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Real-time evaluation of distributed contact forces between rigid or deformable 3D objects is a key ingredient of 6-DoF force-feedback rendering. Unfortunately, at very high temporal rates, there is often insufficient time to resolve contact between geometrically complex objects. We propose a spatially and temporally adaptive approach to approximate distributed contact forces under hard real-time constraints. Our method is CPU based, and supports contact between rigid or reduced deformable models with complex geometry. We propose a contact model that uses a point-based representation for one object, and a signed-distance field for the other. This model is related to the voxmap pointshell method (VPS), but gives continuous contact forces and torques, enabling stable rendering of stiff penalty-based distributed contacts. We demonstrate that stable haptic interactions can be achieved by point-sampling offset surfaces to input "polygon soup'' geometry using particle repulsion. We introduce a multi-resolution nested pointshell construction which permits level-of-detail contact force computation, and enables contact graceful degradation in close-proximity scenarios. Parametrically deformed distance fields are proposed to support contact between reduced deformable objects. We present several examples of 6-DoF haptic rendering of geometrically complex rigid and deformable objects in distributed contact at real-time kilohertz rates.