Splines are curves drawn between two points in a two- or three-dimensional design. The shape of these curves is calculated to be as smooth as possible. Fortunately, design software makes manual calculating unnecessary; you generally just need to plot each point of your design, while your design program calculates and displays the splines dynamically. Joining splines can take at least two forms: flowing the end segments of two separate splines together and interlacing splines to form a network, aka “spline cage,” from which a 3-D surface can be rendered.
Method 1: to smoothly connect the ends of two separate splines
1. Create two separate spline curves in your design app. Make an endpoint of the first fairly close to an endpoint of the second one.
2. Make the two spline objects into a single object: apply the tool in your app that joins two separate objects into one, so that you can see the vertexes of both at the same time. Do not use your app’s tool for grouping objects for this task.
3. Enter the vertex-editing mode for the joined curve object, then select the tool that lets you create new vertices. (This tool will be called “Refine,” “Create” or a similar name.)
4. Draw points defining a new spline curve that connects the existing ones. Ensure that the points of this curve trace over following existing points, in the following order:
The point adjacent to the endpoint of one curve
The endpoint of that curve
The nearest endpoint of the second curve
The second curve’s next-to-end point
5. Add one or two additional points to the joining curve, to make it fit the existing curves.
6. Delete the vertexes of the original curves that coincide with those of the joining curve.
7. Use your app’s tool for welding or fusing vertexes to join the ends of the three separate curves. (Consult your app’s documentation for a tool that automatically does vertex welding when vertexes are close enough to each other.)
8. Use the joined spline as you would any other spline (e.g., to create spline cages, as paths for extrusion, to constrain objects in an animation).
Method 2: to join splines together to form a spline cage
9. Draw a closed shape, such as a square, oval, circle or polygon, with your app’s line tool. (Don’t worry about being exact. Just make sure the shape’s start point coincides with its endpoint.)
10. Enter your app’s vertex-editing mode. Use this mode to add new segments within the shape. Ensure that the new segments connect existing, outer vertexes, and that each inner polygon formed by the new segments contains only 3 or 4 vertexes. Delete vertexes or add segments as needed, to ensure that these conditions are met.
11. Go to a perspective view of the spline curves, and pull at least one of the inner vertexes away from the plane containing the outer vertexes, so that a three-dimensional shape is formed.
12. Select the object containing the joined splines, then apply your app’s tool (aka “modifier”) for creating surfaces from spline cages.
13. Render the final object to view the joined splines as a smooth surface.