MA115-2P AU07 Instructor Handout-1

Advanced Modeling and Surfacing Techniques with Autodesk®

AliasStudio™ (Part I) Uwe Rossbacher - Autodesk

MA115-2P Like the real world, the virtual world too provides different ways to model form. This session takes a classic geometry representation, NURBS (Non-Uniform Rational B-Splines) and looks at it from the perspective of a sculptural material. As a technology, there are strengths and weaknesses, but as a material, the properties of the math become a part of the allure of the medium. Take a fascinating and intimate look at surface modeling and learn why this material has become an essential part of shape definition for all the automotive companies and the top product design firms in the world. About the Speaker: Uwe Rossbacher brings 10 years of experience in industrial design and 3D surface modeling in the automotive industry to his role as Marketing Manager for Modeling/Technical Surfacing at Autodesk, including more than six years with the Alias Studio Tools product development team. Uwe has a deep knowledge of automotive concept design and technical surfacing and currently focuses on creating and delivering demonstrations, technical marketing materials and field education. Uwe also supports Autodesk product management efforts by identifying and defining market and user requirements. During his time with Alias, Uwe focused his efforts on refining the technical surfacing product specifications according to the needs of customers worldwide, and was a key resource in the development of many new surfacing tools within AliasStudio. Before joining Alias, Uwe held marketing and technical positions at ICEM. Most recently Uwe worked at the VW concept studio in Potsdam, Germany. Uwe received a Masters Degree in Engineering and Technical design from the University of Technology in Dresden, Germany.

Before computer came into the game

This problem was particularly acute in shipbuilding: although a skilled artist or draftsman could reliably hand draw such curveson a drafting table, shipbuilders often needed to make life size (or nearly life size) drawings, where the sheer size of therequired curves made hand drawing impossible.

Because of their great size, such drawings were often done in the loftarea of a large building, by a specialist known as a loftsman. The termlofting originally came from the shipbuilding industry where loftsmenworked on "barn loft" type structures to create the keel and bulkheadforms out of wood. This was then passed on to the aircraft thenautomotive industries who also required streamline shapes.

The resulting curves were smooth, and varied in curvature depending on the position of the ducks.

To aid in the task, the loftsman would employ long, thin, flexible strips of wood, plastic, or metal, called splines. The splines wereheld in place with lead weights, called ducks because of their resemblance to the feathered creature of the same name.

As computers were introduced into the design process, the physical properties of such splines were investigated so that theycould be modeled mathematically on the computer.

The �“Ducks�” were replaced with so called ControlVertices (CV).

At first NURBS were only used in the proprietary CAD packages of car companies. Later they became part of standard computergraphics packages.Real time, interactive rendering of NURBS curves and surfaces were first made available on Silicon Graphics workstations in1989. In 1993, the first interactive NURBS modeller for PCs, called NöRBS, was developed by CAS Berlin, a small startup companycooperating with the Technical University of Berlin.

Development of NURBS (Non Uniform Rational Basis, or Bézier Spline) began in the 1950 by engineers who were in need of amathematically precise representation of freeform surfaces like those used for car bodies and ship hulls, which could be exactlyreproduced whenever technically needed.

The pioneers of this development were Pierre Bézier who worked as an engineer atRenault, and Paul de Casteljau who worked at Citroën, both in France. Bézier workednearly parallel to de Casteljau, neither knowing about the work of the other. Butbecause Bézier published the results of his work, the average computer graphicsuser today recognizes splines (which are represented with control points lying offthe curve itself ) as Bézier splines while de Casteljau�’s name is only known and usedfor the algorithms he developed to evaluate parametric surfaces. In the 1960s itbecame clear that non uniform, rational B splines are a generalization of Béziersplines.

The layout of the patches is the basic knowledge

1 How would you make it in foam?

To find the first steps in building a surface model it helps to imagine how this process would be, when using a block of foam anda saw to work out the shape.

Similar to the most preferred sketching view, the NURBS modeler starts to develop the centerline. This is the section of themodel that lays in the middle of it defining the side view. Building the curves of the center line the modeler gets an idea of howmany curves he needs to describe the shape of the object.

Centerline surfaces

1All surfaces crossing the centerline should be build as oneBezier surface. This helps to avoid discontinuities of thesurfaces at the centerline. Lots of designs require a strictradius behavior of the surfaces in a certain area close to thecenterline. The �“one surface across the centerline�”approach has the disadvantage that when CV modificationon the surface is required, always the corresponding CV hasto be picked as well, to maintain the symmetry. This cost abit more time, but the price is, that the surface is always100% smooth across the centerline.

Width of the car

2Different to a classical approach (at first layout some curvesto describe the surfaces building the width of the car) oftenthe use of simple surface planes, their positioning and somedirect modeling is the faster method that fulfills the idea ofmodeling. In clay the designer always sees the material, thevolume. It can be said hat there is always physical property.The same would come with using shadeable property insoftware process. That�’s why it is good to show in virtualworld as soon as possible surfaces that can be shaded.

A modeling workflow based on simple planes requires a fast re parameterization of those planes. When the formerplanes already are shaped and with certain degree, it is often too time consuming to change the position of each CVindividually. A re approximation technique is much faster. The surface will be trimmed and then regarding this trim edgere calculated. The result is a completely re shaped surface done by the internal re approximation algorithm.

Marry the parts

3With this step it becomes clear if the parts defining the widthof the model fit together. For cars it is important, that thecrowning of the side window and the body side fit together.This can be verified building the shoulder surfaces withcorrect angle conditions to both side surfaces.

See tangent angle example that will come in Part 2!

Rocker and Fillets

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connection and muscles

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2 Detect the feature lines and build the slabs first

Sometimes the modeler just gets a scan of a physical model. For further design iterations this scan has to re modeled in NURBS(Reverse Engineering). Using Gaussian Shader the molder can detect the areas of curvature change on the model. This gives agood hint regarding the layout of the surface boundaries.

Scan data (polygons) of a physical model

The colorized areas gives a pretty good hint about the major slab surfaces that have to be build first. Its important to say thatthose physical models usually are filleted and with all transition surfaces. Therefore slabs will not appear anymore with their realsize but partial hidden or trimmed. The modeler must �“extend�” the colorized areas to create the slabs in their original size.It�’s a good method to fit the slabs first on the smaller portion (like they appear on the filleted physical model) to extend themafter fitting. When the fit is with smooth and low degree surfaces, the extend will provide reasonable results.

In AliasSudio Blend curves can be created directly ontop of the polygons (Mesh).

Still there are cases where just a section model isavailable. Here the modeler finds the slabs by�“interpreting�” section lines.

One approach is to isolates main section lines. Thenthey will be rebuild with NURBS curves. This can bedone with all the main section lines and is a savemethod to find the areas where a Slab character turnsinto a Transition character.

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The section line still is one continues line.The blue section in the image beside iswith three �“parts�”, two main pieces andone transition piece (fillet).The modeler needs to find the pointswhere the fillet goes into the maincurves.

Section data (curves, rawdata) of a physical model

Then the modeler build the transitioncurve. It is helpful, when the curve hassome kind of history so that the modelercan move the endpoints of the transitioncurve along the main curve to find the rightpoint, where the transition starts. InAliasStudio the Blend curve type is ideal forthis job.The curvature plots calculated on thecreated curves also can give a good hintabout the transition point.

First the modeler creates the two maincurves. He overbuilds the section line. It iswith the modelers skill to interpret, wherethe main curves �“leaves�” the section line.

With this method all points, where a slabpart goes into a transition part, can bemarked, like in the image beside. Thisknowledge is the base for building mainsurfaces (slabs) and transition surfaces.

For example a simple draft surface will becreated. This first surface doesn�’t have tofully fit the sections yet.

Interpreting every or lots of scan lines seems a bit time consuming. That�’s why there is a second approach using surfaces tointerpret many section lines in one step. For that, the user works with simple surfaces and visual sections ,cut through thesesurfaces. The surfaces has to stay relatively simple (moving hulls instead of moving every single CV) and the visual sections give apermanent feedback about the level of fitting.

Based on the first draft surfaces another draft will be created. It is very helpful when this second draft has a historicalconnection to the first draft. In this case the second surface should just fit the section lines in terms of the right angle (beingparallel).

Fitting the first draft to the sections, the second draft always will follow. The second draft will be fit modifying the first oneonly. With this method the theoretical line can be defined very fast.

Calculate visual sections!

Adjust the draft angle to followthe section lines!

Fit this surface by moving CV�’s!

Finishing a surface model often it comes to areas that are difficult to proceed with. Typically these are areas where more thantwo radii come together, or where transition surfaces are washing out.

3 Close the entire model first in theory

A good method for those cases is to close the model first just using sharp edges. All fillets should be avoided. Often surfacesmust be build that wont even appear after filleting and that usually wont be considered finding the right patch layout.

The next step is to build the fillets as long as they reach without getting complicated or washed out. This step is relatively easy todo. Just areas with a clearly defined fillet situation will be worked on.

The left over regions are washouts or magic corners where many radii come together and have to be blended. To fill these blendregions first the entry lines for the blends have to be marked. As a general advice the natural flow of the fillet edges should becontinued. Its obvious that the surfaces between these continued fillet edges act as a blend and is not a fillet anymore. With thismethod most of those situations can be managed.

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The natural flow of the fillet edges will be maintained andblended into the natural flow of the wheel.

But!

This method has the advantage that the software controls the internal continuity by itself and the digital sculptor has thefreedom to concentrate just on the form he is working on. It seems that the ability of modifying the shape of those �“one surfaceobjects�” are endless but when it comes to concrete engineering or package requirements often this method has limitations. Themodeler checks the technical requirements using analyses tools and adapts the surface model via moving CV�’s. He cannot usethe technical input directly as a base for his model like he could do it using a traditional patch layout.

Sometimes establishing a classical patch layout can become too time consuming. There are shapes where it is better to justsculpt the entire model out of one surface by inserting segments (raising its mathematical complexity). It is comparable tocraftsmanship where the sculptor cuts the form out of one block of foam.

The design of the shower head was defined based on the splitting line along the entire model.

The engineer had difficulties to establish the patch layout based on this line. The most critical area is on the tip of the showerhead where the classical layout just offers are triangle patch. On the other hand, the engineer found too many surfaces. That canbe difficult because the higher number of surfaces makes it more difficult to control the highlight flow through the entire surfaceset.

A digital sculptor used the �“one surface�”approach. He almost matched the split linethat was given as a technical requirement.Literally he came closer and closer byadjusting the CV�’s. Saving patches he couldeasily control the highlight of his patch.

This method is not as accurate as buildingsurfaces based on the split line but it helpsto sculpt organic surfaces.

Surface Evaluation

1 Shading

To evaluate Surfaces in Clay, the molder works with foil, called Dynoc. A little bit of water on top of the smooth clay surface sucksthe Dynoc onto it. Now the environment reflects on the foil and any inconsistencies of the surface shape will be visible. If theshape of the clay should be improved, the Dynoc has to be removed.Using Dynoc in clay process the modeler cannot watch the reflections while he is scraping the Clay. In software process themodeler can modify the surfaces while the reflections (diagnostics) are on. This is a huge advantage to reach surface quality muchfaster.

It is important to know how the evaluation toolcalculates the reflection lines. Additional to that it isgood when the light source creating the reflection linescan be moved above the model.In AliasStudio the Iso Angle Tool is the most accurateevaluation regarding highlights on the surface set, evenwhen these �“highlights�” are not comparable withreflections in the real world.

Most software for NURBS modeling offer shading tools that visualize the selected surfaces. But often the user calculate zebrastripes, which are often spherical environment . This evaluation is not good enough to judge high end surface quality.

�“Reasoning�“ behind Iso angle analyses

Iso angle literally means "a line of constant angle" on asurface. Here is an analogy: on a map of the world,sometimes you can see what are called "iso therms"these are lines of constant temperature. Similarly, "isobars" are lines of constant barometric pressure. Theseline are used to indicate temperature and pressuretrends on the globe.Iso angle, the tool, by default, shows you the line ofzero angle between the surface normals of the surfaceand an infinite "light source direction". In fact, youshould stop thinking of this as a lighting kind ofcalculation, but as an analysis of the surface propertiespurely. The pointed arrow in the interface is there tojust indicate the direction with which the zero angle isbeing evaluated.

Iso angle therefore provides a very tight and accurate way of evaluating the properties of a surface. It will indicate surfaceproperties (like trends, continuity across boundaries etc.) way more accurately than spherical maps of zebra stripes.When used in the multiple band (the colored bands) mode, each colored band is indicating a line of constant angle with thedirection of the vector for example, the white band could be the zero angle, the red one next to it could be the line of constant5 degree angle,the green one next to it the 10 degree angle etc. This kind of evaluation is called iso photes actually, and is used in mathematicalanalysis of surfaces.

2 CV picture

The analogy between �“ducks�” used by loftsman and CV�’s in NURBS technology is a perfect way to understand the importance ofa good CV flow to get good surfaces.

NURBS modeling software often offers various User Interfacecapabilities for surfaces creation and manipulation. But all this isjust amask. The common ground is always the position of the CV�’s.For a loftsman the duck placement was the only possibility to get anice curve with aesthetic acceleration and so is the CV placementfor a NURBS modeler. So the secret of well shaped surface models iswith their CV layout. Choosing a NURBS modeling software itshould be taken care, that CV�’s can be visualized and modeleddirectly.

Common rules about CV spacing

As a first rule it can be said, that the CV�’s has to look nice and they should flow beautifully (there are several exceptions when itcomes to the CV flow). Experienced NURBS modelers can �“read�” the shape of a NURBS model by investigating the CV�’s only.But was is nice and what is beautiful? Some people say: �“Beauty is the phenomenon of the experience of pleasure, through theperception of balance and proportion of stimulus. It involves the cognition of a balanced form and structure that elicits attractionand appeal towards a person, animal, inanimate object, scene, music, idea, etc.�”

Even when the judgment of CV structure is relative there are some rules introducing two parameters.

A �– length of the line that connects two CV�’s with each other �– CV spacingB �– length of the Normal that is between a CV and the underlying curve/surface

A

B

Judging beauty is always depended on the audience and relative. To illustrate this there is a nice quote from Francis Bacon.�“There is no excellent beauty that has not some strangeness in the proportion.�”

Technical surfacing exists between creativity of design and requirements of Engineering. Any definition of Beauty seems to berelative and doesn�’t fit in strict engineering requirements. But the Surface modeler needs to put a good understanding of abeautiful sense in his work to create good surface sets and therefore a lot of inspiration is available.

2. Concentrate CV�’s where the geometry shows more curvature in its shape. A good analogy is to imagine the speed of the handwhen drawing a curve with a pencil. Where the speed is slow, the artist tries to create curved shape, the CV�’s should beconcentrated. Where the speed gets faster, less CV�’s are needed to describe this portion.

1. Both Parameters should change smoothly and within symmetry if appropriate. Drawing the change of A and B in a graph, theresulting curves, must be nice, smooth and not wavy. There is no engineering rule about these curves. The user must considerhis own sense of beauty, symmetry and proportion.

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!A/B

CV#1 CV#2 CV#3# of CV

Position G0

3 Surface Continuity

This continuity specifies if the edge of two surfaces (natural edge or trimmed edge) fit within a given tolerance. If the geometryedge or endpoint fits within a tolerance the result is good in terms of G0 continuity. This measurement can be qualified as adigital check.

When defining a form, an important factor is the continuity between surfaces how smoothly they connect to one another.One example of where surfacing excels is automotive body panels. If two curved areas of the panel have different radii ofcurvature and are blended together, maintaining tangential continuity (meaning that the blended surface doesn't changedirection suddenly, but smoothly) won't be enough. They need to have a continuous rate of curvature change between the twosections, or else their reflections will appear disconnected.

The continuity is defined using the terms G0 �– position (touching)G1 �– tangent (angle)G2 �– curvature (radius)G3 �– acceleration (rate of change of curvature)

Tangency G1

This continuity specifies the angle between corresponding normal's that stands on the edges of the reference and the geometry.If this angle is within a tolerance the measurement is good in terms of G1 continuity. This measurement can be qualified as adigital check.

Additionally to the measurement of the surface normal's there is a check in terms of co linearity of the tangents (lines connectingthe CV�’s). This criterion is interesting just for continuity measurements between two natural edges. Not every NURBS modelingsystem offers this check (AliasStudio) but it should be investigated by every user.

Curvature G2 (radius) Acceleration G3 (rate of change of curvature)

The continuity measurement in terms of curvature should not be judged as a digital check anymore. In here it is more importantto evaluate the flow and the smoothness of the curvature acceleration. A perfect curvature result just can be evaluated usingcurvature plots.

Curvature G2/G3

4 Curvature plots

When it comes to curvature measurement lots of systems offer locators that measure G2 continuity on the patch borders andthese typical zebra stripes to evaluate �“highlights�”.

These two surfaces obviously looks fine together, but this is not true. Theevaluation tools are just not the right ones.The G2 locator simply compares the value of curvature on both surfaceedges within a certain tolerance. This information is not enough in terms ofjudging highlight quality. Even the zebra stripes often are just a sphericalmap on the surface set and doesn�’t give a useful feedback about thesmoothness of the entire surface set. They don�’t show acceleration ofcurvature within the shape.

That�’s why it makes no sense to judge the highlight quality of a surface set just using G2 checker. The surface set must be cut andcurvature combs must be calculated on the sections.

C

Just a curvature plot on a section cut through the surface set shows that theacceleration of the curvature of both surfaces doesn�’t match. Sure G2continuity is achieved, but its is not a good result regarding the flow of thehighlights.

This curvature comb show a wellbalanced G3 result. This judgment iswith the skill level of the operator andcan be qualified as analog, becausethere is not a certain tolerance thatwould make sense all the time.

This result is well balanced too. Thesmall step in the curvature plot (G2break) doesn�’t have a noticeableimpact on the final highlight picture. Infact, this surface set has only G1continuity but it is still good.

It is very helpful to see the two surfaces beside milled out. Often it becomes clear that a strict G2 achievement is not necessary toreach high end surface quality in terms of visual highlights.

Class A

Class A surfaces is a term used in automotive design to describe a set of freeform surfaces of high quality. Although, strictly, it isnothing more than saying the surfaces have curvature and tangency alignment to near perfect aesthetical reflection quality.

The point when Class A quality for the first time is required is not fixed. As more as the design becomes final, as moreengineering and feasibility requirements have to be recognized. A clean and light surface structure is the base to incorporatethese requirements in a digital model. The final result is a surface set that will be given to tooling or to further CAD departmentsand its final quality level is called Class A.

In automotive design, the first virtual surface models appear at the concept stage already. A fast visualization of shape andproportion is valid. Based on sketches, packages and scanned quarter scale models, the digital sculptor creates the first surfacemodel. At this stage technical requirements doesn�’t play such a role. The interpretation of the styling idea is the main approach.Its called Concept Modeling.

1 What is Class A?

2 Two different aspects of Class A

•Curvature combs•G3•Acceleration of highlights•knee ratio

•Tolerances•Split lines•First flange•Panel gap•Fully filleted

The challenge for Class A modeling is to combine the aesthetic superiority with hard requirements from engineering. A surfaceset that appears just beautiful but without meeting engineering requirements will not be considered as Class A.

As the digital design process gets mature less Data Control Models get milled out but the quality level remains. The Studios try topush the point of design freeze more and more backwards to gain time to improve the styling. For Class A modeling this means,that it has to be establish sometimes along the process to be ready when the project is done.

Highlight Quality Engineering requirements

Class A modeling means a lot of investment in time. During extensive design iterations often it makes no sense to require thehighest quality level of surfaces. In the past Class A quality often was required just after the design freeze. This point wasreached with a so called Data Control Model done and available only in clay. This model had the final design features included. Itwas scanned and then the model had to be re captured as NURBS in Class A quality to serve the following CAD processes. So theClass A modeling was mainly using scan data as input and a certain deviation tolerance was given to the molder. It was called asreverse engineering.

Those requirements were ideal for outsourcingthe work. That is why today most of the Class Amodeling work is done with Tear One Suppliersaround the big automotive companies and somost of the knowledge and skills about it. Its aninteresting phenomenon that the best Class Amodelers are working as contractors for thosesuppliers and cannot be found as employees.

3 Reverse Engineering

To make the design process more effective, the studios engage engineers early on look at engineering requirementsto get guidance from it. Another point to make the process more effective is to improve the surface quality of thefirst models to make them re useable for the next design steps. Some automotive companies even don�’t speakabout conceptual design anymore. They established a process where the design modeling flows meaningless intoengineering and tooling.

4 And where could Class A go in the future?

�“A community of modelers has established general criteria for data to be considered class A. Prior to checking edge continuity,curvature, highlights, or shapes it is the surface structure that has to be well established. In presentations regarding class Asurfacing I try to make it clear: The structure of the surface data is the basis of Class A surfacing. �“

Digital Designer Barry Kimball Nissan Design America, Farmington Hills, Michigan

Surface Modeling Paradigms

The image shows two curves having the same shape.The upper curve has 6 CV�’s and 3 segments (4 edit points). It�’s a NURBS curveThe curve below has 6 CV�’s and just 1 segment (2 edit points). It�’s a Bezier curve.

1 NURBS versus Bezier mathematic

Most surface modeling systems have a common mathematical foundation called B Splines. Some of them creates NURBSgeometry and some creates Bezier geometry. Mathematically a single segment NURBS surface is equivalent to a single Beziersurface patch. Mathematically Bezier surfaces are a subset of NURBS. AliasStudio is capable of creating NURBS and Beziersurfaces.

When moving the marked CV�’s it becomes obvious that a Bezier CV influences the entire curve and a NURBS CV just hasinfluence within its segment. This partial influence increases the risk of wavy curvature plot and with this the risk of a badhighlight picture when it comes to surfaces. That�’s why often it is recommended to work with single segmented geometry knowas BEZIER mathematic. It has the disadvantage of more work taking care for the surface connections, but almost guarantees goodhighlights.

Using multi segment geometry can be an advantage in several surface modeling situations. But software is unable to provide G3continuity between the segments when there is not enough mathematical freedom.

To avoid internal G3 breaks (like shown below) the geometry should always have a minimum degree of 5. The degree validationused in here is for AliasStudio. Other software have different rules to specify the degree of a surface. Basically the geometrymust have six Control Vertices to avoid internal G3 breaks.

A solution where the degree of the geometry doesn�’t count is when using strictly single segmentation approach. This is knownas using Bezier Surfaces.

CAD software packages use two basic methods for the creation of surfaces.

The first begins with construction curves (splines) from which the 3D surface is then swept (section along guide rail) or meshed(lofted) through.The second method is direct creation of the surface with manipulation of the surface poles/control points.

Both methods have their strength. Their use depends on the modeling situation.

2 Modeling method

Curve network approach:

•Fits designers who think in feature lines.Gives a fast 3D interpretation of the intended shape.

traditional patch layout based on curves:

•Lacks in controlling the �“inner CV�’s�”•Requires a huge effort of planning to keep history ofedge curves and surface.The surface is a result of curve modification and cannotbe shaped directly.

Surfaces ruled by parameters:

•Additionally to curves surfaces can be defined byparameters like radii, vectors, length.•Serves engineering approach

Procedural modeling

With this technique, NURBS becomes the first legit virtual material.

Direct modeling

Direct modeling lives of of CV manipulation. To do so, it is needed to hold the overall number of CV�’s down. To align two surfacewith each other, a special align or matching command is needed. This implies massaging every surface match individually.Currently it is the best way to ensure a top highlight quality of the entire surface set, but it requires a gentle surface layout that isbased on primary surfaces and secondary surfaces that are dependent on this.It may sound threatening to manipulate all CV�’s individually. But as long as possible, the digital sculptor manipulates entire CVrows or uses tools that allow a modification of many CV�’s based on a rule how the influence on each CV gradually become less.

Practical Modeling Techniques

1 Surfaces might be bigger than they appear on a final model

The basic surfaces (often they are called slabs) appear on the final model always trimmed. A good analogy is the craftsmanship of claymodeling where the modeler moves a fixed template along a guide. The template cuts clay where it touches the volume and it cut �“air�”to. The entire �“surface�” the template is �“cutting is exactly the surface that has to be modeled in software, even when the template cutsair and the corresponding digital surface stands out. The digital surface will be trimmed later, but its basic shape must be modeled first.

This depends on the stage ofthe design process. Productioncars that has been modeledafter design freeze have adifferent layout that notnecessarily following this rule.

The colorized wheel lip shouldget a certain highlight flow. Toachieve this, the �“underlying�”trimmed surfaces must beshaped to support the finalsculpturing of the wheel lipsurface.

The blue fillet surface set must have a nicehighlight flow. But because of the hole in thebumper it looks like there is no surface thetwo middle fillet pieces can be aligned to.

The surfaces �“around�” the hole in thebumper shows are actually bigger and theyare connected establishing a nice highlightflow, even when they are trimmed later ondescribing the hole.But only this curvature connection allows toalign the blue fillets all way long, even therewhere they appear as �“hanging in the air�”(when the model finally is trimmed).

This is an example how surfaces that even wont be seen in the final model �“hold�” a feature (blue fillet) together.

2 Angle conditions along surface boundaries

Final surface sets are always filleted. Those filets often play a significant role expressing features. In the knee of a fillet there mightbe an ultra shiny highlight gloss. The tangent lines of a fillet (the lines where a fillet starts) mark the region where a flat and slowhighlight from the big slab surfaces starts to speed up into the much more curvy fillet.So it is clear that the shape of such fillets are important for the design expression in two ways:

• Nice and determined Radius entry lines• Constant or smooth change of knee radii to ensure a nice highlight.

The shoulder surface usually will be build withposition continuity (FIXED).

Building the fillet just with this simple position continuity is the reason of the problem with the fillet described following.

Fillet to be done

The resulting fillet often has problems regarding the entry lines or the highlight along the fillet knee.

This fillet is a constant fillet. The radius entry lines show anuneven and bad behavior.

This fillet is a chordal fillet. The thickness of the highlight atthe knee varies unevenly.

The reason for this bad fillet behavior is the uneven change of the angle between both surfaces. In this case the angle betweenthe two surfaces becomes smaller and at the end it becomes bigger again. The tangent checker shows an inflection of the anglechange ( in the middle).

This simple example illustrates how a rollingball would mark uneven radius entry line onboth reference surfaces when their angle toeach other is not controlled.

Controlling the angle changing from one end to the other gives a much smoother and controlled result for the quality of the finalfillet. The tangent checker shows just the maximum and the Minimum of the angle exactly at Start and End of the fillet.In Alias this can be controlled using the TANGENT ANGLE option in the surface creation tools.

This fillet is a constant fillet. The radius entry lines are even(linear interpolation between the two ends).

This fillet is a chordal fillet. The thickness of the highlight atthe knee varies evenly (in accordance a linear interpolation).

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Both Slab surfaces will be cut first, using a longblade. The cutting edge of the blade could beimitated in Software by a profile curve.The modeler has to balance the crown of both Slabsto each other. He can do that by examination ofboth surfaces from the side and the top view.The final indication is the sharp edge between bothSlab�’s. Its shape shows if both crowns fit to eachother.

To define the transition (often it�’s a radius) themodeler tapes the two entry lines (Tangent offset)on the smooth slabs. The modeler exams both linesby checking them from the appropriate view.

3 Theory Modeling

4Using a rake, the modeler cuts the clay between thetapes. After he roughly achieved the shape of thetransition, he uses a template blade with a cuttingedge that was made after the profile the transitionalsurface should have or after the specific radius.The modeler slides the blade along both tapes tonot touching the already finished slabs.The last step is to remove the tapes and to carefullysmooth the entire surface set.

When the transition should be a radius, the modeleruses a drawing circle to get the right distance foreach tape from the sharp edge.

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A finished surface model almost has no sharp lines. Everything is with fillets and transition surfaces. But recognizing modeling step 1there must have been a sharp �“theoretical line�” beneath those fillets. Regarding this it is an interesting experiment to inspect the hoodof a car like shown below. The inspector moves along the front of a car and notices there three vital points (A B C) where the feature ofthe hood appears in three different ways.

C

B

A

There is one position (B), where the virtual theoreticalline, and with this even the fillet that is build on top,appears straight. On Position A it appears concave, onposition C it appears convex. So in B the �“theoreticalline�” MUST be straight, means planar.

ABC

A

C

B

Here is an example from industrial design where the theoretical line is not crisp and causes irritation with the final design wherefillets are incorporated.

flat Curved (convex) Curved (concave)

This effect is a basic rule in technical surfacing to make major features appear crisp and strong from all different views. Softwareproducts offer tools that can planarize a curve or a surface edge to get this effect. The plane that is the base for such curvesrarely appears parallel to the three main views (side, front and top). So it is needed to be able to modify a curve set while thecurve still maintains its planar character in 3D.