This paper describes a framework for introducing visually smooth surfaces into sketch-based freeform modeling systems. An existing sketch-based freeform modeling system generates rough polygonal meshes with uneven triangulations after each operation. Our approach generates a dense, visually smooth polygonal mesh by beautifying and refining the original rough mesh. A beautification process generates near-equilateral triangles with a near-uniform distribution of vertices to mask the noise and bad

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... sampling of the uneven mesh. The vertices are distributed on a smoothed surface that approximately interpolates the original mesh. Refinement generates a smooth, dense mesh by subdividing the beautified mesh and moving the vertices to the interpolative surface. The smooth interpolative surface is computed via implicit quadratic surfaces that best fit the mesh locally in a least-squares sense.