Curved screens are increasingly being used for high-resolution immersive visualization enfironments. We describe a new technique to display seamless images using overlapping projectors on curved quadric surfaces such as spherical or cylindrical shape. We exploit a quadric image transfer function and show how it can be used to achieve sub-pixel registration while interactively displaying two or ...

When all planes transverse and nearly perpendicular to the axis of a surface of revolution S intersect it in loops having central symmetry, S must be quadric. Dedicated to Sue Swartz

Algorithms are presented for constructing G t continuous meshes of degree two (quadric) and degree three (cubic) implicitly defined, piecewise algebraic surfaces, which exactly fit any given collection of points and algebraic space curves, of arbitrary degree. A combination of techniques are used from computational algebraic geometry and numerical approximation theory which reduces the problem ...

Estimation of local surface geometry (i.e. principle frame and principle quadric) is discussed. It is shown that surface tting methods are more robust that-nite diierence based approaches for a number of reasons. The local surface geometry is used to segment the surfaces into regions corresponding to smooth patches, separated by visibility boundaries, occluding contours, and ridges. Points with...

X n Given a sequence of points { i}i=l on a regular quadric S: X T A X = 0 C E d, d >1 3, we study the problem of constructing a G I rational quadratic spline curve lying on 5' that interpolates { X ~ } ~ j . It is shown that a necessary condition for the existence of a nontrivial interpolant is ( X ~ A X 2 ) ( X T i A X i + I ) > 0, i = 1 , 2 , . . . , n 1. Also considered is a Hermite interpo...

Quadric surfaces commonly exist in natural objects and artificial components. It is widely needed to evaluate the form quality of a measured data set, but the mostly used least squares method will lead to over-estimation and its results are not consistent with the definitions in ISO standards. In this paper a shape recognition approach is presented to determine the surface type and shape parame...

We give the parameters of any evaluation code on a smooth quadric surface. For hyperbolic quadrics the approach uses elementary results on product codes and the parameters of codes on elliptic quadrics are obtained by detecting a BCH structure on these codes and using the BCH bound. The elliptic quadric is a twist of the surface P ×P and we detect a similar BCH structure on twists of the Segre ...

This paper deals with the constrained shape reconstruction of objects having quadric patches. The incorporation of geometric constraints in object reconstruction was used rst by Porrill 10]. His approach combined the Kalman lter equations with linearized constraint equations. This technique was improved by De Geeter et al 5] to reduce the eeects of linearization error. The nature and the specii...

We present new results on classifying the morphology of the nonsingular intersection curve of two quadrics by studying the roots of the characteristic equation, or the discriminant, of the pencil spanned by the two quadrics. The morphology of a nonsingular algebraic curve means the structural (or topological) information about the curve, such as the number of disjoint connected components of th...

We introduce a novel method to define Dupin cyclide blends between quadric primitives. Dupin cyclides are nonspherical algebraic surfaces discovered by French mathematician Pierre-Charles Dupin at the beginning of the 19th century. As a Dupin cyclide can be fully characterized by its principal circles, we have focussed our study on how to determine principal circles tangent to both quadrics bei...