Abstract: A method traverses a bi-tree stored in a memory to locate application specific data stored in the memory and associated with the bi-tree. The bi-tree comprises a spatial partitioning of an N-dimensional space into a hierarchy of cells. Starting from a root cell enclosing the N-dimensional space, each cell is successively and conditionally partitioned into 2N child cells along the cell's N mid-planes. Each cell of the bi-tree has associated characteristics comprising the application specific data and child cells are indexed directly from a parent cell. First, a set of locational codes, a cell of the bi-tree, and a termination condition are specified. Next, the characteristics of the cell are tested to see if they satisfy the termination condition. If the termination condition is not satisfied, an arithmetic operation on the set of locational codes is performed to directly index a next cell to be tested. Otherwise, the cell identifies a target cell.

Abstract: A method edits a 3D model using 2D images. First, a projected range image is generated from a 3D model. The projected range image is edited using a 2D editor. A projected distance and a cliff distance from a plurality of 3D points to a 3D surface of the 3D model are determined using the edited projected range image. The projected distance and the cliff distance of each of the 3D points are combined to determine a distance from each 3D point to the 3D surface so that the distances forming a distance field of the edited 3D model.

Abstract: A method is described for determining a 2D gradient magnitude image from a range image of an object. The range image includes intensity values at pixel locations. The intensity values correspond to distances to a surface of the object. For each pixel (i,j) in the range image, a horizontal central difference dx value and a vertical central difference dy value are determined. Then, the 2D gradient magnitude image value at each pixel (i,j) is set to 0.5*sqrt(dx2+dy2+4). The range image can be scaled so that a unit intensity value at each pixel corresponds to a unit distance value. The magnitude of a gradient at a 3D point p can then be determined from the scaled range image and the gradient magnitude image. First, a perpendicular projection (x,y) of p onto the scaled range image is computed. Next, a gradient magnitude at (x,y) is interpolated from the corresponding values of the 2D gradient magnitude image near the location (x,y).

Abstract: A method typesets a set of glyphs. A current glyph is selected from the set of glyphs and a current position of the current glyph is selected. A next position of a next glyph is determined, where the next glyph is selected from the set of glyphs. The determination of the next position of the next glyph first represents the current glyph as a two-dimensional distance field and then determines the next position using the current position, an escapement of the current glyph, and an alignment of the two-dimensional distance field. The current glyph is then updated to be the next glyph and the current position is updated to be the next position. The selection of the next glyph and the determination of the next position continue until a termination condition is satisfied.

Abstract: A method and apparatus determine an antialiased intensity of a component of a pixel from a two-dimensional distance field representing an object. A set of sample points in the two-dimensional distance field is associated with the component of the pixel. A distance is determined from the two-dimensional distance field and the set of sample points and then mapped to the antialiased intensity of the component of the pixel.

Abstract: A method and apparatus determine an antialiased intensity of a component of a pixel. A set of objects is represented by a set of two-dimensional distance fields. For each distance field, a corresponding set of sample points is associated with the component and a corresponding distance is determined using the corresponding set of sample points. The corresponding distances are combined to determine a combined distance that is mapped to the antialiased intensity of the component of the pixel.

Abstract: A method generates a two-dimensional distance field within a cell associated with a corner of a two-dimensional object. A set of boundary descriptors for the two-dimensional object is determined. A corner point in the cell is identified from the set of boundary descriptors. The corner point represents the corner of the object. The corner point partitions the set of boundary descriptors into two subsets. The cell is partitioned into two regions where one region is closest to the corner point and the other region is closest to the set of boundary descriptors. Two lines passing through the corner point are determined such that each line corresponds to one of the two subsets of boundary descriptors. These lines delimit the two regions. A set of values and a method using the two regions are specified for reconstructing the distance field within the cell.

Abstract: A method, apparatus, and system for rendering are disclosed. A rendering request is defined, where the rendering request describes an object to be rendered. A progressive cache is queried to determine a cached element most representing a display image satisfying the rendering request. The cached element is sent to a starting stage of a rendering pipeline for the object, where the starting stage is associated with the cached element. An output of the starting stage is sent to an input of a next stage of the rendering pipeline. A final stage of the rendering pipeline determines the display image satisfying the rendering request.

Abstract: A method generates a distance field for a region of a shape descriptor representing an object. The distance field includes a set of cells for which cell types are defined. A configuration of a set of cells for the region is generated. Each cell of the configuration includes a cell type and a method for reconstructing the distance field within the cell. The configuration of the set of cells is modified until an optimal configuration is reached. The modification is based on the shape descriptor, the region, and the set of cell types. The optimal configuration of the set of cells is stored in a memory to generate the distance field for the region. Another method generates a two-dimensional distance field within a cell associated with a two-dimensional object. A set of boundary descriptors for the two-dimensional object is determined and partitioned into a set of segments. The segments are delimited by a set of features of the boundary descriptors.

Abstract: A method and apparatus antialias a region of a two-dimensional distance field representing an object. The two-dimensional distance field is partitioned into cells where each cell includes a method for reconstructing the two-dimensional distance field within the cell. A set of cells of the two-dimensional distance field associated with the region is identified and a set of pixels associated with the region is located. For each pixel, a set of components is specified. For each component, a distance is determined from the set of cells and then mapped to the antialiased intensity of the component of the pixel.

Abstract: A method converts a two-dimensional distance field to a set of boundary descriptors. An iso-contour of the two-dimensional distance field is selected. An ordered list of points is generated from the iso-contour and the two-dimensional distance field. A set of boundary descriptors is initialized to fit the ordered list of points. The set of boundary descriptors is updated by determining an error for each boundary descriptor using the two-dimensional distance field and refining the set of boundary descriptors based on the error for each boundary descriptor.

Abstract: A method generates a two-dimensional distance field from a pen stroke. A pen state is sampled during the pen stroke to generate an ordered list of pen states along the pen stroke. The pen state includes a location of the pen stroke. A set of boundary descriptors is generated from the ordered list of pen states. The two-dimensional distance field is generated from the set of boundary descriptors.

Abstract: A method and apparatus render a region of a distance field representing an object. The distance field is partitioned into a set of cells, where each cell includes a set of distance samples and a method for reconstructing the distance field within the cell using the distance samples. A set of source cells is selected from the set of cells of the distance field to enable the rendering of the region. Each source cell is represented as a geometric element in a world coordinate system. Each geometric element is associated with a texture map, where the texture map includes distance samples of the corresponding source cell of the geometric element. Each geometric element is transformed from the world coordinate system to a pixel coordinate system and texture mapped, using the distance samples, to determine a distance for each component of each pixel associated with the geometric element. The distance of each component of each pixel is mapped to an antialiased intensity of the component of the pixel.

Abstract: A method animates an object as a sequence of frames according to an animation script. The object is represented as a two-dimensional distance field. For each frame in the sequence of frames, a pose of the object is updated according to the animation script. The object is rendered using the updated pose and an antialiasing rendering method.

Abstract: A method renders a region of a composite glyph. The composite glyph is defined by a set of elements. A set of two-dimensional distance fields is generated using the set of elements, where a composition of the set of two-dimensional distance fields represents the composite glyph. The region of the composite glyph is then rendered using the set of two-dimensional distance fields.

Abstract: A method converts a two-dimensional object to a two-dimensional distance field. The object is represented as a set of boundary descriptors and a fill rule. The set of boundary descriptors is preprocessed and a spatial hierarchy is constructed from the preprocessed set of boundary descriptors. A cache of intersections is initialized. The spatial hierarchy is queried at a set of locations to determine a set of distances at the locations. The query invokes a distance function at each location to determine an unsigned distance. A sign of the unsigned distance is determined from the cache of intersections, the location, and the fill rule. The set of distances is used to construct the two-dimensional distance field.

Abstract: A method renders a region of a composite glyph. The composite glyph is defined by a set of elements. A set of two-dimensional distance fields is generated using the set of elements, where each two-dimensional distance field is partitioned into cells and each cell includes a method for reconstructing the corresponding two-dimensional distance field within the cell. A composition of the set of two-dimensional distance fields represents the composite glyph. The region of the composite glyph is then rendered using the set of two-dimensional distance fields.

Abstract: A method and apparatus antialias a region of a set of objects. The set of objects is represented by a set of two-dimensional distance fields. Each distance field is partitioned into cells, where each cell is associated with a method for reconstructing the distance field within the cell. For each distance field, a set of cells associated with the region is identified. A set of pixels associated with the region is located and a set of components is specified for each pixel. For each component of each pixel, a corresponding distance for the component is determined for each distance field using the corresponding set of cells and the corresponding distances are combined to determine a combined distance. The combined distance is mapped to an antialiased intensity of the component of the pixel.

Abstract: A method generates a textured range image by first acquiring a first image of a scene illuminated with ambient light, and acquiring a second image of the scene illuminated with direct light. The first and second images are combined to determine the textured range image.

Abstract: A method edits a graphics object by first representing the graphics object by an adaptively sampled distance field. A portion of the adaptively sampled distance field is selected for editing and converted to a triangle model. The triangle model is then deformed, the adaptively sampled distance field is regenerated from the deformed triangle model.