Abstract: Various systems, methods, and computing units are provided for reduced cost evaluation of Boolean expressions. In one representative embodiment, a method includes: determining a first modified cost measure for a node of a binary tree, the first modified cost measure comprising M cost values, the node in an original condition; pivoting the node; determining a second modified cost measure for the node in a pivoted condition, the second modified cost measure comprising M cost values; and determining a preferred node condition responsive to a comparison of the first and second cost measures.

Abstract: Various systems, methods, and computing units are provided for reduced cost evaluation of Boolean expressions. In one representative embodiment, a method includes: determining a first modified cost measure for a node of a binary tree, the first modified cost measure comprising M cost values, the node in an original condition; pivoting the node; determining a second modified cost measure for the node in a pivoted condition, the second modified cost measure comprising M cost values; and determining a preferred node condition responsive to a comparison of the first and second cost measures.

Abstract: A system and method for controlling the surface and/or volume of a digital clay device is provided. One embodiment, among others, is a method comprising the following steps: determining a desired position of a skeleton structure portion residing in the digital clay device, determining a volumetric change of fluid residing in a fluid cell, the determined volumetric change corresponding to the determined desired position of the skeleton structure portion, opening a valve so that the fluid flows through the valve thereby causing the determined volumetric change of the fluid, and adjusting a position of the skeleton structure portion corresponding to the desired position of the skeleton structure portion, the position adjustment caused by a force generated by the fluid cell on the skeleton structure portion when the volume of the fluid cell changes in response to the determined volumetric change of the fluid residing in the fluid cell.

Abstract: A system and method for controlling the surface and/or volume of a digital clay device is provided. One embodiment, among others, is a method comprising the following steps: determining a desired position of a skeleton structure portion residing in the digital clay device, determining a volumetric change of fluid residing in a bladder, the determined volumetric change corresponding to the determined desired position of the skeleton structure portion, opening a micro-electro mechanical systems (MEMS) valve so that the fluid flows through the MEMS valve thereby causing the determined volumetric change of the fluid, and adjusting a position of the skeleton structure portion corresponding to the desired position of the skeleton structure portion, the position adjustment caused by a force generated by the bladder on the skeleton structure portion when the volume of the bladder changes in response to the determined volumetric change.

Abstract: A system and method for controlling the surface and/or volume of a digital clay device is provided. One embodiment, among others, is a method comprising the following steps: determining a desired position of a skeleton structure portion residing in the digital clay device, determining a volumetric change of fluid residing in a bladder, the determined volumetric change corresponding to the determined desired position of the skeleton structure portion, opening a micro-electro mechanical systems (MEMS) valve so that the fluid flows through the MEMS valve thereby causing the determined volumetric change of the fluid, and adjusting a position of the skeleton structure portion corresponding to the desired position of the skeleton structure portion, the position adjustment caused by a force generated by the bladder on the skeleton structure portion when the volume of the bladder changes in response to the determined volumetric change.

Abstract: A method for execution by a data processor that prepares an object for display. The method includes a step of processing a first model of the object so as to produce a simplified model thereof, the step of processing including the steps of (a) superimposing a first plurality of grid cells on the first model; for any one of the first plurality of grid cells containing more than one vertex of the first model, (b) combining the vertices into a first representative vertex; (c) generating a first simplified model that includes the first representative vertex or first representative vertices; and (d) storing the first simplified model for subsequent use. The method encompasses a number of criteria for use by the step of combining the vertices within a grid cell.

Abstract: Apparatus and method for generating displayable information expressive of a three dimensional solid object. The apparatus includes a processor (12,16) for expressing the object in a Constructive Solid Geometry representation thereof so as to be comprised of one or more primitive objects. The apparatus further includes a processor (18, 20) for repetitively evaluating the one or more primitive objects to determine displayable faces thereof. A depth interval buffer (20) is responsive to the operation of a scan conversion processor (18) for detecting when a predetermined number of repetitive evaluations occur without causing a change in the determination of a displayable face and for causing the operation of the evaluation processor to terminate. Toleranced depth tests are used to remove dangling faces or edges and to properly handle coincident faces. Pixel-centering is employed to improve the accuracy of depth tests and to identify pixels upon which a product projects.

Abstract: A first method for producing wire-frame images of tessellated objects in real time utilizing existing hardware capabilities removes hidden lines by displaying the frame slightly away from the actual edges and toward the viewing direction to ensure the portion of the frame intended to be visible is not obscured by the visible faces and that the hidden portion of the frame is obscured by the visible faces. A second method allows for visible and hidden lines to be shown in unique line styles. This is done by first displaying all lines in the hidden line style while suppressing the faces. Then, the first method is performed and the lines that are visible lines are overwritten in another line style. A third method shows only visible silhouette and intersection edges. The visible silhouette edges are obtained by displaying the frame in thick lines behind the visible faces. Then, intersection edges are displayed in front of the faces so that only visible ones can be seen.

Abstract: A system and method is provided for displaying trimmed surfaces on a computer graphics system. The present invention tessellates a three-dimensional surface into triangles and determines whether a trimming curve intersects any triangles. If an intersection occurs, a polygon trimming mask is formed by performing an exclusive OR operation and rendering the polygon into a mask plane. The XOR operation sets the bits in the mask plane corresponding to the trimming mask to logical 1. The rendering hardware then compares the bits in the mask plane with the bits in the frame buffer and draws those pixels which correspond to the bits set to 1 in the mask plane. Since, the trimming mask is a polygon the rendering hardware can perform shading, or lighting calculations using values for points which are contained on the tessellated triangle. In this manner, consistent lighting of a trimmed surface can be achieved.

Abstract: A method for constructing the Minkowski sum and derivative morphological combinations of arbitray polyhedra uses operations supported in current CAD/CAM systems. The method has application to three-dimensional modeling of very large scale integrated (VLSI) circuits, their design and simulation of fabrication, and to automated mechanical assembly. The method also has application to n-dimensional modeling in robotics as well as other applications of CAD/CAM systems. In one aspect, an exact Minkowski sum of two polyhedra is obtained by a generalization of sweeping a face along an edge. More generally, according to a second aspect, the Minkowski sum of two polyhedra is computed as the union of linear translational sweeps enabled by the first aspect. The method implements techniques and formulas which greatly reduces the overall cost of the computation of Minkowski sums and, in particular, avoids computations involving non-transversal polyhedra.

Abstract: A CSG solid modelling system 10 has a triple z-buffer architecture. For each pixel stored in a pixel memory 12 there are five storage entries grouped into five buffers including a front z-buffer (F) 16 which is employed to store the depths of a front face for a currently processed z-connected product, a back z-buffer (B) 18 which is employed to store the depths of a back face for the currently processed z-connected product and a final z-buffer (Z) 20 which stores the front faces of a displayed solid. Two other buffers are an intensity buffer (T) 22 for storing the intensities associated with the front face of the current z-connected product and a final intensity buffer (I) 24 for storing the intensities of the visible faces of the displayed solid. A bus 26 couples these various buffers together and to a processor 28 which may be a central processing unit or a peripheral processor.