Combinatorial curve reconstruction in Hilbert spaces: A new sampling theory and an old result revisited

An image copying apparatus includes a copier for copying an image and an imager which forms characteristics of the image. The imager includes a liquid crystal image forming and storing system for forming in real time characteristics of an image in response to a prescribed input and for temporarily storing those characteristics for a time adequate for the copier to copy the same and a scanning device to scan the image forming and storing device to apply the characteristics thereto. In one embodiment the liquid crystal is operationally nematic liquid crystal encapsulated or contained in a support medium that has a capacitance characteristic, and the scanning device includes a dynamic electrode which applies surface charge to selected areas of the encapsulated liquid crystal/support medium affecting the liquid crystal structural alignment to create the image characteristics. A graphics copying method includes the steps of applying respective prescribed inputs to selected areas of a sheet-like liquid crystal material to cause the liquid crystal material to effect the transmission, scattering or absorption of incident light thereby to form characteristics of an image, and using a copying process copying the characteristics to form a copy of such image.

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