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The sweeping surface, or generalized cylinder, is important in graphics, computer vision and elsewhere. A rotation minimizing frame, avoid the unnecessary twist given it by the Frenet frame. We give a quadratically convergent algorithm for computing it along a 3D trajectory curve, with an error bound. This is then used to create NURBS-approximated sweeping(More)
We prove that a compactly supported spline function of degree k satisses the scaling equation (x) = P N n=0 c(n)(mx?n) for some integer m 2, if and only if (x) = P n p(n)B k (x?n) where p(n) are the coeecients of a polynomial P(z) such that the roots of P(z)(z ? 1) k+1 are mapped into themselves by the mapping z ! z m , and B k is the uniform B-spline of(More)
This paper gives a practical method of extending an n × r matrix P (z), r ≤ n, with Laurent polynomial entries in one complex variable z, to a square matrix also with Laurent polynomial entries. If P (z) has orthonormal columns when z is restricted to the torus T, it can be extended to a paraunitary matrix. If P (z) has rank r for each z ∈ T, it can be(More)
This paper characterizes the stability and orthonormality of the shifts of a multidimensional (M; c) reenable function in terms of the eigenvalues and eigenvectors of the transition operator W cau deened by the autocorrelation c au of its reenement mask c; where M is an arbitrary dilation matrix. Another consequence is that if the shifts of form a Riesz(More)
Dry, thin films containing all necessary reagents for clinical analysis by colorimetry have been designed. Reagents in a matrix of hydrophilic polymer are coated on top of a transparent plastic base. A white isotropically porous polymer spreading layer, 80% void volume, is coated over the reagent layer(s). In the analysis, a drop (typically 10 microliter)(More)
Medical images of such branching structures as blood vessels are clear to the human visual system, but easily confuse computer vision programs. We present an intuitive, hand-eye coordinated, reach-in interface that allows the user to sketch central curves for arteries, nerves, etc., detectable in volume data and in 3D space, and have this position/shape(More)
Let ℂ denote the complex numbers and $${\mathcal{L}}$$ denote the ring of complex-valued Laurent polynomial functions on ℂ\{0}. Furthermore, we denote by $${\mathcal{L}}_R ,{\mathcal{L}_N} $$ the subsets of Laurent polynomials whose restriction to the unit circle is real, nonnegative, respectively. We prove that for any two Laurent polynomials $$P_1 ,P_2(More)