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It is of interest to fabricate curved surfaces in three dimensions fromeasily available homogeneous material in the form of flat sheets. The aim isnot just to obtain a surface $M$ in $\mathbb{R}^3$ which has a desiredintrinsic Riemannian metric, but to get the desired embedding $M \subset\mathbb{R}^3$ up to translations and rotations (the Riemannian metric aloneneed not uniquely determine this). In this paper, we demonstrate three genericmethods of molding a flat sheet of thermo-responsive plastic by selectivecontraction induced by targeted heating. These methods do not involve anycutting and gluing, which is a property they share with origami. The firstmethod is inspired by tailoring, which is the usual method for making garmentsout of plain pieces of cloth. Unlike usual tailoring, this method produces thedesired embedding in $\mathbb{R}^3$, and in particular, we get the desiredintrinsic Riemannian metric. The second method just aims to bring about thedesired new Riemannian metric via an appropriate pattern of local contractions,without directly controlling the embedding. The third method is based ontriangulation, and seeks to induce the desired local distances. This results ingetting the desired embedding in $\mathbb{R}^3$, in particular, it also givesus the target Riemannian metric. The second and the third methods, and also thefirst method for the special case of surfaces of revolution, are algorithmic innature. We give a theoretical account of these methods, followed by illustratedexamples of different shapes that were physically molded by these methods.

Molding 3D curved structures by selective heating