A novel deformable B-spline curve model based on elasticity

The physically based deformable curve models are widely used to simulate thin one-dimensional objects in computer graphics, interactive simulation, and surgery simulation. These models consider objects to be rods described by an adapted frame curve that contains the rod’s centerline as well as the orthonormal material frame of each point on the centerline. However, they pose challenges including fine discretization, redundancy in modeling slender rods, and maintaining accuracy and stability. In this paper, we propose a novel physically based deformable B-spline curve model that regards curves as rods consisting of parallel fibers and derive elastic potential energy only from curves’ representations. Therefore, our model does not take rotation-based adapted frames into consideration and reduces degree of freedom. Our model divides the curves into infinitesimal elements in parameter space and derives the analytical relationship between elastic potential energy function and curves’ representations through the change of total length of infinitesimal elements’ fibers. Our model can support material attributes in the real world and maintain the reality and stability of the solution. We employ isogeometric analysis to solve the dynamic equations derived from our deformable model as isogeometric analysis is suitable to solve the dynamic equations of parametric models. We compare the scenarios in the real world, our model’s simulation results, and other model’s results to demonstrate the reality of our models. The results are in line with expectation. We design several examples to demonstrate our models’ applications.