Search results for "Computer Science::Graphics"
showing 10 items of 67 documents
Periodic Polynomial Splines
2018
In this chapter, the spaces of periodic polynomial splines and the Spline Harmonic Analysis (SHA) in these spaces are briefly outlined. The stuff of this chapter is used for the design of periodic discrete-time splines and discrete-time-spline-based wavelets and wavelet packets. For a detailed description of the subject we refer to (Averbuch, Neittaanmaki and Zheludev, Spline and Spline Wavelet Methods with Applications to Signal and Image Processing, Springer, Berlin, 2014) [1]. Periodic polynomial splines provide an example of mixed discrete-continuous circular convolution.
Non-periodic Polynomial Splines
2015
In this chapter, we outline the essentials of the splines theory. By themselves, they are of interest for signal processing research. We use the Zak transform to derive an integral representation of polynomial splines on uniform grids. The integral representation facilitated design of different generators of spline spaces and their duals. It provides explicit expressions for interpolating and smoothing splines of any order. In forthcoming chapters, the integral representation of splines will be used for the constructions of efficient subdivision schemes and so also for the design spline-based wavelets and wavelet frames.
Two -methods to generate Bézier surfaces from the boundary
2009
Two methods to generate tensor-product Bezier surface patches from their boundary curves and with tangent conditions along them are presented. The first one is based on the tetraharmonic equation: we show the existence and uniqueness of the solution of @D^4x->=0 with prescribed boundary and adjacent to the boundary control points of a nxn Bezier surface. The second one is based on the nonhomogeneous biharmonic equation @D^2x->=p, where p could be understood as a vectorial load adapted to the C^1-boundary conditions.
Bézier surfaces of minimal area: The Dirichlet approach
2004
The Plateau-Bezier problem consists in finding the Bezier surface with minimal area from among all Bezier surfaces with prescribed border. An approximation to the solution of the Plateau-Bezier problem is obtained by replacing the area functional with the Dirichlet functional. Some comparisons between Dirichlet extremals and Bezier surfaces obtained by the use of masks related with minimal surfaces are studied.
A Geometric Algorithm for Ray/Bézier Surfaces Intersection Using Quasi-Interpolating Control Net
2008
In this paper, we present a new geometric algorithm to compute the intersection between a ray and a rectangular Bezier patch. The novelty of our approach resides in the use of bounds of the difference between a Bezier patch and its quasi-interpolating control net. The quasi-interpolating polygon of a Bezier surface of arbitrary degree approximates the limit surface within a precision that is function of the second order difference of the control points, which allows for very simple projections and 2D intersection tests to determine sub-patches containing a potential intersection. Our algorithm is simple, because it only determines a 2D parametric interval containing the solution, and effici…
A third order partial differential equation for isotropic boundary based triangular Bézier surface generation
2011
Abstract We approach surface design by solving a linear third order Partial Differential Equation (PDE). We present an explicit polynomial solution method for triangular Bezier PDE surface generation characterized by a boundary configuration. The third order PDE comes from a symmetric operator defined here to overcome the anisotropy drawback of any operator over triangular Bezier surfaces.
Triangular Bézier Surfaces of Minimal Area
2003
We study some methods of obtaining approximations to surfaces of minimal area with prescribed border using triangular Bezier patches. Some methods deduced from a variational principle are proposed and compared with some masks.
Calculation of Splines Values by Subdivision
2014
Assume, the samples of a spline \(S(t)\in {}^{p}\fancyscript{S}\) on the grid \(\mathbf{g} =\{k\}_{k\in \mathbb {Z}}\) are available: \(S(k)=y[k]\). Subdivision schemes are proposed to calculate the spline’s values at dyadic and triadic rational points \(S(k/2^m)\) and \(S(k/3^m)\). The SHA technique provides fast and explicit implementation of the subdivision for one- and two-dimensional periodic splines.
Efficiently using connectivity information between triangles in a mesh for real-time rendering
2004
Triangle meshes are the most popular standard model used to represent polygonal surfaces. Drawing these meshes as a set of independent triangles involves sending a vast amount of information to the graphics system. Taking advantage of the connectivity information between the triangles in a mesh dramatically diminishes the amount of information the graphics system must handle. Multiresolution Triangle Strips (MTS) represent a triangle mesh as a collection of multiresolution triangles strips. These strips are the basis of both the storage and the rendering stage. The coherence between the extraction of two levels of detail is used in the model in order to decrease the visualisation time.
Bifurcations of Elementary Graphics
1998
After the regular limit periodic sets, the simplest limit periodic sets are the elementary graphics.