Modeling surfaces of arbitrary topology with dynamic particles

Splines and deformable surface models are widely used in computer graphics to describe free-form surfaces. These methods require manual preprocessing to discretize the surface into patches and to specify their connectivity. We present a new model of elastic surfaces based on interacting particle systems, which, unlike previous techniques, can be used to sptiL join, or extend surfaces without the need for manual intervention. The particles we use have longrange attraction forces and short-range repulsion forces and follow Newtonian dynamics, much tiie recent computational models of fluids and solids. To enable our particles to model surface elements instead of point masses or volume elements, we add an orientation to each particle’s state. We devise new interaction potentials for our oriented particles which favor locally planar or spherical arrangements. We atso develop techniques for adding new particles automatically, which enables our surfaces to stretch and grow. We demonstrate the application of our new particle system to modefing surfaces in 3-D and the interpolation of 3-D point sets.

Chapter 7 - Tribological experiments with friction force microscopy

Statistical mechanics of a lipid monolayer

3D surface reconstruction from point clouds aims to generate continuous surface representations of physical objects from discrete spatial samples. This problem is of fundamental importance across diverse domains, including robotics, industrial design, and cultural heritage preservation. Among various surface representation schemes, Partial Differential equation (PDE)-based surfaces have emerged as a promising approach due to their strong mathematical foundations, compact representation, and high-order continuity properties. Despite these advantages, a key challenge lies in the analytical solution of PDEs used for surface modelling. Existing approaches often rely on numerical solvers, which are computationally expensive and prone to discretization errors. Although analytical solutions to fourth-order PDEs have been applied to parametric surface reconstruction, several limitations remain: (1) comparisons among different PDE orders (e.g., second-, fourth-, and sixth-order) have not been systematically explored; (2) hyperparameters within PDE solutions are typically tuned manually, which is inefficient and often suboptimal; (3) multiple analytical solutions to the same PDE are rarely compared in terms of their fitting accuracy; and (4) PDEs with non-zero sculpting force are rarely investigated for surface reconstruction. To address these issues, this study conducts a comprehensive analysis of closed-form PDE solutions of varying orders for parametric surface reconstruction from point clouds. The Genetic algorithm (GA) is employed to automatically determine optimal hyperparameter values, thereby improving reconstruction quality. Furthermore, we perform an extensive comparison among different PDE orders and among multiple analytical solutions derived from the same PDE. Lastly, we also investigate the impact of the sculpting force in the PDEs for surface reconstruction. Experimental results across several datasets of varying complexity demonstrate that the proposed framework achieves accurate and smooth surface reconstruction while significantly reducing manual intervention. This work provides new insights into the practical use of PDE-based parametric surfaces and establishes a foundation for future research in data-driven geometric modeling and surface reconstruction.

The transport properties of excess electrons in non polar gases or liquids give important information on the electronic states in a disordered medium and on the relationship among the electron-atom interactions and the properties of the fluid. Anomalous density effects on electron mobilities were discovered in a number of compressed gases1. A negative density effect, i. e., the density-normalized zero-field mobility μ 0 N of electrons decreases with increasing the gas density N, is shown by gases such as He and Ne, whose interaction with electrons is dominated by short-range repulsive exchange forces and whose scattering length a is positive. On the other hand, a positive density effect, i. e., μ 0 N increases with N, is shown by Ar, Kr, and Xe, whose scattering length is negative owing to the overwhelming contribution of the long-range attractive polarization forces to the atom-electron interaction.

We examine rotational transitions of HCl in collisions with H2 by carrying out quantum mechanical close-coupling and quasi-classical trajectory (QCT) calculations on a recently developed globally accurate full-dimensional ab initio potential energy surface for the H3Cl system. Signatures of rainbow scattering in rotationally inelastic collisions are found in the state resolved integral and differential cross sections as functions of the impact parameter (initial orbital angular momentum) and final rotational quantum number. We show the coexistence of distinct dynamical regimes for the HCl rotational transition driven by the short-range repulsive and long-range attractive forces whose relative importance depends on the collision energy and final rotational state, suggesting that the classification of rainbow scattering into rotational and l-type rainbows is effective for H2 + HCl collisions. While the QCT method satisfactorily predicts the overall behavior of the rotationally inelastic cross sections, its capability to accurately describe signatures of rainbow scattering appears to be limited for the present system.

The van Kampen analysis of condensation in a fluid of hard spheres with long-range attractions is extended to investigate the statistical mechanics of a fluid of rigid rod-like molecules which interact through both short-range repulsive and long-range attractive forces and which assume only a restricted set of three mutually orthogonal orientations. The thermodynamic properties are derived for the fluid near the liquid-gas critical point and at the nematic-isotropic transition. The model predicts that both isotropic and anisotropic attractive and repulsive interactions contribute to the stabilization of the nematically ordered fluid when a density change accompanies the transition. However, when the transition occurs at constant density, only the anisotropic contributions of the long-range dispersion energy and short-range repulsions are found to stabilize the transition in partial accord with the Maier-Saupe theory. Numerical results for a rigid-rod fluid with length-to-breadth ratio 3 at various packing...

Three-dimensional models have played important roles in medical simulation and education. Surface models can be manipulated in real time and even online; surface models have significant features for an interactive simulation system. The objective surface models are obtainable from accumulation of each structure's outlines, followed by surface reconstruction. The aim of this research was to suggest the arranged methods of surface reconstruction, which might be applied to building surface models from serial images, such as computed tomographic scans and magnetic resonance images. We used recent state-of-the-art sectioned images of a cadaver head in which several structures were delineated. Four reconstruction methods were regulated according to the structure's morphology: all outlines of a structure are overlapped and singular (method 1), overlapped and not singular (method 2), not overlapped but singular (method 3), and neither overlapped nor singular (method 4). From the trials with various kinds of head structures, we strongly suggested methods 1 and 2, in which volume reconstruction before surface reconstruction accelerated the processing speed on 3D-DOCTOR. So as to use methods 1 and 2, how to make the neighboring outlines overlapped in advance was discussed. The surface models of detailed head structures prepared in this investigation will hopefully contribute to various simulations for clinical practice. The value of the surface models are enhanced if they are placed over the original sectioned images, outlined images, and magnetic resonance images of the same cadaver.

In the reverse engineering area, while the reconstruction of surfaces from scanned or digitised data has been developed, a geometric model of an existing object is often unavailable. This paper presents a new approach to the reconstruction of a surface. The proposed methodology finds the basic parts of the surface and blends surfaces between them. Each basic geometric part is divided into triangular patches which are compared using normal vectors for face grouping. Each group is categorised into analytical surfaces such as a part of a cylinder, a sphere or a cone, and plane shapes to represent the basic geometric surface. Each basic geometric surface is then implemented to the infinitive surface (unbounded plane, cylinder, cone, or sphere: cylinder, cone, and sphere are full shapes of analytical surfaces). The infinitive surface's intersections are trimmed by boundary representation model reconstruction. The proposed methodology has several advantages such as computational efficiency and automatic functional modelling in reverse engineering. Reverse engineering should be the 3D equipment of the photocopying process.

For 3D surface reconstruction problems with noisy and incomplete range data measured from complex scenes with arbitrary topologies, a low-level representation, such as level set surfaces, is used. Such surface reconstruction is typically accomplished by minimizing a weighted sum of datamodel discrepancy and model smoothness terms. We introduce a new nonlinear model smoothness term for surface reconstruction based on variations of the surface normals. A direct solution requires solving a fourth-order partial differential equation (PDE), which is very difficult with; conventional numerical techniques. Our solution is based on processing the normals separately from the surface, which allows us to separate the problem into two second-order PDEs. The proposed method can smooth complex, noisy surfaces, while preserving sharp, geometric features, and it is a natural generalization of edge-preserving methods in image processing, such as anisotropic diffusion.

The patterns formed in flat layers of magnetic suspensions and emulsions due to the competing short-range attractions and long-range magnetic repulsion forces are considered. On the basis of calculating energy of the ordered hexagonal and stripe structures of the liquid magnetics it was shown that the stripe phase is energetically preferred at the symmetrical distribution of the particles between concentrated and diluted phases. If one phase prevails the formation of the array of the separate droplets is expected. Results of the numerical calculation of the energies of the stripe and hexagonal patterns are confirmed by the numerical simulation results of the kinetics of the magnetic field induced phase separation. Numerical simulation by the pseudospectral technique of the dynamics of the concentration perturbation show that at nonsymmetrical distribution of the particles between phases the periodic array of the separated droplets arises. Long-range magnetic repulsion forces are crucial for the formation of ordered arrays of the stripes or droplets since if they are absent characteristic coarsening phenomena at late stages of the phase separation are observed.

No abstract available.

We propose an approach to surface reconstruction using active tactile sensing and surface normal information. Unlike previous works which consider primarily the problem of reconstructing a single tensor B-spline patch based on deformed planar or spherical domain, the surface reconstructed here is a network of triangular B-spline patches based on arbitrary topological domain and can maintain tangent plane continuity. The input is unorganized tactile sensing 3D data points with normal information of arbitrary topological type surfaces, which are obtained by a dextrous multifingered hand equipped with force/moment tactile sensors. The surface reconstructed is a parameterization of the data over these patches. An adaptive refinement is explored on the patch network in order to satisfy a given error tolerance. Demonstrations are carried out on simulated and experimental data.

The individual effects of short-range and long-range forces on the structure of water, a prerequisite for developing a perturbation theory, are assessed using a decomposition of realistic water—water potential models into trial potentials. Computer simulations for one typical liquid density and a number of temperatures ranging from the freezing temperature up to supercritical ones, and for several densities on a supercritical isotherm were performed. The trial potentials were constructed from the ST2 and TIP4P potentials and it is shown that for both potentials the results are practically identical. It is shown that (i) regardless of the thermo-dynamic conditions and potential models used, the structure of water and the mutual orientational arrangement of water molecules, given by a set of site—site correlation functions, are determined nearly exclusively only by the short range forces, and (ii) for high density states the effect of the short range electrostatic part of the intermolecular potential on the spatial arrangement of the water molecules rapidly decreases with increasing temperature but does not become negligible.

Image guidance is an important adjunct for endoscopic sinus and skull base surgery. However, current systems require bulky external tracking equipment, and their use can interrupt efficient surgical workflow. To evaluate a trackerless surgical navigation system using 3-dimensional (3D) endoscopy and simultaneous localization and mapping (SLAM) algorithms in the anterior skull base. This interventional deceased donor cohort study and retrospective clinical case study was conducted at a tertiary academic medical center with human deceased donor specimens and a patient with anterior skull base pathology. Participants underwent endoscopic endonasal transsphenoidal dissection and surface model reconstruction from stereoscopic video with registration to volumetric models segmented from computed tomography (CT) and magnetic resonance imaging. To assess the fidelity of surface model reconstruction and accuracy of surgical navigation and surface-CT model coregistration, 3 metrics were calculated: reconstruction error, registration error, and localization error. In deceased donor models (n = 9), high-fidelity surface models of the posterior wall of the sphenoid sinus were reconstructed from stereoscopic video and coregistered to corresponding volumetric CT models. The mean (SD; range) reconstruction, registration, and localization errors were 0.60 (0.24; 0.36-0.93), 1.11 (0.49; 0.71-1.56) and 1.01 (0.17; 0.78-1.25) mm, respectively. In a clinical case study of a patient who underwent a 3D endoscopic endonasal transsphenoidal resection of a tubercular meningioma, a high-fidelity surface model of the posterior wall of the sphenoid was reconstructed from intraoperative stereoscopic video and coregistered to a volumetric preoperative fused CT magnetic resonance imaging model with a root-mean-square error of 1.38 mm. The results of this study suggest that SLAM algorithm-based endoscopic endonasal surgery navigation is a novel, accurate, and trackerless approach to surgical navigation that uses 3D endoscopy and SLAM-based algorithms in lieu of conventional optical or electromagnetic tracking. While multiple challenges remain before clinical readiness, a SLAM algorithm-based endoscopic endonasal surgery navigation system has the potential to improve surgical efficiency, economy of motion, and safety.