One Curve and Surface Basics.- 1.1 Implicit and Parametric Forms.- 1.2 Power Basis Form of a Curve.- 1.3 Bezier Curves.- 1.4 Rational Bezier Curves.- 1.5 Tensor Product Surfaces.- Exercises.- Two B-Spline Basis Functions.- 2.1 Introduction.- 2.2 Definition and Properties of B-spline Basis Functions.- 2.3 Derivatives of B-spline Basis Functions.- 2.4 Further Properties of the Basis Functions.- 2.5 Computational Algorithms.- Exercises.- Three B-spline Curves and Surfaces.- 3.1 Introduction.- 3.2 The Definition and Properties of B-spline Curves.- 3.3 The Derivatives of a B-spline Curve.- 3.4 Definition and Properties of B-spline Surfaces.- 3.5 Derivatives of a B-spline Surface.- Exercises.- Four Rational B-spline Curves and Surfaces.- 4.1 Introduction.- 4.2 Definition and Properties of NURBS Curves.- 4.3 Derivatives of a NURBS Curve.- 4.4 Definition and Properties of NURBS Surfaces.- 4.5 Derivatives of a NURBS Surface.- Exercises.- Five Fundamental Geometric Algorithms.- 5.1 Introduction.- 5.2 Knot Insertion.- 5.3 Knot Refinement.- 5.4 Knot Removal.- 5.5 Degree Elevation.- 5.6 Degree Reduction.- Exercises.- Six Advanced Geometric Algorithms.- 6.1 Point Inversion and Projection for Curves and Surfaces.- 6.2 Surface Tangent Vector Inversion.- 6.3 Transformations and Projections of Curves and Surfaces.- 6.4 Reparameterization of NURBS Curves and Surfaces.- 6.5 Curve and Surface Reversal.- 6.6 Conversion Between B-spline and Piecewise Power Basis Forms.- Exercises.- Seven Conics and Circles.- 7.1 Introduction.- 7.2 Various Forms for Representing Conics.- 7.3 The Quadratic Rational Bezier Arc.- 7.4 Infinite Control Points.- 7.5 Construction of Circles.- 7.6 Construction of Conies.- 7.7 Conic Type Classification and Form Conversion.- 7.8 Higher Order Circles.- Exercises.- Eight Construction of Common Surfaces.- 8.1 Introduction.- 8.2 Bilinear Surfaces.- 8.3 The General Cylinder.- 8.4 The Ruled Surface.- 8.5 The Surface of Revolution.- 8.6 Nonuniform Scaling of Surfaces.- 8.7 A Three-sided Spherical Surface.- Nine Curve and Surface Fitting.- 9.1 Introduction.- 9.2 Global Interpolation.- 9.2.1 Global Curve Interpolation to Point Data.- 9.2.2 Global Curve Interpolation with End Derivatives Specified.- 9.2.3 Cubic Spline Curve Interpolation.- 9.2.4 Global Curve Interpolation with First Derivatives Specified.- 9.2.5 Global Surface Interpolation.- 9.3 Local Interpolation.- 9.3.1 Local Curve Interpolation Preliminaries.- 9.3.2 Local Parabolic Curve Interpolation.- 9.3.3 Local Rational Quadratic Curve Interpolation.- 9.3.4 Local Cubic Curve Interpolation.- 9.3.5 Local Bicubic Surface Interpolation.- 9.4 Global Approximation.- 9.4.1 Least Squares Curve Approximation.- 9.4.2 Weighted and Constrained Least Squares Curve Fitting.- 9.4.3 Least Squares Surface Approximation.- 9.4.4 Approximation to Within a Specified Accuracy.- 9.5 Local Approximation.- 9.5.1 Local Rational Quadratic Curve Approximation.- 9.5.2 Local Nonrational Cubic Curve Approximation.- Exercises.- Ten Advanced Surface Construction Techniques.- 10.1 Introduction.- 10.2 Swung Surfaces.- 10.3 Skinned Surfaces.- 10.4 Swept Surfaces.- 10.5 Interpolation of a Bidirectional Curve Network.- 10.6 Coons Surfaces.- Eleven Shape Modification Tools.- 11.1 Introduction.- 11.2 Control Point Repositioning.- 11.3 Weight Modification.- 11.3.1 Modification of One Curve Weight.- 11.3.2 Modification of Two Neighboring Curve Weights.- 11.3.3 Modification of One Surface Weight.- 11.4 Shape Operators.- 11.4.1 Warping.- 11.4.2 Flattening.- 11.4.3 Bending.- 11.5 Constraint-based Curve and Surface Shaping.- 11.5.1 Constraint-based Curve Modification.- 11.5.2 Constraint-based Surface Modification.- Twelve Standards and Data Exchange.- 12.1 Introduction.- 12.2 Knot Vectors.- 12.3 Nurbs Within the Standards.- 12.3.1 IGES.- 12.3.2 STEP.- 12.3.3 PHIGS.- 12.4 Data Exchange to and from a NURBS System.- Thirteen B-spline Programming Concepts.- 13.1 Introduction.- 13.2 Data Types and Portability.- 13.3 Data Structures.- 13.4 Memory Allocation.- 13.5 Error Control.- 13.6 Utility Routines.- 13.7 Arithmetic Routines.- 13.8 Example Programs.- 13.9 Additional Structures.- 13.10 System Structure.- References.

https://www.springer.com/productFlyer_978-3-540-61545-3.pdf?SGWID=0-0-1297-1491853-0

The NURBS Book

The Visual Display of Quantitative Information

In this paper the main problems and the available solutions are addressed for the generation of 3D models from terrestrial images. Close range photogrammetry has dealt for many years with manual or automatic image measurements for precise 3D modelling. Nowadays 3D scanners are also becoming a standard source for input data in many application areas, but image-based modelling still remains the most complete, economical, portable, flexible and widely used approach. In this paper the full pipeline is presented for 3D modelling from terrestrial image data, considering the different approaches and analysing all the steps involved.

/pdf/image-based-3d-modelling-a-review-5msqumyd5o.pdf

Image-based 3d modelling: a review

Moving from a set of independent virtual worlds to an integrated network of 3D virtual worlds or Metaverse rests on progress in four areas: immersive realism, ubiquity of access and identity, interoperability, and scalability. For each area, the current status and needed developments in order to achieve a functional Metaverse are described. Factors that support the formation of a viable Metaverse, such as institutional and popular interest and ongoing improvements in hardware performance, and factors that constrain the achievement of this goal, including limits in computational methods and unrealized collaboration among virtual world stakeholders and developers, are also considered.

/pdf/3d-virtual-worlds-and-the-metaverse-current-status-and-2tcyj4edj0.pdf

3D Virtual worlds and the metaverse: Current status and future possibilities

This paper proposes a quasi-dense approach to 3D surface model acquisition from uncalibrated images. First, correspondence information and geometry are computed based on new quasi-dense point features that are resampled subpixel points from a disparity map. The quasi-dense approach gives more robust and accurate geometry estimations than the standard sparse approach. The robustness is measured as the success rate of full automatic geometry estimation with all involved parameters fixed. The accuracy is measured by a fast gauge-free uncertainty estimation algorithm. The quasi-dense approach also works for more largely separated images than the sparse approach, therefore, it requires fewer images for modeling. More importantly, the quasi-dense approach delivers a high density of reconstructed 3D points on which a surface representation can be reconstructed. This fills the gap of insufficiency of the sparse approach for surface reconstruction, essential for modeling and visualization applications. Second, surface reconstruction methods from the given quasi-dense geometry are also developed. The algorithm optimizes new unified functionals integrating both 3D quasi-dense points and 2D image information, including silhouettes. Combining both 3D data and 2D images is more robust than the existing methods using only 2D information or only 3D data. An efficient bounded regularization method is proposed to implement the surface evolution by level-set methods. Its properties are discussed and proven for some cases. As a whole, a complete automatic and practical system of 3D modeling from raw images captured by hand-held cameras to surface representation is proposed. Extensive experiments demonstrate the superior performance of the quasi-dense approach with respect to the standard sparse approach in robustness, accuracy, and applicability.

/pdf/a-quasi-dense-approach-to-surface-reconstruction-from-2vi2wm9tw4.pdf

A quasi-dense approach to surface reconstruction from uncalibrated images

Collaborative virtual environments (CVEs) enable two or more people, separated in the real world, to share the same virtual “space” They can be used for many purposes, from teleconferencing to training people to perform assembly tasks Unfortunately, the effectiveness of CVEs is compromised by one major problem: the delay that exists in the networks linking users together Whilst we have a good understanding, especially in the visual modality, of how users are affected by delayed feedback from their own actions, little research has systematically examined how users are affected by delayed feedback from other people, particularly in environments that support haptic (force) feedback The current study addresses this issue by quantifying how increasing levels of latency affect visual and haptic feedback in a collaborative target acquisition task Our results demonstrate that haptic feedback in particular is very sensitive to low levels of delay Whilst latency affects visual feedback from 50 ms, it impacts on haptic task performance 25 ms earlier, and causes the haptic measures of performance deterioration to rise far more steeply than visual The “impact-perceive-adapt” model of user performance, which considers the interaction between performance measures, perception of latency, and the breakdown of perception of immediate causality, is proposed as an explanation for the observed pattern of performance

Modeling the effects of delayed haptic and visual feedback in a collaborative virtual environment

Camera tracking is a fundamental requirement for video-based augmented reality applications. The ability to accurately calculate the intrinsic and extrinsic camera parameters for each frame of a video sequence is essential if synthetic objects are to be integrated into the image data in a believable way. In this paper, we present an accurate and reliable approach to camera calibration for off-line video-based augmented reality applications. We first describe an improved feature tracking algorithm, based on the widely used Kanade-Lucas-Tomasi tracker. Estimates of inter-frame camera motion are used to guide tracking, greatly reducing the number of incorrectly tracked features. We then present a robust hierarchical scheme that merges sub-sequences together to form a complete projective reconstruction. Finally, we describe how RANSAC-based random sampling can be applied to the problem of self-calibration, allowing for more reliable upgrades to metric geometry. Results of applying our calibration algorithms are given for both synthetic and real data.

/pdf/accurate-camera-calibration-for-off-line-video-based-5exkt68jh6.pdf

Accurate camera calibration for off-line, video-based augmented reality

This paper presents a new technique for controlling a user’s navigation in a virtual environment. The approach introduces artificial force fields which act upon the user’s virtual body such that he is guided around obstacles, rather than penetrating or colliding with them. The technique is extended to incorporate gravity into the environment. The problem of negotiating stairs during a walk-through has also been investigated with the new approach. Human subjects were tested in experiments in which they experienced three different kinds of navigation: unconstrained, simple constrained and assisted by force fields. Theresults demonstrate that the force-field technique is an effective approach for effective, comfortable navigation. KEY’VirORDS: 3D interfaces, virtual environments, collision avoidance, navigation, force fields.

Navigation guided by artificial force fields

We propose a new algorithm that uses consumer-level graphics hardware to render shadows cast by synthetic objects and a real lighting environment. This has immediate benefit for interactive Augmented Reality applications, where synthetic objects must be accurately merged with real images. We show how soft shadows cast by direct and indirect illumination sources may be generated and composited into a background image at interactive rates. We describe how the sources of light (and hence shadow) affecting each point in an image can be efficiently encoded using a hierarchical shaft-based subdivision of line-space. This subdivision is then used to determine the sources of light that are occluded by synthetic objects, and we show how the contributions from these sources may be removed from a background image using facilities available on modern graphics hardware. A trade-off may be made at run-time between shadow accuracy and rendering cost, converging towards a result that is subjectively similar to that obtained using ray-tracing based differential rendering algorithms. Examples of the proposed technique are given for a variety of different lighting environments, and the visual fidelity of images generated by our algorithm is compared to both real photographs and synthetic images generated using non-real-time techniques.

Rapid shadow generation in real-world lighting environments

Network architectures for collaborative virtual reality have traditionally been dominated by client-server and peer-to-peer approaches, with peer-to-peer strategies typically being favored where minimizing latency is a priority and client-server where consistency is key. With increasingly sophisticated behavior models and the demand for better support for haptics, we argue that neither approach provides sufficient support for these scenarios nor, thus, a hybrid architecture is required. We discuss the relative performance of different distribution strategies in the face of real network conditions and illustrate the problems they face. Finally, we present an architecture that successfully meets many of these challenges and demonstrate its use in a distributed virtual prototyping application which supports simultaneous collaboration for assembly, maintenance, and training applications utilizing haptics

Roger J. Hubbold

Papers

Modeling the effects of delayed haptic and visual feedback in a collaborative virtual environment

Accurate camera calibration for off-line, video-based augmented reality

Navigation guided by artificial force fields

Rapid shadow generation in real-world lighting environments

A network architecture supporting consistent rich behavior in collaborative interactive applications