Splines

Spline curve creation and editing

Spline – basically, a smooth curve with a constantly changing radius – discussion

Spline curves should be your default tool for sections underlying complex surface forms.  Planar spline are created in Sketcher, 3D splines are created with Curve thru’ Points or Style curves.

Ending a spline – use MMB to finish creating the spline

Where ever possible always start with a 2 point spline – see previous section.  In sketcher create a curve with 2 end points, set end conditions to references, modify the spline shapes through the end vectors.

See Quality Analysis for spline curvature analysis

• Select the spline
• RMB > Modify
• either:
• Choose ‘Modify spline using control points’ from the Modify toolbar – often referred to as a Control Polygon – this returns you to interpolation point control when you exit the Modify environment
• or;
• Choose to switch control to polygon mode to keep the control polygon active when exited from the Modify environment.
• MMB to exit Modify mode

The direction and length (weight or magnitude) of the end vectors controls the spline shape.  The direction of the vector shows the direction of the curve end.  The length of the vector dictates how far into the curve that direction influences the curve shape.

Geometric constraints – vertical, perpendicular, etc. – can be applied to the control polygon

 

 

Setting spline end conditions

Switching to control polygon mode allows you to simply apply geometric constraints to the end vectors – Horizontal, Vertical or Perpendicular are the most useful.

 

Curvature Continuity in Sketcher

 

The curve end condition can be set to Tangency – G1 or Curvature Continuity – G2:

• activate the Equality geometric constraint
• pick the spline
• pick connected line/arc
• Tangency ‘T’ and continuity ‘C’  icons will show

 

Considerations in moving from G1 to G2 continuity

 

In the 1st image we see a simple 2 point spline which has been initially set to G1 end conditions and then the same spline raised to G2 connection. The spline is connected to two straight curves – zero curvature.

With the G1 connection the curves are travelling in the same direction where they meet but have an immediate change in curvature and take the shortest, smoothest route to the 2nd connection. The 2nd image shows the curvature plot for the initial G1 connection. A reasonably constant curvature but a sudden change in curvature at the connection point – zero curvature in the line.

The highlight in the resultant surface with the G1 connection will show as a blurred highlight boundary but with quite a rapid transition from light to shade.

The 3rd image above shows the curvature plot with the connection raised to G2. The start of the plot shows zero curvature and then a bit of a peak in curvature before it relaxes and travels to the second connection.  This forms a smoother transition in the resultant surface highlight but creates a tighter approximate radius.

As below you could increase the length of the length of the control vectors (the degree of influence into the curve of the end condition) to create a more uniform curvature. But these are then very different sections.

 

 

If you want to achieve a similar approximate radius in the G2 connection compared to the G1 then you need to extend the length of the G2 curve. The image below shows both curves achieving the same approximate radius but the G2 connection will have the smoother transition from the zero curvature line to the spline.

 

Resultant extrusion from both curves, observe the transition highlights

Click on image to enlage