Abstract:The Purkinje fibers are located in the ventricular walls of the heart, just beneath the endocardium and conduct excitation from the right and left bundle branches to the ventricular myocardium. Recently, anatomists succeeded in photographing the Purkinje fibers of a sheep, which clearly showed the mesh structure of the Purkinje fibers. In this study, we present a technique for modeling the mesh structure of Purkinje fibers semiautomatically using an extended L-system. The Lsystem is a formal grammar that defines the growth of a fractal structure by generating rules (or rewriting rules) and an initial structure. It was originally formulated to describe the growth of plant cells, and has subsequently been applied for various purposes in computer graphics such as modeling plants, buildings, streets, and ornaments. For our purpose, we extended the growth process of the L-system as follows: 1) each growing branch keeps away from existing branches as much as possible to create a uniform distribution, and 2) when branches collide, we connect the colliding branches to construct a closed mesh structure. We designed a generating rule based on observations of the photograph of Purkinje fibers and manually specified three terminal positions on a three-dimensional (3D) heart model: those of the right bundle branch, the anterior fascicle, and the left posterior fascicle of the left branch. Then, we grew fibers starting from each of the three positions based on the specified generating rule. We achieved to generate 3D models of Purkinje fibers of which physical appearances closely resembled the real photograph. The generation takes a few seconds. Variations of the Purkinje fibers could be constructed easily by modifying the generating rules and parameters.Key words: Purkinje fibers, L-system, heart simulation.A three-dimensional (3D) virtual heart model is often used for computer simulations and visualizations. Computer simulation is one way to understand the electrophysiological properties of the heart or to figure out the mechanisms of fatal arrhythmias [1][2][3][4]. Effective visualization of a 3D heart model is also a useful tool for education and communication between doctors and patients [1,5]. However, the creation of a 3D heart model is difficult and time-consuming because the heart has intricate structures containing various tissues, such as the atrioventricular node, bundle of His, Purkinje fi bers, and contractive myocardium. Our goal was to facilitate this process by providing effective modeling tools. In this study, we focused on the construction of Purkinje fi bers.The Purkinje fi bers are part of the ventricular conduction system and were originally discovered by Tawara [6]. These tissues conduct excitation (electrical activation) rapidly from the bundle of His to the ventricular myocardial tissue. The Purkinje fibers are located in the ventricular walls of the heart, just beneath the endocardium. Figure 1 is a PAS-stained stereomicrograph of a sheep heart provided by Shimada et al. [7], which shows the...

Coarse quad meshes are the preferred representation for animating characters in movies and video games. In these scenarios, artists want explicit control over the edge flows and the singularities of the quad mesh. Despite the significant advances in recent years, existing automatic quad remeshing algorithms are not yet able to achieve the quality of manually created remeshings. We present an interactive system for manual quad remeshing that provides the user with a high degree of control while avoiding the tediousness involved in existing manual tools. With our sketch-based interface the user constructs a quad mesh by defining patches consisting of individual quads. The desired edge flow is intuitively specified by the sketched patch boundaries, and the mesh topology can be adjusted by varying the number of edge subdivisions at patch boundaries. Our system automatically inserts singularities inside patches if necessary, while providing the user with direct control of their topological and geometrical locations. We developed a set of novel user interfaces that assist the user in constructing a curve network representing such patch boundaries. The effectiveness of our system is demonstrated through a user evaluation with professional artists. Our system is also useful for editing automatically generated quad meshes.

We propose an algorithm to quadrangulate an N‐sided patch (2 ≤ N ≤ 6) with prescribed numbers of edge subdivisions at its boundary. Our algorithm is guaranteed to succeed for arbitrary valid input, which is proved using a canonical simplification of the input and a small set of topological patterns that are sufficient for supporting all possible cases. Our algorithm produces solutions with minimal number of irregular vertices by default, but it also allows the user to choose other feasible solutions by solving a set of small integer linear programs. We demonstrate the effectiveness of our algorithm by integrating it into a sketch‐based quad remeshing system. A reference C++ implementation of our algorithm is provided as a supplementary material.

We propose a method for interactive cloning of 3D surface geometry using a paintbrush interface, similar to the continuous cloning brush popular in image editing. Existing interactive mesh composition tools focus on atomic copy-and-paste of pre-selected feature areas, and are either limited to copying surface displacements, or require the solution of variational optimization problems, which is too expensive for an interactive brush interface. In contrast, our GeoBrush method supports real-time continuous copying of arbitrary high-resolution surface features between irregular meshes, including topological handles. We achieve this by first establishing a correspondence between the source and target geometries using a novel generalized discrete exponential map parameterization. Next we roughly align the source geometry with the target shape using Green Coordinates with automaticallyconstructed cages. Finally, we compute an offset membrane to smoothly blend the pasted patch with C 1 continuity before stitching it into the target. The offset membrane is a solution of a bi-harmonic PDE, which is computed on the GPU in real time by exploiting the regular parametric domain. We demonstrate the effectiveness of GeoBrush with various editing scenarios, including detail enrichment and completion of scanned surfaces.