Control Point Splines: Create complex Sketch curves with precision and ease

Avatar jakefowler July 20, 2018

13 min read

For the upcoming July update, we’re extremely excited to introduce a brand new way to create curves in Fusion 360’s sketching environment – the Control Point Spline tool. This new tool promises to provide:


We know that many of you have been anxiously waiting for this tool to arrive, and we really hope this satisfies your hunger for added power and more control in creating complex shapes in Fusion 360.


We also know that this type of spline will be brand new to a lot of people, so we’ve put together together this in-depth FAQ to answer some of the most common questions concerning control point splines: what they are, where they are most useful, and some best practices for designing with them. Note that some of these tips and techniques make use of the unique capabilities and workflows inside Fusion 360, so be sure to check these out even if you’re a seasoned spline pro!



What are control point splines?


Control point splines – also known as CV splines, NURBS curves or style splines – provide a way for defining complex curves in a Sketch.


Until now, this requirement has been met by the existing Spline command. With this tool, you select a series of points, and Fusion will create a smooth curve that passes through them.


Fit Point Spline creation


Control point splines offer an alternative approach for achieving the same result. You select a series of points, and these points will define a ‘control frame’ from which a smooth curve is derived.


Control Point Spline creation


If you’ve ever used Box Display or Control Frame Display in the Sculpt workspace, you’re essentially seeing the same concept there: you manipulate a simple polygonal control frame, and this drives the resultant smooth shape of the surface.


Editing a Sculpt surface using Control Frame Display mode


Since we’ll now have two spline commands, we’re renaming the previous Spline tool to “Fit Point Spline” (i.e. the spline ‘fits’ to the specified points). These are now presented in a Spline flyout in the Sketch tool menu.


Spline flyout menu


As you start to use these two tools together, there are two key differences to keep in mind between fit point splines and control point splines:


1. As shown above, a control point spline will (usually) not pass through the selected points besides the first and last points. Unlike fit points, which define points that the spline must pass through, control points just define the underlying frame used to calculate the curve. You can think of a control point as applying ‘tension’ to the spline in a given direction: pulling a point further away increases the tension on the curve in that area, and pushing it closer relaxes that tension.

Dragging a control point

2. In most cases, you will need more control points than fit points to define a given shape. This is because each individual control point has less influence on the overall curve than a fit point does. What’s more, control point splines do not offer tangent/curvature handles; to apply more refined shape control, you’ll need to add more points (you can do this by right-clicking the spline and selecting Insert Spline Control Point).


For an example of this, see the two curves below. A fit point spline with three points will feel very flexible, and can be easily manipulated into a variety of shapes. A control point spline with three points will feel much more rigid, and the lack of tangent/curvature handles limits the types of shape change possible. In such cases, adding more control points as needed is the required approach to achieving more flexible shape control.


Modifying a three-point fit point spline and a three-point control point spline



Why add a new spline tool to Fusion 360?


Fit points are a very intuitive way to define a spline – the points you create will directly constrain the curve. However, behind the scenes Fusion is taking most of the responsibility for deciding how the spline shape flows as it passes from one fit point to the next.


How a fit point spline shape is determined


As a product designer, sometimes you need to have very precise control of that intermediate shape flow. Fit point splines provide tangent & curvature handles to apply additional control if needed; but occasionally these don’t provide fine-enough control, and manipulating these handles can affect other areas of the spline in unexpected ways.


Fit point spline tangent handle manipulation having impact elsewhere on the spline


Control point splines give you direct access to the underlying control points that define the full shape of the curve. This offers you extremely precise control over specific areas of its shape.


Control point manipulation having localized impact on the spline


We heard from many of you with professional design backgrounds that this fine-tuned control is a must-have for your work. Whether you prefer the interaction of creating fit point splines or control point splines is really down to your previous experience and personal taste – but control point splines offer a clear advantage in the level of shape control they provide.



When should I use control point splines?


The classic school of thought is that control point splines are better than fit point splines for defining the primary surfaces of your model. They provide you the ability to very explicitly control the math of the surface; and by following the best practices discussed below, you can ensure that surfaces created from these splines will be both aesthetically and technically smooth.


Surface created using Sweep with two control point splines as inputs


However, since a control point spline will require more points than a fit point spline to define a given shape, complex shapes with lots of curvature changes may be simpler to draw with the Fit Point Spline tool. An example of this would be a traced logo: for a small & detailed design task like this, the high degree of mathematical smoothness provided by control point splines is probably less important, and the shape can be created and edited with much less work using a fit point spline.


Tracing a logo with a fit point spline


However, for many tasks the choice of spline tool is really a personal preference – while control point splines offer more flexibility for certain scenarios, the two tools fundamentally create the same type of geometry, so you may just gravitate towards one particular tool that suits you best!



What are best practices for using control point splines?


There are a few core rules of thumb to follow in order to create high-quality curves with the Control Point Spline tool.


1. Use the fewest points possible to describe the shape you need
Splines will naturally form the smoothest transition possible between two points. Creating unnecessary intermediate points means you are ‘overriding’ that natural smoothness, which increases the potential for undesired bumps or wobbles in the curve.


Too many control points vs. reduced number of control points

The general rule here is “less is more”. Keep this within balance though – if you’re finding yourself stretching control points a long way from the curve in order to get the shape you want, you may be trying to do too much work with too few control points. In this case, adding one or two more control points can provide a more suitable level of shape control.


2. Try to keep points evenly-spaced where possible
Uneven control point distribution is another factor that can cause smoothness problems in a spline, so wherever possible keep the spacing between adjacent control points even. There are scenarios where you need to have control points more bunched-together in certain areas – namely, in areas where you want a higher-curvature shape. But keep in mind that, where you have transitions from spread-out control points to bunched-together control points, make sure those transitions are smooth and natural to maintain a high-quality curve.


Uneven control point spacing vs. even control point spacing


3. Keep adjacent points relatively close to each other
Avoid having drastic distances or direction changes from one control point to the next – this results in splines that will be difficult to work with or adjust later on. If you find you need drastic distances between points in order to achieve a given shape, it might be better to insert a few additional control points so that all points lie relatively close to the curve and to one another.


Widely-spaced control points vs. closely-spaced control points

In fact, the three rules above apply to all spline-based geometry, including fit point splines and Sculpt geometry – so live by these rules whenever you can.



How do I constrain a control point spline?


A unique characteristic of control point splines is that they are always paired with a visible control frame. To make the most of this, Fusion 360 allows you to apply constraints on both the control frame and the curve itself. Combining these two methods can open up some unique and powerful constraint workflows.


Since the control frame consists of straight lines, and the curve itself is a shape with complex curvature, different constraint types will be more meaningful on the two different object types. As a general rule:



The most frequently-used constraints for describing a relationship to other geometry will be Tangent and Curvature constraints: these will build a smooth connection between a control point spline and another curve or edge on the model.


One important rule for applying tangent or curvature constraints on control point splines is that you will need enough ‘free’ control points for the constraint to succeed. For a Tangent constraint, you must have at least one free control point next to the tangent connection. This is because, when you apply the constraint, Fusion will need to shift that control point to a new aligned position that enforces the tangent relationship. For a Curvature constraint, you’ll need two free control points, for the same reason.


Control point alignment when applying tangent and curvature constraints


After you have created a tangent or curvature constraint like this, those shifted control points will have their degrees of freedom limited in order to maintain the constraint. However, you should still be able to slide the affected control points in a way that adjusts the ‘weight’ of the tangent/curvature relationship. This is a powerful technique for fine-tuning the character of a curve or surface transition.


Moving control points to adjust the weight of a curvature transition


In order to fully define the shape of a control point spline, you’ll need to constrain all control points locations as well – this is where control frame constraints are necessary. You can constrain control frame edges in the same way as any other straight lines in a sketch. For example, apply distance and angle dimensions to the control frame edges to control the spline shape in those areas. Keep adding these until the control frame is fully-constrained, at which point the spline curve shape will – by definition – also be fully-constrained.


Control point spline with dimensioned control frame


Note that control point spline shapes are “repeatable” using matching constraints: i.e. once a control point spline is fully-constrained, if you apply the same set of constraints to a second spline (of the same degree; see more about spline degree below), you’ll get an identical resultant shape.


You can also use constraints on the control frame to describe specific characteristics of the spline shape. For example, adding a horizontal/vertical constraint at one end of the control frame will ensure the spline runs perfectly horizontally/vertically at that end. This can be very useful when creating a spline that will eventually be mirrored.


Control point spline with horizontal and vertical constraints on control frame


If your part requires a draft angle for manufacturing, you can specify an angle between the control frame and a horizontal/vertical datum line to enforce that draft angle on geometry created from the spline.


Control point spline with draft angle applied


To create a symmetric control point spline, rather than relying on Symmetry constraints, you can also apply Equal constraints between matching pairs of control frame edges. This sometimes requires less work and offers more flexibility than standard symmetry constraints. For example, you can create a spline with rotational symmetry by applying a combination of Equal and Parallel constraints, which isn’t otherwise possible using Symmetry constraints.


Control point spline with rotation symmetry using Equal and Parallel constraints


There are many more techniques made possible through combinations of spline curve and control frame constraints – be sure to experiment with these!



What does the Spline Degree control do?


For experienced users of control point splines, we’ve also provided some control over the degree of your splines.


At a technical level, the degree of a spline describes the complexity of the equation used to describe its shape. A high-degree spline is defined by a high-degree equation, which results in a spline that is technically smoother than a lower-degree spline. The downside of high-degree splines is that more points are required to define a given shape, so lower-degree splines tend to be easier to work with.


In Fusion, we’ve provided a choice from the two most commonly used spline degrees – degree 5 and degree 3. You can choose this from the Spline Degree option in the sketch palette while the Control Point Spline tool is active.


Spline Degree access point


Degree 5 is the default option, and will give the best results for most scenarios. This provides an optimal balance of geometry smoothness and ease-of-use. Their high degree of smoothness makes degree 5 splines perfect for defining primary surfaces on your model, and building transition surfaces between existing geometry.


Degree 3 splines usually require fewer control points, so can be easier to work with. The biggest downside is that they are technically less smooth than degree 5 splines – degree 5 splines ensure G4-continuity internal to the curve, while degree 3 splines only guarantee G2-continuity internally.


If you create a degree 3 spline with a large number of control points, you may observe some sharp turns/bumps in the curvature comb: these represent points on the curve that are not G3-continuous (note that degree 3 splines are still guaranteed to be G2-continuous throughout – surfaces created from G2-continuous curves will still have visibly smooth highlights, so these are smooth enough for most use cases!)


Degree 5 spline vs. Degree 3 spline


One special behavior of note regarding Degree 3 splines is that they can give improved matching behavior when working with geometry in the Sculpt workspace. This is because the Sculpt tools are based on T-Splines, a technology which fundamentally is built on degree 3 surfaces. Because of this, we’ll switch the default Spline Degree to Degree 3 when creating control point splines in the Sculpt workspace.


Also note that the chosen Spline Degree setting actually determines the maximum degree of created spline. A spline’s degree will only ever be equal to or less than the number of control points minus 1: e.g. a spline with 4 control points can only be degree 3 or less. As you select points to build your control point spline, its degree with incrementally increase until it hits degree 5 or degree 3 (based on the Spline Degree setting), and will then stay at that degree. So, if your Spline Degree setting is Degree 5, but you finish the spline after selecting four points, the spline degree can only be as high as 3 regardless of the degree setting.


The gif below shows how the spline degree increases as you add control points using both settings:


How spline degree increments when adding control points


You can check the true degree of a control point spline at any time by selecting it and observing the selection info at the bottom-right corner of the canvas.


Selection feedback for control point spline





We hope this has provided a useful overview of the new Control Point Spline tool, and we really hope you enjoy using the new functionality. Be sure to leave any questions or comments below – we’d love to hear what you think, and we’ll continue to iterate and improve this technology based on your feedback!


– Jake and the Fusion 360 team

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