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3D interactive modeling from range data aims at simultaneously producing and visualizing the surface model of an object while data is collected. The current research challenge is producing the final result in real-time. Using a recently proposed framework, a surface model is built in a volumetric structure encoding a vector field in the neighborhood of the object surface. In this paper, it is shown that the framework allows one to locally control the model resolution during acquisition. Using ray tracing, efficient visualization approaches of the multiresolution vector field are described and compared. More precisely, it is shown that volume traversal can be optimized while preventing holes and reducing aliasing in the rendered image.