Chadwick attempts to explain the mystique behind b-splines, and provides
a run-down on software developers supplying the tools that enable them
to be used in the creation of smooth, complex surfaces.
appears that one of the most significant elements in design is the
ability to produce smooth freeform curves in 2 and 3 dimensions, and to
extrude these curves into complex surfaces. Previously considered
possible only with high end CAD software, a number of mid-range software
developers, such EDS with the latest version of Solid Edge, IronCAD,
Tebis and PTC in Wildfire, have all announced enhancements in their
products that can handle b-splines more effectively and through them
create more convoluted smooth surfaces.
of course, has had the capability for a number of years in its hybrid
CAD package – a solid and surface modelling tool that has been used to
design numerous domestic products, from steam irons and kettles to
lawnmowers with complex free-form shapes.
therefore, is the mystique behind b-splines?
we delve into the subject a bit more closely, it is worth bringing up
some comments made by one of the people I discussed the issue with. I
won’t name him, as the remarks were ‘off the record’ and cast a
somewhat more pessimistic eye over the issue, claiming that the vast
majority of design engineers, even those he supplies with software from
one of the suppliers listed above, couldn’t care less about the ‘curves’
remarks made a lot of sense. The majority of products being developed in
the manufacturing industry are designed to be as simple as possible,
with the design engineer making the most important decisions about the
shape of the product – forget, for once, the input from the sales, or
the marketing department.
drives the designers is the ability of the factory to actually produce
the product. Complex curves and shapes make it more costly and difficult
to put into production – especially if the production run is pretty
small. Some industries – and he mentioned Dyson as a case in point –
produce their products in sufficient quantities to absorb the extra
costs involved – but, by and large – curves are taboo!
exception to this, he conceded, is the plastics industry, where complex
shapes can be moulded far more effectively, the shape being used,
automatically, to produce the shell of the mould. In all other
industries, he claimed, the designer sought merely to provide the
simplest shape possible to cover the gubbins inside, from rocker box
covers in an automobile to switch element covers.
for the sudden flush of improved curve and surfacing tools in the new
generations of CAD modelling packages, he put this down to the emergence
of the capability in a more developed state in both the ACIS and
Parasolid kernels upon which most packages are based. Mechnical design
software, he explained, developed around the needs of the industrial
designers above, and it is only recently that the need for more
efficient surfacing tools is starting to be satisfied.
article, therefore, is dedicated to those idiots who fly in the face of
such reason, and persist in trying to design the dramatic looking shapes
that persuade the general public that the contents are as stunning as
are named after the implements that loftsmen used to create the profiles
of small boats a couple of centuries ago (and are still being used by
some specialised boatbuilders – particularly Roger Dongray, the
inventor of the very successful Cornish Crabber).
to draw accurate curves on a drawing board, they took themselves off the
sail loft in the shipyards, where they could lay out the shape of the
hull on the massive floorspace. The splines they used were long pieces
of flexible timbers, which they stretched between two fixed points, and
fixed lead weights (called ducks) at intervals along the spline. With
this they were able to adjust the curve of the spline to produce the
exact curve they were looking for.
The shape was used as a base line for constructing the rest of
has determined that a minimum of ducks was needed to produce a perfect
shape for his purposes, and that over-egging the problem tended to
produce unsatisfactory results.
that is precisely what splines are today – a continuous free-form
shape formed by a number of control points that determine the flow of
the curve. The ‘b’ means, simply, basis.
you were to search the web for a more technical explanation of b-splines,
you would come across a large number of academic sites that provide
extremely complex mathematical reasoning behind the construction of such
curves, accompanied by a bewildering array of intricate equations.
Forget it! All that you need to know is that b-spline curves are an
extension to simple and Bezier curves, which have been around for a long
is a mathematical basis to such curves, owing much to the graphical
representation of cos and sin waves. Because of this, Bezier curves are
constrained by the directions they can travel – there can
only be one value of x and y. B-spline curves, on the other hand,
can loop back on themselves, and create closed curves in any
term that is widely used to describe such curves is NURBs –
Non-Uniform Rational B-splines. They are used to control the smoothness
of the overall curve – a curve that contains no kinks or sharp
corners, and flows smoothly through the intermediate control
is achieved by the software introducing parametric capabilities to the
control points. When one of them is moved, the nearest control points
are also affected. They do not move, but the angle that the curved line
takes as it passes through the control points changes to retain the
overall smoothness of the curve. In
this way, only the part of the curve nearest to the control being moved
is affected, with little or no effect on the parts of the curve furthest
away. The parametric function also means that the direction of the curve
bears a relationship to the adjacent curve, and can eventually return
to basis, mentioned briefly above. The basis function determines the
strength of the influence of a control point at a particular position on
the curve. Mathematical explanations of curves relate to a curve having
a particular period of time as it progresses. If we imagine a particle
travelling along the curve, as it nears a particular control point, the
basis value of the control point determines how much effect it will have
on the curve, tapering away as it passes the point. In this way the
mathematical shape of the curve can be defined.
Enough of this, though! For a more complete definition of b-splines and NURBs I did find a particularly useful exposition on an Apple web site, www.devworld.apple.com written by Philip Schneider of Apple. I have saved the piece, and would happily email it to anyone interested.
able to produce b-spline curves in 3D is a starting point for producing
Class A surfaces, used extensively in automotive design. Below we list
some of the main software suppliers who have installed the best examples
of the technology in their modellers.
of the principal suppliers of surfacing software is ICEM Limited, with
its ICEM Surf software, of which version 4.3 has recently been
Surf now includes parametric curve sketching and editing amongst its new
functions, and G3 curvature matching – an industry standard in Class A
surfacing. The software includes numerous features for adding parametric
data to surfaces and comparison software for comparing the digitally
produced surfaces with digitally scanned tool and die or even physical
model data. Quick Surfacing
takes point cloud data from scanned physical models that can be
converted to surfaces, ready for further design amendments using ICEM
Surf’s surfacing tools.
next generation of ICEM Surf will be based on an object-oriented
software architecture, and will use parametric technology to build on
the capabilities of ICEM Surf. The provision of a free-form modeller
alongside the latter package will, according to ICEM, start to bridge
the gap between stylists and industrial designers. Lee Cureton, ICEM
Chief Executive, says that “…it will spell the end of the divide
that exists between the styling and product design function and the
design engineering function – benefiting everyone involved in the
product development process.”
first real introduction to b-splines and surfaces was with VX
Corporation. In Verison 7 of their hybrid modelling software, released
at the beginning of the year, the company produced enhancements to its
surfacing tools to speed up the surfacing process, with powerful new
tools to enable designers to create even more complex shapes than
users can employ direct surface manipulation, pulling on any point on a
face in any direction – modifying the underlying b-splines – to
create unlimited surface shapes.
software is widely used in mold creation for plastic modelling, and some
of the functions provided with the software are used by designers to
remove faces and fillets, and to repair gaps created when manipulating
the surfaces. Mould designers also have to add draft angles so that
parts can be ejected cleanly from moulds. Using a Remove Faces/Fillets
command, fillets created by the designer can easily be removed, add the
necessary draft and the re-fillet.
6 is another hybrid modeller, that has also introduced powerful
surfacing tools, and, like VX, can turn surfaces into complex faced
solids – and solids into surfaces. IronCAD has integrated both the
ACIS and the Parasolid kernels into the software, providing a wealth of
software capability in one package. Surfaces can be created in both ACIS
and Parasolid, as IronCAD allows the user to specify a specific kernel,
selecting whichever has the most suitable tools for the particular
surfaces being created. One kernel may have an advantage in
designing one type of geometry, whilst the other kernel provides
better results with different geometry – choice of kernel providing
the utmost freedom in design.
says that its surfacing capabilities compare very favourably with other
desktop products on the market today – delivering a perfect blend of
surface styling and solid modelling. It also provides a level of
flexibility not found in other design systems.
software also contains sheet metal design, draughting, seamless
photo-realism and animation in one total design solution, at a very
reasonable price – nearly half the price of most mid-range solid
modellers (and, incidentally, similar to VX’s prices).
has recently released the latest version of Solid Edge – Version 14. A
significant development in the software is the emergence of Rapid Blue
– shape creation technology that, like the other software mentioned,
‘puts the user in control by providing the shape the designer wants,
rather than the one the CAD system wants to provide’. Basically the
same control over b-splines and surfaces that we have already been
Blue contains some unique features, though, called Blue Dots, Blue Surf,
shape-preserving curves, dynamic editing and complementary surface
blending, filleting and analysis capabilities.
The latter tools handle all of the complex problems that come
with combining different surfaces and awkward angles into one homogenous
latest release of Pro/Engineer -
Wildfire – completely redefines the software, adding, amongst many
other new tools, improved modelling capabilities, especially for the
creation of complex surfaces. Wildfire has added easy-to-grab handles to
its models for manipulating shapes – simply grab the model and re-work
is another company that has added control to the creation of B-splines -
by using the defining control points as well as the interpolation points
typically input by the user and through which the curve passes. Alibre
uses a Modify B-spline command - adding and deleting unnecessary points,
but, most usefully, providing the ability to specify the slope of a
point by entering a weight and an angle.
company worth talking to, if you are serious about curves and surfaces
is Tebit – of whom, more, in a future issue.
there you have it! A painless introduction to the technology without a
single equation having to be produced. It gives, I hope, a flavour of
the technology and some of the tools that address it.
Where do Inventor and SolidWorks fit into all of this? Despite the obvious excellent capabilities for creating solid models from either of the two packages, the tools for handling b-spline curves and complex surfaces are rather more limited than with the software listed above.
www.leonardo.co.uk for IronCAD