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Curves from beginning to end
- 1. Curves from Beginning to End Mark Biasotti SolidWorks Corporation Product Definition – New Concepts January 22 nd 2008
- 3. Splines: Can live with them, can live without them! What are they good for and why do we use them?
- 4. Splines: Can live with them, can live without them My Goal: By the end of this presentation I hope to transform your feelings about splines from this… To This
- 5. Why use Splines? When shape can not be described by line, arc, ellipse etc. (or it takes many of them in series to accomplish) Series of arcs Single Spline
- 6. Why use Splines? Single Spline results in smoother overall edge verses series of arcs. Series of arcs Single Spline C1 C2
- 9. 2D verses 3D Sketch 4 degrees of freedom vs. Six Degrees of freedom
- 11. The 2D spline Curvature Comb (Show Curvature) point of inflection Control Polygon Handle Spline point handle widgets Shadow Spline position
- 14. Lets review with a SolidWorks example
- 15. Creating and re-shaping splines
- 18. Applying a Face Tangency Constraint Using Face Tangency Constraint & Equal Curvature *Play Video to show
- 19. Using the Proportional Option
- 20. 3D curve by 2ea. – 2D sketch spline curves
- 21. Curve thru X,Y,Z Points
- 22. Curve thru Reference Points
- 23. Face Curves
- 24. Curve by intersection of surfaces (or planes)
- 28. Application of 2D Sketch Spline “Bridge Spline”
- 29. Getting around problem with constraining to projected curve Initial over constraint Play Video to show
- 30. 3D Sketches – how do they work?
- 31. Editing 3D sketch splines in 3D space
- 34. Using reference surfaces with 3D Sketch
- 37. 3D sketch splines and surfaces
- 38. Andy and I will now take your questions
Editor's Notes
- This is our agenda for today. I want to use our time familiarizing you with the type of curves that are available in SolidWorks, then get into depth with 2D and 3D sketch splines. With 2D and 3D splines, I’ll show you how to create them, modify them and constrain them and then eventually, how to use them in advanced modeling features.
- Why is there such a line of demarcation between, say, lines and arcs and Splines? I submit that although they can be parametrically controlled and constrained, there is stylist judgment that is called for when creating them. I’m not saying that you need to be an artist, but rather you do need to understand how to create splines to conform to the designer’s intent. More often than not the hardest aspect of this is to achieve smoothness or what mathematicians call “fairness.” Because there are many more variables to splines for defining and changing their shape, this makes them more complex than there arc and line counterparts.
- My goal for this presentation is elevate your fears with sketch spline geometry by familiarize you with it, and get you comfortable using them.
- Why not just use a series of arcs and lines to describe a spline; wouldn’t it be easier and get the same basic effect?
- At first they might appear to be the same, but when these curves are used in creating a surface model, the differences become notable. When Show Curvature is displayed on the geometry their abrupt change of curvature is evident. This occurs when two arcs are connected together, because their default tangent connection does not necessarily mean that the curvature on each arc is equal where they meet. This discontinuity shows up in polished or shiny surfaces, especially white, black and chrome materials. In in order to overcome this discontinuity, Surface modeling techniques focus on replacing these series of arcs with one continuous spline that mimics a series of concave and convex arcs, yet allows for small differences that result in continuity and that translates thru to the surface that is created from the spline.
- Let’s look at a familiar example. Many of today’s leading designs are deceivingly simple. They look like simple prismatic shapes but, in fact, they are not. Take the iPhone for example. It can be described as a thin brick, that can be modeled by simply extruding and adding radii to; however, this not the case. Look at the way that the reflections wrap around the corners. If it were just a brick with radiuses applied, the corners reflections would not flow so smoothly as reflections and light passed over them.
- Lets get familiar with the concept of curvature continuity. Here we compare the way the upper left corner of this letter “C” is treated given the following connection possibilities: C0 = a simple connection but no tangency i.e. an edge C1 = Surface boundaries share Common edge with tangency but the curvature (and rate of) is not equal. C2 = a curve continuous connection where the curvature is equal where the two faces meet (but not necessarily the rate of which can suddenly change) C3 (or better) a curve continuous connection in which the curvature is not only equal but the rate is gradual between them. This specified degree is suitable for Class A applications i.e. automotive, aero where scrutiny to aesthetics and functional flow are paramount. Most consumer product design applications do not require this.
- Almost all aspects of the 2D and 3D sketch are identical except when it comes to spatial freedom. 2D sketches are restricted to only planar faces or reference planes, therefore you have, in essence, 4 degrees of freedom. 3DSketch geometry can be placed anywhere in 3D space, and therefore has 6 degrees of freedom. Although vastly more flexible for today’s consumer product shapes, this added flexibility can make them harder to define and control in 3D space.
- Let’s review the kind of curve geometry methods we have available to us in SolidWorks. 2D Sketch Spline – 2D and 3D sketch Splines are distinguished between whether you can apply them on a plane or face or anywhere in 3D space. Project Curve – You can take 2D sketch geometry and project it normal to it’s sketch plane onto a surface or face. Project Curve by 2 – There is a “2 and ½ D” method that has existed for a while that allows you to define two 2D sketches in opposing planes and then subsequently use the two sketches to project a 3D curve into 3D space. Spline on Surface (known in the industry as COS – curve on surface) is a 3D sketch spline that adheres itself (and makes constrains to) to a face or surface as you draw it. Curve thru XYZ Points – There is also a method to use 3D points either from a excel like table of coordinates or defining the points on existing 3D geometry. This is a popular method to take point data from a flow analysis package like ANSYS, for say, a turbine blade, and get those leading edge curves into SolidWorks to create surfaces from. Face Curves Tools>Sketch Tools>Face Curves gives the user the ability to convert a face or surface into a grid of curves. This grid, in its U and V directions can be defined by the user in the Property manager. Convert Entity and Offset Entity is a spline utility that can, in the case of Convert Entity, can project a existing edge or edges into a 2D sketch or in the case of 3D, simply copy the edges into the current 3D sketch. In the case of Offset, it does similarly, but offsets the result by a user given value. The Fit Spline , (Tools>Spline Tools>Fit Spline) like Convert and Offset, is spline utility that can “fit” a spline over existing sketch geometry whether that be a series of arcs and lines or even a 2D or 3D sketch spline. The difference thou, with this powerful command, is that you can adjust the tolerance of the solution. So in the case of a series of arc and lines connected together, you can fit a spline over them, adjust for a loose tolerance and thereby make a curve continuous spline. This is handy if you want continuity, but want to drive the sketch with simple arc dimensions. Intersection Curve can also be created as a result of 2 surfaces, or a surface and plane, that intersect. Finally, there is a Helix Curve that is essential for creating threads and springs and Parabolas for creating optical solutions. Split Lines are considered by some to be a curve. They take current faces and split them in two thereby creating an edge that can be use like other SW curve geometry.
- Let’s look at the 2D sketch spline in depth, and get familiar with it and its various options. When sketching a 2D spline, you can define it by dragging out a series of points. Alternatively, you can sketch a 2D spline by defining a series of Polygon control points, know as a “Control Cage.” Once the initial spline shape is sketch, the user can then fine-tune it’s shape using spline control handles and their widgets. With the “Show Curvature” displayed, you can analyze the rate of curvature change or “smoothness”. A handy “ghosting” effect is built into all SolidWorks sketch geometry that helps the user reference the last change they make to the sketch by comparing the previous position with the relative current move of the spline shape.
- The spline control handles are made up of a vector widget that is used to change the direction (or angle) of the spline at that point. The arrow shaped widget at the end is used to change the magnitude of tangency. Since SW2007, in the case of interim spline points, you can pull these handles asymmetrically, similar to Bezier splines found in Adobe Illustrator. This makes defining complex profiles much easier with without the need to create an excessive number of points. The ball at the end of the widget is for changing both the vector angle and the magnitude at once. Of course, if you desire symmetrical control, you can hold down the <Alt> key on your keyboard and pull the Magnitude (or combined) widget, and both sides of the interim spline point will be equally influence.
- Whenever the spline is selected, it’s PropertyManager panel is available to make changes and adjustments to it’s various aspects. The first two options, For Construction and Show Curvature are duplicate controls for toggling the spline between geometry and construction geometry and for showing the curvature comb respectively. Maintain Internal Continuity is on by default and it attempts to maintain a more “Fair” or smooth solution. If you are striving for smooth curvatures, it is best to keep it checked. Raised Degree is an option that allows for users to create continuity beyond C2. I doesn’t necessarily mean that your curve will be C3 or higher, but only allows for the user to adjust the spline to a higher rate of curvature. The next part of the PM panel is for making adjustments to the spline. The Tangent Driving option when checked (unchecked by default) allows for maintaining the tangent angle of the spline’s point regardless of where your move the point. With it off (default) when moving spline points, the spline’s point re-parameterizes as you drag the splines endpoint to new locations. It is best illustrated by creating a 3 point spline (try this yourself) and then drag one of it’s endpoints with it both enabled and disabled. The next three buttons are important for reiterating the spline’s shape. Reset This Handle removes any user defined vector or magnitude changes and resets it to its most “relax” and “Fair” condition. Reset All Handles is similar to the above but affects all handles of the spline at once. Relax Spline is a important command that relaxes the shape of the spline, and like Handle Resets, helps to make the spline more smooth. It is sometimes also necessary when switching from Polygon Control back to point control editing. This is necessary because Polygon Control editing does not re-parameterize the interim splines points dynamically. This is evident, after Control Polygon editing, when you try to move the interim spline point close to an adjacent spline point and you experience excessive knotting.
- Let’s do a review in SolidWorks of what we just learned. We will: Create a 2D spline Explore the handles and how they affect the spline Explore the various PM options Show Curvature
- Often times we need to “trace” splines over a image of the design intent like this razor sketch. An affect method for creating splines, is to do the following: Create the initial spline (using spline point creation method or Control Polygon method) using a few points as possible. Create points at areas where the shape’s peaks and valleys (or convex or concave apexes) and if necessary at the areas of inflection (where curve goes from concave to convex.) Constrain and adjust the start and end points of the splines. Now move the interim spline points and change there vector widgets to better mimic the initial design intent of the curve in the design sketch. Up to this point, we have on changed the tangent magnitude of any of the interim point handles. Continue to a move the points and adjust the vector widget handles. Now, turn on show curvature and carefully adjust the tangent magnitudes of the interim spline point handles holding down the <Alt> key (symmetrically) Once you’ve gotten this far, you should be pretty close. Now use asymmetrical control of the tangent magnitude handles by pulling them individually. If tangent driving is on, you can adjust the angle numerically in the spline’s PropertyManager. It should be noted that you can also dimension the tangent weight of the handle as well as it’s angle. I would not generally advise this except in the case where you want to specify draft angle at the beginning and end of the spline or need to drive the spline emphatically by an equation or simply need to lock it down at time of final release of a design.
- As mentioned before, starting with SW2007 users can now control spline interim points asymmetrically. This allows for reduction of the amount of points the user needs to specify. (I come from an ID background and some of my favorite programs are Adobe Illustrator and PhotoShop. I love splines in these programs and how you can asymmetrically weight either sides of the spline point. It makes defining shapes really easy. I really wanted these in SW, but our programmers initially had a tough time figuring out how to do this. After all we use NURBS and although Bezier splines, in which Illustrator uses, are a subset of NURBS, it still would present problems with internal continuity etc. I turned out that many ID/SW users that I interviewed in 2004 and 2005 felt the same way that I did. Well, finally our developers found a way and got them into 2007.) Lets take a look…
- With Degree Raising, the user can make a 5th degree spline (default is cubic). This option gives the spline the flexibility to generate a C3 curve, even thou we don’t have a C3 constraint. Raising the degree generally makes a 2 point spline easier to manipulate. You can make it C3 by adjusting the magnitude or control polygon handles. Let’s take a look at an example…
- There is a somewhat undiscoverable, but very useful 3D sketch constrain called “Tangent Face” which eliminates the need for references curves on faces that you are trying to constrain tangent or equal curvature with. You can make a tangent face constrain (as well as a Curvature Equal constrain) if you pick both the spline, edge of the face that the spline is connected to, and then the face. With these three selected, you will get the choice to make it tangent to the face and/or Curvature Equal to the face. What this type of constraint affords the user is the ability to, after the constrain is applied, freely slide around the curve on its edge while maintaining tangency to the face. *(in order to view these videos, you will need to visit www.techsmith.com and download their video codec.)
- The Proportional option is handy if you want to maintain the shape of a multi point spline yet drive it by it’s end points. In the following example, let look at how you can use this option to create a swept surface.
- Before moving on to 3D sketch splines, let’s review the other curve creation types available. Again, an effective method for creating 3D curves from 2D sketches is to use Insert>Curve>Projected. If you have created two 2D sketches in different planes or faces, you can combine them to project a 3D curve.
- Curves created thru XYZ points allow the user to input a table of 3D coordinates and create a single curve from it. There are also a number of macros that have been written by users to take a text or .ibl file that contains a number of curves and create them automatically in a single command. (Search the SW forums for these macros.)
- Curve thru Reference Points is similar to Curve thru X,Y,Z points except that instead of proving SolidWorks with a table of 3D coordinate values, the users specifies existing 3D points to create the curve. Both of these curve creation techniques are limited in that once the curve is created, you can not adjust it and you can not assign vector angle or magnitude values to it. The work around is to convert it to a 3D sketch using Convert Entities and then perform a Simplify Spline (select 3D sketch spline and RMB and select Simplify Spline) on it to convert it to a SolidWorks 3D sketch spline that then can be edited.
- Face Curves (Tools>Sketch Tools>Face Curves) are another curve type that allows users to create a grid network of 3D sketch splines on a face or surface that correspond to the UV of the surface. This is a way of analyzing the mesh of a surface, persistently without having to edit that surface feature.
- You can create curves that are the intersection of two intersecting faces or surfaces, or a surface/face and a plane.
- Fit spline is a powerful utility that allows the user to “Fit” a spline over existing 2D or 3D sketch geometry, and adjust it’s tolerance to that underlying geometry. This is a useful function when users want to create analytical (arcs and lines) sketch geometry, yet want it to result in a smooth and continuous curve. An yes, you can add dimension to your lines and arcs, and drive the Fit spline parametrically.
- Convert and Offsetting Entities converts existing model edges and faces into the 2D sketch plane. Currently only Convert Entities is available in 3D sketches and not Offset. Composite Curve is a curve utility for gathering up a contiguous set of edges into one curve feature. Recent enhancements in 3D sketch combined with Convert Entity make it a more useful method than Composite curve because they essentially both do the same thing. (One caveat is that Composite curve is slightly more robust because in some cases converted 3D sketches overdefine or dangle when dramatic changes are made in parent features.)
- Helix, is of course, useful and necessary when creating paths to create springs and sweep a cut or add material for a thread. Helix has been enhanced of the last few releases to be able to variably change the pitch and diameter as well as tapering.
- Let look a simple application of a 2D sketch spline and how to use it to build a bridge curve* for a surface. In this will look at creating 4 different types of bridge curves using various methods: 2D sketch spline using Intersection Curve in a 2D plane 3D sketch spline for one vertex to another can =Curvature at the edges of those vertices. 3D sketch between the end of one projected curve and another 3D sketch connected freely between one edge to the other and a “Face Tangency” constraint is *Bridge curve is just a generic name for a spline that “bridges to existing surfaces.
- When constraining to projected curves on surfaces or faces, we current (in 2008 SP2) have a problem with overdefining when constraining 3D sketch splines to them. This occurs because projected curves don’t meet the ends of the faces that they project to with sufficient accuracy that the 3D constraint-solver needs and it applies both a constraint to the end of the fore-shorten projected curve as well as the edge of the face causing an over-defined condition. If you zoom in very closely on the constraint, you will see this. It is best to convert them to a 3D sketch curve that will overcome this problem, or you can do the following: Go ahead and create your 3D sketch spline to the projected curve/s. When it goes over-constrained, zoom in on each end of the spline until you can notice the mis-match of the projected curve with the edge of the face. Simply delete the dual constrain to the edge (not to the end of the projected curve), and on either end if necessary, and this will remove the over-defined condition. You can now successfully add tangent and equal curvature constrains.
- Lets take a look at a this simple shape, created from a single 3D sketch…
- Remember that when creating and editing 3D sketch splines, you have 6 degrees of freedom verses 4 degrees in a 2D sketch so it should not be surprising that they are initially more difficult to work with. Let me show you some useful tools for controlling 3d splines using 3D sketch planes and the 3D sketch Triad….
- Another viable method for creating and editing 3D sketch splines is to use a multi-window SolidWorks environment. This is very familiar to Alias and Rhino users because this is how they effectively interact with 3D curves. Let’s take a look at an example of how to do this in SolidWorks…
- Now that we’ve covered the basics of how to create 2D and 3D splines, lets take a look at how they are used to create complex shapes… A point to be made here is that although you can use these interim curves to better define the Boundary surface, in some cases, you don’t need them. Try the Curve Influence option “Next Curve” in the First direction curve selection box to see how to “inflate” the boundary surface. You can also add a connector to better manage the flow of the surface as it moves around the corner. *(in order to view these videos, you will need to visit www.techsmith.com and download their video codec.)
- 3D sketches are very useful for creating reference surfaces (with a single 3D sketch) to control the fill feature as well as other surface features.
- Again, 3D sketches are useful for not only as curves that define surfaces, but also as a quick way to create reference surface that then subsequently control the final surfaces. Let’s look at an example…
- Creating one or two sketch splines in conjunction with the Fill Feature allow the user to create complex surface features. Let’s take a look…
- Thank you for your time and attention.