Abstract: A method for calculating density maps in hierarchical designs includes the steps of deoverlapping objects in the design, providing an area of interest in the design, generating a grid in the area of interest to partition the area of interest into grid elements, determining whether the local properties of each object within the grid elements have been previously calculated, if previously calculated, adding the previously calculated value for the local properties to a corresponding grid element, otherwise, calculating the local properties of the object and summing the local properties of the objects for each associated grid element such that the local properties are calculated only once for a given object throughout the design. A system is also includes for implementing the method.

Abstract: Disclosed are methods and apparatus for fabricating a three-dimensional object in accordance with a computer-generated definition of the object that is stored within a memory. A method includes the steps of (a) evaluating the stored definition of the object to locate any un-supported features of the object; in response to locating an un-supported feature, (b) defining a support structure for the un-supported feature; (c) generating a fabrication tool movement list expressive of movements required by a fabrication tool to fabricate the object and any defined support structures; and (d) translating the fabrication tool in accordance with the generated fabrication tool movement list to fabricate the object and any defined support structures.

Abstract: Apparatus and method for fabricating a three-dimensional object in accordance with a CAD-generated specification of the object. A closed-loop extrusion system (10) includes a nozzle (12) for extruding a material, such as a hot melt adhesive; apparatus (14, 18, 46) for controllably positioning the nozzle in accordance with the specification; and a sensor (60) for generating a feedback signal that is indicative of at least one characteristic of a most recently extruded portion of the material. Visual and non-visual feedback sensors may be employed, including optical sensors, infrared emission sensors, and proximity detection sensors. The specification of the object is converted to a bit-mapped representation thereof to improve accuracy relative to vector-based representations. Methods for determining a need for supporting structures and anti-aliasing features and for integrating the structures and features into the object specification are also disclosed.

Abstract: The lines representing each edge of each face of each object of a model for producing a multiple object image are segmented at line of sight intersections with other lines representing contour edges of visible faces. Each resulting edge line segment is checked against all visible faces to determine which are visible and which are invisible, and information on visibility is stored together with detailed information on each edge line segment for each object. The model is modified by changing the number of component objects and after each change checking the edge line segments for visibility only with respect to the changes associated with the changed component objects. This results in a substantial reduction in the required number of comparisons between segments and faces as compared to prior methods.