Simulation involving interaction with deformable objects often causes stability problems because a slowly-updated force generates additional energy to the human user. This paper proposes a stable and transparent haptic rendering for simulation involving interaction between a rigid tool and deformable objects. This method computes visual and haptic feedback in the simulation and haptic feedback loop, respectively. A local stiffness matrix consisting of points around contact points is constructed based on collision detection between a virtual tool and a deformable object in the simulation loop. The haptic feedback is then computed at a higher update rate in the haptic feedback loop using the local stiffness matrix. Equivalent springs computed by using the equivalent stiffness energy are added to the boundary of the local stiffness matrix to minimize errors in the rendered force. The proposed method is compared with the virtual coupling widely used in simulation involving interaction with deformable objects. The proposed method reduces the x, y, and z-axis maximum force errors by up to 52 %, 80 %, and 70 % compared to the virtual coupling in the simulation involving interaction with the Stanford bunny object consisting of 2087 points and 9997 tetrahedrons.

Previous researches on analysis of stability of haptic simulation largely assume that the virtual environment is passive. But the virtual environment can become non-passive due to various reasons including discretization errors and interaction dynamics between virtual tools and objects. This paper provides an analysis of the stability and performance of the haptic simulation involving non-passive virtual environment. The dynamic interaction between the virtual tools and the objects is modeled using the two-port networks. The analysis is carried out using a velocity and force mapping matrix for six-DOF simulation. New stability condition resulting from the analysis is applied to an example simulation of a one-DOF virtual wall. Maximum stiffness satisfying the stability condition established in the previous literature, and the proposed condition is compared with the maximum stiffness experimentally determined with various time steps. The newly proposed stability condition manifests less standard deviation of errors than the widely applied absolute stability condition.

This paper proposes a one-dimensional fluid simulation method for real-time simulation of the contrast medium in a narrow blood vessel. A narrow vessel is modeled with the branches organized in a hierarchy. The density of the contrast medium on each branch is computed using the one-dimensional fluid model. The density at the last point of branch is conveyed to the first point of the following branches. The position of the density computation is determined to continuously convey the simulation results from a large vessel to a narrow vessel. The average computation time with the proposed method is 16.18 ms that is less than 21.25 ms of the particle-based method.

Digital Twin (DT) technology replicates the real world within a virtual environment, enabling real-time mapping of dynamic states from the real world to its virtual replica. This paper comprehensively reviews recent research methods in modeling, rendering, and simulation of deformable objects within DT technology. While existing DT technologies primarily focus on static or rigid objects, deformable objects exhibit continuous and nonlinear deformations due to external forces and interactions, presenting challenges such as real-time tracking, representation of complex material behavior, and simulation stability. To address these challenges, this review systematically analyzes modeling techniques categorized by input data type (multi-view images, point clouds, voxels, and single-view images), rendering methods emphasizing Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS), and various simulation approaches including Finite Element Method (FEM), Graph neural network (GNN), and differentiable physics-based simulations from recent studies within the last five years. Additionally, the paper investigates integrated cases of these modeling, rendering, and simulation techniques, evaluating their compatibility and discussing their technical limitations. The analysis concludes that 3DGS has recently gained prominence over NeRF due to its faster processing speed and superior rendering quality. Moreover, advancements in machine learning and differentiable physics-based simulations are anticipated to be pivotal in expanding the applicability of DT technologies for deformable objects.