In the past, cyclide surfaces have been used effectively for the variable radius blending of natural quadric intersections. However, attempts to use cyclides for constructing realistic, freeform composite surfaces met with rather limited success. The paper presents a simple procedure for creating and manipulating geometrically complex objects using tubular cyclide pieces. The method described i...

We propose a simple method of explicit description of families of closed geodesics on a triaxial ellipsoid Q that are cut out by algebraic surfaces in R. Such geodesics are either connected components of spatial elliptic curves or of rational curves. Our approach is based on elements of the Weierstrass–Poncaré reduction theory for hyperelliptic tangential covers of elliptic curves, the addition...

Curved screens are increasingly being used for high-resolution immersive visualization environments. 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 ...

This paper addresses the problem of surface reconstruction of highly noisy point clouds. The surfaces to be reconstructed are assumed to be 2-manifolds of piecewise C1 continuity, with isolated small irregular regions of high curvature, sophisticated local topology or abrupt burst of noise. At each sample point, a quadric field is locally fitted via a modified moving least squares method. These...

The method of moving planes and moving quadrics can express the implicit equation of a parametric surface as the determinant of a matrix M . The rows of M correspond to moving planes or moving quadrics that follow the parametric surface. Previous papers on the method of moving surfaces have shown that a simple base point has the effect of converting one moving quadric to a moving plane. A much ...

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...

Assuming that φ : Sym(E) → F is a morphism of vector bundles on a variety X, we compute the class of the locus in X where Ker(φ) contains a quadric of prescribed rank. Our formulas have many applications to moduli theory: (i) we find a simple proof of Borcherds’ result that the Hodge class on the moduli space of polarized K3 surfaces of fixed genus is of Noether-Lefschetz type, (ii) we construc...

Theoretically, metric solid shape is not determined uniquely by shading. Consequently, human vision has difficulty in categorizing shape when shading is the only cue. In the present research, subjects were required to categorize shaded quadric surfaces. We found that they were rather poor at this task; they confused hyperbolic and elliptic (both convex and concave) shapes easily. When a cast sh...

A kinematic mapping of planar displacements is used to derive generalized constraint equations having the form of ruled quadric surfaces in the image space. The forward kinematic problem for all three legged, three degree of freedom planar parallel manipulators thus reduces to determining the points of intersection of three of these constraint surfaces, one corresponding to each leg. The invers...

This paper presents a scan curve algorithm for evaluating the face area of solids in constructive solid geometry (CSG) representation. Compared to previous methods, the algorithm is more accurate and computationally faster. The applicable domain is limited to solids bounded by three classes of surfaces: all quadric surfaces, cylindrical surfaces, and surfaces of revolution which are algebraic s...