Surfaces through a curve network (Gordon surface)

A Gordon surface is one surface that passes through every curve of a network: a set of profiles running one way and a set of guides running the other, crossing like the threads of a net. It is how you shape a hull, a fender or a handle from a few section curves you control directly. It needs the exact kernel (see The exact kernel and the mesh kernel).

Draw the network

1. Draw the profiles: two or more curves running side by side, for example sections on parallel planes. Lines, arcs, circles and splines all work, and a chain of curves joined end to end counts as one curve.
2. Draw the guides: two or more curves running across the profiles. Each guide has to cross every profile once, and each profile every guide once.
3. Make the curves really meet. Draw a guide's sketch so its curve passes through the profiles' points (snap to projected points, or type the coordinates). The network accepts gaps up to the Tolerance (0.01 mm to start with).

One sketch can hold several curves: every separate chain in it is its own curve. So you can draw all the guides in one sketch on the top plane, for instance.

Make the surface

1. Choose More in the Features group, then Gordon surface.
2. PartCraft takes the sketches nobody uses yet: those in planes parallel to the first become profiles, the others guides. Check the list on the right and set each sketch to Profiles, Guides or Not used.
3. To use edges of the part, click Pick edges as profiles (or as guides), click the edges in the view, then press Esc.

The result is a surface body. Thicken turns it into a solid, Stitch sews it to other surfaces, and Trim surface cuts it.

Close it to a solid

When the profiles are closed curves (circles, closed splines, closed chains) and the first and last profile each lie flat in a plane, tick Close to a solid. The ends are capped with flat faces and the closed shape joins, cuts, intersects or becomes a new body like any other feature. This is how you make a loft that follows guide curves. The same works with closed guides.

What is exact and what is fitted

The panel says which of these applies, and how far the surface strays from your curves.

• Exact: when every curve is polynomial (lines, splines and chains of them) and the guides cross all the profiles at the same parameters, the surface is exactly the Gordon surface of those curves. A network of iso curves cut from a bicubic surface gives that surface back, and four straight lines give a flat or twisted (bilinear) patch.
• Fitted: arcs, circles and edges of the part are not polynomial, and curves that cross at different parameters have to be re-timed so the crossings line up. Those curves are fitted by cubic B-splines within one ten-millionth of the network's size (about 0.00001 mm for a 100 mm part). A cylinder patch made from arcs and lines stays within 0.00001 mm of the true cylinder.

Between the curves the surface is whatever the method gives: the profiles blended across, plus the guides blended across, minus the blend of their crossing points. It is smooth everywhere except where a curve has a sharp corner. Where two Gordon surfaces share a boundary curve they meet edge to edge (G0), not tangent.

When a network does not fit

Limits

• One B-spline face per network: no G1 or G2 tangency to neighbouring surfaces.
• A closed network's seam, at the first guide, is joined edge to edge but not tangent.
• The Loft feature itself has no guide rails; use a Gordon surface closed to a solid instead.
• Very wiggly curves, or crossings spaced very unevenly along one curve compared to another, can need too many points to fit; the feature then says so.