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.

Precise alignment between virtual reality (VR) and haptic interfaces is essential for delivering an immersive visuo-haptic mixed reality experience. Existing methods typically depend on markers, external trackers, or cameras, which can be intrusive and hinder usability. In addition, previous network-based approaches generally rely on image data for alignment. This paper introduces a deep neural network-based alignment method that eliminates the need for such external components. Unlike existing methods, our approach is designed based on coordinate transformation and leverages a network model for alignment. The proposed method utilizes the head-mounted display (HMD) position, fingertip position obtained via hand tracking, and the six-degrees-of-freedom (6-DOF) pose of a haptic device’s end-effector as inputs to a neural network model. A shared multi-layer perceptron and max pooling layer are employed to extract global feature vectors from the inputs, ensuring permutation invariance. The extracted feature vectors are then processed through fully connected layers to estimate the pose of the haptic device’s base. Experimental results show a mean positional error of 2.718 mm and the mean rotation error of 0.5330°, which equates to 1.3% relative to the haptic device’s maximum length. The proposed method demonstrates robustness against noise, demonstrating its applicability across various domains, including medical simulations, virtual prototyping, and interactive training environments.