Comput. Methods Appl. Mech. Engrg. 199 (2010) 224–228

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Comput. Methods Appl. Mech. Engrg.

journal homepage: www.elsevier .com/locate /cma

MCAD: Key historical developments

Elaine Cohen a, Tom Lyche b, Richard F. Riesenfeld a,*

a School of Computing, University of Utah, USAb Centre of Mathematics for Applications, Department of Informatics, University of Oslo, Norway

a r t i c l e i n f o a b s t r a c t

Article history:Received 1 April 2009Received in revised form 9 May 2009Accepted 5 August 2009Available online 9 August 2009

Keywords:CADModeling

0045-7825/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.cma.2009.08.003

* Corresponding author.E-mail addresses: cohen@cs.utah.edu (E. Cohen

rfr@cs.utah.edu (R.F. Riesenfeld).

With an eye toward future developments, the most salient events in the history of MCAD, the ones withvery largest impact, are presented to create a concise review identifying the major factors that haveshaped its current incarnation in the workplace. In anticipation of the unification of CAD and engineeringanalysis, something that is likely to evoke a sea change involving many aspects in both fields, this historyis intended to provide some cultural and scientific context to facilitate the accommodations that will berequired for a rapid and smooth transition.

� 2009 Elsevier B.V. All rights reserved.

1. Background

Mechanical Computer Aided Design (MCAD), or simply CAD aswe refer to it in this specific context, is quite separate in its origins,problems, and landmark advances from Computer Aided CircuitDesign, also sometimes labeled CAD when its context is clear with-in its distinct electrical engineering domain. Like many disruptivetechnology trends driven by compelling application needs and cat-alyzed by a propitious stage set with prerequisite technologicaldevelopments, the origins of CAD sprang forth in a variety ofplaces. The time for CAD had come. In most salient terms, we pri-marily try to provide understanding and context for tracing whereCAD came from and how it got here. Advisedly we undertake a per-ilous endeavor to highlight its most significant origins and devel-opments, those that have had a lasting impact toward forgingcommercial CAD as it is known in the workplace today. Emphasisis being given to the sequence of pivotal technical developmentsover providing a historically detailed and comprehensively accu-rate record so that the cultural as well as scientific scope associatedwith its history is brought into clarifying relief. This is being suc-cinctly portrayed with anticipation of the impending unificationof geometric representation and engineering analysis, a missionto which this special issue is committed. There have been othermore detailed surveys, particularly in the mathematical aspectsof curve and surface design, e.g., [4].

The emergence of modern CAD does not hinge on any singletechnical advance. Rather it came about through the intertwinedevolution and driving interplay of several sister technology

ll rights reserved.

), tom@ifi.uio.no (T. Lyche),

streams, each, in turn, pacing and prodding along new requisitedevelopments in a synergistically guided course of history. The sig-nificant advances in CAD include, among others, the followingingredients: a creative imagination for a revolutionary technologystimulated by a large, complex and interconnected, intractableapplication problem; increasingly powerful computer and com-puter graphics systems; innovative, nontraditional mathematicalformulations for representing shape and their underlying concom-itant developments in theory; computationally robust evaluationalgorithms; fundamentally new interactive 3D design techniquesand methodologies suitable for design engineering; and the emer-gence of geometric modeling, with a facilitating, direct linkage toengineering analysis, as a bona fide discipline of its own. CAD jour-nals, conferences, courses and important reference books emerged.Above all, with its multifarious nature, CAD had become a fertileand academically legitimate focus for highly interdisciplinary re-search. Inasmuch as the early exploratory efforts required majorcapital investments, the advent of CAD research was typically asso-ciated with an industrial sector characterized by a large scale,heavily leveraged, business in which design and manufacture ofcomplicated sculptured forms were mainline activities, and forwhom a breakthrough in technology could engender distinguish-ing, massive, long term, competitive advantage. Partly for thesereasons – broad scope, process complexity, technical difficulty,costly market entry, long amortization horizon, keenly competitionmarket but potentially large returns – early leading explorationswere primarily associated with the ‘‘Big 3 CAD Industries,” namely,automotive, aeronautical, and naval engineering and manufactur-ing. Sparse academic research was largely confined to well-fundedprojects, ones with strong application orientations. Overall, theacademic setting was fertile for a few of the more theoretical inves-tigations centered on CAD representations and algorithms.

E. Cohen et al. / Comput. Methods Appl. Mech. Engrg. 199 (2010) 224–228 225

2. Early systems

During the 1960s, when Europe, the US, and Japan gave rise toimportant progenitor projects, we find the earliest seeds of modernCAD technology. Early systems were doubtless justified on anexploratory research basis with an eye toward future trends andbenefits rather than present day cost savings. For its time, the ad-vanced Norwegian Autokon system was extraordinary in variousrespects. Aimed at a then profitable shipbuilding industry, it wasmarketed as one of the first nonproprietary and externally (tothe customer), developed systems used in commercial applica-tions. Sold as a generic CAD tool mainly to shipbuilders, Autokonwas licensed worldwide, and became a harbinger of a lucrativeCAD software business model that would eventually become stan-dard CAD practice. Remarkably for this time in the 1960s whensplines were hardly known or used, Mehlum [23], the system de-signer and architect, based the internal shape representation on aform of nonlinear spline that he had specifically formulated for thisapplication. It marked an extremely early tie between freeformshape representations and physically inspired mathematical splinefunctions.

During the beginning stage between the late 1960s and early1970s, some other systems appeared. In France two seminallyimportant systems embodying completely novel CAD-basedschemes of enduring effect were essentially concurrently but inde-pendently introduced by Bézier [2] at Renault, and de Casteljau [9]in an internal technical report at A. Citroën. The work of de Castel-jau was unknown for many years because Citroën kept it corporateconfidential for decades.

Both Bézier’s approach in the Unisurf system as well as deCasteljau’s work rely on a notion of specifying a curve/surface bylaying down a control polygon/net that crudely mimics the desiredshape. Drawing on his background as a mathematician, deCasteljau’s recognized that approximation methods, not just inter-polation schemes, can play a fundamental role in shape represen-tation and design. A mechanical engineer by training, Bézierdemonstrated a profound link between CAD model prototypingand numerically controlled machining (CAM).

Other systems slowly emerged like the Japanese system TIPS[24], an internal automotive system at GM, various Coons Patchbased approaches in the aircraft industry, the shoe industry, andso forth.

In the 1970s as pioneering visionaries foresaw experimental ap-proaches slowly migrate into mainstream industrial production,pervasive CAD, still a nascent, unproven concept had already ig-nited in its community a growing imperative to transform radicallythe overall design and manufacture process. As critical capabilitycomponents began to emerge, incipient systems could begin thepath toward their envisaged future incarnation. In the US a high-end CAD software business had been broadly launched by thedominating, historically influential, Computervision sequence ofCADS systems, as well of some other early competitors whose his-tories were much briefer. In France the progeny of the present dayCATIA was being born through the work of Brun and Théron [8].Other early CAD ventures were getting launched as vendorsproliferated.

Still precariously inchoate, a CAD market was gradually form-ing, although obvious cost and business issues threatened itsgrowth. Early systems, nearly exclusively written in Fortran basedmodules grown in painfully tedious development environments,were major, highly labor intensive, software enterprises leadingto relatively low performance design (drafting, actually) systemsthat were expensive to acquire, operate and maintain. These earlyCAD systems provided an interactively slow and awkward to usedesign environment, even though they were hosted on expensive

mainframe computer configurations enhanced with the latestcostly computer graphics satellite subsystems. When successfullyintegrated technically in a commercial development process, theeconomic rationalization of the elusive CAD dividend, occasionallythe target of skeptical remarks remained a formidable manage-ment challenge and a technology thrust whose survival often de-pended principally on a protective umbrella of commitmentaccorded by a high level management champion who simply be-lieved strongly in the cause. Too often a benchmark task could havebeen accomplished more cost effectively, and maybe even moreexpeditiously using traditional processes not requiring expensive,state-of-the-art CAD environments. An immutable indictmentthreatening CAD could only be deflected by highly committedexecutives and lead engineers, many anonymous today, who fer-vently believed that the future realization of CAD returns wouldoffset massive, early CAD investments.

A section on early systems cannot conclude without referencingthe American businessman Pat Hanratty, founder of a companyMCS, whose contributions, although principally entrepreneurial,had significant historical impact. In a succession of business trans-actions his core proprietary CAD code was sold and rebranded tobecome the heart of several popular early systems, the ANVIL ser-ies being the best known.

3. CAD representations

In prefacing this section, we mention two events that bear con-siderable importance in the development of CAD. Since B-splinesplay such a large role in CAD, we feel compelled to referenceSchoenberg, whose extraordinarily broad, seminal work with Curryintroduces nonuniform B-splines in 1947, but curiously does notpublish it until 20 years later [16]. Subsequently this led to decadesof prolific activity in approximation theory including two definitivebooks on B-splines [5,26].

The second development occurred in 1974 when Barnhill andRiesenfeld convened a group of international researchers in an areathey collectively termed Computer Aided Geometric Design (CAGD,1974) [1]. A rather disparate collection of leaders who wereaddressing various issues involving computing techniques fordesigning freeform shapes, these researchers came from a varietyof disciplines in industry, government and academic institutions.Most of the attendees, including leading figures like Bézier andCoons, had known of a few other participants by reputation only.Still fewer participants enjoyed any prior personal acquaintance,the close relevance of common endeavors and interestsnotwithstanding.

In describing this 1974 meeting, [19] remarks, ‘‘The term CAGDwas coined by Barnhill and Riesenfeld in 1974 when they organizeda conference on that topic at the University of Utah. That conferencebrought together researchers from the US and from Europe and maybe regarded as the founding event of the field. It resulted in the widelyinfluential proceedings.”

Over the course of several decades CAD research activity gener-ated a plethora of geometric representations, although here, forbrevity, we only recount those of lasting commercial impact. Partlyfor lack of available alternatives, earliest systems, especially in theUS, generally employed Coons Patches. During this era usersgained experience with piecewise approaches to shape representa-tion and fully digitally specified surfaces. They also struggled withthe formidable challenge of manifesting internal patch parameters(the so-called ‘‘twist partition,” e.g.) to produce desired designforms. Intrigued by future possibilities, users were confrontedessentially with the task of designing 3D geometric shapes literally‘‘by the numbers,” as it were. Meaningfully specifying notoriouslyarcane ‘‘twist partition” values for the mixed partial derivatives

226 E. Cohen et al. / Comput. Methods Appl. Mech. Engrg. 199 (2010) 224–228

of a Coons patch representation was a much discussed technicalenigma of the time. The Coons Patch [14] reigned supreme for acouple of decades, but eventually was superseded in favor of new-er, more intuitively understandable, approaches that were moreamenable to interaction. Historically its role can be viewed asinstrumental to piquing enormous interest during the foundationaldevelopment of many early systems. The Coons Patch era alsohelped to set the CAD stage for the eventual migration towardmore locally behaved parametric representations embodyingbuilt-in smoothness. This was a time when global methods werede rigueur and interactive graphics was tantamount to wireframeimages rendered on line drawing graphics terminals.

Relatively concurrently in what historically appears to be inde-pendent developments in Paris, Bézier working at Renault and deCasteljau at Citroën devised intuitively understandable, predict-able interface schemes for defining shapes (cf. Section 2). Thesedevelopments had considerable impact inasmuch as they intro-duced a breakthrough, interactive design scheme amenable toCAD and conducive to designing aesthetically pleasing shapes.The succinct design output was simply the coefficients of a para-metric polynomial basis. This was probably the first approach togeometric design that provided an intuitive, easy-to-use, tractable,scheme for creating mathematically well-defined freeform curvesand surfaces. This method gave predictable control and an intui-tively simple interface providing highly acceptable shape behavior.It was truly a revolutionary development that triggered consider-able investigation and follow on activities.

Unlike nearly all other schemes based on interpolation formula-tions, these two French schemes generated curves theoreticallyguaranteed not to introduce any undesirable, historically vexing,extraneous shape undulations. These extraordinary properties, vir-tually unseen previously in CAD applications, quickly attractedmathematical interest in gaining fundamental understanding fortheir attractive behaviour. In analyzing Bézier’s Method, Forrest[20] exposed an underlying relationship to the Bernstein polyno-mial basis, which similarly applies to de Casteljau’s approach.

Thus, many major developments in Europe were shown to bebased on global polynomial approximation in contrast to the Amer-ican generated Coons Patch activity closely related to generalizedpiecewise Hermite interpolation. The former schemes had superior,aesthetically pleasing, shape properties while the latter heraldedsplines with local control properties.

Endeavoring to distill a copious body of research to the mostsalient and enduring, commercially important events affectingindustrial practice, we identify just a few subsequent develop-ments of similar importance. The next major development oc-curred when Riesenfeld [25] introduced the B-spline Method asthe proper spline counterpart of the Bézier design scheme, andthus introduced B-spline representations to the world of CAD.Albeit more complicated mathematically and algorithmically,B-spline curves and surfaces offered the benefits of Bézier’smethod as a proper special case while providing an array of addi-tional desirable capabilities due to their underlying, local splinebehavior. Structured as a companion thesis, Versprille’s disserta-tion [28] proposed Nonuniform Rational B-splines, now com-monly called NURBS, as the corresponding rational extension ofRiesenfeld’s Nonuniform B-splines. Within its expressive power,this important extension to NURBS exactly captured all conicssections, a commonly employed construction in pre-CAD designengineering.

While Voelcker and Requicha [29] spent many years developingthe PADL system in the US, Braid [7] in England implementedBUILD, a closely related doctoral thesis project carried out withinthe historic CAD Group at Cambridge University. Both efforts fea-tured the concept of modeling with primitive 3D elements of geo-

metric form like cubes, cylinders and spheres, and subsequentboolean combinations thereof. Although the notion of modelingreal-world designs exclusively with simple 3D solid primitives, so-lid modeling, as it were, proved too restrictive as a viable schemefor design engineering, the most enduring legacy of their modelingapproaches may be the solid modeling paradigm itself, i.e., thenotion of using an hierarchical tree of algebraic boolean combina-tions to specify a complex model built up from atomic geometricprimitives.

Evincing a somewhat artistic flare reminiscent of sketching ini-tially with long rough stokes that become recursively sharpened byshorter more refined ones, subdivision representations for curvesand surfaces grew from a relatively separate stream of contribu-tors. Generally speaking, the subdivision genre can be character-ized by the approach of defining a curve or surface as arepeatedly applied recursive procedure, typically a simple templateor set of rules. Defined by weighting neighboring existing vertices,additional, more closely clustered, vertices provide further refiningand smoothing at each recursive level. Subdivision surfaces defiedmore straightforward classification by traditional mathematicalanalysis because the resulting shapes are given as a limit of arecursive geometric construction procedure, not a traditionalclosed form surface equation. In time, subdivision schemes becameassociated with closed mathematical forms formulations and abetter taxonomical understanding ensued.

Although subdivision was first proposed by deRham [17], Chai-kin’s Method [11] evoked some crossover investigation from thespline community and likely gave impetus to Catmull and Clark[10] for their eponymous scheme. Working in England aroundthe same period of time, Doo and Sabin [18] published a subdivi-sion algorithm of their own. The schemes of Catmull and Clark,as well as Doo and Sabin, are historically important and heavilyreferenced as pioneering works that have become landmark resultsin subdivision surfaces.

Developed for the purpose of rendering and facilitating booleanoperations on them, the Lane–Riesenfeld Algorithm [21] for subdi-vision is intimately linked in its mathematical structure to Bézierand uniform B-spline surfaces. Most widely known and used inthe subdivision genre, Loop Subdivision [22] is box spline based,except at a few extraordinary points where the regular grid topol-ogy breaks down. The immediate connection to a closed form sur-face representation, namely box splines, is fundamentally revealedin discrete spline theory. A flurry of activity after the aforemen-tioned early schemes, including Dubuc, Gregory, Dyn, and Levinamong many others, led to a vast body of literature on subdivisionmethods, and this subsequently generated a better understandingof their mathematical essence. While popular in some areas out-side engineering, subdivision rarely appears in a CAD setting.

In highlighting just the most prominent advances, one couldactually make a large jump forward in years to the advent ofT-splines proposed by Sederberg et al. [27]. As the name suggests,this construction was developed to properly include B-splinesand NURBS in a generalization admitting more flexible knot lineconfigurations in surfaces. Currently being introduced as an add-on option for some popular commercial design systems, T-splinesuse ‘‘T-junctioned” knot lines to generalize (relax) the topologicallayout of the traditionally constrained rectilinear (tensor product)form imposed by B-splines surfaces. While still a relatively recentmethodology, considerable impact is anticipated from T-splines.The appeal of T-splines lies in a scheme that accommodates localpatch insertion and, thereby, leads to a substantially reduced num-ber of polynomial patches for equivalently complicated geometricshape. T-splines avoid the inherent, tensor product topology in-duced artifact causing new patches to cascade into areas, far fromthe site of a design modification, where they are neither needed

E. Cohen et al. / Comput. Methods Appl. Mech. Engrg. 199 (2010) 224–228 227

nor desired. This simply arises because the act of introducing anadditional patch in a region where additional parameters areneeded locally causes an entire new column and row of patchesto be generated in a surface.

4. B-spline algorithms

Inasmuch as the history and the development of CAD represen-tations and mathematical splines are inextricably intertwined, wenow look at key computational developments that have allowed B-splines and NURBS to become the international de facto standardrepresentation for CAD. Between CAD and B-spline methods, therehas been a significant symbiotic interchange of driving CAD appli-cation problems and approximation theoretic and algorithmic ad-vances. This trenchant overview is, again, guided by thediscipline that referenced events are only among the most signifi-cant in CAD.

The era of B-splines computation was essentially opened up bytwo concurrent developments of similar, numerically stable, recur-sive algorithms by de Boor [6] in the US and by Cox [15] in England.Theoretically useful as well, the Cox–de Boor Algorithm becamecentral to B-splines and to their robust computation, includingthe more general nonuniform form defined over a nonuniform knotvector.

The pioneering contributions of Bézier Curves, Coons Patchesand Riesenfeld’s B-spline Method for geometric design have beenpreviously described. Providing subdivision schemes for Béziercurves and uniform B-splines, Lane–Riesenfeld Subdivision [21] re-mains widely referenced, and has had considerable impact on CADalgorithms. Lane and Riesenfeld described methods, all based onthe same subdivision algorithm, for increasing design flexibilityby increasing the available free parameters, effecting boolean oper-ations, and rendering freeform B-spline objects in high imagequality.

Seeking extensions of Lane–Riesenfeld to B-splines with non-uniformly spaced knots to introduce additional parameters (knots)locally without involving the entire B-spline construction led totwo important algorithms for nonuniform knot vector refinementpublished in 1980: (i) the Böhm Algorithm [3] for serially insertingan arbitrary single knot, and, (ii) the Oslo Algorithms [12] for gen-erally inserting a set of knots in parallel, where the new knots maybe arbitrarily spaced including multiplicities. These algorithmsconsiderably facilitated the use of B-spline curves and surfaceswith nonuniformly spaced knot vectors.

The mere act of inserting one new knot into an existing uni-formly spaced knot vector immediately effects a transition to anonuniformly spaced knot vector regime from a uniform B-splinerepresentation. The larger dividends of using these powerful algo-rithms were only realized when supplanting uniformly spacedknot vector B-splines with an arbitrarily and selectively refinednonuniform knot vector. As noted this seemingly benign local stepactually entails the transition to nonuniform B-splines; that is lar-gely how it transpired in practice. The use of nonuniform B-splines,with their additional complications, only began to take off once aclear benefit was engendered. Leading to an approximate form ofrepresentational closure under boolean style modeling operations,splines, locally refined using one of the two aforementioned algo-rithms, offered a sufficiently attractive property to encourage thegradual transition toward nonuniform B-spline models, thus aban-doning the simpler but rigidly restrictive uniform (knot vector) B-spline models.

Inasmuch as degree raising methods for splines, also known asp-refinement in the FEM literature, are widely invoked as an every-day tool in the engineering analysis community, we cite two fun-

damental references from an arena that has inspired manycontributions [9,13].

5. Conclusions

It would be gratifying, indeed, if this special issue and its mis-sion to advance Isogeometric Analysis were to play a significant rolein triggering the Next Big Thing in CAD. A unification of geometryand analysis models would surely stimulate a sea change, and afresh burst of activity in repositioning CAD with respect to itsnew and expanded modeling responsibilities.

Acknowledgements

The authors are grateful to Tom Hughes for emphasizing theimportance of generating key historical and cultural snapshots, likethe one presented here, to catalyze the fusion needed to make Iso-geometric Analysis commonplace, and for providing helpful com-ments during the writing. Thanks to Yuri Bazilevs and all whohave worked to make this important special issue possible. This pa-per has benefited from a meticulous reviewing process that ren-dered several improvements appreciated by the authors.

This work was supported in part by the National Science Foun-dation (CCF0541402) and the Norwegian Research Council.

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