A Constraint-Based Method for Sculpting Free-Form Surfaces

We discuss the problem of creating editable features for free-form surfaces. The manipulation tool is a user-defined curve on the surface. The surface automatically follows changes of the curve keeping a predefined set of constraints satisfied, specifically the incidence and tangency along one or several surface-curves. We review and update our approach presented earlier [18] and show how the curve-surface composition can be expressed as a linear transformation. In this context, we also describe the so-called “aliasing” problem caused by an incompatibility of a general curve on a surface with the rectangular mesh of degrees of freedom of a tensor product surface. The proposed solution is a local reparametrization in accordance with the feature.

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