Smooth Interpolation of Curve Networks with Surface Normals

International audienceRecent surface acquisition technologies based on microsensors produce three-space tangential curve data which can be transformed into a network of space curves with surface normals. This paper addresses the problem of surfacing an arbitrary closed 3D curve network with given surface normals.Thanks to the normal vector input, the patch finding problem can be solved unambiguously and an initial piecewise smooth triangle mesh is computed. The input normals are propagated throughout the mesh and used to compute mean curvature vectors. We then introduce a new variational optimization method in which the standard bi-Laplacian is penalized by a term based on the mean curvature vectors. The intuition behind this original approach is to guide the standard Laplacian-based variational methods by the curvature information extracted from the input normals. The normal input increases shape fidelity and allows to achieve globally smooth and visually pleasing shapes

Shape reconstruction of meshed smooth surfaces equipped with inertial sensors

Cette thèse porte sur le développement de méthodes pour la reconstruction de formes 3D à l’aide de capteurs inertiels et magnétiques. Lorsqu’ils sont placés sur une forme, ces capteurs fournissent des orientations locales de surface mais leur position absolue dans l’espace 3D est inconnue. Les dispositifs que nous considérons dans cette thèse produisent des orientations locales de surface le long d’un réseau de courbes. Reconstruire des formes 3D à l’aide de telles données pose trois types de défis. Tout d’abord, les mesures des capteurs sont bruitées et incohérentes. Deuxièmement, comme les positions sont inconnues, le réseau de courbes acquis doit être reconstruit à partir des orientations. Enfin, une fois le réseau de courbes reconstruit, il est nécessaire de calculer une surface lisse interpolant ce réseau de courbes et les orientations associées. Pour relever ces défis, on formule les différentes étapes de reconstruction comme un ensemble de problèmes d’optimisation. En utilisant des représentations discrètes, ces problèmes sont résolus efficacement et interactivement.Nous présentons deux contributions principales. Tout d’abord, nous introduisons une méthode produisant un réseau de courbes lisses et cohérentes en utilisant les mesures d’orientation et de distance, ainsi qu'un ensemble de contraintes topologiques fournies par l’utilisateur. Notre méthode se base notamment sur une procédure de lissage des orientations motivée par un principe simple: les positions et les normales des courbes doivent coïncider en chaque intersection d'un réseau.Une fois le réseau de courbes reconstruit, nous proposons une méthode permettant de calculer une surface lisse interpolant ce réseau de courbes, ainsi que les orientations associées. Cette méthode a trois étapes. Tout d’abord grâce aux orientations, les cycles de courbes entourant les patchs surfaciques sont déterminés sans ambiguïté. Ensuite les orientations connues le long des courbes sont propagées à travers le maillage initial et utilisées pour estimer la courbure moyenne. Enfin le maillage final est calculé par une méthode basée sur le Laplacien et utilisant l’information de courbure. Les orientations connues sur le réseau de courbes permettent d’obtenir des maillages lisses et de diminuer les erreurs de reconstruction.Les approches précédentes utilisaient des dispositifs statiques placés le long d’un réseau de connectivité fixe entre les capteurs (ruban, grille). Nous explorons dans cette thèse une nouvelle configuration dynamique, consistant à déplacer un dispositif ponctuel sur la surface. En conséquence, il est possible d’acquérir des données le long d’un réseau arbitraire de courbes lisses sur une surface. Les méthodes proposées dans cette thèse ont été testées sur des données réelles acquises avec ces dispositifs mobiles. Des surfaces physiques fabriquées à partir de modèles numériques nous ont permis de faire une évaluation quantitative en calculant l’erreur de reconstruction entre la vraie surface et notre modèle reconstruit. Même pour des formes complexes, l’erreur moyenne reste autour de 1%.This thesis presents a complete framework for 3D shape reconstruction using inertial and magnetic sensors. When placed onto a shape, these sensors provide local surface orientations along a curve network on the shape, but their absolute position in the world space is unknown. The challenges with this type of 3D acquisition are threefold. First, sensor measurements are noisy and inconsistent. Second, since positions are unknown, the acquired curve network has to be reconstructed from orientations. Finally, the smooth surface needs to be inferred from a collection of curves with normals. To compute the shape from measured data, our main insight is to formulate the reconstruction as a set of optimization problems. Using discrete representations, these optimization problems are resolved efficiently and at interactive time rates.We present two main contributions. First, we introduce a novel method for creating well-connected networks with cell-complex topology using only orientation and distance measurements and a set of user-defined constraints. By working directly with orientations, our method robustly resolves problems arising from data inconsistency and sensor noise. Our approach is driven by a simple principle mostly overlooked in previous works: at each intersection in a curve network, the positions and the normals of two intersecting curves have to coincide.Second, we address the problem of surfacing a closed 3D curve network with given surface normals. Thanks to the normal vector input, the patch-finding problem can be solved unambiguously and an initial piecewise smooth triangle mesh is computed. The input normals are propagated throughout the mesh. Together with the initial mesh, the propagated normals are used to estimate mean curvature vectors. We then compute the final mesh by combining the standard Laplacian-based variational methods with the curvature information extracted from the input normals. The normal input increases shape fidelity and allows to achieve globally smooth and visually pleasing shapes.Previous approaches used static devices placed along a network with fixed connectivity between the sensors (ribbon, grid). We explore a new dynamic setup, which used a single mobile node of sensors. As a consequence, a dense set of data can be acquired along an arbitrary smooth curve network on a surface.The proposed framework was tested on real-world data acquired using two devices equipped with mobile sensors. A quantitative evaluation was performed by computing the error of reconstruction for fabricated surfaces with known ground truth. Even for complex shapes, the mean error remains around 1%

Reconstruction de surfaces lisses maillées à partir de capteurs inertiels

This thesis presents a complete framework for 3D shape reconstruction using inertial and magnetic sensors. When placed onto a shape, these sensors provide local surface orientations along a curve network on the shape, but their absolute position in the world space is unknown. The challenges with this type of 3D acquisition are threefold. First, sensor measurements are noisy and inconsistent. Second, since positions are unknown, the acquired curve network has to be reconstructed from orientations. Finally, the smooth surface needs to be inferred from a collection of curves with normals. To compute the shape from measured data, our main insight is to formulate the reconstruction as a set of optimization problems. Using discrete representations, these optimization problems are resolved efficiently and at interactive time rates.We present two main contributions. First, we introduce a novel method for creating well-connected networks with cell-complex topology using only orientation and distance measurements and a set of user-defined constraints. By working directly with orientations, our method robustly resolves problems arising from data inconsistency and sensor noise. Our approach is driven by a simple principle mostly overlooked in previous works: at each intersection in a curve network, the positions and the normals of two intersecting curves have to coincide.Second, we address the problem of surfacing a closed 3D curve network with given surface normals. Thanks to the normal vector input, the patch-finding problem can be solved unambiguously and an initial piecewise smooth triangle mesh is computed. The input normals are propagated throughout the mesh. Together with the initial mesh, the propagated normals are used to estimate mean curvature vectors. We then compute the final mesh by combining the standard Laplacian-based variational methods with the curvature information extracted from the input normals. The normal input increases shape fidelity and allows to achieve globally smooth and visually pleasing shapes.Previous approaches used static devices placed along a network with fixed connectivity between the sensors (ribbon, grid). We explore a new dynamic setup, which used a single mobile node of sensors. As a consequence, a dense set of data can be acquired along an arbitrary smooth curve network on a surface.The proposed framework was tested on real-world data acquired using two devices equipped with mobile sensors. A quantitative evaluation was performed by computing the error of reconstruction for fabricated surfaces with known ground truth. Even for complex shapes, the mean error remains around 1%.Cette thèse porte sur le développement de méthodes pour la reconstruction de formes 3D à l’aide de capteurs inertiels et magnétiques. Lorsqu’ils sont placés sur une forme, ces capteurs fournissent des orientations locales de surface mais leur position absolue dans l’espace 3D est inconnue. Les dispositifs que nous considérons dans cette thèse produisent des orientations locales de surface le long d’un réseau de courbes. Reconstruire des formes 3D à l’aide de telles données pose trois types de défis. Tout d’abord, les mesures des capteurs sont bruitées et incohérentes. Deuxièmement, comme les positions sont inconnues, le réseau de courbes acquis doit être reconstruit à partir des orientations. Enfin, une fois le réseau de courbes reconstruit, il est nécessaire de calculer une surface lisse interpolant ce réseau de courbes et les orientations associées. Pour relever ces défis, on formule les différentes étapes de reconstruction comme un ensemble de problèmes d’optimisation. En utilisant des représentations discrètes, ces problèmes sont résolus efficacement et interactivement.Nous présentons deux contributions principales. Tout d’abord, nous introduisons une méthode produisant un réseau de courbes lisses et cohérentes en utilisant les mesures d’orientation et de distance, ainsi qu'un ensemble de contraintes topologiques fournies par l’utilisateur. Notre méthode se base notamment sur une procédure de lissage des orientations motivée par un principe simple: les positions et les normales des courbes doivent coïncider en chaque intersection d'un réseau.Une fois le réseau de courbes reconstruit, nous proposons une méthode permettant de calculer une surface lisse interpolant ce réseau de courbes, ainsi que les orientations associées. Cette méthode a trois étapes. Tout d’abord grâce aux orientations, les cycles de courbes entourant les patchs surfaciques sont déterminés sans ambiguïté. Ensuite les orientations connues le long des courbes sont propagées à travers le maillage initial et utilisées pour estimer la courbure moyenne. Enfin le maillage final est calculé par une méthode basée sur le Laplacien et utilisant l’information de courbure. Les orientations connues sur le réseau de courbes permettent d’obtenir des maillages lisses et de diminuer les erreurs de reconstruction.Les approches précédentes utilisaient des dispositifs statiques placés le long d’un réseau de connectivité fixe entre les capteurs (ruban, grille). Nous explorons dans cette thèse une nouvelle configuration dynamique, consistant à déplacer un dispositif ponctuel sur la surface. En conséquence, il est possible d’acquérir des données le long d’un réseau arbitraire de courbes lisses sur une surface. Les méthodes proposées dans cette thèse ont été testées sur des données réelles acquises avec ces dispositifs mobiles. Des surfaces physiques fabriquées à partir de modèles numériques nous ont permis de faire une évaluation quantitative en calculant l’erreur de reconstruction entre la vraie surface et notre modèle reconstruit. Même pour des formes complexes, l’erreur moyenne reste autour de 1%

Academic roots of chemical engineering in XVIII and XIX century in middle Europe

Roots of chemical engineering in Middle Europe lead to the first mining and metallurgy academies, established in VIII century in Upper Hungaria and in Bohemian Kingdom. Chemical engineering skills originate from ancient Egyptian handicraft, alchemy, technical chemistry, pneumochemistry and phlogiston chemistry. Development of mining and metallurgy coincided with great scientific discoveries and industrial revolution. In Middle Europe, the first such academies were opened in St. Joachimstahl and in Schemnitz, and the first Serbian mining engineers Djordje Branković, Vasilije Božić and Stevan Pavlović studied, as well as the first chemistry professor of the High School in Belgrade, Mihajlo Rašković. Eminent professors were employed by the Schemnitz academy, such as: Nicol Jacquin, Giovanni Scopoli, Ignaz von Born and Christian Doppler. It is important to emphasize that Shemnitz practiced the first modern, practical laboratory education. In VIII century, Schemnitz Mining and metallurgy academy was the most contemporary educational insistution for engineers. However, in XIX century, mining and metallurgy academies stagnated, due to the replacement of professional academies with polytechnic schools, technical universities and scientific research institutes

Integer-Grid Sketch Simplification and Vectorization

Abstract A major challenge in line drawing vectorization is segmenting the input bitmap into separate curves. This segmentation is especially problematic for rough sketches, where curves are depicted using multiple overdrawn strokes. Inspired by feature-aligned mesh quadrangulation methods in geometry processing, we propose to extract vector curve networks by parametrizing the image with local drawing-aligned integer grids. The regular structure of the grid facilitates the extraction of clean line junctions; due to the grid's discrete nature, nearby strokes are implicitly grouped together. We demonstrate that our method successfully vectorizes both clean and rough line drawings, whereas previous methods focused on only one of those drawing types

Laboratory determination of sorption isotherms and simulation of copper transport using HYDRUS 1D model

Vertikalna raspodjela elemenata u tragovima u tlu na zagrebačkom području opsežno je istraživana u okviru više projekata (ROMIĆ & ROMIĆ, 2003 ; ROMIĆ et al., 2007) kako bi se pokušala definirati njihova mobilnost kroz tlo u podzemnu vodu. Rezultati navedenih istraživanja pokazala su da koncentracije olova, cinka, kroma i bakra variraju s dubinom. Većina istraživanja kakvoće podzemne vode u okviru zagrebačkog vodonosnog sustava, obuhvaćalo je istraživanje utjecaja odlagališta Jakuševec na podzemne vode (NAKIĆ et al., 2007) te istraživanja na području budućeg crpilišta Črnkovec i Kosnica (NAKIĆ, 2003). Na području Jakuševca, NAKIĆ et al. (2007) su utvrdili da visoke koncentracije elemenata u tragovima pokazuju da se u reduktivnim uvjetima aluvija metali snažno otpuštaju. DAS et al. (2013) napravili su sorpcijski eksperiment kako bi uz pomoć aluvijalnog tla rijeke Bhagirathi uklonili bakar iz otopine. Zaključili su kako se najveća sorpcija bakra odvija pri uvjetima pH od 2 do 6. Za modeliranje transporta onečišćivala u nesaturiranoj zoni bitni su procesi sorpcije (adsorpcija, apsorpcija i ionska zamjena). U svrhu određivanja sorpcije elemenata u tragovima u ovom slučaju bakra napravljen je eksperiment na uzorcima tla u laboratoriju. Ovim eksperimentom dobili su se linearni Freundlich-ovi sorpcijski koeficijenti distribucije (Kd). Najveći Freundlich-ov koeficijent distribucije određen je u prvom horizontu što je u podudarnosti sa sorpcijom bakra. Efekt sorpcije potencijalno toksičnih elemenata pod utjecajem je kapaciteta kationske zamjene (CEC), pH tla, redoks potencijala, sadržaja glinovite komponente, tipa minerala glina, sadržaja organske tvari, željezno manganskih oksihidroksida i karbonata (BRADL, 2004). IRHA et al. (2009) su izvršili eksperiment sorpcijskog kapaciteta određenih elemenata (Cd, Pb, Cu, Cr) na pet vrsta Estonskih tla. Njihovi rezultati pokazuju dobru korelaciju s linearnim Freundlich-ovim izotermama. Iz sorpcijskog eksperimenta može se zaključiti da bakar u aluvijalnom tlu na lokaciji Kosnica ima linearan trend rasta s povećanjem koncentracije. Od svih šest horizonata najbrže rastući trend ima najplići horizont, koji je ujedno i najmanje gustoće te prahovito-ilovaste teksture. Postepeno svaki dublji horizont ima sve blaži trend rasta. Zadnji horizont pokazuje veći trend zbog toga što je ilovasto-pjeskovite teksture dok su ostali horizonti prahovito-ilovasti, pa je sorpcija veća u horizontu s manjim zrnima. S određenim parametrima transporta onečišćivala napravljen je prognozni model korištenjem HYDRUS 1D softvera. Prognozni numerički model transporta bakra u tlu na istraživanom području simuliran je za 2005. godinu. S obzirom na pretpostavljene početne koncentracije elemenata (1 mg/cm3) na vrhu profila, na dnu profila modelom se dobila koncentracija od oko 0, 01 mg/cm3 kroz godinu dana. Propisana granična vrijednost prema Pravilniku o parametrima sukladnosti i metodama analize vode za ljudsku potrošnju (NN125/13) za bakar iznosi 2 mg/l, odnosno 0, 002 mg/cm3. Ukoliko se usporedi dobivena koncentracija bakra prognoznim modelom transporta na dnu profila tla, odnosno na granici s otvorenim vodonosnikom, sa MDK granicom iz pravilnika onda se može zaključiti da postoji velika opasnost od onečišćenja bakrom na istraživanoj lokaciji. Kod interpretacije rezultata modela transporta bakra kroz nesaturiranu zonu potrebno je imati na umu pretpostavke koje su definirane da bi se mogli ostvariti postavljeni ciljevi prognoznog numeričkog modela. Temeljem rezultata sorpcijskog eksperimenta u laboratoriju utvrđene su linearne sorpcijske izoterme sa izuzetno dobrim faktorima korelacije preko 0, 99 za svaki horizont. S obzirom na dobivene rezultate iz prognoznog modela transporta bakra sa površine profila, može se zaključiti da će se oko 1% od početne koncentracije bakra transportirati do podzemne vode. Uspoređujući MDK granice pravilnika za bakar s dobivenim podacima, može se zaključiti da postoji velika opasnost od onečišćenja podzemne vode na istraživanoj lokaciji. U slučaju potencijalnih akcidentnih situacija izlijevanja otopine bakra koncentracije 1000 mg/l, rizik onečišćenja vodonosnika je visok. Laboratorijska istraživanja unutar ovog rada obuhvatila su samo absorpcijski dio sorpcijskog eksperimenta. U nekim budućim istraživanjima trebalo bi napraviti i desorpciju, te usporediti sa ovim dobivenim rezultatima

Shape from sensors: Curve networks on surfaces from 3D orientations

International audienceWe present a novel framework for acquisition and reconstruction of 3D curves using orientations provided by inertial sensors. While the idea of sensor shape reconstruction is not new, we present the first method for creating well-connected networks with cell complex topology using only orientation and distance measurements and a set of user- defined constraints. By working directly with orientations, our method robustly resolves problems arising from data inconsistency and sensor noise. Although originally designed for reconstruction of physical shapes, the framework can be used for “sketching” new shapes directly in 3D space. We test the performance of the method using two types of acquisition devices: a standard smartphone, and a custom-made device

Surfacing Curve Networks with Normal Control

International audienceRecent surface acquisition technologies based on microsensors produce three-space tangential curve data which can be transformed into a network of space curves with surface normals. This paper addresses the problem of surfacing an arbitrary closed 3D curve network with given surface normals. Thanks to the normal vector input, the patch finding problem can be solved unambiguously and an initial piecewise smooth triangle mesh is computed. The input normals are propagated throughout the mesh. Together with the initial mesh, the propagated normals are used to compute mean curvature vectors. We then compute the final mesh as the solution of a new variational optimization method based on the mean curvature vectors. The intuition behind this original approach is to guide the standard Laplacian-based variational methods by the curvature information extracted from the input normals. The normal input increases shape fidelity and allows to achieve globally smooth and visually pleasing shapes

Morphorider: a new way for Structural Monitoring via the shape acquisition with a mobile device equipped with an inertial node of sensors

International audienceWe introduce a new kind of monitoring device, allowing the shape acquisition of a structure via a single mobile node of inertial sensors and an odometer. Previous approaches used devices placed along a network with fixed connectivity between the sensor nodes (lines, grid). When placed onto a shape, this sensor network provides local surface orientations along a curve network on the shape, but its absolute position in the world space is unknown. The new mobile device provides a novel way of structures monitoring: the shape can be scanned regularly, and following the shape or some specific parameters along time may afford the detection of early signs of failure. Here, we present a complete framework for 3D shape reconstruction. To compute the shape, our main insight is to formulate the reconstruction as a set of optimization problems. Using discrete representations, these optimization problems are resolved efficiently and at interactive time rates. We present two main contributions. First, we introduce a novel method for creating well-connected networks with cell-complex topology using only orientation and distance measurements and a set of user-defined constraints. Second, we address the problem of surfacing a closed 3D curve network with given surface normals. The normal input increases shape fidelity and allows to achieve globally smooth and visually pleasing shapes. The proposed framework was tested on experimental data sets acquired using our device. A quantitative evaluation was performed by computing the error of reconstruction for our own designed surfaces, thus with known ground truth. Even for complex shapes, the mean error remains around 1%