Computer-aided geometric design (CAGD) is a new field that initially
developed to bring the advantages of computers to industries such as
automotive, aerospace, and shipbuilding. CAGD expanded rapidly and now
pervades many areas, from pharmaceutical design to animation. We are
surrounded by products that were first visualized on a computer. These
products were modified and refined entirely within the computer, so that
when the product entered production, the tools and dies were produced
directly from the geometry stored in the computer. This process is known
as virtual prototyping. Computer visualizations of new products reduce
the design cycle by easing the process of design modification and tool
production. CAGD is based on the creation of curves and surfaces and is
accurately described as curve and surface modeling. Using CAGD tools
with elaborate user interfaces, designers create and refine their ideas
to produce complex results. They combine large numbers of curve and
surface segments to realize their ideas. However, the individual
segments they use are relatively simple, and it is at this level that
the study of CAGD is concentrated.

Automobile, aircraft, aerospace, and ship designers use CAGD techniques
in the design of various types of vehicles. Wire-frame drawings are used
to model indivdual components and plan surface contours for automobiles,
airplanes, spacecraft, and ships.

Individual surface sections and vehicle components can be designed
separately and fitted together to display the total object.
Simulations of the operation of a vehicle are often run to test the
vehicle performance as in the figure. Realistic renderings allow the
designer to see how the finished product will appear.

Computer-aided geometric design has mathematical roots that stretch back
to Euclid and Descartes. Its practical application began with automated
machinery to compute, draft, and manufacture objects with free-form
surfaces. Production pressures in the aircraft industry during World
War II stimulated many new devices to enhance and accelerate design and
manufacturing. For example, in 1944, Liming designed fuselage spars with
a "superelliptic" method that could be implemented with an
electromechanical calculator.

Shipbuilders also became interested in CAGD early on for many reasons.
One example, that may sound trivial but was a serious impediment to ship
design, was that the only place large enough to draw full-scale plans
for a ship was in the loft of the shipbuilders' dry dock. The huge
drawings would warp and shrink in the moist air, causing very real
manufacturing problems. Computers provided the greatest stimulus because
of their power to enable new ideas.

In 1963, Ferguson developed one of the first surface patch systems by
which individual curvilinear patches are joined smoothly to create the
surface "quilt". He also introduced the notion of
parametrically defined surfaces, which has become the standard because
it provides freedom from an arbitrarily fixed coordinate system.
Vertical tangent vectors can be defined by differentiation, for
instance, which is not possible in explicit Cartesian form.

In the mid 1960s, automotive companies became involved in CAGD as a way
to drive milling machines. Car bodies were designed by artists using
clay models. Painstaking measurements produced data that could drive
numerically controlled milling machines to produce stamp molds.

The initial use of CAGD was to represent the data as a smooth surface
for numerical control. It soon became apparent that the surfaces could
be used for the design.

In 1971, Pierre Bézier reformulated Ferguson's ideas so that a
draftsman without any extensive mathematical training could design a
surface. Bézier's system, UNISURF, was used by Renault and
became a milestone in the development of CAGD. It epitomized the
difference between surface fitting and surface design. The purpose of
design was to provide the draftsman, who had strong intuition about
shape but limited mathematical training, with computer tools that
empowered him or her to use the sophisticated mathematics of surface
representation.

In the meantime, the mathematical underpinnings of CAGD continued to
advance. DeCasteljau examined triangular patches and developed
evaluation techniques. Coons unified much of the previous work into a
general scheme that became the basis of the early modeler PDGS made by
Ford. At General Motors in 1974, Gordon and Riesenfeld exploited the
properties of B-spline curves and surfaces for design.

Driven primarily by the automotive, shipbuilding, and aerospace
industries, both the mathematics of CAGD and the designer interface
tools continued to improve through the 1970s. The first CAGD conference
was organized by Barnhill and Riesenfeld in 1974, where the term "CAGD"
was first used.

In the 1980s, the power and versatility of computer aided designing
seemed suddenly to be discovered by anyone who had a free-form geometric
surface application. Industrial designers were smitten with the power of
computer design, and many commercial modelers became the basis of
several substantial applications, including CATIA, EUCLID, STRIM, ANVIL,
and GEOMOD. Geoscience used CAGD methods to represent seismic horizons;
computer graphics designers modeled their objects with surfaces, as did
molecule designers for pharmaceuticals. Architects discovered CAGD, word
processing and drafting programs based their interface protocols on
free-form curves (PostScript), and even moviemakers discovered the power
of animating with such surfaces, beginning with TRON, continuing through
Jurassic Park, and beyond.