Presents a method for the construction of multiple levels of tetrahedral meshes approximating a trivariate scalar-valued function at different levels of detail. Starting with an initial, high-resolution triangulation of a 3D region, we construct coarser representation levels by collapsing edges of the mesh. Each triangulation defines a linear spline function, where the function values associated with the vertices are the spline coefficients. Error bounds are stored for individual tetrahedra and are updated as the mesh is simplified. Two algorithms are presented that simplify the mesh within prescribed error bounds. Each algorithm treats simplification on the mesh boundary. The result is a hierarchical data description that is suited for the efficient visualization of large data sets at varying levels of detail.

We present a method for the construction of multiple levels of tetrahedral meshes approximating a trivariate function at different levels of detail. Starting with an initial, high-resolution triangulation of a three-dimensional region, we construct coarser representation levels by collapsing tetrahedra. Each triangulation defines a linear spline function, where the function values associated with the vertices are the spline coefficients. Based on predicted errors, we collapse tetrahedron in the grid that do not cause the maximum error to exceed a use-specified threshold. Bounds are stored for individual tetrahedra and are updated as the mesh is simplified. We continue the simplification process until a certain error is reached. The result is a hierarchical data description suited for the efficient visualization of large data sets at varying levels of detail.

We present a method to produce a hierarchy of triangle meshes that can be used to blend different levels of detail in a smooth fashion. The algorithm produces a sequence of meshes M/sub 0/, M/sub 1/, M/sub 2/..., M/sub n/, where each mesh M/sub i/ can be transformed to mesh M/sub i+1/ through a set of triangle-collapse operations. For each triangle, a function is generated that approximates the underlying surface in the area of the triangle, and this function serves as a basis for assigning a weight to the triangle in the ordering operation and for supplying the points to which the triangles are collapsed. The algorithm produces a limited number of intermediate meshes by selecting, at each step, a number of triangles that can be collapsed simultaneously. This technique allows us to view a triangulated surface model at varying levels of detail while insuring that the simplified mesh approximates the original surface well.

Presents a new method to produce a hierarchical set of triangle meshes that can be used to blend different levels of detail in a smooth fashion. The algorithm produces a sequence of meshes /spl Mscr//sub 0/, /spl Mscr//sub 1/, /spl Mscr//sub 2/..., /spl Mscr//sub n/, where each mesh /spl Mscr//sub i/ can be transformed to mesh /spl Mscr//sub i+1/ through a set of triangle-collapse operations. For each triangle, a function is generated that approximates the underlying surface in the area of the triangle, and this function serves as a basis for assigning a weight to the triangle in the ordering operation, and for supplying the point to which the triangles are collapsed. This technique allows us to view a triangulated surface model at varying levels of detail while insuring that the simplified mesh approximates the original surface well.

Given a three dimensional (3D) array of function values F/sub i,j,k/ on a rectilinear grid, the marching cubes (MC) method is the most common technique used for computing a surface triangulation T approximating a contour (isosurface) F(x, y, z)=T. We describe the construction of a C/sup 0/ continuous surface consisting of rational quadratic surface patches interpolating the triangles in T. We determine the Bezier control points of a single rational quadratic surface patch based on the coordinates of the vertices of the underlying triangle and the gradients and Hessians associated with the vertices.