A three-dimensional finite-strain rod model. Part II: Computational aspects
Computer Methods in Applied Mechanics and Engineering
What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Large steps in cloth simulation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Super-helices for predicting the dynamics of natural hair
ACM SIGGRAPH 2006 Papers
Oriented strands: dynamics of stiff multi-body system
Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation
A Survey on Hair Modeling: Styling, Simulation, and Rendering
IEEE Transactions on Visualization and Computer Graphics
CoRdE: Cosserat rod elements for the dynamic simulation of one-dimensional elastic objects
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
ACM SIGGRAPH 2008 papers
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Interactive simulation of surgical needle insertion and steering
ACM SIGGRAPH 2009 papers
ACM SIGGRAPH 2010 papers
NumGfun: a package for numerical and analytic computation with D-finite functions
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
A hybrid iterative solver for robustly capturing coulomb friction in hair dynamics
Proceedings of the 2011 SIGGRAPH Asia Conference
3D Euler spirals for 3D curve completion
Computational Geometry: Theory and Applications
Computer Graphics Forum
Hi-index | 0.00 |
Thin elastic filaments in real world such as vine tendrils, hair ringlets or curled ribbons often depict a very smooth, curved shape that low-order rod models --- e.g., segment-based rods --- fail to reproduce accurately and compactly. In this paper, we push forward the investigation of high-order models for thin, inextensible elastic rods by building the dynamics of a G2-continuous piecewise 3D clothoid: a smooth space curve with piecewise affine curvature. With the aim of precisely integrating the rod kinematic problem, for which no closed-form solution exists, we introduce a dedicated integration scheme based on power series expansions. It turns out that our algorithm reaches machine precision orders of magnitude faster compared to classical numerical integrators. This property, nicely preserved under simple algebraic and differential operations, allows us to compute all spatial terms of the rod kinematics and dynamics in both an efficient and accurate way. Combined with a semi-implicit time-stepping scheme, our method leads to the efficient and robust simulation of arbitrary curly filaments that exhibit rich, visually pleasing configurations and motion. Our approach was successfully applied to generate various scenarios such as the unwinding of a curled ribbon as well as the aesthetic animation of spiral-like hair or the fascinating growth of twining plants.