No presente trabalho, utilizou-se o Método da Fronteira Imersa, o qual utiliza dois tipos de malhas computacionais: euleriana (utilizada para o fluido) e lagrangiana (utilizada para representar a interface de separação de dois fluidos). O software livre GMSH foi utilizado para representar um sólido por meio da sua superfície externa e também para gerar uma malha triangular, bidimensional e não estruturada para discretizar essa superfície. Essa superfície foi utilizada como condição inicial para a malha lagrangiana (fronteira imersa). Os dados da malha lagrangiana são armazenados em uma estrutura de dados chamada Halfedge, a qual é largamente utilizada em Computação Gráfica para armazenar superfícies fechadas e orientáveis. Uma vez que a malha lagrangiana esteja armazenada nesta estrutura de dados, passa-se a estudar uma hipotética interação dinâmica entre a fronteira imersa e o escoamento do fluido. Esta interação é estudada apenas em um sentido, considera-se apenas a condição de não deslizamento, isto é, a fronteira imersa acompanhará passivamente um campo de velocidades pré-estabelecido (imposto), sem exercer qualquer força ou influência sobre ele. Foi utilizado um campo de distância local com sinal (função indicadora de fluidos) para identificar o interior e o exterior da superfície que representa a interface entre os fluidos. Este campo de distância é atualizado a cada passo no tempo utilizando idéias de Geometria Computacional, o que tornou o custo computacional para calcular esse campo otimal independente da complexidade geométrica da interface. Esta metodologia mostrou-se robusta e produz uma definição nítida das distintas fases dos fluidos em todos os passos no tempo. Para acompanhar e visualizar de forma mais precisa o comportamento dos fluidos na vizinhança da superfície que representa a interface de separação dos fluido, foi utilizado um algoritmo chamado de Refinamento Adaptativo de Malhas para fazer um refinamento dinâmico da malha euleriana na vizinhança da malha lagrangiana. / The scientific motivation of the present work is the mathematical modeling and the computational simulation of multiphase flows. Specifically, the equations of a two-phase flow are written by combining the Immersed Boundary Method with a suitable fluid indicator function. It is assumed that the fluid equations are discretized on an Eulerian mesh covering completely the flow domain and that the interface between the fluid phases is discretized by a non-structured Lagrangian mesh formed by triangles. In this context, employing tools commonly found in Computational Geometry, the computation of the fluid indicator function is efficiently performed on a block-structured Eulerian mesh bearing dynamical refinement patches. Formed by a set of triangles, the Lagrangian mesh, which is initally generated employing the free software GMSH, is stored in a Halfedge data structure, a data structure which is widely used in Computer Graphics to represent bounded, orientable closed surfaces. Once the Lagrangian mesh has been generated, next, one deals with the hipothetical situation of dealing with the one-way dynamical interaction between the immersed boundary and the fluid flow, that is, considering the non-slip condition, only the action of the flow on the interface is studied. No forces arising on the interface affects the flow, the interface passively being advect with the flow under a prescribed, imposed velocity field. In particular, the Navier-Stokes equations are not solved. The fluid indicator function is given by a signed distance function in a vicinity of the immersed boundary. It is employed to identify interior/exterior points with respect to the bounded, closed region which is assumed to contain one of the fluid phases in its interior. The signed distance is update every time step employing Computational Geometry methods with optimal cost. Several examples in three dimensions, showing the efficiency and efficacy in the computation of the fluid indicator function, are given which employ the dynamical adaptive properties of the Eurlerian mesh for a moving interface.

No presente trabalho, utilizou-se o Método da Fronteira Imersa, o qual utiliza dois tipos de malhas computacionais: euleriana (utilizada para o fluido) e lagrangiana (utilizada para representar a interface de separação de dois fluidos). O software livre GMSH foi utilizado para representar um sólido por meio da sua superfície externa e também para gerar uma malha triangular, bidimensional e não estruturada para discretizar essa superfície. Essa superfície foi utilizada como condição inicial para a malha lagrangiana (fronteira imersa). Os dados da malha lagrangiana são armazenados em uma estrutura de dados chamada Halfedge, a qual é largamente utilizada em Computação Gráfica para armazenar superfícies fechadas e orientáveis. Uma vez que a malha lagrangiana esteja armazenada nesta estrutura de dados, passa-se a estudar uma hipotética interação dinâmica entre a fronteira imersa e o escoamento do fluido. Esta interação é estudada apenas em um sentido, considera-se apenas a condição de não deslizamento, isto é, a fronteira imersa acompanhará passivamente um campo de velocidades pré-estabelecido (imposto), sem exercer qualquer força ou influência sobre ele. Foi utilizado um campo de distância local com sinal (função indicadora de fluidos) para identificar o interior e o exterior da superfície que representa a interface entre os fluidos. Este campo de distância é atualizado a cada passo no tempo utilizando idéias de Geometria Computacional, o que tornou o custo computacional para calcular esse campo otimal independente da complexidade geométrica da interface. Esta metodologia mostrou-se robusta e produz uma definição nítida das distintas fases dos fluidos em todos os passos no tempo. Para acompanhar e visualizar de forma mais precisa o comportamento dos fluidos na vizinhança da superfície que representa a interface de separação dos fluido, foi utilizado um algoritmo chamado de Refinamento Adaptativo de Malhas para fazer um refinamento dinâmico da malha euleriana na vizinhança da malha lagrangiana. / The scientific motivation of the present work is the mathematical modeling and the computational simulation of multiphase flows. Specifically, the equations of a two-phase flow are written by combining the Immersed Boundary Method with a suitable fluid indicator function. It is assumed that the fluid equations are discretized on an Eulerian mesh covering completely the flow domain and that the interface between the fluid phases is discretized by a non-structured Lagrangian mesh formed by triangles. In this context, employing tools commonly found in Computational Geometry, the computation of the fluid indicator function is efficiently performed on a block-structured Eulerian mesh bearing dynamical refinement patches. Formed by a set of triangles, the Lagrangian mesh, which is initally generated employing the free software GMSH, is stored in a Halfedge data structure, a data structure which is widely used in Computer Graphics to represent bounded, orientable closed surfaces. Once the Lagrangian mesh has been generated, next, one deals with the hipothetical situation of dealing with the one-way dynamical interaction between the immersed boundary and the fluid flow, that is, considering the non-slip condition, only the action of the flow on the interface is studied. No forces arising on the interface affects the flow, the interface passively being advect with the flow under a prescribed, imposed velocity field. In particular, the Navier-Stokes equations are not solved. The fluid indicator function is given by a signed distance function in a vicinity of the immersed boundary. It is employed to identify interior/exterior points with respect to the bounded, closed region which is assumed to contain one of the fluid phases in its interior. The signed distance is update every time step employing Computational Geometry methods with optimal cost. Several examples in three dimensions, showing the efficiency and efficacy in the computation of the fluid indicator function, are given which employ the dynamical adaptive properties of the Eurlerian mesh for a moving interface.

The ability of a robot to navigate itself in the environment is a crucial step towards its autonomy. Navigation as a subtask of the development of autonomous robots is the subject of this thesis, focusing on the development of a method for simultaneous localization an mapping (SLAM) of mobile robots in six degrees of freedom (DOF). As a part of this research, a platform for 3D range data acquisition based on a continuously inclined laser rangefinder was developed. This platform is presented, evaluating the measurements and also presenting the robotic equipment on which the platform can be fitted. The localization and mapping task is equal to the registration of multiple 3D images into a common frame of reference. For this purpose, a method based on the Iterative Closest Point (ICP) algorithm was developed. First, the originally implemented SLAM method is presented, focusing on the time-wise performance and the registration quality issues introduced by the implemented algorithms. In order to accelerate and improve the quality of the time-demanding 6DOF image registration, an extended method was developed. The major extension is the introduction of a factorized registration, extracting 2D representations of vertical objects called leveled maps from the 3D point sets, ensuring these representations are 3DOF invariant. The extracted representations are registered in 3DOF using ICP algorithm, allowing pre-alignment of the 3D data for the subsequent robust 6DOF ICP based registration. The extended method is presented, showing all important modifications to the original method. The developed registration method was evaluated using real 3D data acquired in different indoor environments, examining the benefits of the factorization and other extensions as well as the performance of the original ICP based method. The factorization gives promising results compared to a single phase 6DOF registration in vertically structured environments. Also, the disadvantages of the method are discussed, proposing possible solutions. Finally, the future prospects of the research are presented.

Les avancées technologiques dans le domaine informatique (logiciel et matériel) et, en particulier, de la géolocalisation ont permis la démocratisation des modèles numériques. L'arrivée depuis quelques années de véhicules de cartographie mobile a ouvert l'accès à la numérisation 3D mobile terrestre. L'un des avantages de ces nouvelles méthodes d'imagerie de l'environnement urbain est la capacité potentielle de ces systèmes à améliorer les bases de données existantes 2D comme 3D, en particulier leur niveau de détail et la diversité des objets représentés. Les bases de données géographiques sont constituées d'un ensemble de primitives géométriques (généralement des lignes en 2D et des plans ou des triangles en 3D) d'un niveau de détail grossier mais ont l'avantage d'être disponibles sur de vastes zones géographiques. Elles sont issues de la fusion d'informations diverses (anciennes campagnes réalisées manuellement, conception automatisée ou encore hybride) et peuvent donc présenter des erreurs de fabrication. Les systèmes de numérisation mobiles, eux, peuvent acquérir, entre autres, des nuages de points laser. Ces nuages laser garantissent des données d'un niveau de détail très fin pouvant aller jusqu'à plusieurs points au centimètre carré. Acquérir des nuages de points laser présente toutefois des inconvénients :- une quantité de données importante sur de faibles étendues géographiques posant des problèmes de stockage et de traitements pouvant aller jusqu'à plusieurs Téraoctet lors de campagnes d'acquisition importantes- des difficultés d'acquisition inhérentes au fait d'imager l'environnement depuis le sol. Les systèmes de numérisation mobiles présentent eux aussi des limites : en milieu urbain, le signal GPS nécessaire au bon géoréférencement des données peut être perturbé par les multi-trajets voire même stoppé lors de phénomènes de masquage GPS liés à la réduction de la portion de ciel visible pour capter assez de satellites pour en déduire une position spatiale. Améliorer les bases de données existantes grâce aux données acquises par un véhicule de numérisation mobile nécessite une mise en cohérence des deux ensembles. L'objectif principal de ce manuscrit est donc de mettre en place une chaîne de traitements automatique permettant de recaler bases de données géographiques et nuages de points laser terrestre (provenant de véhicules de cartographies mobiles) de la manière la plus fiable possible. Le recalage peut se réaliser de manière différentes. Dans ce manuscrit, nous avons développé une méthode permettant de recaler des nuages laser sur des bases de données, notamment, par la définition d'un modèle de dérive particulièrement adapté aux dérives non-linéaires de ces données mobiles. Nous avons également développé une méthode capable d'utiliser de l'information sémantique pour recaler des bases de données sur des nuages laser mobiles. Les différentes optimisations effectuées sur notre approche nous permettent de recaler des données rapidement pour une approche post-traitements, ce qui permet d'ouvrir l'approche à la gestion de grands volumes de données (milliards de points laser et milliers de primitives géométriques).Le problème du recalage conjoint a été abordé. Notre chaîne de traitements a été testée sur des données simulées et des données réelles provenant de différentes missions effectuées par l'IGN / Technological advances in computer science (software and hardware) and particularly, GPS localization made digital models accessible to all people. In recent years, mobile mapping systems has enabled large scale mobile 3D scanning. One advantage of this technology for the urban environment is the potential ability to improve existing 2D or 3D database, especially their level of detail and variety of represented objects. Geographic database consist of a set of geometric primitives (generally 2D lines and plans or triangles in 3D) with a coarse level of detail but with the advantage of being available over wide geographical areas. They come from the fusion of various information (old campaigns performed manually, automated or hybrid design) wich may lead to manufacturing errors. The mobile mapping systems can acquire laser point clouds. These point clouds guarantee a fine level of detail up to more than one points per square centimeter. But there are some disavantages :- a large amount of data on small geographic areas that may cause problems for storage and treatment of up to several Terabyte during major acquisition,- the inherent acquisition difficulties to image the environment from the ground. In urban areas, the GPS signal required for proper georeferencing data can be disturbed by multipath or even stopped when GPS masking phenomena related to the reduction of the portion of the visible sky to capture enough satellites to find a good localization. Improve existing databases through these dataset acquired by a mobile mapping system requires alignment of these two sets. The main objective of this manuscript is to establish a pipeline of automatic processes to register these datasets together in the most reliable manner. Co-registration this data can be done in different ways. In this manuscript we have focused our work on the registration of mobile laser point cloud on geographical database by using a drift model suitable for the non rigid drift of these kind of mobile data. We have also developped a method to register geographical database containing semantics on mobile point cloud. The different optimization step performed on our methods allows to register the data fast enough for post-processing pipeline, which allows the management of large volumes of data (billions of laser points and thousands geometric primitives). We have also discussed on the problem of joint deformation. Our methods have been tested on simulated data and real data from different mission performed by IGN

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-06-07T15:41:47Z No. of bitstreams: 1 lucianowalentyxaviercejnog.pdf: 14234810 bytes, checksum: 492ebb7393b5f0e7cfc6e822067fe492 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-06-24T13:12:44Z (GMT) No. of bitstreams: 1 lucianowalentyxaviercejnog.pdf: 14234810 bytes, checksum: 492ebb7393b5f0e7cfc6e822067fe492 (MD5) / Made available in DSpace on 2017-06-24T13:12:44Z (GMT). No. of bitstreams: 1 lucianowalentyxaviercejnog.pdf: 14234810 bytes, checksum: 492ebb7393b5f0e7cfc6e822067fe492 (MD5) Previous issue date: 2015-09-21 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho visa melhorar um método clássico para o problema de registro rígido, o ICP (iterative Closest Point), fazendo com que a busca dos pontos mais próximos, uma de suas fases principais, considere informações aproximadas da geometria local de cada ponto combinadas à distância Euclidiana originalmente usada. Para isso é necessária uma etapa de pré-processamento, na qual a geometria local é estimada em tensores de orientação de segunda ordem. É definido o CTSF, um fator de similaridade entre tensores. O ICP é alterado de modo a considerar uma combinação linear do CTSF com a distância Euclidiana para estabelecer correspondências entre duas nuvens de pontos, variando os pesos relativos entre os dois fatores. Isso proporciona uma capacidade maior de convergência para ângulos maiores em relação ao ICP original, tornando o método comparável aos que constituem o estado da arte da área. Para comprovar o ganho obtido, foram realizados testes exaustivos em malhas com características geométricas variadas, para diferentes níveis de ruído aditivo, outliers e em casos de sobreposição parcial, variando os parâmetros do método de estimativa dos tensores. Foi definida uma nova base com malhas sintéticas para os experimentos, bem como um protocolo estatístico de avaliação quantitativa. Nos resultados, a avaliação foi feita de modo a determinar bons valores de parâmetros para malhas com diferentes características, e de que modo os parâmetros afetam a qualidade do método em situações com ruído aditivo, outliers, e sobreposição parcial. / This work aims to enhance a classic method for the rigid registration problem, the ICP (Iterative Closest Point), modifying one of its main steps, the closest point search, in order to consider approximated information of local geometry combined to the Euclidean distance, originally used. For this, a preprocessing stage is applied, in which the local geometry is estimated in second-order orientation tensors. We define the CTSF, a similarity factor between tensors. Our method uses a linear combination between this factor and the Euclidean distance, in order to establish correspondences, and a strategy of weight variation between both factors. This increases the convergence probability for higher angles with respect to the original ICP, making our method comparable to some of the state-of-art techniques. In order to comprove the enhancement, exhaustive tests were made in point clouds with different geometric features, with variable levels of additive noise and outliers and in partial overlapping situations, varying also the parameters of the tensor estimative method. A dataset of synthetic point clouds was defined for the experiments, as well as a statistic protocol for quantitative evaluation. The results were analyzed in order to highlight good parameter ranges for different point clouds, and how these parameters affect the behavior of the method in situations of additive noise, outliers and partial overlapping.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-06-07T17:49:03Z No. of bitstreams: 1 fernandoakiodearaujoyamada.pdf: 21095203 bytes, checksum: 1842e801a538bdeef0368c963b9d98b7 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-06-24T13:47:22Z (GMT) No. of bitstreams: 1 fernandoakiodearaujoyamada.pdf: 21095203 bytes, checksum: 1842e801a538bdeef0368c963b9d98b7 (MD5) / Made available in DSpace on 2017-06-24T13:47:22Z (GMT). No. of bitstreams: 1 fernandoakiodearaujoyamada.pdf: 21095203 bytes, checksum: 1842e801a538bdeef0368c963b9d98b7 (MD5) Previous issue date: 2016-03-15 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / No problema de registro rígido por pares é preciso encontrar uma transformação rígida que alinha duas nuvens de pontos. A sulução clássica e mais comum é o algoritmo Iterative Closest Point (ICP). No entanto, o ICP e muitas de suas variantes requerem que as nuvens de pontos já estejam grosseiramente alinhadas. Este trabalho apresenta um método denominado Shape-based Weighting Covariance Iterative Closest Point (SWC-ICP), uma melhoria do ICP clássico. A abordagem proposta aumenta a possibilidade de alinhar corretamente duas nuvens de pontos, independente da pose inicial, mesmo quando existe apenas sobreposição parcial entre elas, ou na presença de ruído e outliers. Ela se beneficia da geometria local dos pontos, codificada em tensores de orientação de segunda ordem, para prover um segundo conjunto de correspondências para o ICP. A matriz de covariância cruzada computada a partir deste conjunto é combinada com a matriz de covariância cruzada usual, seguindo uma estratégia heurística. Para comparar o método proposto com algumas abordagens recentes, um protocolo de avaliação detalhado para registro rígido é apresentado. Os resultados mostram que o SWC-ICP está entre os melhores métodos comparados, com performance superior em situações de grande deslocamento angular, mesmo na presença de ruído e outliers. / In the pairwise rigid registration problem we need to find a rigid transformation that aligns two point clouds. The classical and most common solution is the Iterative Closest Point (ICP) algorithm. However, the ICP and many of its variants require that the point clouds are already coarsely aligned. We present in this work a method named Shape-based Weighting Covariance Iterative Closest Point (SWC-ICP), an improvement over the classical ICP. Our approach improves the possibility to correctly align two point clouds, regardless of the initial pose, even when there is only a partial overlapping between them, or in the presence of noise and outliers. It benefits from the local geometry of the points, encoded in second-order orientation tensors, to provide a second correspondences set to the ICP. The cross-covariance matrix computed from this set is combined with the usual cross-covariance matrix following a heuristic strategy. In order to compare our method with some recent approaches, we present a detailed evaluation protocol to rigid registration. Results show that the SWC-ICP is among the best methods compared, with superior performance in situations of wide angular displacement, even in situations of noise and outliers.

The Iterative Closest Point (ICP) algorithm has been an extremely popular method for 3D points or surface registration. Given two point sets, it simultaneously solves for correspondences and estimates the motion between these two point sets. However, by only registering two such views at a time, ICP fails to exploit the redundant information available in multiple views that have overlapping regions. In this thesis, a multiview extension of the ICP algorithm is provided that simultaneously averages the redundant information available in the views with overlapping regions. Variants of this method that carry out such simultaneous registration in a causal manner and that utilize the transitivity property of point correspondences are also provided. The improved accuracy in registration of these motion averaged approaches in comparison with the conventional ICP method is established through extensive experiments. In addition, the motion averaged approaches are compared with the existing multiview techniques of Bergevin et. al. and Benjemaa et. al. The results of the methods applied to the Happy Buddha and the Stanford Bunny datasets of 3D Stanford repository and to the Pooh and the Bunny datasets of the Ohio (MSU/WSU) Range Image database are also presented.

Point cloud registration is a technique to align two sets of points with manifold applications across a range of industries. However, due to a lack of adequate sensing technology, this technique has seldom found applications in the automotive sector up to now. With the advent of solid-state Light Detection and Ranging (LiDAR) sensors that are easily integrable in series production vehicles as means to sense the surrounding environment, this technique can be functional to automate their operations. Maneuvering a vehicle in the proximity of a reference object is one such operation, which can only be performed by accurately estimating its position and orientation relative to the vehicle itself. This project deals with the design and the implementation of an algorithm to accurately locate an aircraft parked on an airfield apron in real time. This is achieved by registering the point cloud model of the plane to the measurement point cloud of the scene produced by the LiDAR sensors on board the vehicle. To this end, the Iterative Closest Point (ICP) algorithm is a well-established approach to register two sets of points without prior knowledge of the correspondences between pairs of points, which, however, is notoriously sensitive towards outliers and computationally expensive with large point clouds. In this work, different variants are presented that improve on the standard ICP algorithm, in terms of accuracy and runtime performance, by leveraging different data structures to index the reference model and outlier rejection strategies. The results show that the implemented algorithms can produce estimates of centimeter precision in milliseconds based only on partial observations of the aircraft, outperforming another established solution tested. / Punktmolnregistrering är en teknik för att anpassa två uppsättningar punkter med mångfaldiga applikationer inom en rad branscher. På grund av bristen på adekvat sensorsteknik har denna teknik hittills sällan används inom automotivesektorn. Med tillkomsten av solid-state LiDAR -sensorer som enkelt kan integreras i serieproduktionsfordon för att kunna känna av den omgivningen, kan denna teknik automatisera verksamheten. Att manövrera ett fordon i närheten av ett referensobjekt är en sådan operation, som bara kan utföras genom att exakt uppskatta dess position och orientering i förhållande till själva fordonet. Detta projekt handlar om design och implementering av en algoritm för att exakt lokalisera ett flygplan parkerat på ett flygfält i realtid. Detta uppnås genom att registrera planetens molnmodell till mätpunktsmolnet på scenen som produceras av LiDAR -sensorerna ombord på fordonet. För detta ändamålet är Iterative Closest Point (ICP) -algoritmen ett väletablerat tillvägagångssätt för att registrera två uppsättningar punkter utan föregående kännedom om överensstämmelserna mellan parpar, vilket dock är notoriskt känsligt för avvikelser och beräknat dyrt med stora punktmoln. I detta arbete presenteras olika varianter som förbättrar standard ICP - algoritmen, när det gäller noggrannhet och runtime performance, genom att utnyttja olika datastrukturer för att indexera referensmodellen och outlier -avvisningsstrategier. Resultaten visar att de implementerade algoritmerna kan producera uppskattningar av centimeters precision i millisekunder baserat endast på partiella observationer av flygplanet, vilket överträffar en annan etablerad lösning som testats.

This thesis concerns the analytical and practical aspects of applying the Closest Point Method to solve elliptic partial differential equations (PDEs) on smooth surfaces and domains with smooth boundaries. A new numerical scheme is proposed to solve surface elliptic PDEs and a novel geometric multigrid solver is constructed to solve the resulting linear system. The method is also applied to coupled bulk-surface problems. A new embedding equation in a narrow band surrounding the surface is formulated so that it agrees with the original surface PDE on the surface and has a unique solution which is constant along the normals to the surface. The embedding equation is then discretized using standard finite difference scheme and barycentric Lagrange interpolation. The resulting scheme has 2nd-order accuracy in practice and is provably 2nd-order convergent for curves without boundary embedded in ℝ². To apply the method to solve elliptic equations on surfaces and domains with boundaries, the "ghost" point approach is adopted to handle Dirichlet, Neumann and Robin boundary conditions. A systematic method is proposed to represent values of ghost points by values of interior points according to boundary conditions. A novel geometric multigrid method based on the closest point representation of the surface is constructed to solve the resulting large sparse linear systems. Multigrid solvers are designed for surfaces with or without boundaries and domains with smooth boundaries. Numerical results indicate that the convergence rate of the multigrid solver stays roughly the same as we refine the mesh, as is desired of a multigrid algorithm. Finally the above methods are combined to solve coupled bulk-surface PDEs with some applications to biology.

Now a days where technological advancements are growing at a rapid pace, it has become a common norm for all the manufacturing companies to be abreast with these advancements for being competitive in market. This thesis deals with development of one such common norm for one of the products (Roof rack component) for company Thule. The main aim of the thesis is to curtail the products lead time to market and this was achieved by using an artificial intelligence technique i.e., Case-based reasoning (CBR). Roof rack component which is mounted on car roof is mainly constituted by two parts foot pad and bracket, this thesis main interest was concerned with only brackets and its geometry. This thesis is based on contemplating the already implemented concepts in this context, designer requirements and exploring better solutions. The methods of implementation adopted here was using CBR concept which is based on indexing , retrieve, adapt, review, retain and employing these concepts in form of an algorithm. The concept for developing the algorithm was based on Iterative closest point (ICP) approach which emphasise on assigning lower weight to pairs with greater point to point distance. The results portrayed are with respect to geometry and also with respect to application interface developed, which both together provides us a better solution.