Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the convolution of an exponential B-spline with a compact-support distribution. As a direct consequence of this factorization theorem, we show t...

A new method for manipulation of curves in several degrees is presented. When a point of curve is moved, it a ects a relative local segment, which size could depends of the propagation of the point through their lower resolution curves. So, for the same displacement of the point, could be generated relative local segments of di erent sizes, only varying a local parameter such sti ness constant....

This paper focuses on interpolating vertices and normal vectors of a closed quad-dominant mesh1 G2continuously using regular Coons B-spline surfaces, which are popular in industrial CAD/CAM systems. We first decompose all non-quadrangular facets into quadrilaterals. The tangential and second-order derivative vectors are then estimated on each vertex of the quads. A least-square adjustment algor...

Recently, Runions and Samavati [7] proposed Partion of Unity Parametrics (PUPs), a generalization of NURBS which replaces B-spline basis functions with arbitrary Weight-Functions (WFs) while preserving affine invariance. A key problem identified by Runions and Samavati was the identification of classes of weight-functions which are well-suited to geometric modeling. In this paper, we propose a ...

This paper discusses a design methodology of cooperative path planning for dynamical multi-agent systems with spatial and temporal constraints. The cooperative behavior of the multi-agent systems is specified in terms of the objective function in an optimization formulation. The path of achieving cooperative tasks is then generated by the optimization formulation constructed based on a differen...

A constructive approach is adopted to build B-spline like basis for cubic spline curves with a more general continuity than beta-continuity. This method provides not only a large variety of very interesting shape controls like biased, point, and interval tensions but, as a special case, also recovers a number of spline methods like nu-spline of Nielson[9], beta-splines[1], gamma-splines of Boeh...

The application of collocation methods using spline basis functions to solve differential model equations has been in use for a few decades. However, the application of spline collocation to the solution of the nonlinear, coupled, partial differential equations (in primitive variables) that define the motion of fluids has only recently received much attention. The issues that affect the effecti...

We study the curvature variation functional, i.e., the integral over the square of arc-length derivative of curvature, along a planar curve. With no other constraints than prescribed position, slope angle, and curvature at the endpoints of the curve, the minimizer of this functional is known as a cubic spiral. It remains a challenge to effectively compute minimizers or approximations to minimiz...

Non-uniform basis functions for construction of interpolating and approximating spline curves and surfaces are presented. The construction is based on the theory of B-splines and enables a continuous change from interpolation to approximation of given data. It is also possible to change the tension of the curves and surfaces.

We present a new method for computing intersections of two parametric B-Spline curves. We use an intersection of the control polygons as an approximation for an intersection of the curves in combination with knot insertion. The resulting algorithm is asymptotically Newton-like, but without the need of a starting value. Like Newton’s method, it converges quadratically at transversal intersection...