52 research outputs found
O zakrivljenostima na trokutnim mrežama
A face-based curvature estimation on triangle meshes is presented in
this paper. A flexible disk is laid on the mesh around a given
triangle. Such a bent disk is used as a geodesic neighborhood of the
face for approximating normal and principal curvatures. The radius
of the disk is free input data in the algorithm. Its influence on
the curvature values and the stability of estimated principal
directions are investigated in the examples.U članku je prikazana procjena zakrivljenosti na trokutnim mrežama, bazirana na stranicama. Gipki disk položen je na
mrežu oko danog trokuta. Takav prilagodljiv disk koristi se
kao geodetska okolina stranice za aproksimaciju normalnih i
glavnih zakrivljenosti. Polumjer diska je nezavisni ulazni
podatak u algoritmu. U primjerima se istražuje njegov utjecaj na vrijednosti zakrivljenosti i na stabilnost procijenjenih glavnih
smjerova
B-splajn dijelovi koji pristaju na plohe i triangularne mreže
In this paper a technique for the construction of quartic polynomial B-spline patches fitting on analytical surfaces and triangle meshes is presented.The input data are curvature values and principal directions at a given surface point which can be computed directly, if the surface is represented by a vector function. In the case of discrete surface representation, i.e. on a triangle mesh the required input data are computed from a circular neighborhood of a specified triangle face. Such a surface patch may replace a well defined region of the mesh, and can be used e.g. in re-triangulation, mesh-simplification and rendering algorithms.U ovom se radu prikazuje metoda za konstrukciju kvartnog polinoma B-splajn dijela podesnog za analitičke plohe i mreže trokuta. Ulazni podaci su vrijednosti zakrivljenosti i glavni smjerovi u danoj točki plohe, koji se mogu izravno računati za plohu zadanu vektorskom funkcijom. Za slučaj diskretne reprezentacije plohe, tj. za triangularnu mrežu, odgovarajući ulazni podaci računaju se iz kružne okoline određ-enog trokuta mreže. Takvi dijelovi mogu zamijeniti dobro definirano područje mreže, i mogu se upotrijebiti npr. u retriangulaciji, simplifikaciji mreže i renderiranju
Geodesic computation on implicit surfaces
Geodesics have a wide range of applications in CAD, shape design and machine learning. Current research on geodesic computation focuses primarily on parametric surfaces and mesh representations. There is little work on implicit surfaces. In this paper, we present a novel algorithm able
to compute the exact geodesics on implicit surfaces. Although the existing Fast Marching Method can generate a geodesic path on a Cartesian grid that envelopes the implicit surface in question, this method, as well as
other existing methods, is unable to compute a geodesic on the original surface. The computed geodesic path is actually a polyline offsetting from the surface. Our approach provides a solution to two existing fundamental
problems, which are (1) to produce a Cartesian grid that can tightly embed the implicit surface concerned, which remains challenging; and (2) to formulate exact geodesics on the original implicit surface itself. Our algorithm consists of two steps, Cartesian grid based geodesic
computation and geodesic correction. The later corrects an approximate geodesic path so that it can be on the implicit surface. In addition, in comparison with other existing work, our methods can handle both low dimensional and high dimensional surfaces (hyper-surfaces)
Extraction and Visualization of Swirl and Tumble Motion from Engine Simulation Data
Figure 1: Unsteady visualization of vortices from in-cylinder tumble motion in a gas engine and its relationship to the boundary. During the valve cycle (left to right), the piston head that shapes the bottom of the geometry moves down (not shown). The volume rendering shows vortices using a two-dimensional transfer function of λ2 and normalized helicity (legend). The main tumble vortex is extracted and visible as off-center and with an undesired diagonal orientation. The flow structure on the boundary is visualized using boundary topology. A direct correspondence between the volume and boundary visualizations can be observed. In the third image, the intersection of the main vortex with the boundary results in critical points on the front and back walls. Optimizing the combustion process within an engine block is central to the performance of many motorized vehicles. Associated with this process are two important patterns of flow: swirl and tumble motion, which optimize the mixing of fluid within each of an engine’s cylinders. Good visualizations are necessary to analyze the simulation data of these in-cylinder flows. We present a range of methods including integral, feature-based, and imagebased schemes with the goal of extracting and visualizing these tw
Exact Geosedics and Shortest Paths on Polyhedral Surface
We present two algorithms for computing distances along a non-convex polyhedral surface. The first algorithm computes exact minimal-geodesic distances and the second algorithm combines these distances to compute exact shortest-path distances along the surface. Both algorithms have been extended to compute the exact minimalgeodesic paths and shortest paths. These algorithms have been implemented and validated on surfaces for which the correct solutions are known, in order to verify the accuracy and to measure the run-time performance, which is cubic or less for each algorithm. The exact-distance computations carried out by these algorithms are feasible for large-scale surfaces containing tens of thousands of vertices, and are a necessary component of near-isometric surface flattening methods that accurately transform curved manifolds into flat representations.National Institute for Biomedical Imaging and Bioengineering (R01 EB001550
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