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This paper systematically presents a novel haptics-based volumetric modeling framework, which is founded upon volumetric implicit functions and powerful physics-based modeling. The volumetric implicit functions incorporate hierarchical B-splines, CSG-based functional composition, and knot insertion to facilitate multiresolution editing and level of details (LODs) control. Our dynamic volumes are semi-algebraic sets of implicit functions and are governed by the principle of dynamics, hence responding to sculpting forces in a natural and predictive manner. The versatility of our volumetric modeling affords users to easily modify both the geometry and the topology of modeled objects, while the inherent physical properties can offer an intuitive mechanism for direct manipulation. Moreover, we augment our modeling environment with a natural haptic interface, in order to take advantage of the additional realism associated with 3D haptic interaction. Coupling physics and haptics with implicit functions can realize all the potentials exhibited by volumetric modeling, physics-based modeling, and haptic interface. Furthermore, in order to directly manipulate existing volumetric datasets as well as point clouds, we develop a hierarchical fitting algorithm to reconstruct and represent discrete datasets using our continuous implicit functions, which permit users to further design and edit those 3D models in real-time using a large variety of haptic toolkits and visualize their interactive deformation at arbitrary resolution.