Cost-optimal parallel B-spline interpolations (original) (raw)

A unified architecture for the computation of B-spline curves and surfaces

IEEE Transactions on Parallel and Distributed Systems, 1997

B-Splines in general, and Non-Uniform Rational B-Splines in particular, have become indispensable modeling primitives in computer graphics and geometric modeling applications. In this paper a novel high-performance architecture for the computation of uniform, non-uniform, rational and non-rational B-Spline curves and surfaces is presented. This architecture has been derived through a sequence of steps. First, a systolic architecture for the computation of the basis function values, the basis function evaluation array (the BFEA), is developed. Using the BFEA as its core, an architecture for the computation of non-uniform rational B-Spline curves is constructed. This architecture is then extended to compute NURBS surfaces. Finally, this architecture is augmented to compute the surface normals so that the output from this architecture can be directly used for rendering the NURBS surface. The overall linear structure of the architecture, its small I/O requirements, its non-dependence on the size of the problem (in terms of the number of control points and the number of points on the curve/surface that has to be computed), and its very high throughput make this architecture highly suitable for integration into the standard graphics pipeline of high-end workstations. Results of the timing analysis indicate a potential throughput of one triangle with the normal vectors at its vertices, every two clock cycles.

Speedup of Bicubic Spline Interpolation

Lecture Notes in Computer Science, 2018

The paper seeks to introduce a new algorithm for computation of interpolating spline surfaces over non-uniform grids with C 2 class continuity, generalizing a recently proposed approach for uniform grids originally based on a special approximation property between biquartic and bicubic polynomials. The algorithm breaks down the classical de Boor's computational task to systems of equations with reduced size and simple remainder explicit formulas. It is shown that the original algorithm and the new one are numerically equivalent and the latter is up to 50% faster than the classic approach.

Curve network interpolation by C1 quadratic B-spline surfaces

Computer Aided Geometric Design, 2015

In this paper we investigate the problem of interpolating a B-spline curve network, in order to create a surface satisfying such a constraint and defined by blending functions spanning the space of bivariate C 1 quadratic splines on criss-cross triangulations. We prove the existence and uniqueness of the surface, providing a constructive algorithm for its generation. We also present numerical and graphical results and comparisons with other methods.

Interpolation possibilities using rational B-spline curve

1998

The aim of this paper is to solve some interesting interpolation problems using rational B-spline curve. If a sequence of planar points and vectors are given then a free-form curve can calculated which interpolates the points and has the given tangent vectors in these points. Our method gives a fast interpolation of these data using extra control points. Then we provide a method which allows to interpolate the same set of data without any predefined order of the points, i.e. a set of scattered points with the vectors. In this latter problem we use an artificial neural network to order the data.

B-LUT: Fast and low memory B-spline image interpolation

Computer Methods and Programs in Biomedicine, 2010

We propose a fast alternative to B-splines in image processing based on an approximate calculation using precomputed B-spline weights. During Bspline indirect transformation, these weights are efficiently retrieved in a nearestneighbors fashion from a look-up table, greatly reducing overall computation time. Depending on the application, calculating a B-spline using a look-up table, called BLUT, will result in an exact or approximate B-spline calculation. In case of the latter the obtained accuracy can be controlled by the user. The method is applicable to a wide range of B-spline applications and has very low memory requirements compared to other proposed accelerations. The performance of the proposed BLUT's was compared to conventional B-splines as implemented in the popular ITK toolkit for the general case of image intensity interpolation. Experiments illustrated that highly accurate B-spline approximation can be obtained all while computation time is reduced with a factor of 5 to 6. The BLUT source code, compatible with the ITK toolkit, has been made freely available to the community.

Computation of interpolatory splines via triadic subdivision

Advances in Computational Mathematics, 2010

We present an algorithm for the computation of interpolatory splines of arbitrary order at triadic rational points. The algorithm is based on triadic subdivision of splines. Explicit expressions for the subdivision symbols are established. These are rational functions. The computations are implemented by recursive filtering. Keywords Triadic subdivision • Splines Mathematics Subject Classifications (2000) 65D17 • 65D07 • 93E11 = S j k3 −(j+1) , k ∈ Z. Note that the value of a spline at any point can be expressed as a linear combination of its values at grid points. In other words, any value f j+1 k can be Communicated by Tim Goodman.

Geometric Algorithm for Curve Interpolation With Non Uniform B-Splines

The interpolation of a sequence of points is an important task in Engineering. In this work, three different interpolation methods are studied and expanded. The first method is the conventional interpolation Spline. The second method is a subdivision based geometric algorithm. The third method interpolates a given set of points with additional point normal constraints. The last two methods were implemented with uniform B-Splines curves. In this work, both methods are expanded to use non uniform B-Spline curves. Three critical curves are used to test the developed methods: circle involute, bowditch and epitrochoid. The results show that the non uniform B-Spline implementations have better quality with smaller errors, once the value of the distance error of the curve is in the order of 10 −15 % of the bound box diagonal of the initial input data points and the normal error is around 10 −4 rad in the worst case.

Efficient cubic spline interpolation implemented with FIR filters

Classical Cubic spline interpolation needs to solve a set of equations of high dimension. In this work we show how to compute the interpolant using a FIR digital filter, with a reduced number of operations per interpolated point and high accuracy. Additionally, the computation can be made on real time as the signal samples are acquired. Following this approach, we show how to obtain easily the derivatives of the interpolant in a similar way, and also signal approximations to reduce the oscillations that appear when using high order splines. These techniques are very well suited to compute continuous representations of image contours on closed shapes and to find its curvature and singularities.

Cubic Basic Splines and Parallel Algorithms

International Journal of Advanced Trends in Computer Science and Engineering, 2020

The relevance of using parallel computing systems is reflected, the main approaches to parallelizing processes and data processing methods are reflected, the principles of parallel programming technologies are described, the main parameters of parallel algorithms are studied using cubic splines calculation example, a comparative analysis of the effectiveness of using parallelism technologies is given.

New algorithms for polynomial and trigonometric interpolation on parallel computers

BIT, 1992

An interpolation polynomial of order N is constructed from p indepen dent subpolynomials of order n '" Nip. Each such subpolynomial is found independently and in parallel. Moreover, evaluation of the polynomial at any given point is done independently and in parallel, except for a final step of summation of p elements. Hence, the algorithm has almost no commu ,:.. nication overhead and can be implemented easily on any parallel computer. We give examples of finite-difference interpolation, trigonometric interpola 'tion, and Chebyshev interpolation, and conclude with the general Hermite interpolation problem.