Solid reconstruction using recognition of quadric surfaces from orthographic views

International audienceThe reconstruction of 3D objects from 2D orthographic views is crucial for maintaining and further developing existing product designs. A B-rep oriented method for reconstructing curved objects from three orthographic views is presented by employing a hybrid wire-frame in place of an intermediate wire-frame. The Link-Relation Graph (LRG) is introduced as a multi-graph representation of orthographic views, and quadric surface features (QSFs) are defined by special basic patterns of LRG as well as aggregation rules. By hint-based pattern matching in the LRGs of three orthographic views in an order of priority, the corresponding QSFs are recognized, and the geometry and topology of quadric surfaces are recovered simultaneously. This method can handle objects with interacting quadric surfaces and avoids the combinatorial search for tracing all the quadric surfaces in an intermediate wire-frame by the existing methods. Several examples are provided

Converting Hybrid Wire-frames to B-rep Models

International audienceSolid reconstruction from engineering drawings is one of the efficient technologies to product solid models. The B-rep oriented approach provides a practical way for reconstructing a wide range of objects. However, its major limitation is the computational complexity involved in the search for all valid faces from the intermediate wire-frame, especially for objects with complicated face topologies. In previous work, we presented a hint-based algorithm to recognize quadric surfaces from orthographic views and generate a hybrid wire-frame as the intermediate model of our B-rep oriented method. As a key stage in the process of solid reconstructing, we propose an algorithm to convert the hybrid wire-frame to the final B-rep model by extracting all the rest faces of planes based on graph theory. The entities lying on the same planar surface are first collected in a plane graph. After all the cycles are traced in a simplified edge-adjacency matrix of the graph, the face loops of the plane are formed by testing loop containment and assigning loop directions. Finally, the B-rep model is constructed by sewing all the plane faces based on the M¨obius rule. The method can efficiently construct 2- manifold objects with a variety of face topologies, which is illustrated by results of implementatio

Gn blending multiple surfaces in polar coordinates

International audienceThis paper proposes a method of Gn blending multiple parametric surfaces in polar coordinates. It models the geometric continuity conditions of parametric surfaces in polar coordinates and presents a mechanism of converting a Cartesian parametric surface into its polar coordinate form. The basic idea is first to reparameterize the parametric blendees into the form of polar coordinates. Then they are blended simultaneously by a basis function in the complex domain. To extend its compatibility, we also propose a method of converting polar coordinate blending surface into N NURBS patches. One application of this technique is to fill N-sided holes. Examples are presented to show its feasibility and practicability

A New Algorithm for Boolean Operations on General Polygons

International audienceA new algorithm for Boolean operations on general planar polygons is presented. It is available for general planar polygons (manifold or non-manifold, with or without holes). Edges of the two general polygons are subdivided at the intersection points and touching points. Thus, the boundaryof the Boolean operation resultant polygon is made of some whole edges of the polygons after the subdivision process. We use the simplex theory to build the basic mathematical model of the new algorithm. The subordination problem between an edge and a polygon is reduced to a problem of determining whether a point is on some edges of some simplices or inside the simplices, and the associated simplicial chain of the resultant polygon is just an assembly of some simplices and their coefficients of the two polygons after the subdivision process. Examples show that the running time required bythe new algorithm is less than one-third of that bythe Rivero and Feito algorithm

Immune Responses Following Mouse Peripheral Nerve Xenotransplantation in Rats

Xenotransplantation offers a potentially unlimited source for tissues and organs for transplantation, but the strong xenoimmune responses pose a major obstacle to its application in the clinic. In this study, we investigate the rejection of mouse peripheral nerve xenografts in rats. Severe intragraft mononuclear cell infiltration, graft distension, and necrosis were detected in the recipients as early as 2 weeks after mouse nerve xenotransplantation. The number of axons in xenografts reduced progressively and became almost undetectable at week 8. However, mouse nerve xenotransplantation only led to a transient and moderate increase in the production of Th1 cytokines, including IL-2, IFN-γ, and TNF-α. The data implicate that cellular immune responses play a critical role in nerve xenograft rejection but that further identification of the major effector cells mediating the rejection is required for developing effective means to prevent peripheral nerve xenograft rejection

Regional changes in brain apparent diffusion coefficient in fetuses with complex congenital heart disease and normal pregnancy assessed using diffusion-weighted imaging

ObjectivesTo explore changes in brain apparent diffusion coefficient (ADC) in normal fetuses and fetuses with complex congenital heart disease (CHD) during the second and early third trimesters.MethodsThis single-center prospective study was conducted from May 2019 through October 2021. We measured and compared the mean ADC values between 23 fetuses with CHD and 27 gestational age (GA)-matched controls using covariance analyses. ADC density plots and histograms were used to compare brain characteristics. False-discovery rates (FDR, α = 0.05) correction was used for multiple testing.ResultsThe mean ADC in the frontal white matter, temporal white matter, parietal white matter, occipital white matter, cerebellar hemisphere, central area of the centrum semiovale, basal ganglia region, thalamus, and pons were not significantly different (all p > 0.05). Based on histogram analysis, there were no significant differences between the controls and fetuses with CHD after FDR correction. However, the ADC density plots showed significant heterogeneity between the controls and fetuses with CHD.ConclusionThe mean ADC values and ADC histogram analysis did not differ between the CHD and normal groups. The ADC density plots may provide supplementary information and improve the sensitivity for detecting early brain changes in fetuses with CHD

Polar NURBS surface with curvature continuity

International audiencePolar NURBS surface is a kind of periodic NURBS surface, one boundary of which shrinks to a degenerate polarpoint. The specific topology of its control-point mesh offers the ability to represent a cap-like surface, which iscommon in geometric modeling. However, there is a critical and challenging problem that hinders its application:curvature continuity at the extraordinary singular pole. We first propose a sufficient and necessary condition ofcurvature continuity at the pole. Then, we present constructive methods for the two key problems respectively:how to construct a polar NURBS surface with curvature continuity and how to reform an ordinary polar NURBSsurface to curvature continuous. The algorithms only depend on the symbolic representation and operations ofNURBS, and they introduce no restrictions on the degree or the knot vectors. Examples and comparisons demonstratethe applications of the curvature-continuous polar NURBS surface in hole-filling and free-shape modeling

On Gravitational anomaly and Hawking radiation near weakly isolated horizon

Based on the idea of the work by Wilczek and his collaborators, we consider the gravitational anomaly near weekly isolated horizon. We find that there exists a universal choice of tortoise coordinate for any weakly isolated horizon. Under this coordinate, the leading behavior of a quite arbitrary scalar field near horizon is a 2-dimensional chiral scalar field. This means we can extend the idea of Wilczek and his collaborators to more general cases and show the relation between gravitational anomaly and Hawking radiation is a universal property of black hole horizon.Comment: 14 page

Filling n-sided regions with G1 triangular Coons B-spline patches

International audienceFilling n-sided regions is an essential operation in shape and surface modeling. Positional and tangential continuities are highly required in designing and manufacturing. We propose a method for filling n-sided regions with untrimmed triangular Coons B-spline patches, preserving G1 continuity exactly. The algorithm first computes a central point, a central normal, the central, and the corner derivative vectors. Then the region is split into n triangular areas by connecting the central point to each corner of the boundary. These inner curves and all cross-boundary derivatives are computed fulfilling G1 compatibility conditions. And finally, the triangular patches are generated in the Coons B-spline form, one boundary of which is regressed to the central vertex. Neither positional nor tangential error is introduced by this method. And only one degree elevation is needed