Create better guitar neck profiles using control point splines (Bézier Curves) | Fusion 360 Tutorial

hello everyone my name is austin shainer and welcome back to my channel so let's talk about neck profiles now i haven't talked about neck profiles much on this channel because in my design i simply use three point arcs and many of you have reached out to me questioning whether we should be limiting ourselves to three-point arcs as that doesn't leave much room for other common profiles and while arcs can create most neck profiles there is truth in the fact that splines are a faster and more intuitive way to achieve the same result however we often leave them constrained as the dimensions required to define them are either ambiguous or irrelevant to our design now a month or so ago i made a pretty bold claim that splines are overrated that we should almost never use them when the standard tools can achieve the same result now i stand by that statement however after that video i went down the rabbit hole learning how splines function under the hood of fusion particularly control point splines because as it turns out they are straight up bezier curves and while doing that i came across a video by freya homemare called the beauty of bezier curves in that video she does an incredible job showing us the math behind bezier curves using beautiful animations and not sounding like a college lecturer if you haven't seen that video i highly recommend you go watch that first as she will give you a far better understanding of bezier curves than i will and admittedly in a much more entertaining way so armed with the knowledge that control point splines are bezier curves this means that they are actually quite simple and elegant to constrain if you understand how they work and no i don't mean calculating the polynomial functions or rather a more practical method for fusion using just a few construction lines and a simple height dimension so today we are going to cover how we can better utilize and constrain control point splines in fusion to create better neck profiles for guitars so jumping into fusion what you see on the screen here is a control point spline with a single control point this is also known as a quadratic bezier curve and to make this a bit easier to explain i've gone ahead and i've dimensioned all three of these as equal to one inch and that'll make more sense in a second why i did that so let's talk about how these work so if i sketch a point anywhere along this line and anywhere along this line now this is very similar to the variable fill it method which i showed you in the last video where you have a start point and an endpoint and anywhere along that path there's a value so the value at the start would be zero and the value at the end would be one and any point in the middle will have a separate value and this value in the math is known as t and so because this is one inch that's why i dimensioned it one is i could say the value here is point five and that brings that point to exactly halfway along that line's trajectory and so i could say this one is 0.5 and it brings that one along that line's trajectory so it's pretty cool what is actually happening under the hood here because if we draw a line connecting these two we get a third linear interpolation so if i draw a point here and i dimensioned that to 0.5 of the length of this line and effectively i'd put it at the midpoint and now you will notice that this point right here lies exactly on the highest point of this spline no matter how far we zoom in and this line right here is tangent to that peak of this spline and keep that in mind because that's going to be very useful as we start to talk about how to dimension these but let's visualize this a little bit further on how these work so i'm going to add a user parameter now i've already added it in here but let me show you i created one called t value which will let me control both of these with one dimension so right now this is set to 0.5 so let's change this to 0.25 and let's add that to our dimensions so i'm going to say that this value is this value times t value and basically no matter what i change this to it will always be 0.25 of this dimension and so i could say this one is the same thing because remember these need to be symmetric so what we will do is say this one is equal to this dimension times t value as well and you'll notice let's delete this line real quick or that point you'll notice even at 0.25 there's a point where this line is perfectly tangent to this spline so if i add a point and let's not make it to the midpoint let's just add it on here and make it coincident to our spline like that that is exactly the point of where this line touches our spline and so if we go back to our user parameter and we start to change this value so let's change it to like point one pay attention to this point as i go through these numbers so we'll go point one point two point three point four point five point 0.6 0.7 0.8 0.9 and finally we can say 1. so you'll notice that both of these dimensions have now changed to 1 because those points that were connecting those lines have reached their destination and if i change this to zero then these have changed to zero and you don't see any lines across but if i go back to point five this line now stretches from the midpoint here to the midpoint here and this point right here as it moves along um not along this path but as it move interpolates across this line basically sketches as if it was a pencil sketches out this spline and that's exactly how these splines are generated so if i go back to 0.25 or let's do 0.2 0.3 0.4 0.5 you'll notice that basically that is drawing out that shape and so this is really cool to understand because what we can actually do is we can delete these dimensions and let's delete our equal constraints here let's make sure we still have everything and let's make this horizontal so basically as long as this is horizontal and these are midpoints to these lines let's make these points midpoints then no matter how we draw this this line is always the peak of this spline and that is incredibly useful for drawing good neck profile shapes being able to dimension to the tangency of a spline which is actually not an available option so let's delete this line for a second and i can show you exactly what i mean so let's say we wanted to dimension to the tangency of the spline right now we can't really do that because i can draw a line here and if i select these two there is no tangent option available so i can't make that snap to it now i can make points snap to that spline and so i could in theory you know draw this down to like the midpoint here and dimension upwards but there's no guarantee as you can see here that we dimension to the actual highest peak of that so by understanding how these work we can dimension to the tangency of our splines so now you can see we can do that so now let's dimension this as like 0.6 inches and we went a little haywire on us let's bring it back and let's make this like 1.75 so something fairly close to like the first fret of our neck and then we can decide do we want this to be asymmetric or do we want it to be symmetric now symmetric is easy because we can either just create a construction line that connects to the midpoint and make it vertical or what we can do is draw our point in the center here and make these two vertical and that will fully define our quadratic bezier curve or single point control point spline with just a height dimension and a width dimension and if we didn't want it symmetric then what we could do is draw a construction line from this point to this point here and then we could define like an angle so if i go like 60 degrees then the peak of this arc will be at 6 at 60 degrees from the baseline and so that's a really interesting way to be able to generate these shapes now you'll notice that because of the way a quadratic bezier curve works we are not going to end up being tangent to something that comes down so if we imagine that we have our fretboard so let's bring this up let's say our fretboard is like this and let's give this 0.25 so this will represent our fretboard there we go and so it's not coming tangent to that and so that's one limiting factor of a quadratic bezier curve is that it's a triangular shape or it's based off a triangular polygon and so you can't have this come down tangent with this line but that's where cubic bezier curves really start to shine so let's switch over to cubic bezier curves so if i create a spline and i do control point spline a cubic bezier curve just means that we have more than one control point and every control point that you add more than one increases the order of the bezier curve and so i can just hit the check mark here and let's add a few dimensions to make this a little more constrained so we're going to add a construction line make it horizontal and let's make these horizontal as well let's just define the dimension here because we need to know where this is in space it right now it's like 0.75 inches okay and now what we can do is determine let's turn that off now we can determine okay what do we want that overall shape to look like and let's draw our fretboard again obviously a rough representation of it make that vertical and we'll make these collinear there we go so there's our fretboard again and so now we just need to know what is the width so we could say our width is 1.75 inches again and then if we want this to come tangent to this line right here then all we need to do is make this line collinear with this one so we can say collinear or we could just make it vertical if that's how the shape is drawn and so we could say we want this one and this one to be collinear and so now you can see i can get a sort of asymmetric shape or if these two are equal then i can get a symmetrical shape so let's make those equal for the time being and let's dimension this to the same height as this one over here so every single line that connects a control point you have to connect these lines to like you see over here so if i draw from the midpoint to the midpoint here to the midpoint here now i have two more that can still be connected and if i connect those two you will notice that once again we can dimension to the tangency of this spline so now all i have to do is dimension this as let's say 0.75 or if we want to make it the same height as this one we'll go 0.6 and so we're able to get more of a c shape that actually comes down tangent to our fretboard and now if you wanted to make this asymmetric you could make this not equal these two not equal so let's delete this real quick but you'll notice what happens is when these two aren't equal then this line right here is no longer at the peak of this spline so that creates a bit of a problem for us because if we want a symmetric an asymmetric shape but we want to be able to to dimension to the height of this spline then actually what we need to do is add in an additional control point so let's go back and let's make these two equal let's bring this up and let's delete these so you can right click the spline and say inspire insert spline control point and if i hover over that spline it's going to give you a preview so i'd have one two three so let's do that and so now we have three and if i did it again you could see i could divide it by four five six etc but if we leave it with three then what we can do is we can make these equal so that way we can dimension to the top but then we can use this point to give us our asymmetric profile so let's do that so let's make these equal and let's draw a line between here and here and now since we have another one we have to connect here to here keep going around and now we can connect the midpoints of each one of those so here to here like that and then we can connect one more and you'll notice once again we're able to dimension to the tangency of this line so we can dimension this as 0.625 or 0.6 to match the other one and so now you'll notice that these can move up and down so let's make these vertical and so all we need to do is define this and define these heights so what i would recommend doing at least in the context of neck profiles is just making this point horizontal to our tangency line so we'll go horizontal and so all we need to do now is just drag this over to create our asymmetric profile so once again we can add a point to that midpoint here which is the highest point of our spline and we have a couple of options here so we can either draw an angle like we did before which will end up fully defining that so we can go say 60 degrees in fact let's make a little less than that 65 and we can get a pretty nice asymmetric shape or maybe what we care about more is that the distance that the highest point of our neck profile is offset from the center is 0.25 so we could do that too so we could say that the highest point of this spline is off center by 0.25 from here and that could be a really useful way to dimension that as well you could also if you want to although this is less relevant is define any one of these dimensions and it will do the same thing so you could define these as well and you'll achieve the same result so that is a really interesting way to be able to completely define and constrain constru control point splines in fusion 360 whereas before we didn't really have access to do that so effectively what we've done is we've recreated the underlying math that happens that generates this spline which gives us access to much better ways of defining these with dimensions that are actually relevant to our design so let's switch over and here i have a parametric fretboard sketch that i've created that i can come in here and change the scale length i typed that wrong 26 inch scaling 24.75 whatever and it will automatically adjust this for me now let's go ahead and create a neck profile at the start and somewhere at the end so what we can do is we can basically create planes at each one of our frets that we care about having a defined neck profile at so in this case i'm just going to do the start and not the end we'll create one down here so let's sketch on this plane and let's project in that line at the bottom so that way we can generate a closed profile and let's create a cubic control point spline so let's draw up here like this and down once we click that we'll hit the check mark which will close it you never want to hit escape when you're drawing a control point spline so if i click here like this and then i'm like okay good hit escape well all of a sudden what will happen is it deletes it and you're like what happened so make sure you hit the check mark so we're going to draw this this here check mark and we know that we want it to come tangent to our fretboard so let's project that in right here and let's make these collinear make that collinear let's look at it from this angle and so now we can make these equal remember and we can if we want a c shape then all we need to do is connect these three points like that draw from the midpoint here to here let's make these construction lines and now we can just define the height of our neck at the end of our fretboard so let's do and we can get a generic c shape hit okay that one is already done and it's tangent to this surface right here so let's add another one so this is the 12th fret so let's add it at like the 15th fret for example let's create a planet angle and we'll do 90 degrees and let's make sure we're showing our plane so we can actually see it and let's sketch on that plane and let's project in that line to do the same thing we did before and we can project in this surface using intersect so we'll go create project include intersect and that will generate the vertical line of this face where it intersects this plane and we can use that to constrain our control point guides so then we'll go spline control point spline and we'll do the same thing like that see i just hit escape there you never want to do that it can be really irritating like that click and hit the check mark and now let's make these collinear and let's make sure we follow the same rules that we did on this one so we'll make these collinear and we'll make these equal and then let's go ahead and draw our construction lines so from here to here here to here connect those two and now we can just dimension the height here and we'll make that like 0.75 inches so now if you look at it this way now they're not a perfect offset of each other and that's by design and i'll show you one in just a second in fact actually let's just do that now so if i project in this line and let's hide that other sketch and let's hide our fretboard here there we go let's say instead of doing that i just offset this line what would happen well you'd get pretty close but the problem is is your shape starts to change drastically as you get narrower and wider so watch what happens as i get narrower i start to lose my tangency and everything starts to deform a bit and if i drag it too big it turns it much more into a straight radius which we don't want so instead of projecting in the other one and just offsetting it we're generating a new control point spline that follows the same rules but at a different height and so that way what we can do now is just loft between these two so solid loft and hit ok so let's hide the sketch and let's take a look at this in fact let's change our material type here because that's very dark let's make these a bit brighter now right now these are um basically one body unfortunately because i didn't add it as a new component that would have been smart but that's okay so let's take a look at like our curvature so let's go inspect zebra analysis and you can see there is a slight deformity here but that's only because this is g1 not g2 curvature and i can show you how to do that in a moment but you get a pretty nice transition from one side to the other so let's actually go ahead and talk about how to make this g2 curvature so we get a perfect transition to our fretboard so if we go back to let's do the first sketch so what we can do is we need to add two more control points and what that'll effectively do is every control point that is collinear with this line right here adds to the g value let's say so g1 g2 g3 curvature so let's delete these rail real quick and let's add a control point and here and we can do it again and then what we can do is make these either collinear which will achieve the same thing or what we can do is just say we want this spline and this line right here to be curvature and you'll notice it automatically snapped this point to being collinear with this one and so we can say this line right here and this right here we want to be curvature and then basically we can just redo the same thing but what i would recommend doing because the control points or the control lines have to connect between all of these so i would do that first so connect these points here like this we'll just go around keep going there's gonna be a lot of them in this case because we have so many like that keep going this ends up being a lot i apologize but let's make these all construction lines and now let's make this um curvature so we'll do that and we'll make this one curvature to here and let's make sure we drag this up so we can see it better and we need to make sure that these points right here are equal or horizontal to each other and we can make sure this one's horizontal and now we basically have access like we did before so let's make these ones horizontal to here so that way it's in line with that and then we can define the height so let's define the height here like that as point six and you know maybe that is a little too squished so let's delete that horizontal and let's just make these two line segments here equal to each other and that will fully define it for us and that gives us a little bit better result but now we are actually g2 curvature down to this surface so that's kind of a pain in the butt to get g2 and you really don't need it for woodworking but if you really cared about getting a perfect transition into there you could do that and if you're really a glutton for punishment then you can add another two one to each top of these do the same thing kind of make these all equal and draw draw all of your lines and you could end up with a g3 class a surface um transition between your fretboard and your neck so i'm going to actually just undo this and go back to where we were before and let's go ahead and talk about how to make an asymmetric neck profile so just like we did in the example earlier we're going to add one control point spline or control point to this spline and we're going to follow the exact same rules that we did in the example so connect these like that and we'll do another one i hit escape like this and then connect these two as well let's make these construction lines and let's make these horizontal so now we can define this and we can define it like that so let's make these collinear and so now we should be able to just define our height and how asymmetric is it so let's define our height here as 0.6 and how do we how asymmetric do we want this to be so let's go ahead and do the offset method where i add a point here in the middle and we're going to define that as being 0.25 off of center or let's do 0.375 see that went a little too far because now our spline is going to breach past this line a little bit so yeah let's just leave it at 0.25 and hit ok and now you'll notice that our fretboard or another fretboard our neck has updated to an asymmetric type profile where we have this shape on the front side of the fretboard or neck and a c shape on the rear and that might be really useful if you're going to a guitar body that has a more symmetric heel shape so you could have a symmetric shape at the heel but an asymmetric shape at the headstock or we could change this one to be asymmetric as well if you're designing this from scratch and you control the heel shape so let's change this one as well to being asymmetric following the same rules so let's add a control point here and let's make these equal and collinear to this line and this one collinear to that line and let's draw our lines like that and connect them all midpoint to midpoint okay once again let's make all these construction lines and let's define our height as 0.75 inches and we need to define uh the height of these and how asymmetric is it so let's make these horizontal like we did with the other one and how far offset so on this other one we went in this direction so in this one let's go the opposite direction now it is important probably to pay attention to how far you're making this offset because you probably don't want this arc to breach in past the highest point of your one up above because and then what you'll end up doing is having a point at the back of your neck that is actually shorter than the point at the front of the neck so what we can do is just make sure that our offset is stays just either outside or tangent to that line so let's add our point here so let's add our point at the midpoint and let's dimension that as 0.125 and let's check are we okay yes we are so let's hit ok finish and our neck has now updated so now we have a let's look at it from this angle we have an asymmetric going in this direction on this side and an asymmetric going in the opposite direction on that side but just like in many of my headstock transition videos it is quite useful to have these split this face split into two surfaces so you can control the continuity when you're patching or lofting to your headstock or your heel transition so let's go ahead and switch over to the surface tab and let's delete these front and rear faces like that and let's split this body across the height of our splines so what we can do is we can go plane through three points and let's bring these sketches back and so we're gonna say we're gonna go from here to here to the top of this one and so that's gonna give us our angled um plane that we can split this and hit ok and then we will go modify split face and we'll split this top face with this plane hit okay and hide the planes and so now what you'll see is we have our face of our neck split exactly at the highest point of our spline so that way when we're drawing to our headstock and trying to create our like volute or headstock transition or trying to define our heel transition we actually have the proper geometry that we need to go ahead and constrain and define it so the main reason i have historically avoided splines is because they are notoriously difficult to constrain and make parametric infusion but if we recreate the underlying geometry that defines their shape we can give them dimensions that are more relevant to our design making them easier to understand and allowing us to generate more interesting and comfortable neck profiles armed with a cursory understanding of bezier curves i'm now convinced that not all splines are overrated if you'd like to support my channel or download models featured in each of my videos you can find me at patreon.com forward slash austin shaner if you'd like to submit a request for this channel receive help from myself or other viewers on a design that you're working on or simply join a community where we share ideas and push the boundaries of what fusion is capable of you can join our discord server links will be in the description below thank you all for coming this is austin signing out

Channel: Austin Shaner

Views: 2,218

Keywords: Autodesk Fusion 360, CAD, CAD Modeling, CAM, CAM Basics, CNC, CNC Router, DIY, Fusion 360, Fusion 360 Beginner, Fusion 360 CAM Guitars, Fusion 360 Tutorials, Guitars in Fusion 360, Tutorials, fusion 360 tutorial, Autodesk, splines, T-splines, B-splines, Bezier Curve, Sketch constraints, Sketching basics, Fusion 360 sketching, Variable Chamfer, Variable Fillet, Guitar Body, Guitar Neck, Guitar neck profiles, Asymmetric neck profile, C shape profile, V shape profile, D shape profile

Id: iDzxndSBook

Length: 33min 36sec (2016 seconds)

Published: Mon Sep 20 2021