Automatic construction of nurbs surfaces from unorganized points

Modeling with Non Uniform Rational B-Splines (NURBS) surfaces has become a standard in CAD/CAM systems due to its stability, flexibility, and local modification properties. The advantage of fitting with NURBS surfaces is well known, but it is also known that NURBS surfaces have several deficiencies. A NURBS surface cannot be fitted over an unorganized and scattered set of points and the representation of sharp features like edges, corners, and high curvatures is poor. This paper presents a new method for fitting a NURBS surface over an unorganized and scattered cloud of points, preserving its sharp features. In contrast with other methods, ours does not need either to construct a network of NURBS patches or polygon meshes. By reducing the dimensionality of the point cloud using ISOMAP algorithms, our method detects both regions with lacking points, and regions where the cloud is too dense. Then, the cloud is regularized by inserting and removing points, and it is approximated by a NURBS surface. An evolutionary strategy obtains the weights of the NURBS surface in order to improve the representation of sharp features

Integration between Creativity and Engineering in Industrial Design

The objective of the paper is to illustrate which are the key issues today in the industrial design workflow, paying particular attention to the most creative part of the workflow, highlighting those nodes which still make hard the styling activities and giving a brief survey of the researches aimed at smoothing the transfer of the design intent along the whole design cycle and at providing tools even more adhering at the mentality of creative people. Based on the experience gained working in two different European projects, through the collaboration with industrial designers in the automotive and the household supplies fields, a general industrial design workflow will be depicted, highlighting the main differences between the automotive and non-automotive sectors; the problems still present in the design activity will be also illustrated. The paper includes short surveys, in relation to the aesthetic design, in matter of research activities aimed at - identifying the links between shape characteristics of a product and the transmitted emotions - better supporting, in a digital way, the 2D sketching phase and the automatic interpretation and transfer of the 2D sketches into a 3D surface model - improving the 3D Modeling phase

Dynamic axial curve-pair based deformation and its application.

Chan, Man Leung Dunco.Thesis submitted in: Nov 2008.Thesis (M.Phil.)--Chinese University of Hong Kong, 2009.Includes bibliographical references (leaves 87-91).Abstracts in English and Chinese.Abstract --- p.2摘要 --- p.3Acknowledgement --- p.4Content --- p.5List of figures --- p.6Chapter Chapter 1 --- Introduction --- p.9Chapter 1.1 --- Background --- p.9Chapter 1.2 --- Prior work --- p.11Chapter 1.3 --- Objectives --- p.13Chapter 1.4 --- Proposed method --- p.16Chapter 1.5 --- Thesis outline --- p.18Chapter Chapter 2 --- Axial curve-pair deformation --- p.19Chapter 2.1 --- Axial deformation technique --- p.20Chapter 2.1.1 --- Representing objects in axial space --- p.21Chapter 2.1.2 --- Defining the frame --- p.23Chapter 2.2 --- Axial curve-pair deformation technique --- p.24Chapter 2.2.1 --- Framing the curve-pair --- p.25Chapter 2.2.2 --- Construction of orientation curve --- p.26Chapter 2.2.3 --- Manipulation of the axial curve-pair --- p.28Chapter Chapter 3 --- Dynamic axial curve-pair based deformation --- p.32Chapter 3.1 --- The dynamic mass spring model --- p.34Chapter 3.1.1 --- Dynamic NURBS curve --- p.35Chapter 3.1.2 --- Dynamic Free-form deformation --- p.37Chapter 3.1.3 --- Dynamic Axial Curve-pair deformation --- p.38Chapter 3.2 --- The dynamic mass spring model --- p.41Chapter 3.2.1 --- Curve-pair Fitting --- p.41Chapter 3.2.2 --- Construction of dynamic curve-pair --- p.44Chapter 3.2.3 --- The three-degree torsional spring --- p.48Chapter 3.2.4 --- Conserving feature in a twisting deformation --- p.50Chapter 3.2.5 --- Comparison of mass spring model --- p.51Chapter 3.3 --- Internal and external forces --- p.54Chapter 3.3.1 --- Tensile stress --- p.54Chapter 3.3.2 --- Torsional stress --- p.55Chapter 3.3.3 --- External forces --- p.59Chapter 3.4 --- Equations of motion --- p.60Chapter 3.5 --- System solver --- p.63Chapter 3.6 --- Hierarchical representation --- p.67Chapter 3.7 --- Collision detection --- p.72Chapter Chapter 4 --- Implementation and experimental result --- p.75Chapter 4.1 --- Comparison with original mass-spring system --- p.76Chapter 4.2 --- Comparison with dynamic free form deformation --- p.77Chapter 4.3 --- Comparison with the axial curve-pair deformation --- p.78Chapter 4.4 --- Shape restoring power --- p.80Chapter 4.5 --- Applications --- p.81Chapter Chapter 5 --- Conclusion --- p.84Reference --- p.8

Modelización naval mediante CAD, nurbs y elementos finitos : aplicación mediante ANSYS

En el presente PFC se pretende introducir un método para el análisis de problemas gobernados por ecuaciones en derivadas parciales como, por ejemplo, sólidos, estructuras y fluidos. El método tiene muchos rasgos en común con el método de elementos finitos y algunos rasgos en común con “métodos meshless” (MM). Sin embargo, está más geométricamente basado y toma la inspiración del diseño asistido por ordenador (CAD). Un objetivo primario es ser geométricamente exacto, no importa cuán burda sea la discretización. Otro objetivo es simplificar el refinamiento de malla eliminando la necesidad de la comunicación con la geometría CAD una vez que la malla inicial es construida. Incluso, otro objetivo sería entretejer más fuertemente el proceso de generación de malla dentro del CAD. Con este trabajo introducimos ideas en la búsqueda de estos objetivos. Para todo ello y para poder introducirnos de lleno en el tema tratado se pretende realizar una pequeña introducción a cada uno de los temas que influirán en la puesta en común del presente proyecto. Para empezar vamos a introducirnos en el mundo del diseño asistido por computador (CAD/CAM/CAE). La potencia de las herramientas informáticas actuales hace que el proceso productivo en la industria actual deba ser sometido a un análisis específico. En dichos procesos se ha desarrollado lo que hoy en día se conoce como diseño asistido por ordenador (CAD – ComputerAidedDesign). Esta tecnología permite introducir el uso de ordenadores (y de su potencia) a la hora de crear, modificar, analizar y optimizar un proceso productivo. Las herramientas de esta tecnología van desde la modelización geométrica hasta herramientas para el análisis y perfeccionamiento del producto obtenido. A pesar de ello, se debe hacer notar que el objetivo principal de este tipo de tecnología es la modelización, ya que el diseño es la actividad principal de cualquier ciclo productivo. Por otro lado, la fabricación asistida por ordenador (CAM – ComputerAidedManufacturing) es aquella en la que se controla un sistema productivo. En líneas generales el sistema CAM pretende, mediante el uso de sistemas informáticos, planificar, gestionar y controlar las operaciones de una planta de fabricación.Escuela Técnica Superior de Ingeniería Naval y Oceánic

A framework for hull form reverse engineering and geometry integration into numerical simulations

The thesis presents a ship hull form specific reverse engineering and CAD integration framework. The reverse engineering part proposes three alternative suitable reconstruction approaches namely curves network, direct surface fitting, and triangulated surface reconstruction. The CAD integration part includes surface healing, region identification, and domain preparation strategies which used to adapt the CAD model to downstream application requirements. In general, the developed framework bridges a point cloud and a CAD model obtained from IGES and STL file into downstream applications

Calculating the curvature shape characteristics of the human body from 3D scanner data.

In the recent years, there have been significant advances in the development and manufacturing of 3D scanners capable of capturing detailed (external) images of whole human bodies. Such hardware offers the opportunity to collect information that could be used to describe, interpret and analyse the shape of the human body for a variety of applications where shape information plays a vital role (e.g. apparel sizing and customisation; medical research in fields such as nutrition, obesity/anorexia and perceptive psychology; ergonomics for vehicle and furniture design). However, the representations delivered by such hardware typically consist of unstructured or partially structured point clouds, whereas it would be desirable to have models that allow shape-related information to be more immediately accessible. This thesis describes a method of extracting the differential geometry properties of the body surface from unorganized point cloud datasets. In effect, this is a way of constructing curvature maps that allows the detection on the surface of features that are deformable (such as ridges) rather than reformable under certain transformations. Such features could subsequently be used to interpret the topology of a human body and to enable classification according to its shape, rather than its size (as is currently the standard practice for many of the applications concemed). The background, motivation and significance of this research are presented in chapter one. Chapter two is a literature review describing the previous and current attempts to model 3D objects in general and human bodies in particular, as well as the mathematical and technical issues associated with the modelling. Chapter three presents an overview of: the methodology employed throughout the research; the assumptions regarding the data to be processed; and the strategy for evaluating the results for each stage of the methodology. Chapter four describes an algorithm (and some variations) for approximating the local surface geometry around a given point of the input data set by means of a least-squares minimization. The output of such an algorithm is a surface patch described in an analytic (implicit) form. This is necessary for the next step described below. The case is made for using implicit surfaces rather than more popular 3D surface representations such as parametric forms or height functions. Chapter five describes the processing needed for calculating curvature-related characteristics for each point of the input surface. This utilises the implicit surface patches generated by the algorithm described in the previous chapter, and enables the construction of a "curvature map" of the original surface, which incorporates rich information such as the principal curvatures, shape indices and curvature directions. Chapter six describes a family of algorithms for calculating features such as ridges and umbilic points on the surface from the curvature map, in a manner that bypasses the problem of separating a vector field (i.e. the principal curvature directions) across the entire surface of an object. An alternative approach, using the focal surface information, is also considered briefly in comparison. The concluding chapter summarises the results from all steps of the processing and evaluates them in relation to the requirements set in chapter one. Directions for further research are also proposed

Compression of 3D models with NURBS

With recent progress in computing, algorithmics and telecommunications, 3D models are increasingly used in various multimedia applications. Examples include visualization, gaming, entertainment and virtual reality. In the multimedia domain 3D models have been traditionally represented as polygonal meshes. This piecewise planar representation can be thought of as the analogy of bitmap images for 3D surfaces. As bitmap images, they enjoy great flexibility and are particularly well suited to describing information captured from the real world, through, for instance, scanning processes. They suffer, however, from the same shortcomings, namely limited resolution and large storage size. The compression of polygonal meshes has been a very active field of research in the last decade and rather efficient compression algorithms have been proposed in the literature that greatly mitigate the high storage costs. However, such a low level description of a 3D shape has a bounded performance. More efficient compression should be reachable through the use of higher level primitives. This idea has been explored to a great extent in the context of model based coding of visual information. In such an approach, when compressing the visual information a higher level representation (e.g., 3D model of a talking head) is obtained through analysis methods. This can be seen as an inverse projection problem. Once this task is fullled, the resulting parameters of the model are coded instead of the original information. It is believed that if the analysis module is efficient enough, the total cost of coding (in a rate distortion sense) will be greatly reduced. The relatively poor performance and high complexity of currently available analysis methods (except for specific cases where a priori knowledge about the nature of the objects is available), has refrained a large deployment of coding techniques based on such an approach. Progress in computer graphics has however changed this situation. In fact, nowadays, an increasing number of pictures, video and 3D content are generated by synthesis processing rather than coming from a capture device such as a camera or a scanner. This means that the underlying model in the synthesis stage can be used for their efficient coding without the need for a complex analysis module. In other words it would be a mistake to attempt to compress a low level description (e.g., a polygonal mesh) when a higher level one is available from the synthesis process (e.g., a parametric surface). This is, however, what is usually done in the multimedia domain, where higher level 3D model descriptions are converted to polygonal meshes, if anything by the lack of standard coded formats for the former. On a parallel but related path, the way we consume audio-visual information is changing. As opposed to recent past and a large part of today's applications, interactivity is becoming a key element in the way we consume information. In the context of interest in this dissertation, this means that when coding visual information (an image or a video for instance), previously obvious considerations such as decision on sampling parameters are not so obvious anymore. In fact, as in an interactive environment the effective display resolution can be controlled by the user through zooming, there is no clear optimal setting for the sampling period. This means that because of interactivity, the representation used to code the scene should allow the display of objects in a variety of resolutions, and ideally up to infinity. One way to resolve this problem would be by extensive over-sampling. But this approach is unrealistic and too expensive to implement in many situations. The alternative would be to use a resolution independent representation. In the realm of 3D modeling, such representations are usually available when the models are created by an artist on a computer. The scope of this dissertation is precisely the compression of 3D models in higher level forms. The direct coding in such a form should yield improved rate-distortion performance while providing a large degree of resolution independence. There has not been, so far, any major attempt to efficiently compress these representations, such as parametric surfaces. This thesis proposes a solution to overcome this gap. A variety of higher level 3D representations exist, of which parametric surfaces are a popular choice among designers. Within parametric surfaces, Non-Uniform Rational B-Splines (NURBS) enjoy great popularity as a wide range of NURBS based modeling tools are readily available. Recently, NURBS has been included in the Virtual Reality Modeling Language (VRML) and its next generation descendant eXtensible 3D (X3D). The nice properties of NURBS and their widespread use has lead us to choose them as the form we use for the coded representation. The primary goal of this dissertation is the definition of a system for coding 3D NURBS models with guaranteed distortion. The basis of the system is entropy coded differential pulse coded modulation (DPCM). In the case of NURBS, guaranteeing the distortion is not trivial, as some of its parameters (e.g., knots) have a complicated influence on the overall surface distortion. To this end, a detailed distortion analysis is performed. In particular, previously unknown relations between the distortion of knots and the resulting surface distortion are demonstrated. Compression efficiency is pursued at every stage and simple yet efficient entropy coder realizations are defined. The special case of degenerate and closed surfaces with duplicate control points is addressed and an efficient yet simple coding is proposed to compress the duplicate relationships. Encoder aspects are also analyzed. Optimal predictors are found that perform well across a wide class of models. Simplification techniques are also considered for improved compression efficiency at negligible distortion cost. Transmission over error prone channels is also considered and an error resilient extension defined. The data stream is partitioned by independently coding small groups of surfaces and inserting the necessary resynchronization markers. Simple strategies for achieving the desired level of protection are proposed. The same extension also serves the purpose of random access and on-the-fly reordering of the data stream

Simulación dinámica y deformaciones de superfícies paramétricas

Se desarrolla un modelo basado en NURBS, BSplines4D, de representación de superficies parametrizadas en 4D. El objetivo es la representación y simulación dinámica de superficies deformables basadas en el modelo; se realiza un estudio de las ecuaciones del movimiento, asociando un funcional de energía para medir la deformación de objetos, realizando un estudio riguroso sobre los métodos de integración y de discretización, tanto temporal como espacial, determinando su adecuación para resolver el sistema de ecuaciones diferenciales generado. El movimiento y la simulación de la deformación se realizan exclusivamente usando los puntos de control 4D, obteniendo una eficiencia numérica y computacional excelentes. La determinación del modelo BSplines4D se realiza tras un estudio pormenorizado de los modelos existentes. También se ha utilizado para desarrollar un modelo, N-Scodef, de deformaciones de formas libres (FFD), utilizando deformaciones geométricas basadas en restricciones. Se han establecido las condiciones para aplicar restricciones con trayectorias no rectilíneas, representadas por curvas B-Spline 4D. La deformación se adapta de forma precisa a la forma descrita por las curvasEs desenvolupa un model basat en NURBS, Bsplines4D, de representació de superfícies parametritzades en 4D. L'objectiu és la representació i simulació dinàmica de superfícies deformables basades en el model; es realitza un estudi de les equacions del moviment, associant un funcional d'energia per mesurar la deformació d'objectes, realitzant un estudi rigorós sobre els mètodes d'integració i discretització, tant temporal com espacial, determinant la seva adequació per resoldre el sistema d'equacions diferencials generat. El moviment i la simulació de la deformació es realitzen exclusivament utilitzant els punts de control 4D, obtenint una eficiència numèrica i computacional excel·lents. La determinació del model Bsplines4D es realitza després d'un estudi detallat dels models existents. També s'ha utilitzat per desenvolupar un model, N-Scodef, de deformacions de formes lliures (FFD), utilitzant deformacions geomètriques basades en restriccions. S'han establert les condicions per aplicar restriccions amb trajectòries no rectilínies, representades per corbes B-Spline 4D. La deformació s'adapta de forma precisa a la forma descrita per les corbesBsplines4D, a NURBS based model, is presented. The model allows the representation of 4D parameterized surfaces. The objective is the representation and dynamic simulation of deformable surfaces based on this model; a study of the movement equations has been made, associating to them an energy functional to measure the objects' deformation. A rigorous study on the integration and discretization, both temporal and spatial, is made to evaluate its suitability to solve the system of differential equations generated. The movement and simulation of the deformation is performed only using the 4D control points. An excellent numeric and computational efficiency is achieved. The Bsplines4D model is obtained after a detailed study on the existent models. The model has been also used to develop a free-form deformable (FFD) model, N-Scodef, using geometric constraint-based deformations. The conditions to apply constraints with non rectilinear trajectories, based on 4D B-Spline curves, have been established. The deformations fit precisely to the curves form

Triangular NURBS and their dynamic generalizations

Triangular B-splines are a new tool for modeling a broad class of objects de ned over arbitrary, non-rectangular domains. They provide an elegant and uni ed representation scheme for all piecewise continuous polynomial surfaces over planar triangulations. To enhance the power of this model, we propose triangular NURBS, the rational generalization of triangular B-splines, with weights as additional degrees of freedom. Fixing the weights to unity reduces triangular NURBS to triangular B-splines. Conventional geometric design with triangular NURBS can be laborious, since the user must manually adjust the many control points and weights. To ameliorate the design process, we develop a new model based on the elegant triangular NURBS geometry and principles of physical dynamics. Our model combines the geometric features of triangular NURBS with the demonstrated conveniences of interaction within a physics-based framework. The dynamic behavior of the model results from the numerical integration of di erential equations of motion that govern the temporal evolution of control points and weights in response to applied forces and constraints. This results in physically meaningful hence highly intuitive shapevariation. We apply Lagrangian mechanics to formulate the equations of motion of dynamic triangular NURBS and nite element analysis to reduce these equations to e cient numerical algorithms. We demonstrate several applications, including direct manipulation and interactive sculpting through force-based tools, the tting of unorganized data, and solid rounding with geometric and physical constraints