The gap
Why features and curves are not enough
Even with the modelling power that features and curves provide, a class of objects remains out of reach. Free-form parts are characterised by surfaces of intricate shape that no combination of extrusions, revolves, sweeps and lofts will produce directly. For those, surfaces are the appropriate technique.
Surfaces build on curves in both theory and practice. Creating a surface almost always begins with creating the curves that define it, and surface equations extend the parametric representation of curves into a second parameter. The classification carries across too: surfaces, like curves, divide into analytic — plane, ruled surface, surface of revolution, sweep — and synthetic, of which the spline surface is the archetype.
Combining three-dimensional curves with surfaces gives the most advanced modelling capability available, and with it the ability to model almost anything imaginable. Before exercising that freedom, ask whether the part can be manufactured — and then ask the follow-up question, which is whether it can be manufactured at an acceptable cost. A shape that only a five-axis machine or a bespoke tool can produce is a legitimate answer sometimes and an expensive accident the rest of the time.
Definition
What a surface actually is
A surface is a thin planar or non-planar sheet with no thickness. Creating one is not in itself useful. Surfaces are an intermediate step between curves and solids — a means of producing features that curves alone cannot. Like features, surfaces appear in the feature tree, and expanding a surface node reveals the sketch that defines it.
Mastering surface creation reduces to three questions, exactly parallel to those for features: what surfaces does the system offer, what input does each require, and which is right for the problem at hand? The third again admits several workable answers and one best one — where the cross section is constant along a curve, a sweep needs fewer steps than a loft and should be preferred.
| Surface | Input | Typical role |
|---|---|---|
| Planar | A closed planar boundary or set of coplanar edges. | Capping an open end before a knit or conversion. |
| Extruded | Profile plus direction and depth. | Straight-walled boundaries and trimming tools. |
| Revolved | Profile plus axis and angle. | Axisymmetric shells, bowls, containers. |
| Swept | Profile plus path, optionally guide curves. | Constant section following a spatial curve. |
| Lofted | Two or more profiles, optionally guide curves and centreline. | Varying section transitions — the workhorse of free-form form-finding. |
| Boundary | Curves in two directions. | High-quality surfaces with controlled tangency on all four sides. |
| Filled | A closed boundary of edges or curves, with tangency conditions. | Patching a gap while matching the surrounding surfaces. |
| Offset | An existing face plus a distance. | Creating clearance shells and parallel geometry. |
| Radiate | An edge, a reference plane and a distance. | Producing parting surfaces for mould tooling. |
| Ruled | An edge plus a direction and distance. | Draft-related surfaces and tapered walls. |
| Knit | Several adjacent surfaces. | Joining separate patches into one entity, and closing a volume. |
| Trim and extend | Surfaces plus trimming entities. | Cleaning intersections and reaching to a boundary. |
Representation
Parametric surfaces in two parameters
Where a curve needs one parameter, a surface needs two. A point on a surface is written P = P(u, v), with both parameters running over defined ranges. The plane is the simplest case: given three points P0, P1 and P2, every point on the plane is reached by moving a fraction u along one edge vector and a fraction v along the other, both fractions running from zero to one.
Differentiating with respect to each parameter separately gives two tangent vectors, Pu and Pv. For a plane these are constant, as expected. Their cross product gives the surface normal — the vector that determines which side is material, how light reflects, and along which direction a cutting tool should approach.
The ruled surface extends the idea: it is generated by sweeping a straight line between two boundary curves, so one parameter runs along the curves and the other runs along the generating line. Every point on a ruled surface lies on a straight line lying wholly within the surface, which is exactly why ruled surfaces can be cut by wire EDM and by flame or plasma processes that move a straight cutting element.
Inspection
Visualising surface quality
Surfaces are harder to judge than curves, because their curvature runs in two directions at once. CAD systems therefore provide dedicated visual aids.
- Surface mesh
- A grid of constant-u and constant-v curves laid over the surface. A denser grid makes the shape easier to read, but mesh density has no bearing on surface accuracy — the accuracy is fixed by the surface equation, and the system generates the grid from that equation.
- Curvature display
- Every point on a surface has a radius of curvature, and the curvature is its reciprocal. A contour map of curvature is superimposed on the surface, and both values are reported as the pointer moves across it. Abrupt colour changes indicate abrupt curvature changes, which will be visible on a moulded or polished part.
- Zebra striping
- Reflected stripes that reveal continuity between adjacent patches. Broken stripes indicate a position-only join; kinked stripes indicate tangency without curvature continuity; smooth continuous stripes indicate curvature continuity.
- Draft analysis
- Colour-codes faces by their angle relative to a pull direction, which matters as soon as the part is destined for a mould. Covered further in Part 17.
G0 means the patches meet. G1 means they meet and share a tangent plane. G2 means they meet, share a tangent, and share curvature. Consumer products in gloss finishes usually need G2 across visible transitions; structural parts in matte finishes are often satisfied with G1. Knowing which is required prevents both visible defects and wasted modelling effort.
The point of it all
Three routes from surfaces to solids
The goal of creating surfaces is not to have surfaces. It is to produce complex features and solids.
Thicken
Assign a thickness to the surface and the system generates a solid. Simple, and the most likely to fail.
Cut with a surface
Use the surface as a cutting tool to divide an existing solid, discarding one side. Robust, and the standard technique for tooling splits.
Convert a closed surface body
Knit surfaces into a watertight closed volume and convert it to a solid. The surface set must genuinely close — no gaps, no overlaps.
Why thicken fails
Understanding the operation explains the failure. Conceptually the system copies the surface and displaces the copy by the thickness. The cross sections of the resulting solid must remain perpendicular to the surface profile and must not intersect one another. Where the surface has a sharp change in direction, or a radius of curvature smaller than the requested thickness on the concave side, those cross sections do intersect — and the operation fails.
Three checks resolve most failures. Is the thickness larger than the smallest concave radius on the surface? Reduce the thickness or increase the radius. Does the surface contain a sharp crease? Fillet it first. Is the surface set actually closed? Run a check for open edges — a single unnoticed gap is enough to prevent conversion, and the gap is frequently at a capping face that was never created.
Method
A working sequence for free-form parts
- Stage 1 — Define character curves Build the small number of curves that carry the shape: silhouettes, section profiles, feature lines. Keep control points to a minimum and check curvature before proceeding.
- Stage 2 — Build primary surfaces Create the large surfaces from those curves, using boundary or loft where quality matters. Do not attempt to model detail at this stage.
- Stage 3 — Trim and knit Trim surfaces to one another, extend where they fall short, and knit the result. Inspect continuity with zebra stripes.
- Stage 4 — Close and convert Cap open ends with planar or filled surfaces, confirm the body is watertight, and convert to a solid.
- Stage 5 — Add solid features Shell, rib, boss, hole, draft and fillet the solid using ordinary feature operations. Detail belongs here, not in the surfacing.
The most common failure of method is attempting Stage 5 work during Stage 2. Fillets and small details modelled into driving surfaces make those surfaces harder to control and much harder to repair. Keep the surfacing coarse and clean; add detail once the geometry is solid.
Key takeaways
- A surface has no thickness and is an intermediate step, not a deliverable; the deliverable is a solid.
- Surfaces extend curve mathematics into two parameters; the cross product of the two tangent vectors gives the normal.
- Ruled surfaces contain straight lines throughout, which is why they suit wire and flame cutting.
- Judge quality with mesh, curvature contours and zebra stripes, and know whether the job needs G1 or G2 continuity.
- Three routes convert surfaces to solids: thicken, cut, and convert a closed knitted body.
- Thicken fails when displaced cross sections intersect — usually thickness against a small concave radius, or an unfilleted crease.
- Surface coarsely first; add fillets and detail after conversion to a solid.
Series
Continue the pathway
The SOLIDWORKS Design Approach series works through computer aided design as an engineering discipline, from first principles to manufacture.