Regularization of inverse visual problems involving discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
Finite element handbook
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Representing PDE surfaces in terms of B-splines
Computer-Aided Design
Deformable curve and surface finite-elements for free-form shape design
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Functional optimization for fair surface design
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Dynamic NURBS with geometric constraints for interactive sculpting
ACM Transactions on Graphics (TOG) - Special issue on interactive sculpting
Dynamic manipulation of triangular B-splines
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Efficient simplification of point-sampled surfaces
Proceedings of the conference on Visualization '02
Graphics Applied to Medical Image Registration
IEEE Computer Graphics and Applications
Modeling with Triangular B-Splines
IEEE Computer Graphics and Applications
Registration of 3D Intraoperative MR Images of the Brain Using a Finite Element Biomechanical Model
MICCAI '00 Proceedings of the Third International Conference on Medical Image Computing and Computer-Assisted Intervention
Haptic Sculpting of Volumetric Implicit Functions
PG '01 Proceedings of the 9th Pacific Conference on Computer Graphics and Applications
Haptics-Based Dynamic Implicit Solid Modeling
IEEE Transactions on Visualization and Computer Graphics
Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics)
Multiresolution heterogeneous solid modeling and visualization using trivariate simplex splines
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Harmonic volumetric mapping for solid modeling applications
Proceedings of the 2007 ACM symposium on Solid and physical modeling
3D reconstruction from 2D images with hierarchical continuous simplices
The Visual Computer: International Journal of Computer Graphics
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In this paper, we present a novel computational modeling and simulation framework based on dynamic spherical volumetric simplex splines. The framework can handle the modeling and simulation of genus-zero objects with real physical properties. In this framework, we first develop an accurate and efficient algorithm to reconstruct the high-fidelity digital model of a real-world object with spherical volumetric simplex splines which can represent with accuracy geometric, material, and other properties of the object simultaneously. With the tight coupling of Lagrangian mechanics, the dynamic volumetric simplex splines representing the object can accurately simulate its physical behavior because it can unify the geometric and material properties in the simulation. The visualization can be directly computed from the object's geometric or physical representation based on the dynamic spherical volumetric simplex splines during simulation without interpolation or resampling. We have applied the framework for biomechanic simulation of brain deformations, such as the brain shifting during surgery and brain injury under blunt impact. We have compared our simulation results with the ground truth obtained through intra-operative magnetic resonance imaging and real biomechanic experiments. The evaluations demonstrate the excellent performance of our new technique.