Fast and Effi­cient Geometry Opti­miza­tion with Morphing

While some geometry morphing methods have always been avail­able in CAESES, mostly being used in maritime appli­ca­tions, the focus of the majority of our cus­tomers was put on fully para­met­ric modeling. Each one of these approaches bears its own advan­tages and dis­ad­van­tages, and with our recent release of CAESES 5, we devoted sig­nif­i­cant resources to specif­i­cally tackling the existing dis­ad­van­tages of morphing in previous CAESES versions, in order to make this approach more appeal­ing for a wider range of appli­ca­tions and be able to draw a bigger benefit from its advantages.

Morphing vs. Para­met­ric Modeling

Fully para­met­ric modeling is the gen­er­a­tion of a para­met­ric model for the complete geometry, or at least a com­po­nent thereof, from scratch. We speak of fully para­met­ric modeling because the para­me­ters define all features of the final geometry. Some para­me­ters may be at a high level like the length, width, and height of an object. Other para­me­ters may deter­mine details like a tangent angle or cur­va­ture at a par­tic­u­lar location. A para­met­ric model can be looked at as a system that takes para­me­ters as input and produces a shape (variant) as an output.

Fully para­met­ric modeling is very powerful, since it enables both large changes in the early design phase and small adjust­ments when fine-tuning at a later point in time. It provides very detailed and exact control over shape prop­er­ties. Also, it facil­i­tates the inte­gra­tion of con­straints (e.g., related to pack­ag­ing or man­u­fac­tur­ing), allowing for a vari­a­tion of the geometry while auto­mat­i­cally con­serv­ing certain required prop­er­ties. However, it surely doesn’t come as a surprise that setting up a fully para­met­ric model is more time con­sum­ing and can require a tangible level of knowl­edge about modeling tech­niques, as well as the product and its behavior.

In morphing, some­times also called par­tially para­met­ric modeling, we deal with the (para­met­ric) defor­ma­tion of an existing, imported geometry. Hence, only the changes to this existing shape are defined by para­me­ters, that can be con­trolled to generate design variants.

Par­tially para­met­ric models are usually quick, fairly easy, and intu­itive to set up. When compared to fully para­met­ric models, they typ­i­cally contain less intel­li­gence about the product, and it is gen­er­ally more dif­fi­cult to excite large mod­i­fi­ca­tions. As we para­me­ter­ize the changes to the geometry, they might only provide indirect control over shape prop­er­ties and it can be chal­leng­ing to inte­grate constraints.

Morphing before CAESES 5

Before version 5, CAESES provided the fol­low­ing selec­tion of geometry morphing capabilities:

• Shift trans­for­ma­tions change any point of the geometry by adding a certain dis­place­ment depend­ing on the point’s initial position. The dis­place­ment can be a spec­i­fied as a 1D (curve) or 2D (surface) function. Shift trans­for­ma­tions can be con­cate­nated, directly summed up and/​or mul­ti­plied to form complex mod­i­fi­ca­tions. 
  Their primary downside is that the dis­place­ment is limited to a fixed direc­tion, specif­i­cally, one of the prin­ci­pal axis direc­tions in CAESES, and there­fore only make sense for appro­pri­ately oriented geometries.
• The Lackenby shift is a special case of a shift trans­for­ma­tion ded­i­cated to maritime appli­ca­tions, where the dis­place­ment function in lon­gi­tu­di­nal direc­tion is auto­mat­i­cally deter­mined. Its purpose is to modify the dis­place­ment volume of a ship hull and its dis­tri­b­u­tion. In com­par­i­son to the classic Lackenby shift described in lit­er­a­ture (LACKENBY, H (1950), On the Sys­tem­atic Geo­met­ri­cal Vari­a­tion of Ship Forms, Trans. INA, Vol. 92, pp. 289 – 315) the imple­men­ta­tion in CAESES provides addi­tional flex­i­bil­ity and control over the transformation.
• In free-form defor­ma­tion (FFD), also known as box defor­ma­tion, the geometry to be modified is enclosed by a box con­sist­ing of a regular grid of vertices (i.e., rows, columns and layers defining a B‑spline volume). For all parts of the initial shape located within the box, a local coor­di­nate triplet can be deter­mined. By moving any of the vertices, or several of them in a con­certed way, the box changes its shape and, along with it, the baseline is trans­formed.
  FFD is very flexible in terms of the defor­ma­tions that can be achieved, but is a para­mount example for indirect control, as it is basi­cally impos­si­ble (for the user) to exactly predict a priori which effect the dis­place­ment of the box vertices will have on the actual geometry. Addi­tion­ally, depend­ing on the initial geometry, the gen­er­a­tion of a suitable box might require a non-neg­li­gi­ble effort.
• Finally, so-called carte­sian shifts and spot trans­for­ma­tions were avail­able. They basi­cally consist of point sources at which a dis­place­ment is applied either in prin­ci­pal axis or an arbi­trary direc­tion. This dis­place­ment decays towards the border of a region of influ­ence centered at the point source.
  These trans­for­ma­tion objects can be regarded as exper­i­men­tal imple­men­ta­tions, and have probably never been used in a pro­duc­tion sit­u­a­tion, as they are cum­ber­some and imprac­ti­cal to apply in real-life opti­miza­tion problems.

New Morphing Capa­bil­i­ties in CAESES 5

The moti­va­tion to revisit the geometry morphing capa­bil­i­ties for the CAESES 5 release was pri­mar­ily based on reducing the existing dis­ad­van­tages (in previous CAESES versions) related to the pre­ci­sion with which the user is able to control the trans­for­ma­tion and there­fore the final geometry, as well as removing the inherent restric­tions of existing morphing capa­bil­i­ties that make them unsuit­able for all appli­ca­tions. Addi­tion­ally, morphing is a highly con­ve­nient tool for the novice user, who is not yet up to speed with para­met­ric modeling tech­niques and wants to quickly optimize an already existing geometry. It should there­fore be easy and intu­itive to apply.

The guiding visions were a) to achieve a sort of ​“on-demand para­me­ter­i­za­tion” in which the user is able to apply full para­met­ric control, akin to a fully para­met­ric model, to selected areas of an imported geometry, as well as b) a very easy-to-use inter­ac­tive tool for quick shape modifications.

The new morphing toolset was based on so-called radial basis func­tions (RBFs). The RBF defor­ma­tion tech­nique is char­ac­ter­ized by treating space defor­ma­tion as an abstract inter­po­la­tion problem: Given a set of dis­place­ments for a cor­re­spond­ing set of posi­tions, the goal is to smoothly inter­po­late dis­place­ments through space. Within the RBF defor­ma­tion approach the space defor­ma­tion function is con­structed as a linear com­bi­na­tion of radially sym­met­ric kernels, located at a set of centers and appro­pri­ately weighted. A second impor­tant aspect of RBF defor­ma­tions is the kernel place­ment. By directly placing kernels on all handle and fixed vertices it is straight forward to imple­ment a handle-based direct manip­u­la­tion inter­face sat­is­fy­ing all con­straints spec­i­fied by the user easily and exactly.

CAESES supports both discrete (e.g., STL) and NURBS-geome­tries as objects for the defor­ma­tion. The setup for both kinds of geome­tries differs in the details, but the under­ly­ing prin­ci­ple is the same and the usage is quite similar.

A geometry can have more than one trans­for­ma­tion defined. In CAESES one such trans­for­ma­tion is called an ​“RBF region”. First, the user needs to define an area of the geometry that may be freely deformed by the algo­rithm. In the case of discrete geometry, this can be done using the newly created inter­ac­tive paint tool that allows for painting areas onto the geometry, while in the NURBS case the user may select faces from the boundary rep­re­sen­ta­tion that will be sub­jected to the defor­ma­tion. In the fol­low­ing, the area that was marked in this manner will be called the ​“defor­ma­tion area”, while the rest of the geometry will be called the ​“fixed area”, since it will not be a part of the deformation.

Once the defor­ma­tion area is marked, the user needs to select a feature inside that area and specify how that feature is to be trans­formed. While these ​“source” and ​“target” features need to be supplied by the user, the defor­ma­tion area will then be deformed by the algo­rithm in a way that ensures a tangent con­tin­u­ous tran­si­tion between the target feature and the fixed area. Inter­po­la­tion between the source and target geometry are also possible, as well as extrapolation.

Features that may be selected as source and target geome­tries are:

• A point inside the defor­ma­tion area that will be trans­lated to a target location,
• A col­lec­tion of tri­an­gles that may be trans­lated, rotated and scaled to a new location (discrete geometry only),
• A curve on the geometry that is mapped to a target curve some­where in space,
• A sub-surface of the geometry that is mapped to a target surface in space (NURBS geometry only).

As the target geome­tries will be matched exactly, it is straight forward to accu­rately control the shape in a para­met­ric way, espe­cially when using one or more curves as source and target geome­tries. The trans­la­tion of points and triangle sets with the ded­i­cated handle tool, on the other hand, allow for an intu­itive, quick and inter­ac­tive mod­i­fi­ca­tion of the geometry.

Learn More

1. Watch the webinar record­ing about morphing in CAESES® 5 for more details.

2. Download CAESES®, register for a trial license.

3. Test the morphing func­tion­al­ity yourself with the cor­re­spond­ing tuto­ri­als in CAESES®.

Ques­tions?

Please do not hesitate to get in touch with us if you have ques­tions in the context of your specific appli­ca­tion. We look forward to dis­cussing it together with you!