4,064 research outputs found
Revisiting Digital Straight Segment Recognition
This paper presents new results about digital straight segments, their
recognition and related properties. They come from the study of the
arithmetically based recognition algorithm proposed by I. Debled-Rennesson and
J.-P. Reveill\`es in 1995 [Debled95]. We indeed exhibit the relations
describing the possible changes in the parameters of the digital straight
segment under investigation. This description is achieved by considering new
parameters on digital segments: instead of their arithmetic description, we
examine the parameters related to their combinatoric description. As a result
we have a better understanding of their evolution during recognition and
analytical formulas to compute them. We also show how this evolution can be
projected onto the Stern-Brocot tree. These new relations have interesting
consequences on the geometry of digital curves. We show how they can for
instance be used to bound the slope difference between consecutive maximal
segments
Digital waveguide modeling for wind instruments: building a state-space representation based on the Webster-Lokshin model
This paper deals with digital waveguide modeling of wind instruments. It presents the application of state-space representations for the refined acoustic model of Webster-Lokshin. This acoustic model describes the propagation of longitudinal waves in axisymmetric acoustic pipes with a varying cross-section, visco-thermal losses at the walls, and without assuming planar or spherical waves. Moreover, three types of discontinuities of the shape can be taken into account (radius, slope and curvature).
The purpose of this work is to build low-cost digital simulations in the time domain based on the Webster-Lokshin model. First, decomposing a resonator into independent elementary parts and isolating delay operators lead to a Kelly-Lochbaum network of input/output systems and delays. Second, for a systematic assembling of elements, their state-space representations are derived in discrete time. Then, standard tools of automatic control are used to reduce the complexity of digital simulations in the time domain. The method is applied to a real trombone, and results of simulations are presented and compared with measurements. This method seems to be a promising approach in term of modularity, complexity of calculation and accuracy, for any acoustic resonators based on tubes
A note on digitized angles
We study the configurations of pixels that occur when two digitized straight
lines meet each other
Fast Mojette Transform for Discrete Tomography
A new algorithm for reconstructing a two dimensional object from a set of one
dimensional projected views is presented that is both computationally exact and
experimentally practical. The algorithm has a computational complexity of O(n
log2 n) with n = N^2 for an NxN image, is robust in the presence of noise and
produces no artefacts in the reconstruction process, as is the case with
conventional tomographic methods. The reconstruction process is approximation
free because the object is assumed to be discrete and utilizes fully discrete
Radon transforms. Noise in the projection data can be suppressed further by
introducing redundancy in the reconstruction. The number of projections
required for exact reconstruction and the response to noise can be controlled
without comprising the digital nature of the algorithm. The digital projections
are those of the Mojette Transform, a form of discrete linogram. A simple
analytical mapping is developed that compacts these projections exactly into
symmetric periodic slices within the Discrete Fourier Transform. A new digital
angle set is constructed that allows the periodic slices to completely fill all
of the objects Discrete Fourier space. Techniques are proposed to acquire these
digital projections experimentally to enable fast and robust two dimensional
reconstructions.Comment: 22 pages, 13 figures, Submitted to Elsevier Signal Processin
Combinatorics of the Gauss digitization under translation in 2D
International audienceThe action of a translation on a continuous object before its digitization generates several digital objects. This paper focuses on the combinatorics of the generated digital objects up to integer translations. In the general case, a worst-case upper bound is exhibited and proved to be reached on an example. Another upper bound is also proposed by making a link between the number of the digital objects and the boundary curve, through its self-intersections on the torus. An upper bound, quadratic in digital perimeter, is then derived in the convex case and eventually an asymptotic upper bound, quadratic in the grid resolution, is exhibited in the polygonal case. A few signicant examples finish the paper
Local Rules for Computable Planar Tilings
Aperiodic tilings are non-periodic tilings characterized by local
constraints. They play a key role in the proof of the undecidability of the
domino problem (1964) and naturally model quasicrystals (discovered in 1982). A
central question is to characterize, among a class of non-periodic tilings, the
aperiodic ones. In this paper, we answer this question for the well-studied
class of non-periodic tilings obtained by digitizing irrational vector spaces.
Namely, we prove that such tilings are aperiodic if and only if the digitized
vector spaces are computable.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
Adapted slopes
This article focuses on three research questions: 1) Were terraced landscapes built in the analytical or creative
phase of the first human intervention in a place? 2) Does the geometry of the slopes adapted as a terraced landscape apply
in a conscious planning process? 3) What are the patterns and relationships between buildings, settlements, and terraced
landscapes? The first issue was examined at the archaeological site Lepenski Vir, where a settlement and trapezoidal huts
were built on terraces. The terraces were designed more in the creative phase than in the analytical phase because some
of the terraces already had a shape that corresponded to and followed the shape of the huts. The answer to the second
question is based on an understanding of the importance of horizontal and vertical measurements, their symbolism, and the
origins of agriculture. The applied geometry of the slope is one of the indicators that the terraces were built on the basis of
conscious planning and rational order, which is an instrument of basic economics and land delimitation issues. The types of
relationships between buildings, settlements, and terraces are numerous, and sometimes they can represent a pattern that
occurs in a particular region. Because the aim of civil and other initiatives is to protect terraced landscapes from the prejudice
of marginality and ignorance, extended studies may be expected in this vast field of case studies
State-space representation for digital waveguide networks of lossy flared acoustic pipes
This paper deals with digital waveguide modeling of wind instruments. It presents the application of state-space representations to the acoustic model of Webster-Lokshin. This acoustic model describes the propagation of longitudinal waves in axisymmetric acoustic pipes with a varying cross-section, visco-thermal losses at the walls, and without assuming planar or spherical waves. Moreover, three types of discontinuities of the shape can be taken into account (radius, slope and curvature), which can lead to a good fit of the original shape of pipe. The purpose of this work is to build low-cost digital simulations in the time domain, based on the Webster-Lokshin model. First, decomposing a resonator into independent elementary parts and isolating delay operators lead to a network of input/output systems and delays, of Kelly-Lochbaum network type. Second, for a systematic assembling of elements, their state-space representations are derived in discrete time. Then, standard tools of automatic control are used to reduce the complexity of digital simulations in time domain. In order to validate the method, simulations are presented and compared with measurements
The Vanishing Square, The Fibonacci Sequence, and The Golden Ratio
The Golden Ratio has generally been revered as the most aesthetically pleasing relationship that exists between two numbers. The Fibonacci Sequence is a famous collection of integers occurring unusually often in nature, with many amazing properties, and is intimately related to the Golden Ratio. An intriguing puzzle (âThe Vanishing Squareâ) will set the stage. Then we will examine the origins of both the Golden Ratio and the Fibonacci Sequence and discover how their histories are intertwined. ButâŠ.does the Golden Ratio really live up to its reputation
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