Mapping of features such as texture and geometric detail is an important tool that enhances realism of surface geometry in graphics and animation. This essentially involves a transformation of 2D coordinates with associated attributes to a target surface in 3D. Moreover, users are often in need of more powerful techniques that can also enable cut-and-paste functionality to directly map a feature from one surface in 3D to another with high-fidelity. Such an operation should minimize feature deformation on the target surface. In practice, it is also desirable to hide geometric complexities and transformations from ordinary users, requiring minimal input and providing an intuitive interface for painting. This paper develops a generalized feature mapping technique using a physically-based particle system to map both geometry and associative attributes between two curved surfaces with the physically-correct minimum distortion of these attributes over the target surface.