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This paper presents a novel modeling technique for reconstructinga triangular B-spline surface from a set ofscanned 3D points. Unlike existing surface reconstructionmethods based on tensor-product B-splines which primarilygenerate a network of patches and then enforce certaincontinuity (usually, G{1} or C{1}) between adjacent patches,our algorithm can avoid the complicated procedures of surfacetrimming and patching. In our framework, the user simplyspecifies the degree n of the triangular B-spline surfaceand fitting error tolerance 驴. The surface reconstructionprocedure generates a single triangular B-spline patchthat has C{n-1} continuity over smooth regions and C{0} onsharp features. More importantly, all the knots and controlpoints are determined by minimizing a linear combinationof interpolation and fairness functionals. Examples are presentedwhich demonstrate the effectiveness of the techniquefor real data sets.