A quadric error metric is provided that allows fast and accurate geometric simplification of meshes having attribute values. In particular, the quadric error metric is used to determine the position of a new vertex created during an edge collapse, and the order in which edges are collapsed. In addition, the quadric error metric handles meshes with appearance attributes at their vertices, such as normals, colors, and texture coordinates. Thus, the quadric error metric can be used to simultaneously determine both the geometric position of a new vertex and the values of the appearance attributes associated with the new vertex.

A mesh generating method for numerical simulation of one (1) piece of an analysis target, in a short time period, where there are plural numbers of high-density configuration data, each presenting a configuration surface thereof said one (1) piece of analysis target, including the performing of a plurality of sub-steps until when none of the plural numbers of configuration mesh data remains, and mesh data for numerical simulation is generated from the final combined low-density configuration mesh data.

The invention provides a method for integrating an inset geometry within a background geometry. The method comprises the step of identifying a perimeter of the inset geometry. A further step is extending a skirt, having an outer perimeter and an inner perimeter, from the perimeter of the inset geometry out over the background geometry. An additional step is removing portions of the background geometry that are covered by the inset geometry and skirt. Another step is modifying the skirt so that the outer perimeter of the skirt matches background geometry behavior and the inner perimeter matches inset geometry behavior and a continuous transition exists between the outer perimeter and the inner perimeter.

A fast, texture morphing algorithm for real-time computer simulation and video games dynamically generates objects "on the fly" by simplifying and reducing the computational load required for a texture morphing/blending process. Incremental interpolation techniques compute a morph parameter based on previous value and morph change rate. Precomputed initial and incremental morph parameter values for each texel component are applied during real-time morphing procedures using integer arithmetic. Approximation errors are reduced by incrementing/decrementing by an extra integer value when the number of morph iterations is a multiple of a frame counter. The frame counter avoids over-runs, and the morphing procedure is "snapped" the texel value to the precise texture target value to prevent under-runs and corresponding artifacts. Interlacing (applying interpolation to a subset of the texels each frame) significantly reduces computational load without introducing significant image artifacts. The morph texture buffer data structure is initially decomposed off-line to reduce the number of real-time calculations required to manipulate texel component data.

A mill roll analysis system is described that includes a user interface module, a structural analysis engine, and an analysis control script. The user interface module receives mill roll design data from a remote user via a computer network. The analysis control script automatically directs the structural analysis engine to define and evaluate an appropriate analytical model for the mill roll design based on the mill roll design data. The mill roll analysis system presents an intuitive web-based interface for capturing the mill roll design data, and may present predefined mill roll applications and mill roll types for selection for the user. As a result, the remote user need not be familiar with the underlying analytical modeling techniques, which may be highly-complex by nature. Consequently, a user may utilize the system to evaluate and improve mill roll design in order to achieve increased product performance.