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In computer aided geometric design and computer graphics, fitting point clouds with smooth curves (known as curve reconstruction) is a widely investigated problem. Dynamic implicit curve reconstruction is a new approach appearing in the curve reconstruction. In the paper, we introduce algebraic triangular B-splines into the dynamic implicit curve reconstruction, such that the results of the curves are zero sets of some B-spline functions over triangular meshes. We also use reduced gradient distances to measure the error between the curves and the point clouds. The results illustrate that the method can deal with complex topologies.