Google Inc.

Philip S Milne

Svetoslav Ganov

Chet Haase

Gilles Debunne

Svetoslav R Ganov

Mechanisms for more efficiently and accurately performing anti-aliasing techniques. A bounding box for a line can be generated that includes both a central region of the line and one or more boundary regions that have various levels of opacity. Vertices for the bounding box can be provided to any of a variety of appropriate entities to interpolate pixel locations within the bounding box and to determine various levels of opacity for pixels, such as vertex shaders and/or pixel shaders. Various techniques can be used to determine a pixel's membership value within one or more of the boundary regions of a bounding box, such as using a distance from an edge of a central region to a center of the pixel and/or an area of the pixel that is located inside the boundary region.

Anti-aliasing techniques

A layout that specifies rectangular components within a container rectangle may be specified. Each rectangular component has at least one size and a gravity parameter, and can be classified as flexible or non-flexible based on the gravity parameter. The computing device determines a plurality of grid lines from the layout. Each rectangular component of the set of rectangular components is associated with at least two grid lines. The at least two grid lines are based on the at least one size of the rectangular component. The computing device generates a system of constraints, where each constraint is related to at least two grid lines of the plurality of grid lines. The computing device solves the system of constraints to determine a location for each grid line. The computing device generates a display of the rectangular components based on the locations of the grid lines.

Methods and apparatus for flexibility inference in two-dimensional layout systems

Disclosed are apparatus and methods for generating displays based on a layout. A layout is received that specifies a set of rectangular components, where each rectangular component has at least one size. A plurality of grid lines is determined from the layout. A system of constraints related to the plurality of grid lines is generated. A graph is generated with a plurality of nodes corresponding to the plurality of grid lines and a plurality of edges corresponding to the system of constraints. The plurality of edges is topologically sorted. Locations for the grid lines are determined by solving a single-source path-length problem for the graph to using a variant of the Bellman-Ford algorithm configured to operate with the topologically-sorted plurality of edges. A display of the rectangular components based on the locations of the grid lines.

Methods and apparatus for improving the typical running time of the bellman-ford algorithm

Disclosed are apparatus and methods for generating displays based on a layout with inconsistent constraints. The layout specifies a set of rectangular components within a container rectangle. A plurality of grid lines is determined from the layout. Each rectangular component is associated with at least two grid lines that are based on a size of the rectangular component. A system of constraints is generated that includes inconsistent constraints. A graph including a plurality of nodes and a plurality of edges is generated from the plurality of grid lines and the system of constraints. A variant of the Bellman-Ford algorithm configured to operate with the inconsistent constraints solves a single-source path-length problem for the graph to determine locations for the grid lines. A display of the rectangular components is generated based on the locations of the grid lines.

Methods and apparatus for using a variant of the Bellman-Ford algorithm that operates with inconsistent constraints

Disclosed are apparatus and methods for generating displays based on a user-interface layout. A user-interface layout can specify at least first and second rectangular components, both being within a container rectangle, each having respective sizes in a dimension. The computing device determines a plurality of grid lines from the user-interface layout, where the first and second rectangular components are respectively associated with first and second sets of at least two grid lines. The computing device generates at least first and second constraints, respectively related to the first and second sets of at least two grid lines. The computing device solves the system of constraints to determine respective location for the grid lines. The computing device generates and displays a user-interface display including the first and second rectangular components.

Methods and apparatus for general solution of the two-dimensional layout problem by reduction to a single-source path-length problem on a weighted graph

Disclosed are apparatus and methods for generating displays based on a layout specifying rectangular components. A computing device can determine grid lines from the layout, with each rectangular component associated with at least two grid lines. The computing device generates a system of constraints, each constraint related to at least two grid lines, including one or more normal-order constraints that specify a normal order for the grid lines. The computing device solves the system of constraints to determine a first location for each grid line. The computing device can identify a relaxable normal-order constraint. The computing device solves the system of constraints based on the relaxing the relaxable normal-order constraint to determine a second location for each grid line. The computing device generates a display of at least some rectangular components based on the second locations of the grid lines.

Methods and apparatus for reordering of rows and columns in layout grids

Disclosed are apparatus and methods for generating displays based on a layout with space components. A layout is received that specifies a set of rectangular components, each rectangular component having at least one size. The set of rectangular components includes a non-visible space component configured not to react to user-interface events. A plurality of grid lines is determined from the layout. Each rectangular component is associated with at least two grid lines that are based on the at least one size of the rectangular component. A system of constraints is generated, where each constraint is related to at least two grid lines of the plurality of grid lines. The system of constraints is solved to determine a location for each grid line in the plurality of grid lines. A display of the rectangular components is generated based on the locations of the grid lines.

Methods and apparatus for unification of space mechanisms in toolkits using a generic space component

Disclosed are apparatus and methods for generating displays based on a layout. A layout is received that specifies a set of rectangular components within a container rectangle. Each rectangular component has a size. A plurality of grid lines is determined from the layout. Each rectangular component is associated with at least two grid lines that are based on the size of the rectangular component. A system of constraints is generated that includes a minimum constraint and a maximum constraint. Each constraint is related to at least two grid lines of the plurality of grid lines. The minimum and maximum constraints respectively specify a minimum and a maximum value between at least two grid lines. The system of constraints is solved to determine a location for each grid line. A display of the rectangular components is generated based on the locations of the grid lines.

Methods and apparatus for extensions to directed graphs with minimal and maximal constraints are encoded by arcs in opposite directions

Disclosed are apparatus and methods for generating displays based on a layout. A layout is received that specifies a set of rectangular components within a container rectangle. Each rectangular component has at least one size. The computing device determines a plurality of grid lines from the layout. Each rectangular component of the set of rectangular components is associated with at least two grid lines. The at least two grid lines are based on the at least one size of the rectangular component. The computing device generates a system of constraints, where each constraint is related to at least two grid lines of the plurality of grid lines. The computing device solves the system of constraints to determine a location for each grid line in the plurality of grid lines. The computing device generates a display of the rectangular components based on the locations of the grid lines.

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Palo Alto, CA, United States of America

Philip S Milne