## “Equation Based Surface” for Conformal and Non-Planar Antenna Design

ANYSY HFSS provides many options for creating non-planar and conformal shapes. In MCAD you may use shapes such as cylinders or spheres, and with some steps, you can design you antennas on various surfaces. In some applications, it is necessary to study the effect of curvatures and shapes on the antenna performance. For example for wearable antennas it is important to study the effect of bending, crumpling and air-gap between antenna and human body.

## Equation Based Surface

One of the tools that HFSS offers and can be used to do parametric sweep or optimization, is “Draw equation based surface”. This can be accessed under “Draw” “Equation Based Surface” or by using “Draw” tab and choosing it from the banner (Fig. 1)

Once this is selected the Equation Based Surface window that opens gives you options to enter the equation with the two variables (_u, _v_) to define a surface. Each point of the surface can be a function of (_u,_v). The range of (_u, _v) will also be determined in this window. The types of functions that are available can be seen in “Edit Equation” window, by clicking on “…” next to X, Y or Z (Fig. 2). Alternatively, the equation can be typed inside this window. Project or Design Variables can also be used or introduced here.

For example an elliptical cylinder along y axis can be represented by:

This equation can be entered as shown in Fig. 3.

Variation of this equation can be obtained by changing variables R1, R2, L and beta. Two examples are shown in Fig. 4.

## Application of Equation Based Surface in Conformal and Non-Planar Antennas

To make use of this function to transfer a planar design to a non-planar design of interest, the following steps can be taken:

• Start with a planar design. Keep in mind that changing the surface shape can change the characteristics of the antenna. It is a good idea to use a parameterized model, to be able to change and optimize the dimensions after transferring the design on a non-planar surface. As an example we started with a planar meandered line antenna that works around 700MHz, as shown in Fig. 5. The model is excited by a wave port. Since the cylindrical surface will be built around y-axis, the model is transferred to a height to allow the substrate surface to be made (Fig 5. b)
• Next, using equation based surface, create the desired shape and with the same length as the planar substrate. Make sure that the original deisgn is at a higher location. Select the non-planar surface. Use Modeler->Surface->Thicken Sheet … and thicken the surface with the substrate thickenss. Alternatively, by choosing “Draw” tab, one can expand the Sheet dropdown menu and choose Thicken Sheet. Now select the sheet, change the material to the substrate material.
• At this point you are ready to transfer the antenna design to the curved surface. Select both traces of the antenna and the curved substrate (as shown in Fig. 7). Then use Modeler->Surface->Project Sheet…, this will transfer the traces to the curved surface. Please note that the original substrate is still remaining. You need not delete it.
• Next step is to generate the ground plane and move the wave port. In our example design we have a partial ground plane. For ground plane surface we use the same method to generate an equation based surface. Please keep in mind that the Z coordinate of this surface should be the same as substrate minus the thickness of the substrate. (If you thickened the substrate surface to both sides, this should be the height of substrate minus half of the substrate thickness). Once this sheet is generate assign a Perfect E or Finite Conductivity Boundary (by selecting the surface, right click and Assign Boundary). Delete the old planar ground plane.

## Wave Port Placement using Equation Based Curve

A new wave port can be defined by the following steps:

• Delete the old port.
• Use Draw->Equation Based Curve. Mimicking the equation used for ground plane (Fig. 9).
• Select the line from the Model tree, select Draw->Sweep->Along Vector. Draw a vector in the direction of port height. Then by selecting the SweepAlongVector from Model tree and double clicking, the window allows you to set the correct size of port height and vector start point (Fig. 10).
• Assign wave port to this new surface.

Similar method can be used to generate (sin)^n or (cos)^n surfaces. Some examples are shown in Fig. 11. Fig. 11 (a) shows how the surface was defined.

## Effect of Curvature on Antenna Matching

Bending a substrate can change the transmission line and antenna impedance. By using equation based port the change in transmission line impedance effect is removed. However, the overall radiation surface is also changed that will have effects on S11. The results of S11 for the planar design, cylindrical design (Fig. 8), cos (Fig. 11 b), and cos^3 (Fig. 11 c) designs are shown in Fig. 12. If it is of interest to include the change in the transmission line impedance, the port should be kept in a rectangular shape.

Equation based curves and surfaces can take a bit of time to get used to but with a little practice these methods can really open the door to some sophisticated geometry. It is also interesting to see how much the geometry can impact a simple antenna design, especially with today’s growing popularity in flex circuitry. Be sure to check out this related webinar  that touches on the impact of packaging antennas as well. If you would like more information on how these tools may be able to help you and your design, please let us know at info@padtinc.com.

## August 30th, 2017 – 11:00 AM – 12:00 PM MST

The Stratasys J750 3D printer delivers unavailed aesthetic performance including true, full-color capability with the texture mapping and color gradients. Create prototypes that look, feel and operate like finished products, without the need for painting or assembly, thanks to the Stratasys J750’s wide range of material properties.

With this, students can easily experience both the prototyping and testing stages of the manufacturing process, helping to prepare them for what they will experience once they enter the workforce. The high quality materials available with the J750 also allow for the creation of highly intricate and realistic models, perfect for helping medical students with research.

The wide color spectrum, combined with the fine-finish, multi-material capability, let’s the Stratasys J750 produce parts with an incredible array of characteristics. Prototypes that need to look, feel and function like future products are possible in a single print operation, with minimal to no finishing steps, like painting, sanding or assembly.

With such an innovative machine comes a variety of user applications, such as:

•  Rapid Prototyping
• Concept Models
• Medical Models
• Jigs & Fixtures
• Colored Textures

Join PADT’s Sales executive Jeff Nichols and 3D Printing Application Engineer James Barker from 11:00 AM – 12:00 PM MST AZ for an in depth look at how the Stratasys J750 stacks up against it’s competition, and how it’s various attributes help to make it the perfect fit for institutions such as yours!

Don’t miss this unique opportunity to bring the future of manufacturing into your classroom or workplace, secure your spot today!

# Take the Next Step!

### Upgrade to the future of 3D Printing

Performance so good, you won’t believe it’s so easy to use!
The Stratasys F123 3D Printer Series demands less knowledge and experience, while meeting even the most advanced rapid prototyping expectations and needs, helping to make it the perfect machine for the classroom. This Series excels at all stages of the design prototyping process, from draft-concept iterations – to complex design verification – to high-quality functional prototypes.
Enhanced 3D printing capabilities of the F123 series include:
• New user interface
• Remote print monitoring
• Built-in camera
• Auto calibration
• Improved software experience with GrabCAD Print
• Easy material change out
• Auto material changeover

Join PADT’s Application Engineer James Barker and Sales Executive Jeff Nichols for a webinar that will provide an in depth look at all three machines that make up the all new F123 3D Printer Series (F170, F270, & F370).

## Leaving CAD Embedded Simulation Behind – Webinar

With simulation driven product design and development becoming the norm in the world of manufacturing, it has become increasingly relevant for companies to stay on the cutting edge in the search of the next best thing, in order to succeed in their respective industries.

Join PADT’s Co-Owner and Principal Engineer, Eric Miller for a live presentation on the benefits of ditching your current CAD-Embedded Software for state of the art ANSYS Simulation Solutions.

This webinar will dispel common misconceptions surrounding ANSYS Software, explain how to make the move away from CAD-Embedded tools, and present highly requested topics that ANSYS can provide solutions for, such as:

• Understanding fluid flow: accurate and fast CFD
• Real parts that exist in assemblies
• The importance of robust meshing
• Advanced capabilities and faster solvers

## In support of the ANSYS Startup Program, PADT is proud to introduce the PADT Startup Spotlight.

We here at PADT are firm believers in the opinion that today’s startup companies are tomorrow’s industry leaders and thus should be give every possible opportunity to thrive and succeed.

As a result we are offering full access to our promotional capabilities in order to help startup companies developing physical prototypes to grow and develop in a competitive environment.

We will look through those startups that have purchased the ANSYS Startup Package through PADT, and select one to feature and promote, that we believe clearly represents the drive and entrepreneurial spirit that is key in order to succeed in today’s day and age.

## Presenting the first Startup Spotlight:

Since their inception in 2014, Velox Motorsports has always been focused on speed; whether that be the speed of the NASCAR teams they have worked with or the desire their customers have for speed, which drives their competitiveness and fuels the demand for their products.

They even show a passion for speed in the company’s name (Velox), which translates from Latin to “swift or speed”.

Thursday, March 2 is PADT’s annual SciTech Festival Open House, from 5-8pm (click HERE to register). This year, three student groups working on a range of projects will be present to showcase their work, all of which involved some level of 3D printing. Please bring friends and families to meet and discuss ideas with these students from our community.

### Formula SAE Team (Arizona State University)

ASU’s Formula SAE team will be onsite with their 2016 cardemonstrating specifically how they used 3D printing to manufacture the functional intake manifolds on these cars. What is specifically interesting is how they have modified their manifold design to improve performance while leveraging the advantages of 3D printing, and also they have evaluated multiple materials and processes over the recent years (FDM, SLS).

### Prosthetic Arm Project (BASIS Chandler)

Rahul Jayaraman will be back to discuss how he and 30 students at BASIS Chandler manufactured, assembled and delivered about 20 prosthetic hands to an organization that distributes these to children in need across the world. Rahul and PADT were featured in the news for this event.

### Cellular Structures in Nature (BASIS Chandler)

A BASIS Chandler High School senior, Amy Zhang, just started her Senior Research Project with PADT, focusing on a project at the intersection of biology and 3D printing, investigating cellular structures that occur on surfaces in nature, like the wing of a dragonfly or the shell on a turtle or the encasing of a pineapple – all of which are comprised of cellular geometries. Using 3D scanning, image analysis and mathematical methods, Amy hopes to develop models for describing these structures that can then be used in developing design principles for 3D printing. You can learn more on Amy’s blog: http://shellcells.blogspot.com/

## Live Webinar: Stratasys and Aerospace Manufacturing & Design

Next week, Stratasys will be hosting a live webinar with Aerospace Manufacturing and Design.  Hear from drone manufacturer Monarch about the competitive advantages they have gained by using Stratasys 3D Printing in their design process.

Register Here

Monarch is a drone manufacturer who uses 3D printing to provide a wide range of application-focused drone services for the agriculture, energy and land survey industries.  Building these drones with the use of 3D printing gives them the ability to produce a wide range of drones for specialized applications and build custom drones in a short period of time, giving them a tremendous advantage over the competition.  Monarch chose the Stratasys Fortus 400mc 3D printer because of its ability to build large parts that are strong and rugged enough to fly their drones.  They have taken advantage of these capabilities to design and build drones for special applications that include inspecting crops, wind turbines and solar panels, aerial surveying, accident and crime scene mapping, historical building documentation and many others.

When: May 25th at 1:00pm EST

Register Here

## PADT and ASU Collaborate on 3D Printed Lattice Research

Over the past two academic semesters (2015/16), I had the opportunity to work closely with six senior-year undergraduate engineering students from the Arizona State University (ASU), as their industry adviser on an eProject (similar to a Capstone or Senior Design project). The area we wanted to explore with the students was in 3D printed lattice structures, and more specifically, address the material modeling aspects of these structures. PADT provided access to our 3D printing equipment and materials, ASU to their mechanical testing and characterization facilities and we both used ANSYS for simulation, as well as a weekly meeting with a whiteboard to discuss our ideas.

While there are several efforts ongoing in developing design and optimization software for lattice structures, there has been little progress in developing a robust, validated material model that accurately describes how these structures behave – this is what our eProject set out to do. The complex internal meso- and microstructure of these structures makes them particularly sensitive to process variables such as build orientation, layer thickness, deposition or fusion width etc., none of which are accounted for in models for lattice structures available today. As a result, the use of published values for bulk materials are not accurately predictive of true lattice structure behavior.

In this work, we combined analytical, experimental and numerical techniques to extract and validate material parameters that describe mechanical response of lattice structures. We demonstrated our approach on regular honeycomb structures of ULTEM-9085 material, made with the Fused Deposition Modeling (FDM) process. Our results showed that we were able to predict low strain responses within 5-10% error, compared to 40-60% error with the use of bulk properties.

This work is to be presented in full at the upcoming RAPID conference on May 18, 2016 (details at this link) and has also been accepted for full length paper submission to the SFF Symposium. We are also submitting a research proposal that builds on this work and extends it into more complex geometries, metals and failure modeling. If you are interested in the findings of this work and/or would like to collaborate, please meet us at RAPID or send us an email (info@padtinc.com).

## Ovid: A Teaching Tool for 3D Printing

Meet Ovid.  He is a very simple character that we use to explain 3D Printing to kids. Explaining how 3D Printing works to anyone without a technical background can be tough. To help out PADT has created a collection of resources that shows how it is done, including a hands on model for younger kids, that feature Ovid as the object being printed.

Let’s start by getting technical.  3D Printing is a common term for a class of manufacturing methods referred to as Additive Manufacturing.  In 3D Printing you take a computer model and you print it out to get a real world three dimensional object. The way we do it is that we slice the computer model into thin layers, then build up material in the 3D printer one layer at a time.  Here is a simple GIF showing the most common process:

This is Fused Deposition Modeling, or FDM. If a classroom has a 3D Printer it is most likely an FDM printer.

The idea behind these resources is to show the process:

2. Slice it
3. Build it one layer at a time

The materials below can be used by parents or teachers to explain things to kids, K-8. Please use freely and share!

## Presentation

This PowerPoint has slides that explain the 3D Printing process and the video is of the slides being presented, with our narration.

PowerPoint: Ovid-Presentation-3D_Printing

## Making a Hands-On Ovid

Our fun little plexiglass model of Ovid is an example of a manual 3D printing process. Students can stack up the layers to “3D Print” their own Ovid by hand, reinforcing the layered manufacturing process.

We did everything the same as a real 3D Printer, but instead of automatically stacking the layers, we cut each layer on a laser cutter and the students do the cutting.

Here is a video showing the laser cutting.

And this is a zip file containing the geometry we used to make Ovid in STEP, IGES, Parasolid, and SAT.

To put it all together we created a triangular rod with a base and height that are identical.  Figure out the size you need once you have scaled the geometry for your version of Ovid. we glued the rod to a base.

## Files for 3D Printing and Other Information

We also have a video showing how the software for the printer slices the geometry and makes the tool path for each layer:

And to round things out, here is a few minutes of Ovid being made in one of our Stratasys FDM printers:

## Kids, Pizza, Engineering – A Fantastic SciTech Festival Open House at PADT

We thought we would open PADT’s doors to families and maybe a few people would stop by. Over 250 people did just that.  What a great evening of smiling kids and adults enjoying the excitement of engineering.  Exciting engineering? Yes, we know enough to not talk about quality system protocols, matrix inversions, and non-linear turbulence model convergence. We stuck to 3D Printing, elephants on skateboards, and 3D scanners. And we fed everyone pizza.

It was a great evening where everyone learned something.  The focus was on exposing what engineers do, what PADT does, to people who may not be technical. Mostly kids but we also saw it as a way for engineers to show their family members and friends what engineering is about.  The results far exceeded our expectation, mostly because of how great everyone who showed up was.

Some of the quotes from people who have emailed to thank us are:

“Thank you for opening up your office to me.  What a cool place!  Even though I have been familiar with and worked with 3D printing for 20+ years, it is always nice to see the new technology, products, and the output of the products. “

“… to see my son and all of the other kids so excited and amazed was truly awesome. Mason told me it was the best night of his life! And this morning his first words to me where thanking me for taking him to the event and when can we go back.”

“This is such a great opportunity for me to show my grandkids what I spent my life doing, and seeing them get so excited about it is wonderful”

The best part of the event for most of us here at PADT were the fantastic questions.  As one of our engineers said “for 2 hours I was just lost in the joy of positive human interaction.”  We do love what we do here, but it was nice to share it with other people.

Below are some pictures from the evening.  Make sure you sign up for PADT’s email list to get invites to future events.

## Bring the kids for an evening of STEM fun at PADT’s AZ SciTech Festival Open House

PADT is excited to open our doors to the community and show you and your families what engineering is all about.  Bring the family down for a tour of PADT’s Tempe office and we will show them why engineering rocks. This family friendly event is a great way for kids to see what engineers really do all day.  Tour our 3D printing lab and check out how “We Make Innovation Work”.          Register Here

 WHEN: Wednesday, February 24th from 6:00pm to 7:30pm WHERE: PADT Headquarters 7755 S. Research Drive, Suite 110 Tempe, AZ 85284

The Arizona SciTech Festival is a state-wide celebration of science, technology, engineering and math held annually in February and March.  Through a series of over 1,000 expos, workshops, conversations, exhibitions and tours held in diverse neighborhoods throughout the state, the Arizona SciTech Festival excites and informs Arizonans from ages 3 to 103 about how STEM will drive our state for next 100 years. Spearheaded by the Arizona Commerce Authority, Arizona Science Center, the Arizona Technology Council Foundation, Arizona Board of Regents, the University of Arizona and Arizona State University, the Arizona SciTech Festival is a grass roots collaboration of over 700 organizations in industry, academia, arts, civic, community and K-12.

## Arizona Chief Science Officers Design Their Own 3D Printed Name Badges

The Chief Science Officer program is a program for 6th-12th grade students to represent their school in STEM. And what better way is there for them to identify themselves then with 3D Printed name badges?  The program’s sponsors, the AZ SciTech Festival offer a training retreat for the kids who get elected as their school’s CSO and we all thought introducing design and 3D Printing would be a great activity.

As part of the 2015 Fall CSO Institute, PADT’s Jeff Nichols joined local designer and artist John Drury to spend some time with the kids explaining how to work with logos and shapes to convey an idea, and how to design for 3D Printing.  The kids worked out their own design and sent it to PADT for printing.

We converted their sketch into a 3D Model, starting in Adobe Illustrator. The sketch was traced with vector geometry and then a generic name was added. This was then copied 144 times and each name was typed in, with a few extras. This step was the only boring part.

The design worked great because it is a simple extrusion with no need for support material.    The outline of their names were exported as DXF from Illustrator and then imported onto the 3D Model and extruded up to make a solid model of a badge. This was then copied to make a badge for each student. Then the names were imported and extruded on the patterned badges.

STL files were then made and sent off to one of our Stratasys FDM 3D Printers. The FDM (Fused Deposition Modeling) process extrudes an ABS plastic filament, and you can change material during the build. So, to add a bit of contrast, we changed the filament color after the base of the design was done, making the logo and student names stand out.  The final results came out really nice.

This project was a lot of fun because we were able to work with the students. They got what John and Jeff taught them and did a great job.  We know they will be placed with pride on back backs and jackets across Arizona.

To learn more about the CSO program, visit their website: http://chiefscienceofficers.org/ Check out the blog.  Some of these kids can really write well and their insight into Science, Technology, Math, and Education is insightful.

## Programming a Simple Polygon Editor

Part of my job at PADT is writing custom software for our various clients.  We focus primarily on developing technical software for the engineering community, with a particular emphasis on tools that integrate with the ANSYS suite of simulation tools.  Frankly, writing software is my favorite thing to do at PADT, simply because software development is all about problem solving.

This morning I got to work on a fairly simple feature of a much larger tool that I am currently developing.  The feature I’m working on involves graphically editing polygons.  Why, you ask am I doing this?  Well, that I can’t say, but nonetheless I can share a particularly interesting problem (to me at least) that I got to take a swing at solving.  The problem is this:

When a user is editing a node in the polygon by dragging it around on the screen, how do you handle the case when they drop it on an existing node?

Consider this polygon I sketched out in a prototype of the tool.

What should happen if the user drags this node over on top of that node:

Well, I think the most logical thing to do is that you merge the two nodes together.  Implementing that is pretty easy.  The slightly harder question is what to do with the remaining structure of the polygon?  For my use case, polygons have to be manifold in that no vertex is connected to more than two edges. (The polygons can be open and thus have two end vertices connected to only one edge.)  So, what part do you delete?  Well, my solution is that you delete the “smaller” part, where “smaller” is defined as the part that has the fewest nodes.  So, for example, this is what my polygon looks like after the “drop”

Conceptually, this sounds pretty simple, but how do you do it programmatically?  To give some background, note that the nodes in my polygon class are stored in a simple, ordered C++ std::list<>.

Now, I use a std::list<> simply because I know I’m going to be inserting and deleting nodes at random places.  Linked lists are great for that, and for rendering, I have to walk the whole list anyway, so there’s no performance hit there.  Graphically, my data structure looks
something like this:Pretty simple.  For a closed polygon, my class maintains a flag and simply draws an edge from the last node to the first node.

The rub comes when you start to realize that there are tons of different ways a user might try to merge nodes together in either an open or closed polygon.  I’ve illustrated a few below along with what nodes would need to be merged in the corresponding data structure.  In the data structure pictures, the red node is the target (the node on which the user will be dropping) and the green node is the one they are manipulating (the source node).

Here is one example:

Here is another example:

Finally, here is one more:

In all these examples, we have different “cases” that we need to handle.  For instance, in the first example the portion of the data structure we want to keep is the stuff between the source and target nodes.  So, the stuff on the “ends” of the list needs to be deleted.  In the middle case, we just need to merge the source and target together.  Finally, in the last case, the nodes between the source and target need to be deleted, whereas the stuff at the “ends” of the list need to be kept.

This simple type of problem causes shivers in many programmers, and I’ll admit, I was nervous at first that this problem was going to lead to a solution that handled each individual case respectively.  Nothing in all of programming is more hideous than that.  So, there has to be a simple way to figure out what part of the list to keep, and what part of the list to throw away.

Now, I’m sure this problem has been solved numerous times before, but I wanted to take a shot at it without googling.  (I still haven’t googled, yet… so if this is similar to any other approach, they get the credit and I just reinvented the wheel…)  I remember a long time ago listening to a C++ programmer espouse the wonders of the standard library’s algorithm section.  I vaguely remember him droning on about how wonderful the std::rotate algorithm is.  At the time, I didn’t see what all the fuss was about.  Now, I’m right there with him.  std::rotate is pretty awesome!

std::rotate is a simple algorithm.  Essentially what it does is it takes the first element in a list, pops it off the list and moves it to the rear of the list.  Everything else in the list shifts up one spot.  This is called a left rotate, because you can imagine the items in the list rotating to the left until they get to the front of the line, at which point they fall off and are put back on the end of the list.  (Using reverse iterators you can effectively perform a right rotate as well.)  So, how can we take advantage of this to simplify figuring out what needs to be deleted from our list of nodes?

Well, the answer is remarkably simple.  Once we locate the source and target nodes in the list, regardless of their relative position with respect to one another or to the ends of the list, we simply left rotate the list until the target becomes the head of the list.  That is, if we start with this:We left rotate until we have this:That’s great, but what does that buy us?  Well, now that one of the participating nodes is at the head of the list, our problem is much simpler because all of the nodes that we need to delete are now at either end of the list.  The only question left to answer is which end of the list do we trim off?  The answer to that question is trivial.  We simply trim off the shorter end of the list with respect to the source node (the green node in the diagram). The “lengths” of the two lists are defined as follows.  For the head section, it’s the number of nodes up to, but not including the source. (This section obviously includes the target node)  For the tail, it’s the number of nodes from the source to the end, including the source.  (This section includes the source node).  Since we define the two sections this way we are guaranteed to delete either the source or the target, but not both.  Its fine to delete either one of them, because at this point we’ve deemed the geometrically coincident, but we must not accidentally delete both!!

In the example just given, after the rotate, we would delete the head of the list.  However, let’s take a look at our first example.  Here is the original list:

Here is the rotated list:So, in this case, the “end” of the list (including the source) is the shortest.  If it is a tie, then it doesn’t matter, just pick one.  Interestingly enough, if the two nodes are adjacent in the original list, then the rotated list will look like either this: Or this, if the source is “before” the target in the original list:In either case, the algorithm works unchanged, and we only delete one node.  It’s beautiful! (At least in my opinion…)  Modern C++ makes this type of code really clean and easy to write.  Here is the entire thing, including the search to located geometrically adjacent nodes as well as the merge. The standard library algorithms really help out!

```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 // Search lambda function for looking for any other node in the list that is // coindicent to this node, except this node. auto searchAdjacentFun = [this, pNode](const NodeListTool::AdjustNodePtrT &amp;pOtherNode)-&gt;bool { if (pNode-&gt;tag() == pOtherNode-&gt;tag()) return false; return (QVector2D(pNode-&gt;pos() - pOtherNode-&gt;pos()).length() &lt; m_snapTolerance); }; auto targetLoc = std::find_if(m_nodes.begin(), m_nodes.end(), searchAdjacentFun); // If we don't find an adjacent node within the tolerance, then we can't merge if (targetLoc == m_nodes.end()) { return false; } // Tidy things up so that the source has exactly the same position as the target pNode-&gt;setPos((*targetLoc)-&gt;pos());   // Begin the merge by left rotating the target so that it is at the // beginning of the list std::rotate(m_nodes.begin(), targetLoc, m_nodes.end());   // Find this node in the list auto searchThis = [this, pNode](const NodeListTool::AdjustNodePtrT &amp;pOtherNode)-&gt;bool { return (pNode-&gt;tag() == pOtherNode-&gt;tag()); }; auto sourceLoc = std::find_if(m_nodes.begin(), m_nodes.end(), searchThis);   // Now, figure out which nodes we are going to delete. auto distToBeg = std::distance(m_nodes.begin(), sourceLoc); auto distToEnd = std::distance(sourceLoc, m_nodes.end());   if (distToBeg &lt; distToEnd) { // If our source is closer to the beginning (which is the target) // than it is to the end of the list, then we need to delete // the nodes at the front of the list m_nodes.erase(m_nodes.begin(), sourceLoc); } else { // Otherwise, delete the nodes at the end of the list m_nodes.erase(sourceLoc, m_nodes.end()); } // Now, see if we still have more than 2 vertices if (m_nodes.size() &gt; 2) { m_bClosed = true; } else { m_bClosed = false; } return true;```

## PADT Presents 3DPAZ Contest and FIRST Robotics Grant

PADT has always been a proud supporter of STEM education in our community.  This summer we have been busy planning some new activities to help support local schools.  Today we are busy attending the Innovation Arizona Summit which is a joint collaborative of the Arizona SciTech Festival, the MIT Enterprise Forum Phoenix and the Arizona Commerce Authority.

As part of our attendance, we will be promoting our first ever 3D printing contest, 3DPAZ  which will challenge high school students in Arizona with the task of creating or improving an existing engineering product.  We are very excited to be launching this contest and cannot wait to see what students come up with. Please visit our website for more information on how to take part in this contest by clicking here.

We are also very excited to be extending our support to the FIRST Robotics Competition by way of a new grant program for Arizona schools or organizations that are competing in the in the 2014/2015 FRC season.  If you are interested in either the 3DPAZ contest or the FRC Grant program, please email Kathryn Pesta at kathryn.pesta@padtinc.com.