Bezier Curves Intersection Using Relief Perspective

Presented paper describes the method for finding the intersection of class space rational Bezier curves. The problem curve/curve intersection belongs among basic geometric problems and the aim of this article is to describe the new technique to solve the problem using relief perspective and Bezier clipping.Comment: 8 pages, 2 figures, to appear in Proceedings of WSCG'2000 in Plzen, Czech Republi

Routing protocols and quality of services for security based applications using wireless video sensor networks

Wireless video sensor networks have been a hot topic in recent years; the monitoring capability is the central feature of the services offered by a wireless video sensor network can be classified into three major categories: monitoring, alerting, and information on-demand. These features have been applied to a large number of applications related to the environment (agriculture, water, forest and fire detection), military, buildings, health (elderly people and home monitoring), disaster relief, area and industrial monitoring. Security applications oriented toward critical infrastructures and disaster relief are very important applications that many countries have identified as critical in the near future. This paper aims to design a cross layer based protocol to provide the required quality of services for security related applications using wireless video sensor networks. Energy saving, delay and reliability for the delivered data are crucial in the proposed application. Simulation results show that the proposed cross layer based protocol offers a good performance in term of providing the required quality of services for the proposed application

Qualitative Global Illumination of Mock-3D Scenes

In this work, we developed a framework to obtain qualitatively acceptable global rendering effects without an explicit geometry. This framework is particularly useful for 2D artists such as painters and illustrators. They will be able to obtain 3D looking images with complete artistic control as if they are using a 2D digital image manipulation system. The core of this approach is a mock-3D scene representation that allows impossible or stylized shapes as “fuzzy” geometric structures. These fuzzy geometric structures are view dependent shapes that are computed from texture maps which provide normal, thickness and displacement information for all visible points of a shape. The information that is provided by these texture maps, which we call shape maps, do not have to be complete or consistent. Shape maps can be obtaining by (1) converting 3D shapes into 2D images, (2) modeling using a sketch based interface, (3) directly painting a gradient domain image or (4) photographing real objects. The most interesting shape maps are those sketched or painted by an artist, since they can reflect the artist’s intention, even if this does not follow the normal rules of perspective. The major advantage of this approach is the ability to obtain visually acceptable global effects even when shape maps do not correspond to real 3D shapes. We show that computing view dependent fuzzy geometry from shape maps is sufficient to obtain qualitatively convincing global illumination effects even for impossible shapes. The methods we have developed and implemented for global rendering effects include ambient occlusion, local and global shadows, refraction and reflection. Although these methods do not directly correspond to underlying physical phenomena, they ii can provide results that are qualitative proportional to 3D realistic rendering. Our approach is a very 2D artist-friendly representation since the shaders are also defined as images. These images can naturally describe shading parameters and provide a simple 2D control of the shading and rendering processes to intuitively obtain desired visual results. In particular, this representational power helps to easily obtain a wide variety of NPR effects that is still consistent with global illumination

A comparison of hole-filling methods in 3D

This paper presents a review of the most relevant current techniques that deal with hole-filling in 3D models. Contrary to earlier reports, which approach mesh repairing in a sparse and global manner, the objective of this review is twofold. First, a specific and comprehensive review of hole-filling techniques (as a relevant part in the field of mesh repairing) is carried out. We present a brief summary of each technique with attention paid to its algorithmic essence, main contributions and limitations. Second, a solid comparison between 34 methods is established. To do this, we define 19 possible meaningful features and properties that can be found in a generic hole-filling process. Then, we use these features to assess the virtues and deficiencies of the method and to build comparative tables. The purpose of this review is to make a comparative hole-filling state-of-the-art available to researchers, showing pros and cons in a common framework.• Ministerio de Economía y Competitividad: Proyecto DPI2013-43344-R (I+D+i) • Gobierno de Castilla-La Mancha: Proyecto PEII-2014-017-PpeerReviewe

True2Form: 3D Curve Networks from 2D Sketches via Selective Regularization

International audienceTrue2Form is a sketch-based modeling system that reconstructs 3D curves from typical design sketches. Our approach to infer 3D form from 2D drawings is a novel mathematical framework of insights derived from perception and design literature. We note that designers favor viewpoints that maximally reveal 3D shape information, and strategically sketch descriptive curves that convey intrinsic shape properties, such as curvature, symmetry, or parallelism. Studies indicate that viewers apply these properties selectively to envision a globally consistent 3D shape. We mimic this selective regularization algorithmically, by progressively detecting and enforcing applicable properties, accounting for their global impact on an evolving 3D curve network. Balancing regularity enforcement against sketch fidelity at each step allows us to correct for inaccuracy inherent in free-hand sketching. We perceptually validate our approach by showing agreement between our algorithm and viewers in selecting applicable regularities. We further evaluate our solution by: reconstructing a range of 3D models from diversely sourced sketches; comparisons to prior art; and visual comparison to both ground-truth and 3D reconstructions by designers

Use of mixed study techniques in the evaluation of coastline dynamics - the “Porto Cesareo” MPA case of study

In recent decades, the much-discussed climate changes with the consequent variations in sea and weather conditions and the rise of the mean sea level are causing an indisputable set of negative actions on the entire coastal system mainly due to the increase of the erosive phenomenon along the shorelines. These critical scenarios have a major impact even on a local scale, and because of that, we decided to study a well knows tract of rocky/sandy mixed coast, in a highly anthropized area, even if located inside the “Porto Cesareo” Marine Protected Area (MPA) (Ionian Sea, Gulf of Taranto, Puglia Region, Italy). The high naturalistic and archaeological value of this area calls for a greater institutional effort in the study of erosional phenomena. Several historical documents from other studies point out that this coastal area is an ideal place for this kind of research. The effects of coastal erosion and anthropic pressures along this tract of coast require adequate efforts for a consistent and rapid evaluation of the coastal dynamics. The methodologies proposed in this work are based on mixed techniques from different fields of study, integrating recent aero photogrammetry surveys with drones, aerial images acquired by the Italian Military Geographic Institute (IGM), elaboration of paleoshorelines related by underwater archaeological markers and their dating, and finally on the elaboration of satellite products useful for the study of vast areas. The monitoring of coastal areas and the evaluation of shoreline dynamics are core topics in the implementation of managing actions of decision makers on a local, regional, national, and international scale, above all in places like the chosen one, inside an MPA. Remote sensing through the use of RPAS (Remotely Piloted Aircraft Systems or Drones) has proved to be very useful for identifying phenomena that act on a small spatial scale and in supporting and implementing protective measures according to the adaptive management approach, through multi-year surveys on habitats of conservation interest [18]. For the implementation of fine-scale monitoring actions, we have chosen products from the Sentinel satellite of the Copernicus constellation (European Space Agency - ESA). In this context, the use of satellite products provides a recurrent view of the ground, useful in the short and long-term monitoring of changes in wide coastal areas, and in particular, offers a coastline positioning evaluation in near real-time. Local monitoring actions performed in recent years have already shown an erosive trend in the past decades, and even, negative forecasts for the next decade, so further surveys with mixed methodologies could be crucial in the evaluation of the evolution of this particular coastal area by local authorities

A feature-based approach to the Computer-Aided Design of sculptured products

Computer-Aided Design systems offer considerable potential for improving design process efficiency. To reduce the 'ease of use' barrier hindering full realisation of this potential amongst general mechanical engineering industries, many commercial systems are adopting a Feature-Based Design (FBD) metaphor. Typically the user is allowed to define and manipulate the design model using interface elements that introduce and control parametric geometry clusters, with engineering meaning, representing specific product features (such as threaded holes, slots, pockets and bosses). Sculptured products, such as golf club heads, shoe lasts, crockery and sanitary ware, are poorly supported by current FBD systems and previous research, because their complex shapes cannot be accurately defined using the geometrically primitive feature sets implemented. Where sculptured surface regions are allowed for, the system interface, data model and functionality are little different from that already provided in many commercial surface modelling systems, and so offer very little improvement in ease of use, quality or efficiency. This thesis presents research to propose and develop an FBD methodology and system suitable for sculptured products. [Continues.

Shape Machine: shape embedding and rewriting in visual design

Shape grammar interpreters have been studied for more than forty years addressing several areas of design research including architectural, engineering, and product design. At the core of all these implementations, the operation of embedding – the ability of a shape grammar interpreter to search for subshapes in a geometry model even if they are not explicitly encoded in the database of the system – resists a general solution. It is suggested here that beyond a seemingly long list of technological hurdles, the implementation of shape embedding, that is, the implementation of the mathematical concept of the “part relation” between two shapes, or equivalently, between two drawings, or between a shape and a design, is the single major obstacle to take on. This research identifies five challenges underlying the implementation of shape embedding and shape grammar interpreters at large: 1) complex entanglement of the calculations required for shape embedding and a shape grammar interpreter at large, with those required by a CAD system for modeling and modifying geometry; 2) accumulated errors caused by the modeling processes of CAD systems; 3) accumulated errors caused by the complex calculations required for the derivation of affine, and mostly, perspectival transformations; 4) limited support for indeterminate shape embedding; 5) low performance of the current shape embedding algorithms for models consisting of a large number of shapes. The dissertation aims to provide a comprehensive engineering solution to all these five challenges above. More specifically, the five contributions of the dissertation are: 1) a new architecture to separate the calculations required for the shape embedding and replacement (appropriately called here Shape Machine) vs. the calculations required by a CAD system for the selection, instantiation, transformation, and combination of shapes in CAD modeling; 2) a new modeling calibration system to ensure the effective translation of geometrical types of shapes to their maximal representations without cumulative calculating errors; 3) a new dual-mode system of the derivation of transformations for shape embedding, including a geometric approach next to the known algebraic one, to implement the shape embedding relation under the full spectrum of linear transformations without the accumulated errors caused by the current algorithms; 4) a new multi-step mechanism that resolves all cases of indeterminate embeddings for shapes having fewer registration points than those required for a shape embedding under a particular type of transformation; and 5) a new data representation for hyperplane intersections, the registration point signature, to allow for the effective calculation of shape embeddings for complex drawings consisting of a large number of shapes. All modules are integrated into a common computational framework to test the model for a particular type of shapes – the shapes consisting of lines in the Euclidean plane in the algebra U12.Ph.D

Meshfree Approximation Methods For Free-form Optical Surfaces With Applications To Head-worn Displays

Compact and lightweight optical designs achieving acceptable image quality, field of view, eye clearance, eyebox size, operating across the visible spectrum, are the key to the success of next generation head-worn displays. The first part of this thesis reports on the design, fabrication, and analysis of off-axis magnifier designs. The first design is catadioptric and consists of two elements. The lens utilizes a diffractive optical element and the mirror has a free-form surface described with an x-y polynomial. A comparison of color correction between doublets and single layer diffractive optical elements in an eyepiece as a function of eye clearance is provided to justify the use of a diffractive optical element. The dual-element design has an 8 mm diameter eyebox, 15 mm eye clearance, 20 degree diagonal full field, and is designed to operate across the visible spectrum between 450-650 nm. 20% MTF at the Nyquist frequency with less than 3% distortion has been achieved in the dual-element head-worn display. An ideal solution for a head-worn display would be a single free-form surface mirror design. A single surface mirror does not have dispersion; therefore, color correction is not required. A single surface mirror can be made see-through by machining the appropriate surface shape on the opposite side to form a zero power shell. The second design consists of a single off-axis free-form mirror described with an x-y polynomial, which achieves a 3 mm diameter exit pupil, 15 mm eye relief, and a 24 degree diagonal full field of view. The second design achieves 10% MTF at the Nyquist frequency set by the pixel spacing of the VGA microdisplay with less than 3% distortion. Both designs have been fabricated using diamond turning techniques. Finally, this thesis addresses the question of what is the optimal surface shape for a single mirror constrained in an off-axis magnifier configuration with multiple fields? Typical optical surfaces implemented in raytrace codes today are functions mapping two dimensional vectors to real numbers. The majority of optical designs to-date have relied on conic sections and polynomials as the functions of choice. The choice of conic sections is justified since conic sections are stigmatic surfaces under certain imaging geometries. The choice of polynomials from the point of view of surface description can be challenged. A polynomial surface description may link a designer s understanding of the wavefront aberrations and the surface description. The limitations of using multivariate polynomials are described by a theorem due to Mairhuber and Curtis from approximation theory. This thesis proposes and applies radial basis functions to represent free-form optical surfaces as an alternative to multivariate polynomials. We compare the polynomial descriptions to radial basis functions using the MTF criteria. The benefits of using radial basis functions for surface description are summarized in the context of specific head-worn displays. The benefits include, for example, the performance increase measured by the MTF, or the ability to increase the field of view or pupil size. Even though Zernike polynomials are a complete and orthogonal set of basis over the unit circle and they can be orthogonalized for rectangular or hexagonal pupils using Gram-Schmidt, taking practical considerations into account, such as optimization time and the maximum number of variables available in current raytrace codes, for the specific case of the single off-axis magnifier with a 3 mm pupil, 15 mm eye relief, 24 degree diagonal full field of view, we found the Gaussian radial basis functions to yield a 20% gain in the average MTF at 17 field points compared to a Zernike (using 66 terms) and an x-y polynomial up to and including 10th order. The linear combination of radial basis function representation is not limited to circular apertures. Visualization tools such as field map plots provided by nodal aberration theory have been applied during the analysis of the off-axis systems discussed in this thesis. Full-field displays are used to establish node locations within the field of view for the dual-element head-worn display. The judicious separation of the nodes along the x-direction in the field of view results in well-behaved MTF plots. This is in contrast to an expectation of achieving better performance through restoring symmetry via collapsing the nodes to yield field-quadratic astigmatism