We present a method for calculating the envelope surface of a parametric solid object swept along a path in three-dimensional space. The boundary surface of the solid is the combination of parametric surfaces and an implicit surface where the Jacobian of the defining function has a rank-deficiency condition. Using the rank deficiency condition, we determine a set of square sub-Jacobian determin...

We present a method for calculating the envelope of the swept surface of a solid along a path in three-dimensional space. The generator of the swept surface is a trivariate tensorproduct Bèzier solid and the path is a non-uniform rational B-spline curve. The boundary surface of the solid is the combination of parametric surfaces and an implicit surface where the determinant of the Jacobian of t...

We have explored the design and development of magnetically-resonant tag readers for application to tangible computer interfaces. To this end, we constructed a ringdown tag reader and a swept-frequency tag reader, both capable of real-time continuous interaction with multiple tagged objects. Although the ringdown reader worked well for smaller numbers of tags, the swept-frequency tag reader pro...

We present efficient and robust algorithms for intersecting a rational parametric freeform surface with a general swept surface. A swept surface is given as a one-parameter family of cross-sectional curves. By computing the intersection between a freeform surface and each cross-sectional curve in the family, we can solve the intersection problem. We propose two approaches, which are closely rel...

We classify complex projective varieties of dimension 2r ≥ 8 swept out by a family of codimension two grassmannians of lines G(1, r). They are either fibrations onto normal surfaces such that the general fibers are isomorphic to G(1, r) or the grassmannian G(1, r +1). The cases r = 2 and r = 3 are also considered in the more general context of varieties swept out by codimension two linear space...

We present a method for calculating the envelope surface of a parametric solid object swept along a path in threedimensional space. The boundary surface of the solid is the combination of parametric surfaces and an implicit surface where the Jacobian of the defining function has a rankdeficiency condition. Using this condition, we determine a set of square sub-Jacobian determinants that must al...

In this letter, a phase-sensitive, swept-source optical coherence tomography (SS-OCT) system is implemented for the optical measurement of nanostructures. A new approach is proposed to reduce the phase errors, resulting from trigger jitter of the swept source and the asynchronization between the A-scan trigger and OCT signal at the data acquisition end, with a narrowband fiber Bragg grating to ...