Chandrajit L. Bajaj

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We present an isocontouringalgorithm which is near-optimal for real-time interaction and modification of isovalues in large datasets. A preprocessing step selects a subset of the cells which are considered as seed cells. Given a particular isovalue, all cells in which intersect the given isocontour are extracted using a high-performance range search. Each(More)
AJ1STRACT In this paper we apply Galois theoretic algebraic methods to certain fundamental geometric optimization problems whose recognition versions are not even known to be in the class NP. In particular we show that the classic Weber problem, the Line-restricted' Weber probe lem and the 3-Dimension version of this problem are in general not solvable by(More)
In computed tomography, magnetic resonance imaging and ultrasound imaging, reconstruction of the 3D object from the 2D scalar-valued slices obtained by the imaging system is di cult because of the large spacings between the 2D slices. The aliasing that results from this undersampling in the direction orthogonal to the slices leads to two problems known as(More)
We introduce the contour spectrllm, a user interface component that improves qualitative user interaction and provides real-time exad quantification in the visualization of isoconlours. The contour spectrum is a signature consisting of a variety of scalar data and conlour attributes, computed over the range of scalar values wE!R. We explore the use of(More)
Polygonal meshes have been used as the primary geometric model representation for networked gaming and for complex interactive design in manufacturing. Accurate polygonal mesh approximation of a surface with sharp features (holes, highly varying curvatures) requires extremely large number of triangles. Transmission of such large triangle meshes is critical(More)
We present a unified anisotropic geometric diffusion PDE model for smoothing (fairing) out noise both in triangulated two-manifold surface meshes in <i>IR</i><sup>3</sup> and functions defined on these surface meshes, while enhancing curve features on both by careful choice of an anisotropic diffusion tensor. We combine the <i>C</i><sup>1</sup> limit(More)
Many approaches to simpliication of triangulated terrains and surfaces have been proposed which permit bounds on the error introduced. A few algorithms additionally bound errors in auxiliary functions deened over the triangulation. We present an approach to simpliication of scalar elds over unstructured grids which preserves the topology of functions deened(More)
We present an efficient and uniform approach for the automatic reconstruction of surfaces of CAD (computer aided design) models and scalar fields defined on them, from an unorganized collection of scanned point data. A possible application is the rapid computer model reconstruction of an existing part or prototype from a three dimensional (3D) points scan(More)