Urn Models and Beta-splines

Some insight into the properties of beta-splines is gained by applying the techniques of urn models. Urn models are used to construct beta-spline basis functions and to derive the basic properties of these blending functions and the corresponding beta-spline curves. Only the simple notion of linear geometric continuity and with the most elementary beta parameter are outlined. Non-linear geometric continuity leads to additional beta parameters and to more complicated basis functions. Whether urn models can give us any insight into these higher order concepts still remains to be investigated

Shape Preserving Spline Interpolation

A rational spline solution to the problem of shape preserving interpolation is discussed. The rational spline is represented in terms of first derivative values at the knots and provides an alternative to the spline-under-tension. The idea of making the shape control parameters dependent on the first derivative unknowns is then explored. The monotonic or convex shape of the interpolation data can then be preserved automatically through the solution of the resulting non-linear consistency equations of the spline

A rational cubic spline with tension

A rational cubic spline curve is described which has tension control parameters for manipulating the shape of the curve. The spline is presented in both interpolatory and rational B-spline forms, and the behaviour of the resulting representations is analysed with respect to variation of the control parameters

Quantitative analysis of the reconstruction performance of interpolants

The analysis presented provides a quantitative measure of the reconstruction or interpolation performance of linear, shift-invariant interpolants. The performance criterion is the mean square error of the difference between the sampled and reconstructed functions. The analysis is applicable to reconstruction algorithms used in image processing and to many types of splines used in numerical analysis and computer graphics. When formulated in the frequency domain, the mean square error clearly separates the contribution of the interpolation method from the contribution of the sampled data. The equations provide a rational basis for selecting an optimal interpolant; that is, one which minimizes the mean square error. The analysis has been applied to a selection of frequently used data splines and reconstruction algorithms: parametric cubic and quintic Hermite splines, exponential and nu splines (including the special case of the cubic spline), parametric cubic convolution, Keys' fourth-order cubic, and a cubic with a discontinuous first derivative. The emphasis in this paper is on the image-dependent case in which no a priori knowledge of the frequency spectrum of the sampled function is assumed

Smooth parametric surfaces and n-sided patches

The theory of 'geometric continuity' within the subject of CAGD is reviewed. In particular, we are concerned with how parametric surface patches for CAGD can be pieced together to form a smooth Ck surface. The theory is applied to the problem of filling an n-sided hole occurring within a smooth rectangular patch complex. A number of solutions to this problem are surveyed

A 3D COORDINATE APPROACH TO WALKING ANALYSIS

The method developed uses three video cameras (60 fields per second) to record the movement. The body segment co-ordinates are captured manually on each image. No anatomic markers are used for a 14-segment human body representation. The data extracted from the images are interpolated to calculate information for non-recorded instants. The 3D reconstruction is made using the DLT calibration procedure

Appendices - Parametric Keyframe Interpolation Incorporating Kinetic Adjustment and Phrasing Control

These are the unpublished appendices for the paper entitled, Parametric Keyframe Interpolation Incorporating Kinetic Adjustment and Phrasing Control

Effects of Air Pollution on Heart Rate Variability: The VA Normative Aging Study

Reduced heart rate variability (HRV), a marker of poor cardiac autonomic function, has been associated with air pollution, especially fine particulate matter [< 2.5 μm in aerodynamic diameter (PM(2.5))]. We examined the relationship between HRV [standard deviation of normal-to-normal intervals (SDNN), power in high frequency (HF) and low frequency (LF), and LF:HF ratio] and ambient air pollutants in 497 men from the Normative Aging Study in greater Boston, Massachusetts, seen between November 2000 and October 2003. We examined 4-hr, 24-hr, and 48-hr moving averages of air pollution (PM(2.5), particle number concentration, black carbon, ozone, nitrogen dioxide, sulfur dioxide, carbon monoxide). Controlling for potential confounders, HF decreased 20.8% [95% confidence interval (CI), 4.6–34.2%] and LF:HF ratio increased 18.6% (95% CI, 4.1–35.2%) per SD (8 μg/m(3)) increase in 48-hr PM(2.5). LF was reduced by 11.5% (95% CI, 0.4–21.3%) per SD (13 ppb) increment in 4-hr O(3). The associations between HRV and PM(2.5) and O(3) were stronger in people with ischemic heart disease (IHD) and hypertension. The associations observed between SDNN and LF and PM(2.5) were stronger in people with diabetes. People using calcium-channel blockers and beta-blockers had lower associations between O(3) and PM(2.5) with LF. No effect modification by other cardiac medications was found. Exposures to PM(2.5) and O(3) are associated with decreased HRV, and history of IHD, hypertension, and diabetes may confer susceptibility to autonomic dysfunction by air pollution