In Chapter 2 of the manual, the stiffness of a spline curve was compared to the stiffness of springs altering the shape of a wooden spline/batten. This analogy also holds when you think of the fact that if the wooden spline itself were stiffer, its curvature when loaded transversely would be lesser. Similarly: when drawing a smooth shallow curve you could select a stiff spline, and when drawing a curve featuring a high rate of change of curvature you could select a flexible spline.

A Perspex batten is used to draw a spline. Its stiffness determines how much curvature can be drawn.

In Maxsurf there are a number of stiffness levels or “orders” for both the longitudinal and transverse directions of the surface:

The order reflects the number of coefficients used in the polynomial that describes the spline’s shape. For example: the order 2 polynomial “” uses 2 coefficients ‘a’ and ‘b’ and describes a straight line (read: linear curve).

When using NURB surfaces, flexible surfaces are useful for modelling knuckles (a region on a surface with sudden or very high change in curvature) and discontinuities.

 Watch a video that shows you the effects that a change to the surface stiffness has on the shape of a spline. [Web | Disk]

 Watch a video that shows how a change in stiffness affects the shape of the surface. [Web | Disk]

2D Curve

In the section on Basic Fairing we will discuss stiffness further, but first let’s have a look at the effects of stiffness on a curve:

Ø  Maximise the Profile window

Ø  Open SurfaceStiffness2D_start.msd

The model consists of a single chain (or “row”) of control points that produces a spline that lies in a single plane (you can see this in the Plan and Body Plan windows). Thus the model is best viewed in the Profile window. The ‘curve’ produced is simply a jagged line connecting the control points.

Ø  In the Assembly pane on the left, right click the surface 2D Curve and open the Properties dialog. (If the assembly plane is not visible, go to View | Assembly).

Currently, the transverse surface stiffness is set to 2 (linear).

Ø  Increase the longitudinal surface stiffness to 3 (flexible).

The curve now remains closer to the line between end control points. Note that the curve runs at a tangent to the control point net (blue) at the end points. This is true for splines of all stiffness orders. In the case of an order 3 spline, the curve is also tangential to the control point net at the midpoint of the net lines between successive intermediate control points (i.e. at  points A and B below):

Ø  Undo (Ctrl + Z) and Redo (Ctrl + Y) the change in stiffness to best study the effect of the change

Ø  Increase the longitudinal surface stiffness to 4, then 5

Notice how the spline displaces less and less from the line between the end control points.

Ø  Try selecting a stiffness of order 6 from the longitudinal stiffness drop-down menu. What happens?

A stiffness of 6 is not allowed because the order of the surface stiffness in a given direction must be less than or equal to the number of control points in that direction. Here there are 5 control points in a row so the maximum stiffness in the longitudinal direction is 5.

 The reason for this relates to the mathematical definition of a spline of certain stiffness or order. If a polynomial has five constants, at least five points on the curve (or influencing the curve, like the control points) are required to solve the constants and define the curve. 

Note:

Maxsurf will make sure the stiffness of the surface cannot be greater then the number on control points in that direction; i.e. if you have an order 6 surface and you reduce the number of columns from 6 to 5, Maxsurf automatically reduces the surface stiffness from 6 to 5.

3D Surface

To extend the concept of surface stiffness from a curve to a surface,

Ø  Open SurfaceStiffness3D.msd. If prompted to locate the materials and shapes library, click Cancel.

To best view the effect of changing the stiffness of the surface,

Ø  Maximise the perspective window.

Ø  Set pitch to 0, yaw to 60 and roll to –60.

Ø  Go to Display | Net and select Show Net to view all control points and the net.

Ø  Go to Display | Contours  and turn on sections and buttocks.

The surface stiffness is initially set to 2 (linear) in both directions. Notice that the sections and buttocks follow the shape of the control point net perfectly. 

Ø  Change the stiffness is both directions to 3.

Notice how the longitudinal surface edges and the buttocks, as well as the transverse surface edges and the sections have smoothed away from the control point net.

Ø  Change the stiffness in the transverse direction to 4 and in the longitudinal direction to 5 (the limits).

Observe how the edges, sections and buttocks are even smoother and that the entire surface is more planar.

Continue with the section on Surface Precision.