13,046 research outputs found
Implicit equations of non-degenerate rational Bezier quadric triangles
In this paper we review the derivation of implicit equations for non-degenerate quadric patches in rational BĂ©zier triangular form. These are the case of Steiner surfaces of degree two. We derive the bilinear forms for such quadrics in a coordinate-free fashion in terms of their control net and their list of weights in a suitable form. Our construction relies on projective geometry and is grounded on the pencil of quadrics circumscribed to a tetrahedron formed by vertices of the control net and an additional point which is required for the Steiner surface to be a non-degenerate quadric
Conforming restricted Delaunay mesh generation for piecewise smooth complexes
A Frontal-Delaunay refinement algorithm for mesh generation in piecewise
smooth domains is described. Built using a restricted Delaunay framework, this
new algorithm combines a number of novel features, including: (i) an
unweighted, conforming restricted Delaunay representation for domains specified
as a (non-manifold) collection of piecewise smooth surface patches and curve
segments, (ii) a protection strategy for domains containing curve segments that
subtend sharply acute angles, and (iii) a new class of off-centre refinement
rules designed to achieve high-quality point-placement along embedded curve
features. Experimental comparisons show that the new Frontal-Delaunay algorithm
outperforms a classical (statically weighted) restricted Delaunay-refinement
technique for a number of three-dimensional benchmark problems.Comment: To appear at the 25th International Meshing Roundtabl
Three-dimensional unstructured grid generation via incremental insertion and local optimization
Algorithms for the generation of 3D unstructured surface and volume grids are discussed. These algorithms are based on incremental insertion and local optimization. The present algorithms are very general and permit local grid optimization based on various measures of grid quality. This is very important; unlike the 2D Delaunay triangulation, the 3D Delaunay triangulation appears not to have a lexicographic characterization of angularity. (The Delaunay triangulation is known to minimize that maximum containment sphere, but unfortunately this is not true lexicographically). Consequently, Delaunay triangulations in three-space can result in poorly shaped tetrahedral elements. Using the present algorithms, 3D meshes can be constructed which optimize a certain angle measure, albeit locally. We also discuss the combinatorial aspects of the algorithm as well as implementational details
DOT tomography of the solar atmosphere. IV. Magnetic patches in internetwork areas
We use G-band and Ca II H image sequences from the Dutch Open Telescope (DOT)
to study magnetic elements that appear as bright points in internetwork parts
of the quiet solar photosphere and chromosphere. We find that many of these
bright points appear recurrently with varying intensity and horizontal motion
within longer-lived magnetic patches. We develop an algorithm for detection of
the patches and find that all patches identified last much longer than the
granulation. The patches outline cell patterns on mesogranular scales,
indicating that magnetic flux tubes are advected by granular flows to
mesogranular boundaries. Statistical analysis of the emergence and
disappearance of the patches points to an average patch lifetime as long as
530+-50 min (about nine hours), which suggests that the magnetic elements
constituting strong internetwork fields are not generated by a local turbulent
dynamo.Comment: 8 pages, 6 figure
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