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The class of double-curved surfaces (undevelopable surfaces) contains objects that cannot be simply unfolded (developed). Such surfaces can be developed only approximately with some distortions of linear surface elements (see the
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The tangential contact between the surfaces being rolled over one another provides a relation between points on the two surfaces. If this relation is (perhaps only in a
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Development can be generalized further using flat connections. From this point of view, rolling the tangent plane over a surface defines an
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can be rolled around the surface to obtain the tangent plane at other points.
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In particular, if one of the surfaces is a plane, then the other is called a
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Differential
Geometry: Cartan's Generalization of Klein's Erlangen Program
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of each other. Differently put, the correspondence provides an
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188:Sharpe, R.W. (1997).
159:Stretched grid method
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138:local diffeomorphism
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