In traditional CAD environments, geometry can be defined and represented in more ways than one. If you have ever used a 3D modeling program, you’ve most likely worked with meshes, BReps, or both, depending on the task at hand. Although meshes and BReps have their strong points, their weaknesses rear their head as product geometry becomes more complex. Managing the size and performance of complex geometry requires a computationally lighter means of defining and representing geometry. By integrating a field-driven design approach based on the implicit modeling technology, designers can focus on engineering work that matters, and spend less time with non-value-added tasks.

Implicit Geometry

Implicit modeling is a powerful way to define, change and represent 3D geometry. Geometry is defined through equations in such an approach, rather than through a network of vertices, edges, and faces like meshes and BReps. This means that implicits are significantly lighter to compute and maintain their pure form because they are not discretized like meshes and BReps, which don’t always capture continuity perfectly.

For instance, mesh geometry, regardless of its resolution, is a faceted representation of the actual form. At some point in the design-to-manufacturing pipeline, some form of discretization will be required, whether it is through meshes, BReps, or producing slice data for additive manufacturing (AM). By discretizing data from implicit models directly to a manufacturing-ready output, the discretization occurs at the very end of the process instead of at the beginning or throughout. This means that outgoing manufacturing data is more precise. In addition to being orders of magnitude faster to compute, implicit geometry also results in super-lightweight files, as only a minimal amount of information is needed. 

nTopology, implicits, 3D geometry, CAD, meshes, BReps, field-driven design, modeling technology

Shown above is a mesh representation compared to an implicit representation of a sphere. In this example, the mesh face count of the sphere is purposely low to exaggerate the discretization. Note, that if the mesh face count was significantly increased to more accurately represent the sphere then file size would also increase, which is problematic for design and analysis. (Image Credit: nTopology)

nTopology, implicits, 3D geometry, CAD, meshes, BReps, field-driven design, modeling technology

Rather than discretizing implicit geometry, sampling and previewing geometry through “shaders” is a form of rendering that enables users to quickly view geometry at very low or very high resolution, while also leveraging a computer’s graphic processing unit. This improves speed while accurately representing geometry. (Image Credit: nTopology)

Understanding Fields—an analogy taken from the weather

Field-driven design is an empowering concept that builds upon implicit modeling. It has several benefits to end users and organizations, such as increased flexibility and efficiency of design. To better understand the concept of fields, let’s first explain how it works by using weather as an analogy.

Imagine driving along the east coast of the United States from Florida to Maine, with the goal of finding optimal places to camp along the way based on simple weather data. At each mile, using a weather app, you could sample information such as temperature, wind, humidity, visibility and air quality. Each information type, such as temperature, is continuous, meaning it is everywhere. This is a field, and you can sample this temperature field and all other weather fields at every mile, half-mile, yard, foot, inch, etc. The key takeaway is that we can use one type of weather data or combine all of it to inform our decision on where to camp. In a similar way, fields representing different types of data such as distance, force, or velocity values can be used and even combined to enhance implicit geometry for optimal performance.

Although many different types of data can be converted into fields, we’ll only focus on distance fields, since they are the first type of field you’ll encounter in a computational modeling platform. When creating models through a visual programming interface, the output is more than just the representation of implicit geometry. Under the hood of each implicit operation resides an equation that outputs the distance values to the boundary of the geometry.

Like temperature in our environment, distance data is everywhere. It can be sampled at very large or very small increments from any height or depth in any axis. It is everywhere. Why are these distance values relevant to the representation of geometry? Distance values that equal zero define the boundary of geometry. Negative distance values define what is inside, while positive values define what is outside.

nTopology, implicits, 3D geometry, CAD, meshes, BReps, field-driven design, modeling technology

An example of distance fields, sampled at the cross-section of a sphere, torus, and cube. Values beyond the boundary of each primitive are positive, while values internal are negative. The radiating white lines represent the resolution at which the distance field is sampled, in this case, every 2 millimeters. (Image Credit: nTopology)

Distance Fields for Modeling Operations

Other than the zero values that define the boundary of our geometry, how can the positive and negative values of a field be utilized? Imagine wanting to offset a sphere. We now know that the boundary of the sphere is composed of zeros. If we wanted to offset the sphere by one millimeter, we would need the zero values to be one millimeter away from where they are currently.

Boolean operations are some of the first commands any designer or engineer learns when introduced to 3D modeling. But as we become more skilled, we notice that these commands become more volatile as geometric complexity increases. When Boolean-unioning one mesh with another, two networks of vertices, edges, and faces are recalculated into one new network.

nTopology, implicits, 3D geometry, CAD, meshes, BReps, field-driven design, modeling technology

When Boolean unioning two mesh spheres, a new network of vertices, edges, and faces is formed. This network is composed of network geometry from each original sphere and new geometry in order to connect the two. (Image Credit: nTopology)

Combining two simple mesh geometries is easy, but performing this operation among complex mesh parts such as lattices most certainly results in a failure at some point. However, implicit modeling treats these problems entirely differently and they never fail. Computing the Boolean union of two geometries implicitly is just a matter of extracting the minimum values of two overlapping distance fields. Inverting this condition to extract the maximum values between the two fields will result in a Boolean intersect.

nTopology, implicits, 3D geometry, CAD, meshes, BReps, field-driven design, modeling technology

Left: The Boolean union of two fields extracts the minimum values between two fields. Right: The Boolean intersect of two fields extracts the maximum values between two fields. (Image Credit: nTopology)

Innovative Design for Manufacturing

Just as weather data can determine camping conditions, distance fields determine the result of modeling operations such as Booleans, offsets and fillets, to name a few. Engineers and designers using a field-driven approach to driving implicit models are freed from frustrating manual setup, rework and data repair, and have the ability to fine-tune and control their data.

They can focus on creative, breakthrough designs with a smooth pathway to manufacturing. From modeling to simulation to manufacturing, fields are ever-present in core workflows and enable designers to drive geometry with layers of synthesized data. The outcome can be products with highly complex features and characteristics yet with more reliable, robust performance.

Drive World with ESC Launches in Silicon Valley

This summer (August 27-29), Drive World Conference & Expo launches in Silicon Valley with North America’s largest embedded systems event, Embedded Systems Conference (ESC). The inaugural three-day showcase brings together the brightest minds across the automotive electronics and embedded systems industries who are looking to shape the technology of tomorrow.

Will you be there to help engineer this shift? Register today!


  1. I do not even know the way I stopped up here, however I thought this
    post was great. I don’t recognize who you might be
    but definitely you’re going to a famous blogger if you are not
    already. Cheers!

  2. Hi would you mind sharing which blog platform you’re working with?
    I’m looking to start my own blog in the near
    future but I’m having a difficult time selecting between BlogEngine/Wordpress/B2evolution and Drupal.
    The reason I ask is because your design and style seems different then most blogs and I’m
    looking for something completely unique.
    P.S Sorry for getting off-topic but I had to ask!

  3. Have you ever considered about adding a little bit more than just your articles?
    I mean, what you say is important and all. Nevertheless just imagine if you added
    some great pictures or video clips to give your posts more, “pop”!
    Your content is excellent but with images and clips, this site could certainly be one of the
    most beneficial in its field. Fantastic blog!

  4. After looking over a number of the blog articles on your blog,
    I honestly like your technique of writing a blog.
    I book marked it to my bookmark site list and will be checking back
    soon. Take a look at my web site too and tell me how you feel.

  5. What’s up everyone, it’s my first go to see at this web site, and post is
    genuinely fruitful for me, keep up posting these articles or

  6. Awesome blog! Is your theme custom made or did you download
    it from somewhere? A theme like yours with a few simple adjustements would really make my blog shine.
    Please let me know where you got your design. Thanks

  7. Hmm it appears like your website ate my first comment (it was extremely long) so I guess I’ll just sum it
    up what I wrote and say, I’m thoroughly enjoying your blog.
    I as well am an aspiring blog blogger but I’m still new to
    the whole thing. Do you have any tips and hints for rookie blog writers?

    I’d genuinely appreciate it.

  8. A person necessarily assist to make severely posts I would state.
    This is the first time I frequented your web page
    and so far? I amazed with the analysis you made to make this actual put
    up extraordinary. Magnificent task!

  9. An impressive share! I have just forwarded this onto a co-worker who had been conducting a little research
    on this. And he in fact ordered me dinner because I discovered it for him…

    lol. So allow me to reword this…. Thank YOU for the meal!!
    But yeah, thanks for spending some time to talk about this matter here on your web page.

  10. Helpful information. Lucky me I found your site by accident, and I’m
    stunned why this accident did not took place in advance! I bookmarked it.

  11. I blog often and I really thank you for your content. Your article has really peaked my interest.
    I’m going to take a note of your website and
    keep checking for new details about once a week. I subscribed to your Feed as well.

  12. I’m truly enjoying the design and layout of your
    blog. It’s a very easy on the eyes which makes it much more pleasant for me to come here and visit more often. Did you hire out a developer
    to create your theme? Exceptional work!

  13. It is the best time to make some plans for the
    future and it is time to be happy. I’ve read this post
    and if I could I want to suggest you some interesting things or advice.
    Maybe you can write next articles referring
    to this article. I desire to read more things about it!

  14. Thank you for every other wonderful post.
    Where else may just anybody get that type of information in such an ideal means
    of writing? I have a presentation next week, and I’m on the look for such information.

  15. My coder is trying to persuade me to move to .net from PHP.
    I have always disliked the idea because of the expenses.
    But he’s tryiong none the less. I’ve been using Movable-type
    on a variety of websites for about a year and am anxious about switching to another platform.
    I have heard very good things about blogengine.net. Is there a way I can transfer all my wordpress content into it?
    Any help would be really appreciated!

  16. I was curious if you ever thought of changing the page layout of your website?
    Its very well written; I love what youve got to say.
    But maybe you could a little more in the way
    of content so people could connect with it better. Youve got
    an awful lot of text for only having one or two pictures.
    Maybe you could space it out better?

  17. fantastic submit, very informative. I wonder why the other experts of this sector don’t understand this.
    You must continue your writing. I’m confident, you’ve a great
    readers’ base already!

  18. Hey there! I’ve been reading your web site for
    some time now and finally got the courage to go ahead and
    give you a shout out from New Caney Tx! Just wanted to
    say keep up the fantastic work!

  19. I want to to thank you for this great read!! I definitely loved
    every bit of it. I have got you book marked
    to check out new things you post…

  20. Does your website have a contact page? I’m having problems locating it but, I’d like to
    shoot you an e-mail. I’ve got some ideas for your
    blog you might be interested in hearing. Either way, great blog and I
    look forward to seeing it improve over time.

  21. I am not sure the place you’re getting your information, but great topic.
    I needs to spend some time finding out more or figuring out more.
    Thank you for wonderful info I was looking for this info for my mission.

  22. Heya excellent website! Does running a blog like this take
    a massive amount work? I’ve very little knowledge of coding however
    I was hoping to start my own blog in the near future.
    Anyway, if you have any suggestions or tips for new
    blog owners please share. I understand this is off topic however I simply needed to ask.

  23. Hello, Neat post. There’s a problem along with your web site in web explorer, would test this?
    IE nonetheless is the marketplace chief
    and a good part of other folks will omit your fantastic writing because of this problem.

  24. I’ll immediately snatch your rss as I can not
    to find your e-mail subscription hyperlink or newsletter service.
    Do you have any? Please allow me realize so that I may just subscribe.

  25. Good day! Would you mind if I share your blog with my facebook group?
    There’s a lot of people that I think would really enjoy your content.

    Please let me know. Cheers

  26. This is the perfect web site for anyone who really wants to find out about this topic.

    You realize so much its almost hard to argue with you (not that I personally would want to…HaHa).
    You certainly put a fresh spin on a topic which has been written about for years.
    Excellent stuff, just wonderful!

  27. I’ve been surfing online more than 3 hours these days, yet I
    by no means discovered any interesting article like yours.
    It is beautiful value sufficient for me. Personally, if all web owners and bloggers made good content material
    as you probably did, the internet will likely be much more
    helpful than ever before.

  28. It’s a shame you don’t have a donate button! I’d most
    certainly donate to this outstanding blog! I guess for now i’ll settle
    for book-marking and adding your RSS feed to my Google account.
    I look forward to new updates and will share this website with my Facebook group.
    Chat soon!

  29. Wow! This blog looks just like my old one! It’s on a completely different subject but it has pretty much the same
    layout and design. Wonderful choice of colors!

  30. Greate pieces. Keep writing such kind of information on your blog.

    Im really impressed by it.
    Hello there, You have performed a fantastic job.
    I’ll definitely digg it and for my part recommend to my
    friends. I am confident they will be benefited from this site.

  31. May I just say what a comfort to find somebody who
    truly understands what they are talking about on the internet.
    You definitely know how to bring a problem to light and make it
    important. More people should check this out and understand this side of
    your story. I was surprised you aren’t more popular given that you definitely possess the

  32. Thanks for every other great post. The place else could anybody get that type
    of info in such a perfect means of writing? I have a presentation subsequent week, and I am at the look
    for such information.

  33. Today, I went to the beach front with my kids. I found a sea shell and gave it to my 4
    year old daughter and said “You can hear the ocean if you put this to your ear.” She put the shell
    to her ear and screamed. There was a hermit crab inside and it pinched her ear.
    She never wants to go back! LoL I know this is completely off topic but I had to
    tell someone!

  34. I must thank you for the efforts you’ve put in penning this website.
    I am hoping to view the same high-grade content from you later on as well.

    In truth, your creative writing abilities has inspired me to get my own, personal website now 😉

  35. What i don’t realize is in reality how you are now not really much more neatly-favored than you may be now.
    You are very intelligent. You recognize therefore significantly on the
    subject of this matter, made me individually believe it from numerous
    various angles. Its like women and men are not fascinated
    except it is one thing to accomplish with Lady gaga!
    Your personal stuffs great. At all times deal with it up!

  36. Hello! I could have sworn I’ve been to your blog before but after going through a few of the posts I realized it’s new to me.

    Anyways, I’m certainly happy I came across it and I’ll
    be bookmarking it and checking back frequently!

  37. I am extremely impressed with your writing skills as well as with
    the layout on your blog. Is this a paid theme or did you modify it yourself?
    Either way keep up the nice quality writing, it is rare to see a nice blog like this one today.

  38. Thanks for ones marvelous posting! I truly enjoyed reading it, you will be a great author.I
    will always bookmark your blog and definitely will come back
    someday. I want to encourage one to continue your great posts,
    have a nice morning!

  39. Howdy! This is my 1st comment here so I just wanted to give a quick shout out and say I truly enjoy reading your blog
    posts. Can you suggest any other blogs/websites/forums that deal with the same subjects?

  40. A fascinating discussion is definitely worth comment.
    I think that you should publish more on this subject, it might not be a taboo subject
    but typically people do not talk about these issues.
    To the next! Cheers!!

  41. My brother recommended I might like this web site. He was entirely right.
    This post truly made my day. You can not imagine just how
    much time I had spent for this information! Thanks!

  42. May I just say what a relief to find somebody who actually knows what they are discussing online.
    You definitely realize how to bring an issue to light and make it important.
    More and more people ought to check this out and understand
    this side of your story. It’s surprising you aren’t more popular since you
    surely possess the gift.

  43. Have you ever thought about adding a little bit more than just your articles?

    I mean, what you say is fundamental and everything.

    But think of if you added some great graphics or videos to give your posts more, “pop”!
    Your content is excellent but with images and video clips, this website could certainly
    be one of the greatest in its field. Superb blog!

  44. Howdy, i read your blog occasionally and i own a similar one and i was
    just wondering if you get a lot of spam feedback? If so how do
    you protect against it, any plugin or anything you can suggest?
    I get so much lately it’s driving me crazy so any assistance is very much appreciated.

  45. I’ve been browsing online more than three hours today, yet I never found any interesting article like yours.
    It is pretty worth enough for me. In my opinion, if all web owners and bloggers made good content as you did,
    the web will be much more useful than ever before.

  46. Hi there everyone, it’s my first pay a quick visit at this web page, and piece of writing is really fruitful
    in favor of me, keep up posting such content.

  47. Wow! This blog looks exactly like my old one!
    It’s on a completely different subject but it has pretty much the same page layout and design. Superb choice of colors!

  48. Hey I know this is off topic but I was wondering if you knew of any widgets I could add to my blog that automatically tweet
    my newest twitter updates. I’ve been looking for a plug-in like this for quite some
    time and was hoping maybe you would have some experience with something like this.

    Please let me know if you run into anything.
    I truly enjoy reading your blog and I look forward
    to your new updates.

  49. Hey There. I found your blog using msn. This is an extremely well written article.
    I will be sure to bookmark it and return to read more of your useful
    information. Thanks for the post. I will certainly comeback.

  50. That is a good tip especially to those new to the blogosphere.
    Short but very precise information… Thanks for
    sharing this one. A must read article!

  51. Unquestionably consider that which you said. Your favorite justification seemed to be on the net the
    simplest thing to take into account of. I say to you, I definitely get irked whilst other folks consider concerns
    that they plainly do not recognize about.

    You controlled to hit the nail upon the highest as neatly as outlined out the entire
    thing without having side-effects , other people could take a signal.
    Will probably be again to get more. Thank you

  52. Someone essentially lend a hand to make critically posts I would
    state. This is the very first time I frequented your web page and to this point?
    I surprised with the research you made to make this actual put up amazing.
    Magnificent task!

  53. Nice weblog here! Also your web site rather a lot up fast!

    What web host are you the use of? Can I am getting your affiliate link on your
    host? I want my website loaded up as quickly as yours lol

  54. Hmm is anyone else encountering problems with the images on this blog loading?
    I’m trying to figure out if its a problem on my end or if it’s the blog.

    Any feedback would be greatly appreciated.

  55. Thank you for any other informative blog. The place else may I am getting that kind of
    info written in such a perfect way? I have a challenge that
    I’m just now operating on, and I have been at the glance out for such information.

  56. I have read so many posts regarding the blogger lovers however this article is genuinely a pleasant piece
    of writing, keep it up.

  57. It is really a nice and useful piece of info. I am glad that you simply shared
    this useful info with us. Please stay us informed like this.
    Thank you for sharing.

  58. Hiya! Quick question that’s entirely off topic. Do you know how to make
    your site mobile friendly? My website looks weird
    when browsing from my iphone. I’m trying to find a template or plugin that might be able to
    correct this issue. If you have any suggestions, please share.
    Appreciate it!

  59. I loved as much as you’ll receive carried out right here.
    The sketch is attractive, your authored subject matter stylish.

    nonetheless, you command get bought an nervousness over
    that you wish be delivering the following. unwell unquestionably
    come further formerly again as exactly the same nearly very often inside case you shield this hike.

  60. Hi, i feel that i noticed you visited my web site thus i got here to return the favor?.I am trying to
    find things to enhance my site!I suppose its ok to make use of some of your concepts!!

  61. I’m curious to find out what blog platform you have been using?

    I’m experiencing some minor security problems with my latest site and I’d like to find something more risk-free.
    Do you have any recommendations?

  62. Hi! I’m at work surfing around your blog from my new iphone!
    Just wanted to say I love reading your blog and look forward to all your posts!
    Carry on the outstanding work!

  63. I like the helpful information you provide in your articles.
    I’ll bookmark your weblog and check again here regularly.
    I am quite certain I will learn plenty of new stuff right
    here! Good luck for the next!

  64. I’m impressed, I must say. Seldom do I come across
    a blog that’s both equally educative and amusing, and let me tell you,
    you have hit the nail on the head. The problem is
    something that not enough people are speaking intelligently about.
    Now i’m very happy I found this during my search for something regarding this.

  65. I all the time used to read piece of writing in news papers but
    now as I am a user of internet therefore from now I am using net for posts, thanks to web.

  66. I’m really loving the theme/design of your web site. Do you
    ever run into any web browser compatibility issues? A number of my blog audience
    have complained about my website not operating correctly in Explorer but looks great in Firefox.
    Do you have any suggestions to help fix this issue?

  67. Its like you learn my mind! You appear to know so much about this, like you wrote the book in it
    or something. I think that you just can do with a few p.c.
    to force the message home a bit, however instead of that, that is magnificent blog.
    A great read. I’ll definitely be back.

  68. Good post. I learn something new and challenging on sites I stumbleupon on a daily basis.
    It will always be interesting to read articles
    from other authors and practice a little something from other websites.

  69. I have read so many articles or reviews on the topic of
    the blogger lovers but this paragraph is truly a fastidious article, keep it

  70. I was recommended this blog by my cousin. I’m not sure whether this post is written by him
    as no one else know such detailed about my problem.
    You are amazing! Thanks!

  71. I do believe all the concepts you have introduced to your
    post. They’re really convincing and can definitely work.
    Still, the posts are too brief for newbies.

    Could you please extend them a little from subsequent time?
    Thanks for the post.

  72. hello there and thank you for your information – I’ve
    definitely picked up something new from right here.
    I did however expertise some technical issues using this web site, as I experienced to reload the site lots of times
    previous to I could get it to load properly.
    I had been wondering if your web host is OK? Not that I’m complaining, but slow loading
    instances times will very frequently affect your placement in google and can damage
    your quality score if advertising and marketing with Adwords.

    Well I am adding this RSS to my email and could look out for
    much more of your respective fascinating content. Make sure you update
    this again very soon.

  73. Good day! This post couldn’t be written any better!
    Reading this post reminds me of my old room mate! He always kept chatting about this.

    I will forward this write-up to him. Pretty sure he will have a good read.
    Thank you for sharing!

  74. I’ll immediately seize your rss as I can not in finding your e-mail subscription link or e-newsletter service.
    Do you’ve any? Please let me recognise so that I may
    just subscribe. Thanks.

  75. Hi there just wanted to give you a brief heads up and let you know a few
    of the pictures aren’t loading properly. I’m not sure
    why but I think its a linking issue. I’ve tried it in two different browsers and both show the same results.

  76. I know this if off topic but I’m looking into starting
    my own blog and was curious what all is required to get setup?
    I’m assuming having a blog like yours would cost a pretty penny?
    I’m not very web savvy so I’m not 100% positive. Any recommendations or advice would be greatly
    appreciated. Cheers

  77. Heya terrific blog! Does running a blog similar to this take a massive amount work?
    I have virtually no understanding of coding but I had been hoping to start my own blog in the
    near future. Anyhow, if you have any ideas or techniques
    for new blog owners please share. I understand this is off subject however I simply wanted to
    ask. Thanks a lot!

  78. Howdy! Quick question that’s completely off
    topic. Do you know how to make your site mobile friendly?
    My web site looks weird when browsing from my iphone 4. I’m trying to find a
    theme or plugin that might be able to correct this
    issue. If you have any recommendations, please share.
    Thank you!

  79. It is in point of fact a nice and useful piece of information. I am satisfied that you shared this helpful information with us.
    Please keep us up to date like this. Thanks for sharing.

  80. May I simply just say what a comfort to find someone that really knows what they’re talking
    about online. You certainly realize how to bring an issue to light and make it important.
    A lot more people need to read this and understand this side of the
    story. It’s surprising you’re not more popular given that
    you definitely have the gift.

  81. Very good site you have here but I was wondering if you knew of any message boards that cover the same topics
    talked about here? I’d really love to be a part of online community
    where I can get responses from other experienced individuals that share the same interest.
    If you have any suggestions, please let me know.
    Many thanks!

  82. Hello there I am so glad I found your site, I really found you by accident, while I was browsing
    on Yahoo for something else, Anyhow I am here now and would just like to say many thanks for a tremendous post and a
    all round enjoyable blog (I also love the theme/design), I don’t have time to read through it all at the minute but I have saved it and
    also added in your RSS feeds, so when I have time I will be back to read more, Please
    do keep up the excellent work.

  83. Hey there! Do you know if they make any plugins to protect against hackers?
    I’m kinda paranoid about losing everything I’ve worked hard
    on. Any recommendations?

  84. Excellent blog right here! Also your site lots up fast! What
    host are you the usage of? Can I get your associate hyperlink on your host?
    I desire my web site loaded up as fast as yours lol

  85. Great web site you have got here.. It’s difficult to find high-quality writing like yours these days.

    I really appreciate people like you! Take care!!

Leave a Reply

Your email address will not be published.