Abstract: A non-transitory computer-readable storage medium may comprise instructions stored thereon. The instructions, when executed by at least one processor, may be configured to cause the first computing system to at least generate a collection of inverse transformations of an index of the document, the collection of inverse transformations being based on at least one asymmetric local edit to the document by the first computing system, determine a location within the document to perform a remote edit by the second computing system based on the collection of inverse transformations of the index of the document, perform the remote edit to the document at the determined location based on the remote edit by the second computing system, and perform at least one local edit to the document based on the at least one asymmetric local edit to the document by the first computing system.

Abstract: A non-transitory computer-readable storage medium may comprise instructions stored thereon. The instructions, when executed by at least one processor, may be configured to cause the first computing system to at least generate a collection of inverse transformations of an index of the document, the collection of inverse transformations being based on at least one asymmetric local edit to the document by the first computing system, determine a location within the document to perform a remote edit by the second computing system based on the collection of inverse transformations of the index of the document, perform the remote edit to the document at the determined location based on the remote edit by the second computing system, and perform at least one local edit to the document based on the at least one asymmetric local edit to the document by the first computing system.

Abstract: A system of curve generation takes a sequence of control points and constraint codes for each control point, and outputs a curve in which each of the constraints is satisfied. The set of constraints is chosen from the tangent angle, curvature, first derivative of curvature, and second derivative of curvature. The interactive curve design uses as its primitive, a curve whose curvature is a polynomial function of arclength (whose intrinsic equation is a polynomial). At each control point, a choice of G2 curvature continuity (tangent angle and curvature) or G4 curvature continuity (tangent angle and curvature plus first and second derivatives of curvature are continuous) is input. The desired curve is expressed as the solution to the chosen set of constraints.

Abstract: A data optimization method transforms an input Data File containing an Arbitrary Order Signal Sequence into a Streamable Signal Sequence having the same or compatible format as the original input Data File. The Streamable Signal Sequence, which represents the same information as contained in the original Arbitrary Order Signal Sequence, can be sequentially processed using less memory. In one embodiment, a Data File containing a PDF (portable document format) file, i.e., an Arbitrary Order Signal Sequence document is transformed from an arbitrary order organization into a Streamable Signal Sequence organization, more suitable for printing. Reordering an Arbitrary Order Signal Sequence into a Streamable Signal Sequence reduces the memory required to print a document as compared to the same document represented by an Arbitrary Order Signal Sequence.