I fought the Law and…

I won!  Surfacing Laws can be evasive, so this is my humble attempt to make them clear.

If you have been given the task of creating a surface that smoothly transitions from one

closed curve to the next, while controlling the intermediate cross-sections, Laws are for YOU!

Simply put, the concept is to match the Law to the planar area of the Generating curves

in a Surf2+Curve+Crv-Crv.

In order to do this, you must first analyze the enclosed area of the sections by creating a planar face with Limit2.

With the Analysis+Inertia routine, using the default density of 1.00, determine and record the areas of the G-Curve

generated Faces.  Be sure to keep these in order in your notes, since their order is important to the definition process.

The next step is to create a plane through each of the planar G-Curves, and place them adjacent to the curves for clarity

and reference.  Place a Limit point on one of the planes at the furthest extremity in the stack of G-Curves.

Now, use Curve2+Spine to define the flow from one section to the next by selecting the point and first through last

planes in order (The point lies on the first plane in the series).

 

After generating the Spine, Analysis+Numeric the curvilinear length of the Spine curve.

Limit1+Break the Spine at each section plane, and analyze the length of each segment,

keeping good records of each span and which pair of G-Curves each span lies between.

Limit1+Concatenate+Curve the Spine back together, since you need it intact for the Law

to be distributed along.

 

Now for the FUN part!  Solve the following equation for R on each section:

Sqrt of Area/Pi = R.  The conversion of the Area to a Radius value is necessary for the

successful completion of the Law.

 

In 2D, somewhere slightly away from the part, draw a line the same length as the Spine you

analyzed earlier.  Use Point+Limits to create end points on the line.  With Point+Spaces,

select the line and the start point, followed by the value equal to the first segment of the Spine

length, and so on.  At one end of the line, use Point+Coord to select the end point and key in

0,(Radius value) to establish the first point offset for the Law.  Continue this process, basing the

coordinate point on the next consecutive value of R that you solved earlier.  In other words,

you are charting a gap defining the Radius resultant for each consecutive G-Curve Area, at the

specific point that it will occur along the Spine.

 

Once these points are charted, an Arc can be calculated through these points, and it is a good

idea to impose tangency at each end, so that the area is held momentarily as the surface exits

the final G-Curve.

 

Law+Create+Area:  In 3D mode, select the Varying Arc that you just calculated through the

Radius points, then the Line that was initially created in 2D, then the Spine that was concatenated,

Yes:Compute and type in a name for the Law.

This law can now be used in Surf2+Curve+Crv-Crv as one of the variables controlling your

new surface.  You will notice that Area is an input parameter in your FK Menu after Spine

selection and before G-Curve selection.  For a complete list of possible inputs, look at the

Analysis panel with Alt+ on the 10-key pad (Alt- removes the analysis panel).