The geometry engine

In this article, the usage of matrices and matrix operations in computer graphics is shown. A brief overview of geometric transformations in computer graphics is given. The "Matrix - Computer Graphics" application software is created for the representation and easier understanding of relations between geometric transformations and matrix calculus.

Solving the initial value problem of discrete geodesics

Mesh parameterization is one of the fundamental operations in computer graphics (CG) and computeraided design (CAD). In this paper, we propose a novel local/global parameterization approach, ARAP++, for singleand multi-boundary triangular meshes. It is an extension of the as-rigid-as-possible (ARAP) approach, which stitches together 1-ring patches instead of individual triangles. To optimize the spring energy, we introduce a linear iterative scheme which employs convex combination weights and a fitting Jacobian matrix corresponding to a prescribed family of transformations. Our algorithm is simple, efficient, and robust. The geometric properties (angle and area) of the original model can also be preserved by appropriately prescribing the singular values of the fitting matrix. To reduce the area and stretch distortions for high-curvature models, a stretch operator is introduced. Numerical results demonstrate that ARAP++ outperforms several state-of-the-art methods in terms of controlling the distortions of angle, area, and stretch. Furthermore, it achieves a better visualization performance for several applications, such as texture mapping and surface remeshing.

Efficient piecewise higher-order parametrization of discrete surfaces with local and global injectivity

Given a collection of points in the plane, pick an arbitrary horizontal segment and move it vertically until it hits one of the points (if at all). This form ofsegment-dragging is a common operation in computer graphics and motion-planning, it can also serve as a building block for multidimensional data structures. This note describes a new approach to segment-dragging which yields a simple and efficient solution. The data structure requiresO(n) storage andO(n logn) preprocessing time, and each query can be answered inO(logn) time, wheren is the number of points in the collection. The method is best understood as the end result of a sequence of transformations applied to a simple but inefficient starting solution.

Tracing a ray through a scene and finding the closest intersection with the scene geometry is a fundamental operation in computer graphics. During the last two decades, significant efforts have been made to accelerate this operation, with interactive ray tracing as one of the major driving forces. At the heart of a fast method for intersecting a scene with a ray lies the acceleration structure. Many different acceleration structures exist, but research has focused almost exclusively on a few well-tried and well-established techniques: regular and hierarchical grids, bounding volume hierarchies and kd-trees. Spectacular advances have been made, which have contributed significantly to making interactive ray tracing a possibility. However, despite the success of these acceleration structures, several problems remain open. Handling deforming and dynamic geometry still poses significant challenges, and the local vs. global complexity of acceleration structures is still not entirely understood. One therefore wonders whether other acceleration structures, that leave the beaten path of efficient grids, bounding volume hierarchies and kd-trees, can provide viable alternatives.Next to computer graphics, the ray shooting problem is also studied in computational geometry. Ray shooting queries against a large collection of polyhedra are answered by tracing the ray through a simplicial complex such as a constrained tetrahedralization. This is a well-known technique, see e.g. the chapter Ray shooting and lines in space by Pellegrini in Handbook of Discrete and Computational Geometry. However, relevant work in computational geometry is usually theoretical, and practical implementations and experimental results are typically not available.In this work we explore the idea of accelerating the operation of intersecting a scene with a ray using constrained tetrahedralizations. This is illustrated in figure 1. A constrained tetrahedralization of a scene is a tetrahedralization that respects the faces of the scene geometry. The closest intersection of a ray with a scene is found by traversing this tetrahedralization along the ray, one tetrahedron at a time, until a constrained face is encountered. We show that constrained tetrahedralizations are a viable alternative to state-of-the-art acceleration structures, such as kd-trees, and that constrained tetrahedralizations have a number of interesting and unique properties that set them apart from traditional acceleration structures. Constrained tetrahedralizations are not hierarchical yet adaptive; the complexity of traversing them is a function of local geometric complexity rather than global geometric complexity; constrained tetrahedralizations support deforming geometry without any effort (see figure 2); and they have the potential to unify several data structures currently used in global illumination.Although constrained tetrahedralizations are not a silver bullet, and although they are in general not yet faster than the most optimized kd-trees, constrained tetrahedralizations offer several new perspectives on acceleration structures for ray tracing and deserve attention.

Discretization and reconstruction are fundamental operations in computer graphics, enabling the conversion between sampled and continuous representations. Major advances in signal-processing research have shown that these operations can often be performed more efficiently by decomposing a filter into two parts: a compactly supported continuous-domain function and a digital filter. This strategy of “generalized sampling” has appeared in a few graphics papers, but is largely unexplored in our community. This survey broadly summarizes the key aspects of the framework, and delves into specific applications in graphics. Using new notation, we concisely present and extend several key techniques. In addition, we demonstrate benefits for prefiltering in image downscaling and supersample-based rendering, and analyze the effect that generalized sampling has on the noise due to Monte Carlo estimation. We conclude with a qualitative and quantitative comparison of traditional and generalized filters.

In the paper "On the Increasing Role of Geometry", published in the electronic "Journal of Natural Science Research" in 2017, it was outspoken a hypothesis that now, at the time of innovative technologies, the importance of geometry is constantly increasing. The significance of geometry is also demonstrated by numerous Ph.D. and doctoral dissertations in the specialty No 05.01.01 - “Engineering Geometry and Computer Graphics”. It can be affirmed that all and everyone dissertations of technical and technological profile contain a geometric component to one degree or another. The "Geometry and Graphics" journal turned 8 (it was founded in June 2012). During this time, on its pages have been published numerous scientific papers, developing namely geometry and its branches: from simplest geometric constructions based on new properties of both lines and surfaces, to imaginary elements. Investigations were conducted in the following areas: “New Directions in Geometry”, “Fractal Geometry”, “Multidimensional Geometry”, “Geometric Constructions”, “Construction and Research of Surfaces”, “Imaginary Geometry”, “Practical Application of Geometry”, “Computer Graphics”, “Descriptive Geometry as Basis of other Branches of Geometry” ,”Geometry of Phase Spaces”. The journal publishes both recognized scientists and candidate for Ph.D. and doctor degrees. The considered array of papers clearly confirms the statement of the majority of authors, published in the journal, about geometry continuous development, which knocks out the ground for skeptics who decided that geometry is the science of the past centuries. As long as objects with shapes and surfaces surround us, geometry will be in demand. This, as they say, is unequivocal.

The history and famous landmarks of computer graphics hardware are well known. Starting with Ivan Sutherland's Sketchpad system in the early 1960's, the first generation of computer graphics hardware consisted of calligraphic (vector) displays capable of drawing complex three-dimensional wireframe models at interactive rates. In the early 1970's expensive color frame buffers with the capability for displaying static color images were introduced. Although more and more intelligence was added to these frame buffers, Jim Clark's geometry engine and the first graphics workstations were not introduced until the 1980's. During the 1970's, only the very costly and specialized hardware used for military and aerospace simulations was capable of real-time surface color display.

Aiming at the modeling representation in cooperative plant design within heterogeneous CAD systems, a modeling representation method based on XML is proposed. The schema of the representation document is also defined. By the schema, the description rules of basic graphic element, graphic operation, parametric modeling, and constraint are defined. This verifies the feasibility of standardizing modeling representation in cooperative plant design.

Image downscaling via co-occurrence learning

Theories for graphics processors in TIPS-1

PREFACECGDIP 2018 was held in Bangkok, Thailand from July 27-29, 2018. CGDIP 2018 was organized by the Asia Pacific Institute of Science and Engineering (APISE). The conference provides a useful and wide platform both to display the latest research and for the exchange of research results and thoughts in Computer Graphics and Digital Image Processing. The participants of the conference were from almost every part of the world, with backgrounds in either academia or industry, even well-known enterprise. The success and prosperity of the conference is reflected in the high level of the papers received.The proceedings are a compilation of the accepted papers and represent an interesting outcome of the conference. This book covers two chapters: 1. Applications & Visualization; 2. Image Processing, Detection and Recognition.We would like to acknowledge all of those who supported CGDIP 2018. Each individual and institutional help were very important for the success of this conference. Especially we would like to thank the organizing committee for their valuable advice in the organization and helpful peer review of the papers.We sincerely hope that CGDIP 2018 will be a forum for excellent discussions that will put forward new ideas and promote collaborative researches. We are sure that the proceedings will serve as an important research source of references and the knowledge, which will lead to not only scientific and engineering progress but also other new products and processes.Prof. Shahram Latifi, University of Nevada, Las Vegas, USA

The Indian Conference on Computer Vision, Graphics and Image Processing (ICVGIP) is India's premier conference in Computer Vision, Graphics, Image Processing and related fields. Started in 1998, it is a biennial international conference providing a forum for the presentation of technological advances and research findings in these areas.

During the three decades since Ivan Sutherland introduced the Sketchpad system [7], there has been an outpouring of computer graphics systems for use in architecture [3, 5]. In response to this development, most of the major architectural firms around the world have embraced the idea that computer literacy is mandatory for success. We would argue, however, that most of these recent developments have failed to tap the potential of the computer as a design tool. Instead, computers have been relegated largely to the status of drafting instruments, so that the "D" in CAD stands for drafting rather than design. It is important that future architectural design systems consider design as a continuous process rather than an eventual outcome.The advent of computer graphics technology has had an impact on the architectural profession. Computer graphics has revolutionized the drafting process, enabling the rapid entry and modification of designs (see Figure 1). In addition, modeling and rendering systems have proven to be invaluable aids in the visualization process, allowing designers to walk through their designs with photorealistic imagery (see Figure 2) [6, 2, 3]. Computer graphics systems have also demonstrated utility for capturing engineering information, greatly simplifying the analysis and construction of proposed designs. However, it is important to consider that all of these tasks occur near the conclusion of a larger design process. In fact, most of the artistic and intellectual challenges of an architectural design have already been resolved by the time the designer sits down in front of a computer. In seeking insight into the design process, it is generally of little use to revisit the various computer archives and backups. Instead, it is best to explore the reams of sketches and crude balsa models that fill the trash cans of any architectural studio.In architecture, as in most other fields, the initial success of computerization has been in areas where it frees humans from tedious and mundane tasks. This includes the redrawing of floor plans after minor modifications, the generation of largely redundant, yet subtly different engineering drawings and the generation of perspective renderings.We believe that there is a largely untapped potential for computer graphics as a tool in the earlier phases of the design process. In this essay, we argue that computer graphics might play a larger role via applications that aid and amplify the creative process.