No real objects have perfectly sharp features. All edges, even those on seemingly sharp objects, have some finite radius of curvature. Though inevitable in real life, this unavoidable lack of precision presents a difficult problem for computer graphics and computer animation. Some modeling methods, e.g., the use of piecewise linear surfaces (polygon meshes) work well for objects with sharp boundaries. Other methods, e.g., NURBS (non-uniform rational B-splines) work well (i.e., are more accurate and compact) for modeling curved surfaces, but fair less well and are less efficient for modeling objects with sharp features.
In recent work, Hoppe, et al. have shown that piecewise smooth surfaces incorporating sharp features, including edges, creases, darts and corners, can be efficiently modeled using subdivision surfaces by altering the standard Loop subdivision rules in the region of such sharp features. Hoppe, et al., Piecewise Smooth Surface Reconstruction, Computer Graphics (SIGGRAPH '94 Proceedings), pgs. 295-302. The modified subdivision surface technique developed by Hoppe, et al, provides for an efficient method for modeling objects containing both curved surfaces and sharp features. The resulting sharp features are, however, infinitely sharp, i.e., the tangent plane is discontinuous across the sharp feature.
Even the method of Hoppe, et al. does not, therefore, solve the problem of modeling real objects with finite radius edges, creases and corners. To model such objects with existing techniques, either subdivision surfaces, NURBS, or polygons, requires vastly complicating the model by including many closely spaced control points or polygons in the region of the finite radius contour. As soon as one moves away from infinite sharpness, which can be modeled easily and efficiently with subdivision surfaces following Hoppe, et al. most, if not all of the advantages of the method are lost, and one must create a vastly more complicated model to enjoy the incremental enhancement in realism. Accordingly, there is a need for a way to efficiently model objects with semi-sharp features and, more generally, there is a need for a way to sculpt the limit surface defined by subdivision without complicating the initial mesh.
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