I propose a new equation to estimate the normal at a vertex of a polygonal approximation to a smooth surface, as a weighted sum of the normals to the facets surrounding the vertex. It accounts for the difference in size of these facets by assigning larger weights for smaller facets. When tested on random cubic polynomial surfaces, it is superior to other popular weighting methods.

A computer animated movie was produced, illusrrating both 20 and 30 Hilbert curves, and showing the transition from 20 to 30 with the help of volume rendering.

This paper enhances the voxel-to-voxel radiance shooting, propagation, and scattering algorithm of Max [20]. It reduces the memory requirements by storing the radiance only on the occupied cells of a sparse voxel octree and by sampling only 24 propagation direction bins instead of 96 or more. It gives a modification of the propagation algorithm to compensate for the larger solid angle of the direction bins and allows for position-dependent fully anisotropic scattering. For a volume of n3 voxels, the computation time is O(n3(logn)3/2).

This paper presents an efficient algorithm for filtering multi-layer depth images (MDIs) in order to produce approximate penumbras. The filtering is performed on a MDI that represents the view from the light source. The algorithm is based upon both ray tracing and the z-buffer shadow algorithm, and is closely related to convolution methods. The method's effectiveness is demonstrated on especially complex objects such as trees, whose soft shadows are expensive to compute by other methods. The method specifically addresses the problem of light-leaking that occurs when tracing rays through discrete representations, and the inability of convolution methods to produce accurate self-shadowing effects.

Selective visualization is a solution for visualizing data of large size and dimensionality. In this paper a new method is proposed for effectively rendering certain chosen parts among the full set of data in terms of a colour buffer, referred to as the virtual plane, for storing intermediate results. By this method, scientists may concentrate their attention on the contents of data in which they are interested. Besides, the method could be easily integrated with all the current direct volume rendering techniques, especially progressive refinement methods and selective methods.

This paper describes a volume rendering system for unstructured data, especially finite element data, that creates images with very high accuracy. The system will currently handle meshes whose cells are either linear or quadratic tetrahedra. Compromises or approximations are not introduced for the sake of efficiency. Whenever possible, exact mathematical solutions for the radiance integrals involved and for interpolation are used. The system will also handle meshes with mixed cell types: tetrahedra, bricks, prisms, wedges, and pyramids, but not with high accuracy. Accurate semitransparent shaded isosurfaces may be embedded in the volume rendering. For very small cells, subpixel accumulation by splatting is used to avoid sampling error. A revision to an existing accurate visibility ordering algorithm is described, which includes a correction and a method for dramatically increasing its efficiency. Finally, hardware assisted projection and compositing are extended from tetrahedra to arbitrary convex polyhe

A hardware polygon rendering pipeline can be used with hardware compositing to volume render arbitrary unstructured grids composed of convex polyhedral cells. This technique is described, together with the global sorting necessary for back-to-front compositing, and the modifications that must be made to approximate curvilinear cells, whose faces may not be planar.

We present an adaptive signed distance transform algorithm for curves in the plane. A hierarchy of bounding boxes is required for the input curves. We demonstrate the algorithm on the isocontours of a turbulence simulation. The algorithm provides guaranteed error bounds with a selective refinement approach. The domain over which the signed distance function is desired is adaptively triangulated and piecewise discontinuous linear approximations are constructed within each triangle. The resulting transform performs work only where requested and does not rely on a preset sampling rate or other constraints.