Continuous Mapping of Three-dimensional surfaces

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If I have two sampled surfaces in $\mathbb{R}^3$ (discrete points) is there a nice way (or algorithm) to form a continuous map between the two, if the surfaces are of different sizes? That is, what is the best way to construct a continuous map between $\{ x_i^1, y_i^1, z_i^1 \}_{i=1}^n$ and $\{x_j^2, y_j^2, z_j^2\}_{j=1}^m$? Also, how about when I construct bivariate splines for both surfaces, is there a nice way to construct a map between the two as well?