Solving Free-Form Face-to-Edge Gap Problems with Geomenon's Patent Pending Technology

Deformable healing solves the most difficult of CAD database problems, reducing gap sizes between free-form surfaces and the edges that bound them while preserving the original input curve and surface shapes.

Face-to-edge gaps are inevitable wherever any free-form surface connects to another free-form surface with a different parametric representation (e.g. different knot vector), through a trimmed edge, or to a non-planar analytic surface. This is true for B-splines, NURBs, and any other CAD free-form surface representation. These gaps are not due to database errors or to the algorithms that built them. Rather these gaps are inherent to the representation just like a piecewise linear poly-line must have gaps when approximating a circular arc, as shown below. And like the poly-line approximation of a circular arc, free-form face-to-edge gaps can be minimized by carefully optimizing the shape of the free-form surface. Once gaps are optimized, increasing the sampling density can further reduce their size. These gaps cannot be eliminated.

Deformable healing solves the problem of moving the control-points of a free-form surface to minimize its face-to-edge gaps while also minimizing any changes to the original input shape. If the optimized gaps are still too large, the surface is subdivided and the shape re-optimized until the gap sizes are acceptable.

In a simple form, deformable healing changes the shape of a surface to interpolate all of its bounding edges. More complicated aspects of deformable healing include deforming some edges to lie on the surface, deforming curves and surfaces simultaneously, and in a solid modeling context using other techniques where appropriate, such as surface-surface intersection to replace offending edge shapes.

Global Operator: Deformable Healing changes surface shape by a very small amount over the entire surface to minimize gaps. Fixing gaps with localized changes in shape, places bends and hooks into the shapes being healed making them difficult to use for subsequent modeling and manufacturing applications.

Tangent Edges: Deformable Healing can enforce G1 and G2 continuity across edge boundaries.

General Boundaries: Deformable Healing can be applied to surfaces with any number of iso-parameter and trimmed edge boundaries. The edges may be distributed into any number of loops and may self intersect.

Over Sample Reduction: Many CAD free-form curves and surfaces are generated in an over-sampled fashion using more control points than required to represent their shape. Deformable healing can remove unneeded control points to help reduce database size.

Improved Parameterizations: Many CAD free-form curves and surfaces are generated with poor underlying parameterizations including uneven element sizes, highly varying parameter speeds, and even multi-valued parameterizations. Deformable healing replaces poor parameterizations with regular parameterizations that help improve CAD application performance.