes can adapt to complex domains with high precision even for a small count of elements thanks to the added flexibility afforded by more control points and higher order basis functions.

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A novel virtual cutting method for deformable objects using high‐order elements combined with mesh optimisation

Wang

Liu

2022

Robotics Computer Surgery

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Background: Virtual cutting of deformable objects plays an important role in many applications, especially in digital medicine, such as soft tissue cutting in virtual surgery training system. Methods:We developed a novel virtual cutting algorithm, combined with mesh optimisation. A new local mesh processing method is used to control the number and quality of the elements created during the cutting process. At the same time, high-order tetrahedral elements are used to fit the cutting surface and reduce the mesh size. Results:In this paper, single cut, multiple cut and intersecting cut are performed on the mesh model, combined with a force feedback device, and the result obtained is that the visual feedback is higher than 30 Hz, and the tactile feedback is 800~1000 Hz. Conclusions:Experimental results show that the method proposed in this paper can effectively eliminate low-quality elements and control the mesh size, thereby ensuring real-time simulation. K E Y W O R D Sdeformable objects, high-order element, mesh optimisation, virtual cutting | INTRODUCTIONThe cutting simulation of physics-based deformable objects has always been an important research topic, and it has important applications in the fields of sculpture, computer animation, cloth simulation, crack growth simulation, virtual surgery and so on.Maintaining physical rationality during the cutting process and achieving stable and efficient simulation is still a challenging topic.Especially in virtual surgery, the soft tissue model needs to interact with surgical tools to achieve deformation and cutting and meet the requirements for real-time and authenticity of the simulation of real surgery. Therefore, it is essential to develop an efficient virtual cutting method.The current virtual cutting methods for deformable objects are mainly divided into mesh-based methods and meshless methods. This article focuses on mesh-based methods. The mesh-based virtual cutting method is mainly implemented through algorithms such as element deletion, 1 node snapping, 2 mesh subdivision 3-9 and virtual node algorithm. [10][11][12][13] The element deletion algorithm and the virtual node algorithm can achieve stable cutting realisation and they are easy to implement. However, element deletion and duplication will cause changes in the mass or stiffness of the model, which cannot satisfy the law of conservation of mass, and there will be a jagged surface during display. The mesh subdivision method can maintain the physical correctness of the model by dividing the mesh at the cutting track and can simulate the cutting surface correctly due to the adaptability of the tetrahedron. However, meshing will introduce a large number of additional elements, resulting in a substantial increase in computational costs. In addition, the division of tetrahedral meshes will inevitably introduce low-quality elements. The existence of low-quality elements greatly limits the ability of finite element calculations, thereby reducing the stability of cutting simulation.

show abstract

Interactive deformable models with quadratic bases in Bernstein–Bézier-form

Cited by 15 publications

References 6 publications

Deformation simulation using cubic finite elements and efficient p-multigrid methods

Deformation simulation using cubic finite elements and efficient p-multigrid methods

Curved optimal delaunay triangulation

A novel virtual cutting method for deformable objects using high‐order elements combined with mesh optimisation

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