Abstract: A method and system renders a 3D model of a 3D object as an image including image samples. The 3D model is a distance field, and the distance field includes surface cells representing portions of a surface of the 3D object. A set of image samples in the image is determined in an object-order phase for each surface cell. Each surface cell is then processed independent of other surface cells. The processing casts a ray, in an image order phase from each image sample in the set of image samples, through the surface cell to determine a contribution of the surface cell to the image sample, and then the image is rendered.

Abstract: A method converts an outline character to a stylized stroke character by first identifying regions of the outline character, wherein each region is closed and disjoint. For each region, candidate locations for stroke bodies and terminals of the stylized stroke character are determined. The stroke bodies are then initialized and organized into a hierarchical tree stricture, and modified in an order of the hierarchical tree structure. End positions of the modified stroke bodies are then adjusted to match the outline character, and lastly, the terminals are selected for the adjusted stroke bodies.

Abstract: A method generates a distance field of an object, where the distance field includes a set of cells and the object includes a set of stylized strokes. Each stylized stroke includes a centerline, a set of profiles, and a set of terminals. A processor is included for performing steps of the method. A first cell of the set of cells enclosing the object is determined. An outside reconstruction method is associated with the first cell. For each stylized stroke, centerline cells of the set of cells are determined, where each centerline cell encloses a portion of the centerline of the stylized stroke. A centerline reconstruction method is associated with each centerline cell. For each terminal of each stylized stroke a terminal distance field is generated, the terminal distance field including a terminal reconstruction method. Reconstructed distances are determined using the reconstruction methods to generate the distance field of the object.

Abstract: A method performed on a processor reconstructs a distance field of an object at a sample point, where the object is a swept volume generated by moving a shape along a path. The shape is represented by a shape distance field. The path is represented by a parametric function. Distance data at the sample points is determined, where the distance data characterizes the distance field of the object at the sample point. An optimal set of parameters defining an optimal placement of the shape along the path is determined in a continuous manner. The shape distance field is transformed to the optimal placement to produce a transformed shape distance field. The distance data is determined at the sample point from the transformed shape distance field to reconstruct the distance field at the sample point.

Abstract: Provided is a method performed on a processor for simulating the milling of an object by moving a shape along a path intersecting the object. A composite adaptively sampled distance field (ADF) is generated to represent the object, where the composite ADF includes a set of cells. Each cell in the composite ADF includes a set of distance fields and a procedural reconstruction method for reconstructing the object within the cell. The shape is represented by a shape distance field. The path is represented by a parametric function. A swept volume distance field is defined in a continuous manner to represent a swept volume generated by moving the shape along the path according to a swept volume reconstruction method which reconstructs the swept volume distance field at a sample point. The composite ADF is edited to incorporate the swept volume distance field into the composite ADF to simulate the milling.

Abstract: Provided is a method performed on a processor for simulating the milling of an object by moving a shape along a path intersecting the object. A composite adaptively sampled distance field (ADF) is generated to represent the object, where the composite ADF includes a set of cells. Each cell in the composite ADF includes a set of distance fields and a procedural reconstruction method for reconstructing the object within the cell. The shape is represented by a shape distance field. The path is represented by a parametric function. A swept volume distance field is defined in a continuous manner to represent a swept volume generated by moving the shape along the path according to a swept volume reconstruction method which reconstructs the swept volume distance field at a sample point. The composite ADF is edited to incorporate the swept volume distance field into the composite ADF to simulate the milling.

Abstract: A method performed on a processor reconstructs a distance field of an object at a sample point, where the object is a swept volume generated by moving a shape along a path. The shape is represented by a shape distance field. The path is represented by a parametric function. Distance data at the sample points is determined, where the distance data characterizes the distance field of the object at the sample point. An optimal set of parameters defining an optimal placement of the shape along the path is determined in a continuous manner. The shape distance field is transformed to the optimal placement to produce a transformed shape distance field. The distance data is determined at the sample point from the transformed shape distance field to reconstruct the distance field at the sample point.

Abstract: A method generates a distance field of an object, where the distance field includes a set of cells and the object includes a set of outlines. A processor is included for performing steps of the method. A first cell of the set of cells enclosing the object is determined. An outside reconstruction method is associated with the first cell. A set of boundary cells of the set of cells is determined, where each boundary cell encloses a portion of a particular outline in the set of outlines. A boundary reconstruction method is associated with each boundary cell. A final cell of the set of cells is determined enclosing the object. An inside reconstruction method is associated with the final cell. The outside and boundary reconstruction methods are used to determine combined distances, which are further processed by the inside reconstruction method to generate the distance field of the object.

Abstract: A method generates a distance field of an object, where the distance field includes a set of cells and the object includes a set of stylized strokes. Each stylized stroke includes a centerline, a set of profiles, and a set of terminals. A processor is included for performing steps of the method. A first cell of the set of cells enclosing the object is determined. An outside reconstruction method is associated with the first cell. For each stylized stroke, centerline cells of the set of cells are determined, where each centerline cell encloses a portion of the centerline of the stylized stroke. A centerline reconstruction method is associated with each centerline cell. For each terminal of each stylized stroke a terminal distance field is generated, the terminal distance field including a terminal reconstruction method. Reconstructed distances are determined using the reconstruction methods to generate the distance field of the object.

Abstract: A method generates a distance field of an object, where the distance field includes a set of cells and the object includes a set of outlines. A processor is included for performing steps of the method. A first cell of the set of cells enclosing the object is determined. An outside reconstruction method is associated with the first cell. A set of boundary cells of the set of cells is determined, where each boundary cell encloses a portion of a particular outline in the set of outlines. A boundary reconstruction method is associated with each boundary cell. A final cell of the set of cells is determined enclosing the object. An inside reconstruction method is associated with the final cell. The outside and boundary reconstruction methods are used to determine combined distances, which are further processed by the inside reconstruction method to generate the distance field of the object.

Abstract: A method converts an outline character to a stylized stroke character by first identifying regions of the outline character, wherein each region is closed and disjoint. For each region, candidate locations for stroke bodies and terminals of the stylized stroke character are determined. The stroke bodies are then initialized and organized into a hierarchical tree stricture, and modified in an order of the hierarchical tree structure. End positions of the modified stroke bodies are then adjusted to match the outline character, and lastly, the terminals are selected for the adjusted stroke bodies.

Abstract: A method and system renders a 3D model of a 3D object as an image including image samples. The 3D model is a distance field, and the distance field includes surface cells representing portions of a surface of the 3D object. A set of image samples in the image is determined in an object-order phase for each surface cell. Each surface cell is then processed independent of other surface cells. The processing casts a ray, in an image order phase from each image sample in the set of image samples, through the surface cell to determine a contribution of the surface cell to the image sample, and then the image is rendered.

Abstract: Described is a method for recognizing a shape from a path of a digitizing device. A set of points along a path of the digitizing device is acquired and a parametric representation is fit to the path. The parametric representation is compared to a set of known shapes to determine that the path of the digitizing device represents a particular shape. Fitting the parametric representation to the path includes generating a vector distance field representation of a set of objects corresponding to the set of digitized points, initializing a parametric representation to fit the set of objects, determining a fitting error from the vector distance field representation and adjusting the parametric representation to reduce the fitting error. The fitting error indicates an accuracy of the fit of the parametric representation to the set of objects.

Abstract: Described is a method for sketching with a digitizing device. A set of digitized points along a path of the digitizing device are acquired and a parametric representation is fit to the path. Fitting includes generating a vector distance field representation of a set of objects corresponding to the set of digitized points and initializing a parametric representation for the set of objects. A fitting error indicating an accuracy of the fit of the parametric representation to the set of objects is determined from the vector distance field representation. The parametric representation is adjusted and the fitting error is again determined in an iterative manner until an acceptable fitting error is achieved. The method has numerous technical advantages such as robustness, speed, simplicity relative to standard approaches, and the ability to manage constraints such as maintaining corners and enforcing continuity.

Abstract: Described is a method for fitting a parametric representation to digital data. A vector distance field is generated to represent a set of objects and a parametric representation for the set of objects is initialized. A fitting error is determined from the vector distance field representation. The fitting error indicates the accuracy of the fit of the parametric representation to the set of objects. The parametric representation is adjusted and the fitting error is again determined in an iterative manner until an acceptable fitting error is achieved. The method has numerous technical advantages such as robustness, speed, simplicity relative to standard approaches, and the ability to manage constraints such as maintaining corners and enforcing continuity.

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 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 is described for modeling interactions between models. A first adaptively sampled distance field having a first spatial hierarchy for a first model is generated, and a second adaptively sampled distance field having a second spatial hierarchy for a second model is generated. During each time step, a potential overlap region is determined using the spatial hierarchies of the first and second adaptively sampled distance fields. When the potential overlap region is non-empty, a third adaptively sampled distance field is generated from the first and second adaptively sampled distance fields using a first interaction procedure and first properties and a fourth adaptively sampled distance field is generated from the first and second adaptively distance fields using a second interaction procedure and second properties to model the interactions between the first and second models.

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 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.