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 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 optimizes a system. Performances of design parameters of an objective function modeling the system are represented in a multi-dimensional search space. A set of vertices are positioned in the search space. Each vertex has an associated one of the performances. The vertices in the set are sorted in a worst to best performance order. Each vertex in the ordered set is moved to a next position if the performance at the next position is better than a current performance of the vertex. The sorting and moving are repeated in a cycle until a termination condition is reached.

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.

Abstract: A system interactively edits a graphics object. The system includes a user interface for setting editing parameters, and providing a model of the graphics object. An adaptively sample distance field is generated from the model, and an interactive editor manipulates the adaptively sampled distance field. The manipulated adaptively sampled distance field is then converted to rendering primitives to be rendered by a rendering engine.

Abstract: A method, using a filter function, generates an anti-aliased discrete image from a continuous image including an edge. The method defines a line sample. A progressive convolution is derived from the filter function and the line sample. A pixel at a predetermined location in the discrete image is selected, and the line sample is oriented with respect to the selected pixel. A distance is measured from a point in the continuous image corresponding to the selected pixel to the edge along the oriented the line sample. The progressive convolution is evaluated at the measured distance to produce a weighted coverage value, and the weighted coverage value is associated with the pixel to anti-alias the pixel in the discrete image.

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: In a server-client web-enabled networked computing system including a database containing eyeglass frame image information for a plurality of eyeglass frames, a system and method allows for a customer to virtually try on eyeglass frames by enabling a computer system to provide an esthetically realistic rendition of the customer wearing the eyeglass frames through virtual digital imaging means for display on the customer's computer so the customer can view his/herself in the selected eyeglass frames. An eye-care professional first visits a customer at a customer location to obtain all necessary measurements and account creation data. Subsequently, the user may access the virtual try-on system. A utility enabling side-by-side comparison permits the customer to view side-by-side displays of the customer virtually fitted with esthetically realistic images of eyeglass frames to aid in choosing a preferred eyeglass frames for purchase.

Abstract: A method edits a surface of a graphics object with a computer implemented tool by first generating an adaptively sampled distance field from the graphics object, and defining a tool path. A gradient for each point on the surface nearest to each location of the tool on the tool path is determined, as well as the distance between each point and each location. The tool is iteratively moved along the tool path in a direction of the gradient and an amount proportional to the distance to maintain the tool on the surface of the object while editing the surface of the object.

Abstract: A method dynamically generates rendering elements for a graphics model. The model is first converted to an adaptively sampled distance field including surface cells representing a surface of the model. A visibility element is determined for each surface cell. A set of active cells is determined, where each active cell is associated with one of the surface cells of the adaptively sample distance field, and each active cell has a corresponding visibility element. Rendering elements are determined for each active cell. Active cells are added and deleted from the set of active cells dynamically according to a weight determined for each active cell by a weighting function. The weight of each active cell can depend on viewing and shading parameters. Rendering elements are dynamically generated when active cells are added to the set of active cells and dynamically deleted when active cells are deleted from the set of active cells.

Abstract: A method determines a distance from a 3D point to a 3D surface from a 2D projected range image. A projected distance and a cliff distance from the 3D point to the 3D surface are determined using the projected range image. The projected distance and the cliff distance are then combined to determine the distance from the 3D point to the 3D surface.

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 camera generates a textured range image. The camera includes a single lens, and a flash substantially co-located with the lens. The camera acquires a first image of a scene from a point of view with ambient light, and a second image of the scene from the point of view with direct light of the flash. The first image and the seconds image are then combined by a divider to generate the textured range image.

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 for modeling a graphics object generates a model of the graphics object. An adaptively sampled distance field is generated from the model according to an error measure. The adaptively sampled distance field includes interior, surface, and exterior cells. Each cell stores distance values, and the distance values of the surface cells always satisfy the error measure. A subset of cells are selected from the adaptively sampled distance field. The subset of cells only include interior and exterior cells. The selected cells are subdivided and the distance values for the subdivided cells are regenerated, until the distance values of the subdivided cells satisfy the error measure.

Abstract: A method edits a graphics object with a computer implemented tool by first representing the graphics object by an adaptively sampled distance field, and defining a mask by a distance field. Then, the tool is iteratively moved with respect to the object while constraining the movement according to the mask to edit the object.

Abstract: A method sculpts an object expressed as a model. A hierarchical distance field is generated from the model according to generation parameters. The hierarchical distance field is edited according to editing parameters, and the hierarchical distance field is rendered while editing. To generate the hierarchical distance field, the object distance field is enclosed with an object bounding box. The enclosed object distance field is partitioned into a plurality of cells. Each cell has a size corresponding to detail of the object distance field and a location with respect to the object bounding box. A set of values of the enclosed object distance field is sampled for each cell. A method for reconstructing the portion of the distance field enclosed by the cell is specified for each cell.

Abstract: A method memoizes a computation as follows. A set of input parameters is provided to the computation. A determination is made to see whether a memo contains results of the computation on sets of memoized parameters near the set of input parameters. If true, the computation for the set of input parameters is reconstructed using the results of the computations on the sets of memoized parameters near the set of input parameters. If false, the computation is performed using the set of input parameters. A result of the computation on the set of input parameters is then memoized, and that result is provided as output of the computation.

Abstract: A method optimizes a system. Performances of a plurality of design parameters of an objective function modeling the system are represented in a search space. A set of vertices are positioned in the search space, and each vertex has an associated performance. The model also includes a plurality of constraints. The constraints and the objective function are grouped according to a plurality of unique hierarchical levels. The group including the objective function has a highest level. The performance of a particular vertex is evaluated, in a low to high order of the levels, according to the groupings of the constraints and the objective function. The evaluated performance and the associated level is assigned to the particular vertex as soon as the evaluated performance is negative, unless the associated level is the highest level, in which case the assigned performance is evaluated from the objective function to partition the search space into a plurality of partitions according to the levels.

Abstract: An image processing system enables the manipulation of individual anonymous laser pointers in interactive visual games. The system includes a display system that displays an image on a display screen. A camera acquires a sequence of images of the display screen. Participants in the game aim individual laser pointers at the screen; the laser pointers form dots on the display screen. A warp module corrects the acquired images for distortion. A registration module registers the corrected sequence of images with the displayed image, and modifies the displayed image in response to a distribution of the laser dots on the display screen.