Great. We’ve got Conics. Now what?

One of the mantras I’ve adopted in my time with the SolidWorks product is “be careful of what you ask for”. Sometimes the answer is to simply remove the functionality you complain about. Or maybe create a whole new set of problems to make you forget about the old problems. Their answer has rarely been either trouble free, or something I had imagined/hoped for. I like the “Show Flat Tree View”. So far that hasn’t had any unintended consequences.

But “the Conic” has been for some users the holy grail of “stuff other CAD programs have”. I personally have never worked with conics. People claim they are great, and in concept I can see some of the value, but in practice, they just seem to be an endless font of excuses.

SolidWorks 2013 added the conic sketch entity to the toolset. Literally the first thing I tested after sketching one was if you could then connect it to a spline and add a curvature continuity relation between them. In beta and prerelease, it turned out that you couldn’t. To me, a sketch entity that is supposed to enhance smoothness without the ability to assign c2 is nearly pointless.

But then I did some searching, and it turned out that you also couldn’t make c2 relations to partial ellipses or parabolas. We never cried about parabolas because parabolas sucked so bad when they were introduced that they were an embarrassment.  After some time, the parabola got partially fixed, although I have to say I don’t remember when that was. The work flow to draw a parabola still includes placing 4 points, and still starts with a point that isn’t on the curve, and ends with the two end points. Surely there’s something better than that.

Come SW2013 and now we’ve got the ability to draw the sacred “conic”. They did at least figure out to make the two endpoints the first stages of the workflow, thanks for that. 2013 sp2 reportedly added the functionality I felt was missing, so I got all excited. It turns out they also added the ability to make splines c2 to partial ellipses and parabolas. But the excitement was short lived. It turns out you can make a c2 relation between a conic and a spline if they are both in the same sketch, or if the conic is in a closed sketch and the spline is in the active sketch. But you can’t make c2 between a conic and anything else if the “anything else” is outside the sketch, or is a dead entity like a converted entity. One of two things will happen if you try to create a situation that it won’t support. One possibility is that the relation will just go “unsolvable”. Red. Overdefined. Another option is that SolidWorks will simply ignore it altogether. It won’t add the relation, but it won’t fail either.

In the end, you only have a couple situations when the new conic sketch entity is worth using, and that’s when you sketch spline-conic-spline within a single sketch, or when you just draw a conic and make a surface from it, then build on that later with other features. But a conic is meant to function almost like a fillet, and you never draw the fillet before you draw the lines on either side.

This is why the limitations of a function are almost more important than knowing what it will do.

There may be a reason conics were not implemented in SolidWorks for so long. There may actually be GOOD reasons. The problem is no one (who actually knows) has taken the time to communicate with users. This is one of the underlying complaints I have about the software. Convincing people who are fans of conic sketch entities from other programs would undoubtedly be difficult. But SolidWorks to me has if nothing else, been an adventure of discovery. I’ve had to piece everything I’ve learned together from little bits, and from reverse engineering. Lots of things make sense when they are explained. Maybe what I’ve really learned is how loosely a CAD program is tied together. There are very few people who actually know how things work, and those people may not even work for the company that develops the software.

The math for conic sections is simple enough.

Circle: x^2 + y^2 = r^2
ellipse: (x/a)^2 + (y/b)^2 = 1
parabola: y=x^2
hyperbola: x^2/a^2 – y^2/b^2 = 1
straight line: y=mx+b


The math is high school math. LOTS of us who use this software have had LOTS of math after high school math, and would understand stuff like this if it was explained somewhere. The slope of the tangent of a conic curve at its end point is easy to figure out from first derivative, which is easy for all these. The curvature at the end of the curve is also easy to figure out for a second order equation, as second derivative. But there has to be a single equation for the whole set of conic entities.

From Wikipedia,

In the Cartesian coordinate system, the graph of a quadratic equation in two variables is always a conic section – though it may be degenerate, and all conic sections arise in this way. The equation will be of the form

Ax^2 + Bxy + Cy^2 +Dx + Ey + F = 0\text{ with }A, B, C\text{ not all zero.} \,

But we need something with a rho-like single variable in it.

At another link,

given three control points, a, b, and c, and a parameter
Lambda, the parametric equation for a conic is given as
              a (1-t)^2 + b \Lambda 2t(1-t) + c t^2
    eta(t) = -------------------------------------       
                 (1-t)^2 + \Lambda 2t(1-t) + t^2

Anyway, I’m sure its doable. So many other things are really difficult, but most of this is understandable. If this is just plain wrong, please someone explain why.

I’ve created a lot of stuff without the conic in the past, and I have the feeling I’ll create a fair amount of stuff without the conic in the future. If they can’t create a conic sketch entity that can get c2 without limitations, I don’t think I’ll find a whole lot of use for it. They might have saved themselves the trouble of working on it if they had just talked to users. I really don’t need what was delivered. It will be another curiosity in the dust  bin like the parabola.


15 Replies to “Great. We’ve got Conics. Now what?”

  1. Matt,
    you can look at the conic creation in this respect: while you are drawing the conic in Solidworks, you are gradually defining the constants in the general conic equation (ax^2+bxy+cy^3+dx+ey+f=0). not all a,b,c are zero, so we can divide it with either a or b or c which isn’t zero. therefore, eliminating one of those constants. so we are left with 5 constants(unknowns). and we need 5 equations to make up our system of 5 equations,5 unknowns, and solve it to obtain those constants and fully define the curve. Placing the start point on the graphics area, means that the general equation should be valid when u input the coordinates(x,y) of the start point into the equation, so that’s one equation in our system of 5 equations. placing the end point, generates the second equation. adding start tangent and end tangent, generate 2 more equations, and finally inputting the value for rho, generates the fifth and last one. so we fully defined the conic with these inputs. if the equation had a couple more of unknown constants, we could enforce the C2 condition. but simply we don’t have them in a conic. that’s why you can’t force C2 on conic ends. it can be the driving element as you say, but cant be driven.

  2. Solidworm,
    Solidworks boundary surface butt cracks and hogbacks tend to have small dihedral angles and influence the shape over a large area. The airplane fuselage had the nasty problem visible several inches from the centerline. This is apparent when curvature combs are turned on when creating the surface. Curls and tits tend to be very small and vanish with the CAM software, but persist in solidworks to prevent thickening the surface.

    I get the best shapes by defining the boundaries of a surface with relatively low order curves, usually a 3rd order spline projected on another spline or a conic. This produces a higher order 3D curve that is controllable. When the corner conditions of these curves is correct very nice surfaces are possible. The big goal is controllable smooth and accurate geometry.

    GW3D conic surfaces do generate nurbs surfaces. These are nearly conics in one direction. I have never seen a butt crack, hogback, wrinkle, ripple or tit feature from one of these surfaces. I have seen a tiny ribbon defect very near a singular point. I suspect that this is due to one curve not exacly intersecting the other. The fact that singular points usually form excellent terminations of the conic surface is amazing.

  3. …indeed many butts aren’t all they are cracked up to be.
    cleavage can also be unnecessarily distracting as well but I haven’t noticed anyone complaining about that here…perhaps that can be the subject of another blog post.. 😉

  4. @Rick McWilliams
    >”The boundary surface is a trimmed nurbs surface that has very high order shapes at the edges ”
    the trimmed surface part shouldn’t be true i think. and not higher order,they are all degree 3 as far as i know, but with excessive number of spans or knots, in fact if they were higher order, it could be better, because they could use fewer number of spans and the resulting surface would be of higher quality, of course if they could handle the “egg carton” effect.
    I bet the conic surfaces you make with GW3D Add-in are made of overly complex degree 3 nurbs surfaces as well.
    Plus all of these surfaces, are an input for the CAM system you use, and the CAM system, will probably reparametrize all of these surfaces to its own standards and those famous butt cracks may appear there. and all those but cracks are going to get machined with an endmill with a diameter definitely larger than butt crack width, so it wont go in there, but goes over the butt crack, so its betters not to get too obsessive about the those butt cracks.

  5. The solidworks conic curve sketch item is useful. My complaint is that a boundary surface with entirely conic profiles does not produce conic intermediate shapes. It will produce butt cracks and hogbacks. These nasty shapes can be somewhat rounded with a normal to profile edge condition. The boundary surface is a trimmed nurbs surface that has very high order shapes at the edges and sometimes gaps. It takes some skill to detect minor surface geometry errors, curvature combs, curvature, and zebra stripes. They are not ignorable in the final product.

    I use the GW3D add in to create beautiful conic surfaces, and other surfaces that were forgotten by Solidworks.

  6. @didi
    I know all that. For years I hear we need conics.Then Conics are introduced. Conplaints about only being c1. Then made c2 workable upto a point. Complaints well not enough yet bla bla bla….. As Matt is well versed with solid edge now I thought it would be good to be given a direct comparison

  7. @Ronan
    Ronan, these guys are complaining about SW. For they doesn’t really matter if D-Cubed (Siemens owned) doesn’t support what they are asking for. In many areas, SW have more capabilities than SE, using same solver (D-Cubed). Strange, right?

  8. Next is the cloud! See this Draftsight marketing email:


    “What is a flipbook? It’s a learning resource that’s easy-to-use, with cloud-based rich media that you can bookmark while using DraftSight. Flip through the pages or click a tab to quickly jump through the sections. Our flipbooks are accessible via the web, tablet, and mobile devices, and can be easily shared through email or social media.”

    Here’s the flipbook

    Interesting material with nice videos, but I’d like to see it offline. I’m offered to either print it or save it to pdf. If I save it to pdf then I cannot see the videos.

    I’m too traditional, the cloud is not for me…

  9. If they are serious about SW then they would have overhauled the reference system a long time ago. Not having the option to replace sketch entities is a bare minimum.

    Conics are a nice-to-have, but so are splines where you can dimension the control polygon…

  10. Conic curves a nice because they are completely defined in various useful ways. The form that I use the most is the two points with two slopes and rho. GW3D gives 15 choices on how to define the conic curve. I use conics often instead of two point splines because they are easier to control.

    Conic surfaces are wonderful. It will never generate a wiggly rippled shape. I apply a conic surface spanning between two general edge curves. The edge slope can be determined by normal to plane, tangential to surface, or a slope curve. The conic shape can be controlled by rho, linear changing rho, shoulder curve and others. A change of rho is a powerful and easy style control for the sharpness of corners. Conics are not just for airplanes. I have used them for seat cushions. It would make an excellent puffy box.

    Some other GW3D shapes are useful. The blend surface does very delicate fillets but it will make a ruled surface suitable for a wing skin. Without sags that can happen with a SW loft. The blend surface is nicer than SW fill for complex shapes. It is fussy as the corners must be correct or no C2 for you. I have heard that the GW3D for 2013 includes a cone spline. There is a mirror feature that can mirror curves, something forgotten by SW.

    SW splines can become very tricky to control. Moving one handle should not move others. The tangent to a line or circle should stay tangent. What is a Sw spline and why do they need relaxation? Adobe style splines work better.

    Conic surfaces are so versatile and beautiful it is very hard to go back to SW surfaces.

  11. Well conics are useful if you need conics. And I think your criticism is somewhat misplaced because you actually don’t need them.

    For example, drawing a conic arc starting from the endpoints is nice, but not if you want to draw an arc of ellipse starting from the ellipse foci. For the same reason the parabola tool (which is a conic so there’s no need for a separate parabola arc tool) can be useful if the points used to define the parabola are not the endpoints. There are specific fields where being able to draw a conic arc is very useful, and also fields where being able to define a conic starting from her geometry roots (foci and axes) can be a time saver.

    That said, you can draw all conics with a degree 2 nurbs curve, it’s an exact representation, only not as easy to manage as a proper conic definition.

  12. Well you must be looking to wind up your audience…
    Conics were the next obvious thing to include in SW.
    If you were wanting to do something to extend geometric functionality, as you have been keen to do over other frivolous things its the obvious choice.
    I don’t actually believe they seriously intended to put conics in SW at this stage though.
    Its more of a demonstration to the SW community that SW is still getting some attention and something of a stocking filler seeing as how the arrival of Catia lite drags on year after year.
    The problem is I think that this is something of a hastily resurrected project that simply hasn’t managed to deliver enough. It looks like a conic and makes conic noises but it doesn’t taste of conic when you bite into it.
    I am surprised though to hear you want to cast them aside because they arent as accomplished as you would like. There are a number of things in SW that aren’t particularly thrilling in their present state like tangle prone connectors and flip out splines that don’t get a lot of love from any quarter and yet people persist with them as a given.
    Perhaps if they were more complete/refined you would be keen to utilise it in a creative/constructive fashion. I’m pretty sure I would make use of conics if they dovetailed well with other tools and maintained a decent fairness. Conics are cool however its got to be said DS is not. Don’t let them degrade your geometry experience while they are distracted with socialised industry experiences and other nonsense.
    I agree I am not convinced they are that serious about conics. On the other side of that I am not sure if they were serious whether I would be motivated to resume subs to make use of them. The looming spectre of SW redundancy plays larger on my mind. If I identify things that ought to be improved about conics I am not sure they will ever arrive and frankly if they were to my effort might only be of short term benefit for those who persist with SW well after I’ve left for a more rational/stable/focused wares. Having said that many people including myself have made what we believe is a useful contribution to refining a range of SW tools by giving fobust feedback only to be marginalised by SW pursuing their own different ideas or other priorities. All said and done conics aren’t particularly convincing and really don’t reassure or advance DS credibility problems. I haven’t moved beyond kicking the tires and offering a passing opinion about the power to weight ratio. I think its unlikely you will get me to sit down in the sales office at this stage of the game…
    What would you rather they have done if conics are a waste of time?

  13. As conics are part of the d-cubid constraint engine (Siemens owned) as far as I understand .
    What is the c2 conic functionality like in solid edge?

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