Les A. Piegl

• University of South Florida

Peer review is a widely utilized pedagogical feedback mechanism for engaging students, which has been shown to improve educational outcomes. However, we find limited discussion and empirical measurement of peer review in visualization coursework. In addition to engagement, peer review provides direct and diverse feedback and reinforces recently-lea...

Assessing the quality of 3D printed models before they are printed remains a challenging problem, particularly when considering point cloud-based models. This paper introduces an approach to quality assessment, which uses techniques from the field of Topological Data Analysis (TDA) to compute a topological abstraction of the eventual printed model....

Assessing the quality of 3D printed models before they are printed remains a challeng- ing problem, particularly when considering point cloud-based models. This paper introduces an approach to quality assessment, which uses techniques from the field of Topological Data Analy- sis (TDA) to compute a topological abstraction of the eventual printed mo...

Scalar fields are used to describe a variety of data from photographs, to laser scans, to x-ray, CT or MRI scans of machine parts and are invaluable for a variety of tasks, such as fatigue detection in parts. Analyzing scalar fields can be quite challenging due to their size, complexity, and the need to understand both local and global details in c...

The advancement of technology and its application to the field of education has caused many to re-examine the merits and pitfalls of cyberlearning environments. Though there is a wealth of research both for and against its mainstream use, there is a consensus that much work remains to be done in key areas such as collaboration, course content, pers...

This paper revisits a more than half a century old problem: slice a free-form object into layers for manufacturing. A point based approach is taken that would have been prohibitive even a decade ago. Due to modern hardware, plenty of storage and a plethora of software packages, the time has come to ditch complicated and error prone numerical code a...

We present a new approach for accessing and visualizing point-based data in CAD applications. Instead of developing a traditional database around spatial data structures, our approach augments a data indexing engine to enable quick access to data. The primary advantage of an indexing engine is flexibility. The approach enables both range queries fo...

This article presents the design of a web-based knowledge management system as a training and research tool for the exploration of key relationships between Western and Traditional Chinese Medicine, in order to facilitate relational medical diagnosis integrating these mainstream healing modalities. The main goal of this system is to facilitate deci...

3-D printing, also known as additive manufacturing, has gained a lot of attention both within and outside CAD research. Even popular media have touted the technology as one of the game changer technologies of the 21st century. Simply stated, most printing devices add material to an unfinished part, layer by layer, until the entire object is complet...

Three dimensional printing has gained considerable interest lately due to the proliferation of inexpensive devices as well as open source software that drive those devices. Public interest is often followed by media coverage that tends to sensationalize technology. Based on popular articles, the public may create the impression that 3D printing is...

There has been much attention on sophisticated algorithm design to compute geometric arrangements with both time and space efficiency. The issue of robustness and reliability has also been the subject of some interest, although mostly at the level of theory rather than practice and commercial grade implementation. What seems to have received very l...

Given a set of axis-aligned rectangles in the plane, this paper presents an algorithm for the removal of rectangle containment as well as rectangle enclosures. That is, given a query rectangle Rq, this algorithm removes all rectangles Rk, … , Rl from the rectangle set that are contained in Rq. It also removes Rq if there is a rectangle Rj that encl...

We reveal the basement membrane, a specialized connective tissue structure found in all tissue systems, as a framework in an adaptive computer aided design (CAD) strategy for the reverse engineering of 3 dimensional (3D) tissue structures. Our approach to the creation of functional 3D tissue structures is centered on our previous models of vascular...

NURBS were introduced into CAD/CAM systems predominantly for the representation of conventional objects, such as conics and quadrics. Among these, the circle played a critical role in representing a myriad of parts used in the every-day practice. Being the most universally used object, the circle has enjoyed the most popularity in science and engin...

This paper presents a methodology to repair flawed migrated models that are designed with knowledge-guided NURBS (KGN). Incompatible traditional CAD packages that are based on NURBS technology have been for many years carrying out the exchange of models and data through either neutral file formats (IGES or STEP) or proprietary formats. The exchange...

This paper presents a robust algorithm to solve the line-curve intersection problem used frequently in design, manufacturing, graphics, art, etc. A global solution is proposed, i.e. all the intersections are found and computed to high accuracy requirements. The emphasis is on robustness, reliability and to handle geometric as well as numerical anom...

This paper presents a framework and a methodology to increase the robustness of CAD systems based on the de facto standard of NURBS. Contrary to popular belief, the solution to robustness does not lie in either the mathematical tool used in computations or in the form of arithmetic chosen, but rather, it depends on how much and what types of inform...

A knowledge-guided approach is presented to compute the distance between a point and NURBS curves and surfaces. Given a set of query points, a global algorithm is introduced that finds the required distances. The method has the following major components: (1) a discrete version of a physical wave model is implemented to find nearest regions, (2) a...

This paper outlines the fundamentals of a knowledge-guided modeling system based on NURBS. NURBS have become standard tools in shape representation in almost all fields where shape information is processed, however, the representation has been largely numerical with no sufficient information attached to aid the design and production processes. The...

Currently, there are no comprehensive and harmonized regulations for unmanned aviation, instead there are many groups and agencies developing standards and policies. These include among others, the International Civil Aviation Organization (ICAO), the US Federal Aviation Administration (FAA), the American Society of Testing Materials (ASTM), the Ra...

The primary goal of regulating UAS operations is to assure an appropriate level of safety. This goal is quantified by most national aviation agencies as an “Equivalent Level of Safety” with that of manned aviation, also known as the ELOS principle. Although ELOS is difficult to define, some insight may be gained by analyzing accident statistics of...

The concept of a flying machine originates in ancient Greece and China, whereas the first modern unmanned aircraft was demonstrated less than 15 years after the first flight by the Wright brothers. For several years these unmanned systems were used as target drones and it wasn’t until the 1950s that the first reconnaissance drones were developed, l...

Current manned aviation regulation includes provisions for airworthiness certification of different aircraft types, maintenance requirements, aircraft registration and marking, pilot certification, airspace classification, operating rules and special classes of vehicles among others.

There are a number of issues any UAS integration roadmap must take into account. UAS are different in their construction, applications, flight characteristics and failure modes and these differences must be acknowledged. The risk reference systems used in manned aviation also don’t apply due to the lack of people on board the aircraft. An appropria...

Using the methodologies described in Chap. 5, it is possible to derive reliability requirements for UAS of different sizes and designs and under different scenarios. In general, conservative risk estimates are over-restrictive in the case of small systems, while many UAS would have problems maintaining appropriate safety levels over major populated...

This paper presents a solution to the autonomous vertical autorotation problem of unmanned helicopters using a novel nonlinear model predictive controller (NMPC) enhanced by a recurrent neural network (RNN) that handles the nonlinear optimization. The controller utilizes an internal, nonlinear autorotation model and is capable of handling input and...

This paper deals with the challenging task of computing accurate contours from CT and MRI scans using B-spline curve approximation. To date bio-modeling and visualization have been performed primarily on voxel and facet (triangle) based models. On the other hand, traditional CAD has reached a level of sophistication where just about any object can...

Small unmanned helicopters are suitable for a variety of applications including search and rescue, surveillance, communications, traffic monitoring as well as inspection of buildings, power lines and bridges. This paper presents an on-line, model-based, real-time autonomous autorotation controller, tailored for small helicopters. The approach selec...

Safe operations of unmanned rotorcraft hinge on successfully accommodating failures during flight, either via control reconfiguration or by terminating flight early in a controlled manner. This paper focuses on autorotation, a common maneuver used to bring helicopters safely to the ground even in the case of loss of power to the main rotor. A novel...

Small unmanned helicopters are suitable for a variety of applications including search and rescue, surveillance, communications, traffic monitoring as well as inspection of buildings, power lines and bridges. This paper presents an on-line, model-based, real-time autonomous autorotation controller, tailored for small helicopters. The approach selec...

A method to compute curvature minima and maxima of parametric curves (represented in NURBS format) is presented in this paper. Since the curvature changes vary rapidly along the path of (even smooth) curves, a biarc filter is employed to approximate the curvature function with a piecewise constant function. This allows the isolation of curvature ex...

In vitro biomedical engineering of intact, functional vascular networks, which include capillary structures, is a prerequisite for adequate vascular scaffold production. Capillary structures are necessary since they provide the elements and compounds for the growth, function and maintenance of 3D tissue structures. Computer-aided modeling of stereo...

Two-dimensional micro-computed tomography (micro-CT) slices can be reconstructed into three-dimensional (3D) models that demonstrate capillary beds. This study focused on the acquisition of data necessary to create scaffolding that directly mimics the unique structural patterns of a microvascular tree system. The Microfil vascular contrasting metho...

UAV accidents have been steadily rising as demand and use of these vehicles increases. A critical examination of UAV accidents reveals that human error is a major cause. Advanced autonomous systems capable of eliminating the need for human piloting are ...

This is the only book that presents in a comprehensive way current manned aviation regulation, airworthiness certification, special aircraft categories, pilot certification, federal aviation requirements, operation rules, airspace classes and regulation development models. It is the first book that discusses unmanned aircraft systems levels of safe...

Unmanned Aircraft Systems (UAS) have seen unprecedented levels of growth during the last decade in both military and civilian domains. It is anticipated that civilian applications will be dominant in the future, although there are still barriers to be overcome and technical challenges to be met. Integrating UAS into, for example, civilian space, na...

Currently many countries are developing regulation to allow unmanned aircraft systems (UAS) operations in their National Airspace System (NAS). Successful integration requires UAS to achieve, at a minimum, an equivalent level of safety to that of manned aviation. Safety is primarily defined in terms of the risk to human life, although potential col...

Any aircraft, manned or unmanned, may enter safely and legally into the US National Airspace System (NAS) provided that it has been issued an airworthiness certificate complying with Federal Aviation Administration (FAA) requirements. Unfortunately corresponding requirements, procedures and regulations for airworthiness certification of unmanned ai...

An algorithm to interpolate data points with directional constraints is given in this paper. The interpolating B-spline curve passes through the data points and assumes tangent directions at arbitrarily selected points. The advantages of the method is that the user is free to select any number of directional constraints and the method produces full...

This paper presents a method for converting a NURBS curve of any degree to a non-rational B- spline curve of any other degree. The conversion is parametric rather than geometric, i.e. the geometry as well as the parametrization are approximated. The algorithm contains straightforward computations only, i.e. it does not rely on discrete sampling, gu...

The objective for this research is to streamline design for manufacturing (DfM) analysis across all manufacturing domains and to provide transparency for DfM measures and evaluation process used. Generic steps are identified for performing manufacturability ...

This short paper presents 10 challenging research areas in the general field of computer-aided design. The research problems come from the author's personal experience, and as such are highly subjective. All findings and opinions are those of the author and do not represent any of the institutions the author is affiliated with.

Given a point data set that contains several fairly unevenly distributed random points, this paper presents a new paradigm of curve interpolation to fit a curve to the data with end tangent vector constraints. The method uses a base curve, which is subjected to constrained shape manipulations to achieve interpolation, while maintaining end point an...

Robust computations have been haunting CAD system builders for decades. The common belief among researchers is that the source of the problem lies in rounded arithmetic and that new forms of computations may be necessary to ensure consistency and accuracy in commercial systems. This paper argues that, although floating point arithmetic is not perfe...

Given a random data set that covers a surface patch, a method is presented to fit a B-spline surface to the data. The surface fit can be an interpolating or an approximating surface, depending on the number of points involved. The general technique is to apply a base surface and to modify this surface, via constrained shaping, to achieve interpolat...

A method to approximate a circular arc of any sweep angle with integral B-spline curves of any degree is presented. The idea is to interpolate end derivatives as well as some internal points with integral B-splines of given degree and continuity. The critical element is the choice of the right end derivative directions and magnitudes. The points an...

An algorithm for approximating arbitrary NURBS curves with biarcs is presented. The main idea is to approximate the NURBS curve with a polygon, and then to approximate the polygon with biarcs to within the required tolerance. The method uses a parametric formulation of biarcs appropriate in geometric design using parametric curves. The method is mo...

Surface skinning is a powerful tool that allows the designer to pass a B-spline surface through a set of curves. Although this technique has been in use for about two decades, its many problems raise questions about its usefulness as a design tool. The contribution of this paper is twofold: (1) several skinning problems are studied and analyzed, an...

Algorithms for fitting circular arcs and straight line segments to measured data are presented. Algebraic as well as geometric methods are discussed leading to efficient techniques for arc and line fitting. A thorough empirical analysis reveals that the best circle fit is via algebraic minimization followed by distance minimization, whereas the bes...

A very simple algorithm for computing all k nearest neighbors in 2-D is presented. The method does not rely on complicated forms of tessellation, it only requires simple data binning for fast range searching. Its applications range from scattered data interpolation to reverse engineering.

n -sided region with G ɛ continuous NURBS patches that interpolate boundary curves and approximate given cross-boundary derivatives. The NURBS surfaces joining along inner or boundary curves have normal vectors that do not deviate more than the user-specified angular tolerance ɛ. The method is general in that there are no restrictions on the number...

This paper presents algorithms for computing offsets of NURBS curves and surfaces. The basic approach consists of four steps: (1) recognition of special curves and surfaces; (2) sampling the offset curve or surface based on bounds on second derivatives; (3) interpolating these points; and (4) removing all unwanted knots using the offset tolerance....

Algorithms for computing the derivative of NURBS with respect to a knot are presented. Rational and nonrational curves and surfaces as well as basis functions are differentiated with respect to a knot. The derivative entities are computed by control point or basis function differencing divided by appropriate knot spans.

An algorithm for obtaining a piecewise triangular approximation of a trimmed NURBS surface is presented. The algorithm is geometry based, i.e. the surface is subdivided into triangular facets based on its geometric characteristics and not on its parametrization. No assumption is made about the surface's parametrical representation; it does not have...

Although the study of the visual system has been popular for a number of years, data derived from human factors or applied vision research continue to be insufficient to establish guidelines for developing biologically correct three-dimensional images. Current techniques look at monocular and binocular attributes in depth, but overlook how the actu...

Symbolic operators for NURBS curves and surfaces are presented in this paper. The operators are used to compute NURBS entities by performing algebraic operations using NURBS curves and surfaces as variables. Dot and cross products, sum/difference and derivative operators are presented. An application to construct ruled surfaces to rational rail cur...

In the previous twelve chapters we introduced different aspects of modeling with NURBS. These chapters covered basically two things: (1) the underlying mathematics, and (2) algorithms illustrating how the tools can be turned into computer code. Although the pseudocodes presented in each chapter are fairly detailed, containing all the necessary info...

The central theme of this chapter is the relationship of NURBS geometry, as practiced in this book, to other methods of representing curves and surfaces, and to several important standard formats for the exchange of geometric data between two systems. We have used a specific form of knot vector throughout this book; Section 12.2 discusses another t...

An algorithm for approximate skinning through cross-sectionalNURBS curves is presented. The method eliminates the problem of dealing with huge amounts of control points obtained during the curvecompatability process. It also allows the designer to specify large numbers of cross-sections and approximately fit a smooth surface to these curves to any...

A procedural method for scattered data interpolation is presented. The interpolating surface represents terrain surfaces used in Digital Terrain Modeling (DTM). The construction provides visually continuous surfaces whose shape can be locally or globally controlled, can interpolate disconnected domains, and can maintain break lines or break triangl...

Triangulation in two and higher dimensions began with Dirichlet, Voronoi, Thiessen, and Delaunay. A number of textbooks and papers have extensively covered the properties of triangulations and algorithms for their construction. Most dealt with theoretical aspects of the algorithms and gave upper bounds on their complexity. Here we present a new alg...

An algorithmic approach to degree reduction of B-spline curves is presented. The method consists of the following steps: (a) decompose the B-spline curve into Bézier pieces on the fly, (b) degree reduce each Bézier piece, and (c) remove the unnecessary knots. A complete algorithm and precise error control are provided.

The purpose of this chapter is to develop tools which allow a designer to interactively make local modifications to an existing NURBS curve or surface, in a way that is natural and intuitive. A NURBS curve or surface is defined by its control points, weights, and knots; modifying any of these changes the shape of the curve or surface. Generally des...

In Chapters 7 and 8 we showed how to construct NURBS representations of common and relatively simple curves and surfaces such as circles, conics, cylinders, surfaces of revolution, etc. These entities can be specified with only a few data items, e.g., center point, height, radius, axis of revolution, etc. Moreover, the few data items uniquely speci...

Sections 2 through 5 of this chapter cover the NURBS representation of the four surface types: bilinear surfaces, general cylinders (extruded surfaces), ruled surfaces, and surfaces of revolution. As the reader surely realizes by now, these representations are not unique. Considerations such as parameterization, convex hull, continuity, software de...

The central theme of this chapter is the relationship of NURBS geometry, as practiced in this book, to other methods of representing curves and surfaces, and to several important standard formats for the exchange of geometric data between two systems. We have used a specific form of knot vector throughout this book; Section 12.2 discusses another t...

In the previous twelve chapters we introduced different aspects of modeling with NURBS. These chapters covered basically two things: (1) the underlying mathematics, and (2) algorithms illustrating how the tools can be turned into computer code. Although the pseudocodes presented in each chapter are fairly detailed, containing all the necessary info...

In this chapter we present five tools which axe fundamental in the implementation of B-spline curves and surfaces; these are knot insertion, knot refinement, knot removal, degree elevation, and degree reduction. We devote a section to each topic, and the layout of each section is roughly: a statement of problems (curves); a list of applications; cl...

In this chapter we cover various topics which are rather fundamental in implementing NURBS geometry.

In this chapter we define nonrational B-spline curves and surfaces, study their properties, and derive expressions for their derivatives. For brevity we drop the word nonrational for the remainder of this chapter. The primary goal is to acquire an intuitive understanding of B-spline curves and surfaces, and to that end the reader should carefully s...

Curves consisting of just one polynomial or rational segment are often inadequate. Their shortcomings are: a high degree is required in order to satisfy a large number of constraints; e.g., (n-1)-degree is needed to pass a polynomial Bé curve through n data points. However, high degree curves are inefficient to process and are numerically unstable;...

The conic sections and circles play a fundamental role in CADCAM applications. Undoubtedly one of the greatest advantages of NURBS is their capability of precisely representing conic sections and circles, as well as free-form curves and surfaces. We assume a knowledge of conics and circles; the purpose of this chapter is to study them in the framew...

The two most common methods of representing curves and surfaces in geometric modeling are implicit equations and parametric functions.

In this chapter we cover several advanced surface construction techniques, namely swung, skinned, swept, Gordon, and Coons surfaces. Roughly speaking, the idea in this chapter is to take one or two curves, or sets of curves, and to create a NURBS surface which interpolates these curves; i.e., the given curves are isoparametric curves in the NURBS s...

Until recently B-spline curves and surfaces (NURBS) were principally of interest to the computer aided design community, where they have become the standard for curve and surface description. Today we are seeing expanded use of NURBS in modeling objects for the visual arts, including the film and entertainment industries, art, and sculpture. NURBS...

A direct algorithm for computing constrained Delaunay triangulation in 2-D is presented. The algorithm inserts points along the constrained edges (break lines) to maintain the Delaunay criterion. Since many different insertions are possible, the algorithm computes only those that are on the Delaunay circles of each intersected triangle. A shelling...

A software-engineering approach to the degree elevation of B-spline curves is presented. A general method is introduced that consists of the following steps: (a) decompose the B-spline curve into piecewise Bézier curves by a modified version of knot insertion, (b) perform the necessary operation (degree elevation) on each Bézier segment, and (c) re...

A fast algorithm for triangulating multiply connected polygonal domains is presented. The algorithm is an application of the ideas presented in [25], to arbitrary domains. The main contributions are the extension of range searching to handle arbitrary domains and constraint edges, and the generation of the output on the fly without storing triangle...

An algorithm for triangulating 2-D data points that is based on a uniform grid structure and a triangulation strategy that builds triangles in a circular fashion is discussed. The triangulation strategy lets the algorithm eliminate points from the internal data structure and decreases the time used to find points to form triangles, given an edge. T...

A direct algorithm for computing the Delaunay triangulation of 2D data points is presented. The algorithm is based on a sparse-matrix data structure and on a circular-triangulation strategy, called shelling, that guarantees that the triangulation is complete and correct, and allows the dynamic update of the internal sparse-matrix data structure dur...