Abstract: A system, method, and computer program product are provided for generating display data. The data processing system loads coefficient values corresponding to a behavior of a selected function in pre-defined ranges of input data. The data processing system then determines, responsive to items of input data, the range of input data in which the selected function is to be estimated. The data processing system then selects, through the use of a vector permute function, the coefficient values, and evaluates an index function at the each of the items of input data. It then estimates the value of the selected function through parallel mathematical operations on the items of input data, the selected coefficient values, and the values of the index function, and, responsive to the one or more values of the selected function, generates display data.

Abstract: The present invention renders a triangular mesh for employment in graphical displays. The triangular mesh comprises triangle-shaped graphics primitives. The triangle-shaped graphics primitives represent a subdivided triangular shape. Each triangle-shaped graphics primitive shares defined vertices with adjoining triangle-shaped graphics primitives. These shared vertices are transmitted and employed for the rendering of the triangle-shaped graphics primitives.

Abstract: A system, method, and computer program product are provided for generating display data. The data processing system loads coefficient values corresponding to a behavior of a selected function in pre-defined ranges of input data. The data processing system then determines, responsive to items of input data, the range of input data in which the selected function is to be estimated. The data processing system then selects, through the use of a vector permute function, the coefficient values, and evaluates an index function at the each of the items of input data. It then estimates the value of the selected function through parallel mathematical operations on the items of input data, the selected coefficient values, and the values of the index function, and, responsive to the one or more values of the selected function, generates display data.

Abstract: A method and apparatus in a data processing system for processing perspective transformations. An estimate of a depth coordinate is obtained. A determination is made as to whether the estimate is sufficiently accurate for the perspective transformation. An algebraic operation is performed on the estimate if the estimate is insufficiently accurate for the perspective transformation, wherein the algebraic operation increases the accuracy of the estimate.

Abstract: A method, system, and computer program product for reducing a boundary of a subspace in a binary space partitioning tree is provided. In one embodiment a space containing an object for which an image is to be rendered and displayed to a user is divided into subspaces. The boundaries of each subspace are recalculated to remove at least a portion of the dead space from within the subspace. The recalculation is performed by analyzing the spatial extent of the object or objects within the each subspace and recalculating the boundaries of each subspace to be coextensive with the boundaries of the object or objects within the subspace.

Abstract: A method, system, and program product for creating a child node of a binary space partitioning (BSP) tree node that better approximates the size of an object to be rendered is provided. In one embodiment, a a binary space partitioning tree is created. A rendering process then determines whether either a top node or a child node in a first level of child nodes is a good approximation of the object to be rendered. If not, then the rendering process modifies the binary space partitioning tree to include a new child node having boundaries that are closer to the maximum coordinates of primitives defining the object than are the boundaries of the top node or of the child nodes in the first level of child nodes. This new child node may have a bounding volume that overlaps the bounding volumes of other child nodes in the BSP tree.

Abstract: An apparatus and method for three-dimensional graphic rendering are implemented. For each vertex on a surface of a graphic to be rendered, the scalar product of the unit normal to the surface and a half vector (the vector bisecting an angle between a unit vector in a direction of observation, the “eye” vector and a unit vector in a direction of a light source, the “light vector”), is generated outside of a graphics engine. Additionally, a second scalar product, between the unit normal and the unit vector in the direction of the light source is generated. These scalar products are loaded into two predetermined components of the unit normal, and sent to the graphics engine in lieu of the corresponding values of the components of the unit normal. In the graphics engine, components of the light vector and the half vector are assigned respective predetermined values, wherein the calculation of the two scalar products by the graphics engine produces the correct results.

Abstract: A method, system, and computer program product for reducing a boundary of a subspace in a binary space partitioning tree is provided. In one embodiment a space containing an object for which an image is to be rendered and displayed to a user is divided into subspaces. The boundaries of each subspace are recalculated to remove at least a portion of the dead space from within the subspace. The recalculation is performed by analyzing the spatial extent of the object or objects within the each subspace and recalculating the boundaries of each subspace to be coextensive with the boundaries of the object or objects within the subspace.

Abstract: A method, system, and program product for creating a child node of a binary space partitioning (BSP) tree node that better approximates the size of an object to be rendered is provided. In one embodiment, a a binary space partitioning tree is created. A rendering process then determines whether either a top node or a child node in a first level of child nodes is a good approximation of the object to be rendered. If not, then the rendering process modifies the binary space partitioning tree to include a new child node having boundaries that are closer to the maximum coordinates of primitives defining the object than are the boundaries of the top node or of the child nodes in the first level of child nodes. This new child node may have a bounding volume that overlaps the bounding volumes of other child nodes in the BSP tree.

Abstract: A method of and system for testing a graphic primitive for trivial acceptance or rejection. An initial bounding volume, such as a rectangular parallelepiped, is defined by the graphic primitive's maximum and minimum x, y, and z coordinates in an initial coordinate system. A first bounding volume is then defined by the graphic primitive's maximum and minimum x′, y′, and z′ coordinates in a first coordinate system, where the first coordinate system is transformed with respect to the initial coordinate system. Preferably this transformation comprises a 45° rotation about a common axis such as the z-axis. The initial bounding volume and the first bounding volume are then intersected to form a modified bounding volume. The vertices of the modified bounding volume are then available for use in determining whether the graphic primitive may be trivially rejected or accepted within a specified viewing volume.

Abstract: A method and means are provided for utilizing, in a color imaging environment, such as ray tracing, display adapter hardware which is capable of interpolating color values for pixels lying in an area between previously color imaged pixels. A computer system CPU performs ray tracing calculations, or the like for a predetermined number of the total pixels, rather then each pixel, as is the case with conventional ray trace image systems. The system CPU then turns over the color imaged pixels to a display adapter, capable of color interpolating therebetween. In this way, previously idle display adapter hardware can be utilized to determine pixel color values and allow the system CPU to continue color imaging other more critical areas of a scene to be displayed. Therefore, an image can be rendered at a much faster rate than possible with conventional systems, with relatively no visible loss in quality.

Abstract: A method and means are provided for utilizing, in a color imaging environment, such as ray tracing, display adapter hardware which is capable of interpolating color values for pixels lying in an area between previously color imaged pixels. A computer system CPU performs ray tracing calculations, or the like for a predetermined number of the total pixels, rather then each pixel, as is the case with conventional ray trace image systems. The system CPU then turns over the color imaged pixels to a display adapter, capable of color interpolating therebetween. Additionally, a prioritization scheme is provided which allows a graphics system user to assign priority values to particular areas or objects included in a scene description. In this way, the areas having higher priority values are subject to a greater concentration of ray tracing operations, thereby allowing these object to be displayed at a much faster rate.