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To address the problem of low overall machining efficiency of free-form surfaces and difficulty in ensuring machining quality, this paper proposes a MATLAB-based free-form surface division method. The surface division is divided into two stages: Partition area identification and area boundary determination. In the first stage, the free-form surface is roughly divided into convex, concave, and saddle regions according to the curvature of the surface, and then the regions are subdivided based on the fuzzy c-means clustering algorithm. In the second stage, according to the clustering results, the Voronoi diagram algorithm is used to finally determine the boundary of the surface patch. We used NURBS to describe free-form surfaces and edit a set of MATLAB programs to realize the division of surfaces. The proposed method can easily and quickly divide the surface area, and the simulation results show that the proposed method can shorten machining time by 36% compared with the traditional machining method. It is proved that the method is practical and can effectively improve the machining efficiency and quality of complex surfaces.

Funder: Natural Environment Research Council; doi: http://dx.doi.org/10.13039/501100000270, Conformal Geometric Algebra (CGA) provides a unified representation of both geometric primitives and conformal transformations, and as such holds significant promise in the field of computer graphics. In this paper we implement a simple ray tracer in CGA with a Blinn–Phong lighting model, before putting it to use to examine ray intersections with surfaces generated from the direct interpolation of geometric primitives. General surfaces formed from these interpolations are rendered using analytic normals. In addition, special cases of point-pair interpolation, which might find use in graphics applications, are described and rendered. A closed form expression is found for the derivative of the square root of a scalar plus 4-vector element with respect to a scalar parameter. This square root derivative is used to construct an expression for the derivative of a pure-grade multivector projected to the blade manifold. The blade manifold projection provides an analytical method for finding the normal line to the interpolated surfaces and its use is shown in lighting calculations for the ray tracer and in generating vertex normals for exporting the evolved surfaces as polygonal meshes.

Generative models that produce point clouds have emerged as a powerful tool to represent 3D surfaces, and the best current ones rely on learning an ensemble of parametric representations. Unfortunately, they offer no control over the deformations of the surface patches that form the ensemble and thus fail to prevent them from either overlapping or collapsing into single points or lines. As a consequence, computing shape properties such as surface normals and curvatures becomes difficult and unreliable. In this paper, we show that we can exploit the inherent differentiability of deep networks to leverage differential surface properties during training so as to prevent patch collapse and strongly reduce patch overlap. Furthermore, this lets us reliably compute quantities such as surface normals and curvatures. We will demonstrate on several tasks that this yields more accurate surface reconstructions than the state-of-the-art methods in terms of normals estimation and amount of collapsed and overlapped patches., 14 pages

Surface curvature affects adhesion forces, deformations of surfaces in contact, leakage of mechanical seals, friction, wear, paintability, and electrical conductivity. However, potential benefits of surface curvature have not yet been fully utilized. One problem is the lack of comparison data helping to make an informed decision on the selection of curvature characterization method. In this paper, five multiscale curvature characterization methods, namely Nowicki, Bigerelle-Nowicki, Gleason-Heron, Kalin, and Bartkowiak are compared. The comparison was conducted on large image databases of computer-generated fractal surfaces, sine waves and real engineering surfaces. Specifically, the methods were evaluated for their ability to differentiate between surfaces that: (i) exhibit increasing curvature complexity, (ii) have varying curvatures at a single scale, and (iii) represent minute multiscale curvature changes encountered in real engineering applications. The results obtained indicate that the Bigerelle-Nowicki method exhibits the best overall performance.

Highresolution X-ray tomography can be used to measure the local mean curvature of fluid–fluid interfaces within the pores of opaque, permeable porous media. Thereof, the pore-scale capillary pressure can be estimated via the Young– Laplace equation. We critically review the aforementioned method by processing experimental data acquired with an X-ray cone-beam laboratory station and compare capillary pressure estimates with results of pore-scale numerical simulations. The method looks promising but is rather sensitive to the attainment of an equilibrium state for the fluid mixture and to the numerical calculation of curvature. Numerical simulation results provide evidence that dynamic effects result in a larger discrepancy between values of the capillary pressure computed from first principles (i.e., pressure difference across the interface) and from geometric considerations (i.e., curvature estimation and Young– Laplace equation).

UMR BFP - Equipe OrFE; International audience; In Arabidopsis (Arabidopsis thaliana), reduced expression of the transcriptional regulator PEAPOD2 (PPD2) results in propeller-like rosettes with enlarged and dome-shaped leaves. However, the molecular and cellular processes underlying this peculiar phenotype remain elusive. Here, we studied the interaction between PPD2 and NOVEL INTERACTOR OF JAZ (NINJA) and demonstrated that ninja loss-of-function plants produce rosettes with dome-shaped leaves similar to those of ppd mutants but without the increase in size. We showed that ninja mutants have a convex-shaped primary cell cycle arrest front, putatively leading to excessive cell division in the central leaf blade region. Furthermore, ppd and ninja mutants have a similar increase in the expression of CYCLIN D3;2 (CYCD3;2), and ectopic overexpression of CYCD3;2 phenocopies the ppd and ninja rosette and leaf shape phenotypes without affecting the size. Our results reveal a pivotal contribution of NINJA in leaf development, in addition to its well-studied function in jasmonate signaling, and imply a new function for D3-type cyclins in, at least partially, uncoupling the size and shape phenotypes of ppd leaves.

© Springer Nature Switzerland AG 2019. Conformal Geometric Algebra (CGA) provides a unified representation of both geometric primitives and conformal transformations, and as such holds great promise in the field of computer graphics [1–3]. In this paper we implement a simple ray tracer in CGA with a Blinn-Phong lighting model and use it to examine ray intersections with surfaces generated from interpolating between objects [7]. An analytical method for finding the normal line to these interpolated surfaces is described. The expression is closely related to the concept of surface principal curvature from differential geometry and provides a novel way of describing the curvature of evolving surfaces.

In this work, the behaviour of bovine serum albumin (BSA) interacting with zinc oxide (ZnO) particles functionalized with 3-mercaptopropionic acid (3-MPA) and without any coating has been investigated. Two kinds of ZnO particles of different size and morphology were obtained: microwires (MW) and nanoparticles (NP). The effect of surface modification on the fluorescence properties of ZnO was studied. Typical ZnO green emission due to defects was not observed in the functionalized NP spectrum. Structure alterations of the protein interacting with ZnO particles were evaluated by fluorescence spectroscopy and circular dichroism (CD). Though BSA structure was not significantly perturbed in any case, some conformational changes were observed for BSA interacting with not functionalized MW. Fil: Simonelli, Gabriela. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Tucumán. Facultad de Ciencias Exactas y Tecnología. Departamento de Física. Laboratorio de Física del Sólido; Argentina Fil: Arancibia, Eleuterio Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán. Instituto de Química del Noroeste. Universidad Nacional de Tucumán. Facultad de Bioquímica, Química y Farmacia. Instituto de Química del Noroeste; Argentina. Universidad Nacional de Tucumán. Facultad de Ciencias Exactas y Tecnología. Departamento de Ingeniería en Procesos y Gestión Industrial; Argentina

Highlight Isolation and characterization of a novel Arabidopsis mutant is reported. This has a cup-shaped leaf surface, as opposed to the flat leaves of wild-type plants., The leaf surface usually stays flat, maintained by coordinated growth. Growth perturbation can introduce overall surface curvature, which can be negative, giving a saddle-shaped leaf, or positive, giving a cup-like leaf. Little is known about the molecular mechanisms that underlie leaf flatness, primarily because only a few mutants with altered surface curvature have been isolated and studied. Characterization of mutants of the CINCINNATA-like TCP genes in Antirrhinum and Arabidopsis have revealed that their products help maintain flatness by balancing the pattern of cell proliferation and surface expansion between the margin and the central zone during leaf morphogenesis. On the other hand, deletion of two homologous PEAPOD genes causes cup-shaped leaves in Arabidopsis due to excess division of dispersed meristemoid cells. Here, we report the isolation and characterization of an Arabidopsis mutant, tarani (tni), with enlarged, cup-shaped leaves. Morphometric analyses showed that the positive curvature of the tni leaf is linked to excess growth at the centre compared to the margin. By monitoring the dynamic pattern of CYCLIN D3;2 expression, we show that the shape of the primary arrest front is strongly convex in growing tni leaves, leading to excess mitotic expansion synchronized with excess cell proliferation at the centre. Reduction of cell proliferation and of endogenous gibberellic acid levels rescued the tni phenotype. Genetic interactions demonstrated that TNI maintains leaf flatness independent of TCPs and PEAPODs.

Matrix nanotopography plays an important role in regulating cell behaviors by providing spatial as well as mechanical cues for cells to sense. It has been proposed that nanoscale topography is possible to modulate the tensions which direct the formation of cytoskeleton and the organization of the membrane receptor within the cell, which in turn regulate intracellular mechanical and biochemical signaling. With current studies on this topic being performed mainly in 2D platforms, the question on how nanotopography can influence cell bahaviors in 3D environments has yet to be addressed. In this paper, we explored this question by placing cells in 3D hollow spherical polydimethylsiloxane scaffolds. After culturing rat embryonic fibroblast cells in two kinds of scaffold, one with smooth surface and the other with numerous nano-spikes, we observed that cells in the smooth scaffold have more anchoring sites and more focal adhesions than in the etched scaffold. Moreover, we found the presence of correlation between cortical actin, the important component for supporting cell attachment, and local cell geometry. MOE (Min. of Education, S’pore)

Vascular morphology characterization is useful for disease diagnosis, risk stratification, treatment planning, and prediction of treatment durability. To quantify the dynamic surface geometry of tubular-shaped anatomic structures, we propose a simple, rigorous Lagrangian cylindrical coordinate system to monitor well-defined surface points. Specifically, the proposed system enables quantification of surface curvature and cross-sectional eccentricity. Using idealized software phantom examples, we validate the method's ability to accurately quantify longitudinal and circumferential surface curvature, as well as eccentricity and orientation of eccentricity. We then apply the method to several medical imaging data sets of human vascular structures to exemplify the utility of this coordinate system for analyzing morphology and dynamic geometric changes in blood vessels throughout the body. Graphical abstract Pointwise longitudinal curvature of a thoracic aortic endograft surface for systole and diastole, with their absolute difference.

This paper presents a novel method for surface curvature estimation. By using the k-nearest neighbors algorithm, an 8 neighbors ring is selected from point cloud for each point. Surface normal vector is estimated by neighbors coordinates. Local surfaces are classified using the point of interest and its 8 neighbors ring coordinates. In this paper surface curvature is calculated based on normal vector and neighbors ring coordinate. Surface curvature calculated using the novel method is called umbrella curvature. To evaluate how this method performs, the curvature of a sample surface was estimated by the umbrella curvature and surface variance method. The results show that the umbrella curvature performs well and is superior in terms of accuracy. However the method in computation is more expensive than variance method.

Although much is known about the embryo during implantation, the architecture of the uterine environment in which the early embryo develops is not well understood. We employed confocal imaging in combination with 3D analysis to identify and quantify dynamic changes to the luminal structure of murine uterus in preparation for implantation. When applied to mouse mutants with known implantation defects, this method detected striking peri-implantation abnormalities in uterine morphology that cannot be visualized by histology. We revealed 3D organization of uterine glands and found that they undergo a stereotypical reorientation concurrent with implantation. Furthermore, we extended this technique to generate a 3D rendering of the cycling human endometrium. Analyzing the uterine and embryo structure in 3D for different genetic mutants and pathological conditions will help uncover novel molecular pathways and global structural changes contributing to successful implantation of an embryo.

Local solid shape applies to the surface curvature of small surface patches—essentially regions of approximately constant curvatures—of volumetric objects that are smooth volumetric regions in Euclidean 3-space. This should be distinguished from local shape in pictorial space. The difference is categorical. Although local solid shape has naturally been explored in haptics, results in vision are not forthcoming. We describe a simple experiment in which observers judge shape quality and magnitude of cinematographic presentations. Without prior training, observers readily use continuous shape index and Casorati curvature scales with reasonable resolution. ispartof: i-Perception vol:6 issue:5 pages:1-17 ispartof: location:United States status: published

Unsteady mixed convection flow over a rotating vertical slender cylinder under the combined effects of buoyancy force and thermal diffusion with injection/suction has been studied where the slender cylinder is inline with the flow. The effect of surface curvature is also taken into account, especially for the applications such as wire and fiber drawing, where accurate predictions are desired. The governing boundary layer equations along with the boundary conditions are first converted into dimensionless form by a non-similar transformation, and then resulting system of coupled nonlinear partial differential equations is solved by an implicit finite difference scheme in combination with the quasi-linearization technique. The effects of various parameters on velocity and temperature profiles and on skin friction coefficients and heat transfer rate at the wall are reported in the present study. � 2007 Elsevier Ltd. All rights reserved.

The time-independent nonhomogeneous diffusion equation is solved for the equilibrium distribution of wound-induced growth factor over a hemispherical surface. The growth factor is produced at the inner edge of a circular wound and stimulates healing in regions where the concentration exceeds a certain threshold value. An implicit analytic criterion is derived for complete healing of the wound.

Gewebsbildung ist ein wichtiger Prozess für die Entstehung und Aufrechterhaltung unserer Organe. Die verschiedenen Gewebe unseres Körpers werden kontinuierlich von Zellen aufgebaut, umgebaut und repariert, beispielsweise während Morphogenese, Wundheilung oder Knochenumbau. Obwohl diese biologischen Prozesse genetisch codiert sind, spielen auch die biochemische Zusammensetzung und die physikalischen Eigenschaften der Umgebung eine wichtige Rolle bei der Gewebebildung und ermöglichen den Zellen, ihre Aktivität den externen Anforderungen anzupassen. Beispielsweise werden Muskel- und Knochenaufbau durch sportliche Aktivitäten verstärkt. Andererseits können Fehler im Gleichgewicht des Knochenumbaus die mechanische Funktion des Organs beschädigen, etwa bei Osteoporose. Indem wir verstehen, wie Gewebewachstum gesteuert wird, können wir viele biologische Prozesse und damit verbundene Krankheiten besser erklären.Trotz des kontinuierlichen Umbaus bleiben die geometrischen Eigenschaften von Organen wie etwa Knochen grundsätzlich erhalten. Geometrie wurde deswegen als ein mögliches Signal für die Kontrolle der Gewebsbildung vorgeschlagen. Es wurde bereits gezeigt, dass dieser physikalische Parameter biologischen Mechanismen auf subzellulärer, zellulärer und mehrzelliger Ebene beeinflussen kann. Über die Rolle von Geometrie auf der Gewebeskala ist jedoch bis jetzt nur ein wenig bekannt. Diese Arbeit zielt daher darauf ab zu verstehen, wie die Geometrie eines Substrats die Bildung und Organisation von Knochengewebe beeinflusst.Osteoblasten wurden kultiviert, um Knochengewebe im dreidimensionalen Gerüsten aus Hydroxyapatit in-vitro wachsen zu lassen. Parallel dazu wurde die Hypothese „die Geometrie einer Oberfläche beeinflusst die lokale Gewebsbildung“ in ein Rechenmodell für krümmungsabhängiges Wachstum umgesetzt. Ein Vergleich der experimentellen und simulierten Wachstumsmuster zeigt nicht nur die Relevanz des geometrischen Modells für die quantitative Beschreibung des Gewebewachstums auf komplexen Oberflächen, sondern auch, dass durch Optimierung der Geometrie des Substrats eine schnellere Gewebebildung erzielt werden kann.Außerdem wurde mathematisch bewiesen, dass ein einfaches Anlagern linearer dehnbarer Elemente, die für längliche kontraktile Zellen stehen - das sogenannte Sehnenmodell - äquivalent zu krümmungsabhängigem Wachstum ist. Eine qualitative Analyse der Zellorganisation im Gewebe unterstützt die biologische Relevanz dieses geometrischen Modells. Eine Ausweitung der strukturellen Untersuchungen auf die extrazelluläre Matrix hat zusätzliche Erkenntnisse zu den Mechanismen geliefert, die an der Gewebestrukturierung und -organisation beteiligt sind. Beispielsweise wurde gezeigt, dass die mechanische Spannung, die durch die Zellen aufgebaut wird, essentiell für die Organisation der Fibronektin und Kollagenfasern und ganz allgemein für die mechanische Stabilität des Gewebes ist.Schließlich wurde ein Computermodell des Wachstums in Abhängigkeit von der mittleren Krümmung der dreidimensionalen Oberfläche vorgeschlagen, um das aktuelle experimentelle System besser zu beschreiben und um zukünftige Untersuchungen über den Einfluss der dritten Dimension zu motivieren.Ein besseres Verständnis, wie Geometrie an der Gewebsbildung beteiligt ist, ist nicht nur interessant für die biomedizinische Forschung, sondern ist auch eine wichtige Inspirationsquelle für Tissue Engineering., Tissue formation is a key process for the genesis and the maintenance of our organs. As in morphogenesis, wound healing and bone remodelling, the various tissues of our body are continuously modelled, remodelled and repaired by the cells. Even if these biological processes are encoded in genetics, the biochemical composition and the physical cues of the surroundings also play a major role in tissue formation and enable cells to adapt their activity in response to external stimuli. For example, muscle and bone formation is enhanced in individuals practicing physical activities. On the other hand, a failure in the balance of bone remodelling can impair the mechanical function of the organ like in osteoporosis. Understanding how tissue formation is controlled is thus determining to clarify many biological processes and their associated pathologies. The geometrical features of organs like bones are generally conserved despite a continuous remodelling. As geometry also sets the boundary conditions for the mechanical environment that cells respond to, geometry has been proposed as a potential cue controlling tissue formation. This physical parameter has been shown to influence biological mechanisms at the sub-cellular, cellular and multi-cellular levels, but only a little is known about the tissue scale. This thesis aims therefore at understanding how the geometry of a substrate influences the deposition and organisation of tissue. Osteoblasts were cultured to grow bone tissue in three-dimensional hydroxyapatite scaffolds in-vitro. In parallel, the hypothesis that geometry locally influences tissue deposition on a surface was implemented into a computational model of curvature-driven growth. Comparing the experimental and simulated growth patterns not only confirmed the relevance of the geometrical model to describe quantitatively tissue growth on complex surfaces, but also proved that faster tissue formation can be obtained by optimising the geometry of the substrate. Moreover, a simple construction assembling tensile elements that represent elongated contractile cells – the chord model – was demonstrated to be equivalent to the curvature-driven growth simulation. A qualitative analysis of cells organisation in the tissue supported the biological relevance of this geometrical model. Extending the structural investigations to the extracellular matrix further clarified the mechanisms involved in tissue patterning and organisation. For example, the tension built by the cells was shown to be essential for organising the fibronectin and collagens fibres and more generally for the mechanical stability of the tissue. Finally, a computational model of growth driven by the mean curvature of the three-dimensional surface was proposed to better describe the current experimental system and inspire future investigations to evaluate the effects of the third dimension. Understanding how geometry is involved in tissue formation will not only benefit to biomedical research but will also profit to tissue engineering., La formation de tissu est un processus clé de la genèse et la maintenance de nos organes. Pendant la morphogenèse, la cicatrisation et le remodelage osseux, les divers tissus de notre organisme sont continuellement modelés, remodelés et réparés par les cellules. Bien que ces processus biologiques soient encodés génétiquement, la composition biochimique et les propriétés physiques des milieux jouent aussi un rôle important dans la formation de tissu et permettent aux cellules d’adapter leur activité en réponse aux stimulations extérieures. Par exemple, la formation de muscle et d’os est accrue chez les personnes pratiquant une activité physique. D’autre part, un déséquilibre du remodelageosseux peut affecter la fonction mécanique de l’os, c’est le cas dans l’ostéoporose.Les caractéristiques géométriques d’organes comme l’os sont généralement conservées malgré un remodelage continuel. Comme la géométrie impose également les conditions aux limites de l’environnement mécanique auquel répondent les cellules, la géométrie a été proposée comme étant potentiellement impliquée dans le contrôle de la formation du tissu. Il a été montré que ce paramètre physique influence des mécanismes biologiques aux échelles subcellulaire, cellulaire et multicellulaire, mais très peu est connu à l’échelle tissulaire. Cette thèse a donc pour but de comprendre comment la géométrie d’un substrat influence la déposition et l’organisation des tissus.Des ostéoblastes ont été cultivés in-vitro pour produire du tissu osseux dans des structures tridimensionnelles en hydroxyapatite. L’hypothèse proposant que la géométrie influence localement la formation de tissu sur une surface a été transcrite dans un modèle numérique de croissance contrôlée par la courbure. La comparaison des motifs de croissance expérimentaux et simulés a non seulement confirmé la pertinence du modèle géométrique pour décrire la croissance du tissu de manière quantitative sur des surfaces complexes, mais a aussi montré qu’une croissance plus rapide du tissu peut être obtenue en optimisant la géométrie du substrat.Il a également été montré qu’un « modèle des cordes » consistant à assembler des éléments sous tension qui représentent les cellules contractiles, est équivalent à la simulation de croissance contrôlée par la courbure. Une analyse qualitative de l’organisation des cellules dans le tissu a conforté la pertinence de ce modèle géométrique. Etendre les études structurelles à la matrice extracellulaire a permis de clarifier les mécanismes impliqués dans l’organisation du tissu. Par exemple, la tension générée par les cellules s’est montrée indispensable à l’organisation des fibres de fibronectine et de collagènes, et de manière générale à la stabilité mécanique du tissu.Enfin, un modèle de croissance contrôlée par la courbure moyenne d’une surface en trois dimensions a été proposé pour décrire le système expérimental et inspirer de nouvelles études pour évaluer les effets de la troisième dimension.Comprendre comment la géométrie est impliquée dans la formation du tissu profitera à la fois à la recherche biomédicale et à l’ingénierie tissulaire.

We report on the ability of human observers to discriminate local second-order shape of quadratic stereo-defined surfaces. Local second-order shape can be specified by two parameters: the curvedness (a scale-dependent quantity describing overall curvature of a shape) and the shape index (a scale-independent quantity describing the shape's appearance). We measured shape index discrimination thresholds of shapes subject to attitude and curvedness transformations. Results show that neither slant nor curvedness manipulations affect or bias observers' judgements of surface shape. Furthermore, ideal detector simulations show that observers do not perform optimally: they do not exploit all available information.