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Dive into the research topics where John A. Roulier is active.

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Featured researches published by John A. Roulier.


ACM Transactions on Mathematical Software | 1981

An Algorithm for Computing a Shape-Preserving Osculatory Quadratic Spline

David F. McAllister; John A. Roulier

An algorithm is presented for calculating an osculatory quadratm sphne that preserves the monotonmlty and convexity of the data when consmtent with the given derivatives at the data points A method is also presented for calculatmn of an mterpolatory quadratm sphne with monotonicity and convexity consistent with that of the data Included is a discussion of pathologms that can occur when these algorithms are maplemented. Examples are given that illustrate the dependence of the method on only local informatmn and its usefulness m geometrm design.


SIAM Journal on Numerical Analysis | 1977

MONOTONE AND CONVEX SPLINE INTERPOLATION

Eli Passow; John A. Roulier

For a set of monotone (and/or convex) data, we consider the possibility of finding a spline interpolant, of pre-determined smoothness, which is monotone (and/or convex). The investigation is carried out by constructing an auxiliary set of points and using the well-known monotonicity and convexity preserving properties of Bernstein polynomials. In § 3 we consider the problem of piecewise monotone interpolation.


Mathematics of Computation | 1977

Algorithms for Computing Shape Preserving Spline Interpolations to Data

David F. McAllister; Eli Passow; John A. Roulier

Algorithms are presented for computing a smooth piecewise polynomial interpolation which preserves the monotonicity and/or convexity of the data.


Mathematics of Computation | 1978

Interpolation by convex quadratic splines

David F. McAllister; John A. Roulier

Algorithms are presented for computing a quadratic spline interpolant with variable knots which preserves the monotonicity and convexity of the data. It is also shown that such a spline may not exist for fixed knots.


IEEE Computer Graphics and Applications | 1983

Shape-Preserving Spline Interpolation for Specifying Bivariate Functions on Grids

S. L. Dodd; David F. McAllister; John A. Roulier

Compared with other methods, this technique for smooth surface interpolation over grid data reduces the number of extraneous local optima and inflection points of the surface.


Journal of Approximation Theory | 1978

Lipschitz and strong unicity constants for changing dimension

Myron S Henry; John A. Roulier

;I Tf,}& with lim,,m /! f -h 11 = 0 that lim,+, A(h) = h(f). For fixed f and n, Henry and Roulier [5] investigate the behavior of X(f) for changing intervals.


Computer-aided Design | 1991

Designing faired parametric surfaces

Thomas Rando; John A. Roulier

Abstract The paper presents the theoretical foundation for the development of systems for the automatic fairing of parametric surfaces. Three fairness metrics are derived; each metric is a geometric property of the designed surface, which can be expressed explicitly in terms of the shape properties of the designed surface. The metrics are based on the surface areas of derived surfaces constructed from the geometric invariants of the designed surface. Consequently, these metrics can be evaluated in the original parameterization of the surface.


IEEE Computer Graphics and Applications | 1987

A Convexity-Preserving Grid Refinement Algorithm for Interpolation of Bivariate Functions

John A. Roulier

This article presents an algorithms to refine bevariate grid data that is convex (and monotonic) along the grid lines so that the refined data exhibits the same convexity (and monotonicity). The algorithm is based on some observations about univariate data and an algorithm for shape-preserving quadratic splines for such data. It can be used as is or with standard surface-path techniques.


ACM Transactions on Mathematical Software | 1981

Algorithm 574: Shape-Preserving Osculatory Quadratic Splines [E1, E2]

David F. McAllister; John A. Roulier

DESCRIPTION This algorithm is a FORTRAN implementation for the procedure developed in [3]. Let n data points {(x,, y,)} n.1 and n first derivatives {rn,),-1 at these data points be given, with x, <_-X,+l, 1 __ i __. n-1. The algorithm constructs a smooth osculatory quadratic spline S, which satisfies (1) S(x,) = y,, 1 <_ i <_ n; (2) S(xi) = m,, 1 <_ i <_ n; (3) S preserves monotonicity and convexity in the case that the slopes rn, are consistent with the shape of the data; (4) the knots of the spiine S include the data points and at most two additional knots between adjacent data points. The spline S is a piecewise quadratic Bernstein polynomial with a continuous first derivative. Permission to copy without fee all or part of this material is granted provided that the copras are not made or distributed for direct commercial advantage, the ACM copyright notice and the htle of the publication and its date appear, and notice is given that copying Is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission.


Computing | 2007

Preserving computational topology by subdivision of quadratic and cubic Bézier curves

Edward L. F. Moore; Thomas J. Peters; John A. Roulier

Non-self-intersection is both a topological and a geometric property. It is known that non-self-intersecting regular Bézier curves have non-self-intersecting control polygons, after sufficiently many uniform subdivisions. Here a sufficient condition is given within ℝ3 for a non-self-intersecting, regular C2 cubic Bézier curve to be ambient isotopic to its control polygon formed after sufficiently many subdivisions. The benefit of using the control polygon as an approximant for scientific visualization is presented in this paper.

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David F. McAllister

North Carolina State University

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J. Li

University of Connecticut

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Thomas Rando

University of Connecticut

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Bruce R. Piper

Rensselaer Polytechnic Institute

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Myron S. Henry

North Carolina State University

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Yates Fletcher

North Carolina State University

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Calvin Lee Doss

North Carolina State University

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