CPU–GPU mixed implementation of virtual node method for real-time interactive cutting of deformable objects using OpenCL
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Surgical simulators need to simulate interactive cutting of deformable objects in real time. The goal of this work was to design an interactive cutting algorithm that eliminates traditional cutting state classification and can work simultaneously with real-time GPU-accelerated deformation without affecting its numerical stability.
A modified virtual node method for cutting is proposed. Deformable object is modeled as a real tetrahedral mesh embedded in a virtual tetrahedral mesh, and the former is used for graphics rendering and collision, while the latter is used for deformation. Cutting algorithm first subdivides real tetrahedrons to eliminate all face and edge intersections, then splits faces, edges and vertices along cutting tool trajectory to form cut surfaces. Next virtual tetrahedrons containing more than one connected real tetrahedral fragments are duplicated, and connectivity between virtual tetrahedrons is updated. Finally, embedding relationship between real and virtual tetrahedral meshes is updated. Co-rotational linear finite element method is used for deformation. Cutting and collision are processed by CPU, while deformation is carried out by GPU using OpenCL.
Efficiency of GPU-accelerated deformation algorithm was tested using block models with varying numbers of tetrahedrons. Effectiveness of our cutting algorithm under multiple cuts and self-intersecting cuts was tested using a block model and a cylinder model. Cutting of a more complex liver model was performed, and detailed performance characteristics of cutting, deformation and collision were measured and analyzed.
Our cutting algorithm can produce continuous cut surfaces when traditional minimal element creation algorithm fails. Our GPU-accelerated deformation algorithm remains stable with constant time step under multiple arbitrary cuts and works on both NVIDIA and AMD GPUs. GPU–CPU speed ratio can be as high as 10 for models with 80,000 tetrahedrons. Forty to sixty percent real-time performance and 100–200 Hz simulation rate are achieved for the liver model with 3,101 tetrahedrons. Major bottlenecks for simulation efficiency are cutting, collision processing and CPU–GPU data transfer. Future work needs to improve on these areas.
KeywordsSurgical simulation Deformable object Interactive cutting Virtual node method GPU acceleration OpenCL
The work described in this paper is supported by the Science and Technology Development Programme of Shandong Province (Grant No. 2014GGX101048) and the Natural Science Foundation of China (Grant No. 61303078).
Conflict of interest
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- 4.Müller M, Dorsey J, McMillan L, Jagnow R, Cutler B (2002) Stable real-time deformations. In: Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on computer animation, pp 49–54Google Scholar
- 5.Müller M, Hennix BHM, Ratcliff J (2006) Position based dynamics. In: Proceedings of virtual reality interactions and physical simulations, pp 71–80Google Scholar
- 7.Becker M, Ihmsen M, Teschner M (2009) Corotated SPH for deformable solids. In: Proceedings of the fifth eurographics conference on natural phenomena, pp 27–34Google Scholar
- 14.Wu J, Westermann R, Dick C (2014) Physically-based simulation of cuts in deformable bodies: a survey. Eurographics 2014 State-of-the-Art Report, pp 1–19Google Scholar
- 16.Bielser D, Gross MH (2000) Interactive simulation of surgical cuts. In: Proceedings of pacific graphics, pp 116–125Google Scholar
- 17.Mor AB (2001) Progressive cutting with minimal new element creation of soft tissue models for interactive surgical simulation. Doctoral dissertation. Robotics Institute, Carnegie Mellon UniversityGoogle Scholar
- 18.Steinemann D, Harders M, Gross M, Szekely G (2006) Hybrid cutting of deformable solids. In: Proceedings of IEEE conference on virtual reality, pp 35–42Google Scholar
- 22.Molino N, Bao Z, Fedkiw R (2004) A virtual node algorithm for changing mesh topology during simulation. In: ACM transactions on graphics—proceedings of the 2004 SIGGRAPH conference 2004, vol 23(3), pp 385–392Google Scholar
- 23.Sifakis E, Der KG, Fedkiw R (2007) Arbitrary cutting of deformable tetrahedralized objects. In: Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on computer animation, pp 73–80Google Scholar
- 26.Kaufmann P, Martin S, Botsch M, Grinspun E, Gross M (2009) Enrichment textures for detailed cutting of shells. In: ACM transactions on graphics—proceedings of ACM SIGGRAPH 2009, vol 28(3), pp 50:1–50:10Google Scholar
- 28.Dick C, Georgii J, Westermann R (2011) A hexahedral multigrid approach for simulating cuts in deformable objects. IEEE Trans Vis Comput Graph 17(11):1663–1675Google Scholar
- 33.Teschner M, Heidelberger B, Mueller M, Pomeranets D, Gross M (2003) Optimized spatial hashing for collision detection of deformable objects. In: Proceedings of vision, modeling, and visualization, pp 47–54Google Scholar
- 34.Heidelberger B, Teschner M, Keiser R, Mueller M, Gross M (2004) Consistent penetration depth estimation for deformable collision response. In: Proceedings of vision, modeling, and visualization, pp 339–346Google Scholar