Related papers: Mathematical models of the complex surfaces in sim…
This paper presents a new technique for the virtual reality (VR) visu-alization of complex volume images obtained from computer tomography (CT) and Magnetic Resonance Imaging (MRI) by combining three-dimensional (3D) mesh processing and…
Finding the distribution of the velocities and pressures of a fluid by solving the Navier-Stokes equations is a principal task in the chemical, energy, and pharmaceutical industries, as well as in mechanical engineering and the design of…
Statistical Shape Models of faces and various body parts are heavily used in medical image analysis, computer vision and visualization. Whilst the field is well explored with many existing tools, all of them aim at experts, which limits…
Modular forms are highly self-symmetric functions studied in number theory, with connections to several areas of mathematics. But they are rarely visualized. We discuss ongoing work to compute and visualize modular forms as 3D surfaces and…
Current trends in the computer graphics community propose leveraging the massive parallel computational power of GPUs to accelerate physically based simulations. Collision detection and solving is a fundamental part of this process. It is…
BSplines are one of the most promising curves in computer graphics. They are blessed with some superior geometric properties which make them an ideal candidate for several applications in computer aided design industry. In this article,…
Straight lines are common features in human made environments, which makes them a frequently explored feature for control applications. Many control schemes, like Visual Servoing, require the 3D parameters of the features to be estimated.…
Surface parametrization is a crucial part in various fields, having applications in computer graphic, medical imaging, scientific computing and computational engineering. The majority of surface parametrization approaches are performed on…
Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials. These include: tightly containing a cloud of points (e.g., representing an…
Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an…
In recent years, the use of expressive surface visualizations in the representation of vascular structures has gained significant attention. These visualizations provide a comprehensive understanding of complex anatomical structures and are…
Neural reconstruction and rendering strategies have demonstrated state-of-the-art performances due, in part, to their ability to preserve high level shape details. Existing approaches, however, either represent objects as implicit surface…
In this contribution, I give an overview of the various approaches toward the numerical modelling of turbulence, particularly, in the interstellar medium. The discussion is placed in a physical context, i. e. computational problems are…
We give necessary and sufficient conditions on the curvature and the torsion of a regular curve of the space forms $\h^3$ and $\s^3$ to be contained in a totally umbilical surface. In case that the curve has constant torsion, we obtain the…
The quest for regular models of arithmetic surfaces allows different viewpoints and approaches: using valuations or a covering by charts. In this article, we sketch both approaches and then show in a concrete example, how surprisingly…
Accurately simulating real world object dynamics is essential for various applications such as robotics, engineering, graphics, and design. To better capture complex real dynamics such as contact and friction, learned simulators based on…
The paper is concerned with three types of cubic splines over a triangulation that are characterized by three degrees of freedom associated with each vertex of the triangulation. The splines differ in computational complexity, polynomial…
Human figures have been animated using a variety of geometric models including stick figures, polygonal models, and NURBS-based models with muscles, flexible skin, or clothing. This paper reports on experimental results indicating that a…
Statistical models of 3D human shape and pose learned from scan databases have developed into valuable tools to solve a variety of vision and graphics problems. Unfortunately, most publicly available models are of limited expressiveness as…
A hyperbolic framed curve is a smooth curve with a moving frame in hyperbolic 3-space. It may have singularities. By using this moving frame, we can investigate the differential geometry properties of curves, even at singular points. In…