VSLib provides deformable modeling as part of a library using the constrained optimization techniques of the calculus of variations. The library supports several very different geometric operations:

Gap Refinement

• Reduce surface/edge gap sizes to a specified tolerance by modifying the shape of an existing surface a minimal amount without introducing sharp surface bends or dog-legs.
• Helps repair poorly made databases.

Deformable Modeling

• Design fair curve and surface shapes by setting and moving constraint point locations.
• Any number of constraint points can be located anywhere on the shape and each may constrain any combination of the shape’s differential properties: position, tangents, normals, curvatures, etc. The shape is deformed to interpolate all the constraints while keeping the surface/curve shape smooth and fair.
• Deform surfaces while interpolating any number of arbitrarily placed trim curves.
• Helps enable interactive sculpting applications using a tight loop of user input to modify constraint point values, automated surface recomputation, followed by surface rendering.

Improved Curve and Surface Approximations

• Create smooth and nicely parameterized low-control point count BSpline curve and surface approximations from high-count sample point sets. Individual sample points can contain any combination of position, tangency, normal, or curvature values.
• Each sample point value, in any combination, can either be interpolated or approximated.
• The number of output control points is decoupled from the number of input sample points. Output control point count depends only on shape complexity and desired tolerance. For example, a simple bi-Cubic surface sampled by 10,000 points can be approximated by a Bspline surface with 16 control points.

Global Deformations

• Create variations of existing Brep models by embedding them into a deformable 3 space. Change the shape of the Brep into a new valid Brep by smoothly deforming the space in which it is embedded. The user interface for bending space mimics the user interface for sculpting surfaces allowing space to be deformed by pulling on constraint points while constraining the space to interpolate an arbitrary set of 3d points, curves, and surfaces.

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From the staff of Solid Modeling Solutions

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