AT512060B1 - METHOD FOR PRODUCING A PATTERN STRUCTURE - Google Patents

Abstract

A method of producing a fabric by means of a computer-controlled weaving machine, wherein a fabric pattern with a square base figure, which corresponds to a crossing point of threads, is arranged several times in the tissue, characterized in that the computer control is such that on a square output figure, the is composed of a plurality of square basic figures, that is, a plurality of crossing points of threads, in a page center, an edge-side rotation point is set to the three copies of this initial figure successively rotated by 90 °, 180 ° and 270 ° and positioned in a fan-like manner one behind the other To obtain composite figure, which is then set as the starting figure for a corresponding subsequent fan-like composition of their successively rotated copies by 90 °, 180 ° and 270 °, so iteratively to develop arbitrarily large figures from crossing points of threads corresponding to the tissue, wherein in the tissuethe threads cross each other aperiodically and asymmetrically above and below.

Description

Description: [0001] The invention relates to a method for producing a tissue with the aid of a computer-controlled weaving machine, wherein a tissue pattern with a square basic figure, which corresponds to a crossing point of threads, is arranged several times in the tissue.

The aim of the invention is to propose a method as stated above, with which inhomogeneous fabric materials, with aperiodic differences in weaving density, can be produced.

For this purpose, the invention provides a method, as indicated above, with the Merkma¬len that the computer control takes place such that at a square Ausgangsfi¬gur, which is composed of several square basic figures, ie several intersections of threads , is set in a page center, an edge-side rotation point to the three copies of this initial figure successively rotated by 90 °, 180 ° and 270 ° and fächcherartig positioned one behind the other to obtain a composite figure, which then as a starting point for a corresponding subsequent fan-like composition of its successively rotated copies by 90 °, 180 ° and 270 ° is set so iterativbeliebig big figures from crossing points of threads corresponding to the tissue to un¬ develop, wherein the threads in the tissue aperiodisch and asymmetrically above and below cross. It is further advantageous for ease of implementation if the output figures of each iteration are rotated in a clockwise direction; and / or if the most central eastern, i. farthest right point of the starting figures is defined as a rotation point.

With the proposed procedure, inhomogeneous woven textile materials can be obtained in which the aperiodic differences in weaving density result in corresponding aperiodic textile concentrations. In this way, it is possible to obtain a tissue material which, due to the inhomogeneity, is difficult to tear apart in a tear process, in contrast, for example, with known fabrics, in particular with silk.

The invention is based on a subsequently explained in more detail geometric method, the method of so-called. Inductive rotation (IR) or short IR method. A starting point for this is the so-called tiling, cf. For example, US 4 133 152 A, where a set of "tiles" of predetermined shape will be used to assemble a surface covering. In the present method, this known tiling method is still exceeded, and an aperiodic pattern production is made possible by iteration of initial figures with rotation of the output figures and subsequent composite figures.

In detail, three different recursive methods - IR methods - are conceivable in order to generate aperiodic, asymmetrical patterns, in each case starting from a single output figure.

This basic procedure and furthermore the special procedure in the case of the method according to the invention will be explained in more detail by way of example with reference to the drawing.

In detail, in the drawing: Fig. 1A is a basic or output figure for a three-step IR method as used in the invention; Fig. 1B shows various stages using this three-step method, starting from the basic figure (output figure) of FIG. 1A;

FIG. 1C shows the repeated application of the inductive rotation according to FIG. 1B to obtain more complex structures; FIG. FIGS. 2A to 2C are views for comparison of a starting figure and steps of an application of another, namely two-step 1 R method; FIGS. [0013] FIGS. 3A to 3C for further explanation corresponding representations in application of a five-step IR method; 4 shows a representation similar to FIG. 1 C, wherein the starting figure for the three

Step method is divided into parts indicated by different arrows, so as to make the achievable pattern - also with regard to the asymmetry and aperiodicity in the present weaving process - better recognizable; 5, starting from a part of an initial figure according to the three

Step method according to FIG. 1 and FIG. 4 with additional illustration of a web node; Fig. 6 shows the composite output figure according to FIGS. 4 and 5 in FIG

Connection to a set of four-web nodes as the initial figure for tissue fabrication; and Fig. 7 shows a section of a textile fabric produced according to the three-step IR method.

In principle, three IR methods can be named as follows: 1. The three-step IR method which, starting from a single quadratic output figure (= start prototype), carries out a rotation in three steps: 90 °, 180 ° and 270 °; s. FIGS. 1 and 4.

2. The two-step IR method, which executes a rotation in two steps starting from a single star-shaped Aus¬gangsfigur (= starting prototype): 120 ° and 240 °; s. Fig.2.

3. The five-step IR method, which executes a rotation in five steps starting from a single hexagonal Aus¬gangsfigur (= starting prototype): 60 °, 120 °, 180 °, 240 ° and 300 °; s. Fig. 3.

The start prototeil, i. The output figure is structured in each case with sub-parts which are not invariant during rotation in order to recursively generate aperiodic, asymmetrical flat patterns or parquet patterns. For each iteration of the recursive process, a fulcrum is chosen around which the output figure, e.g. is rotated in two, three or five steps according to the IR method used in each case according to FIG. 1A, 2A and 3A, respectively. Due to a precise overlapping of the figures, the IR method simultaneously creates a second, parallel, concealed, aperiodic and asymmetrical tiling, the so-called background tiling, which lies exactly behind it and is different from the tiling visible in the foreground.

The aforementioned IR methods will be described in more detail below to illustrate their geometric and practical applications by developing examples and to better explain the principles of the IR methods. The following definitions and examples are only special cases to apply the respective IR method, e.g. with a clockwise rotation and a rotation axis in the central most easterly point of the (initial) figure; however, the IR method can also be used e.g. using the counterclockwise rotation or defining the axis of rotation as the central westerly point of the figures.

As a result, different tilings or patterns are produced which have similar periodic and asymmetric structures. FORMAL DEFINITIONS: Let a, b, c be figures, X = (x, y) rotation axis, w an integer; For a, X, w define [0027] 0 [a, X, w]: = rotate a by X clockwise by w degrees.

For figures a, b, define [0029] a U b: = Figure b is positioned behind the figure a.

For all figures a, b, c, the following applies: (a U b) U c = a U (b U c) = a U b U c.

In the three-step IR method (see Figures 1A-1C and 4), the initial or basic figure (= prototeil) of the recursion R is a quadratic figure Q, s. Fig. 1A; Without restricting the generality, Q should have the side length = 2 with the center o = (0,0) and be formed of four quadratic sub-parts with side length = 1, which should not be invariant on rotation.

For n = 0, set R (0): = Q (R - recursion).

For each iteration of the recursion R, the point of rotation is defined as the central most easterly point of the basic figure, i. the exact center of the right-hand side, around which the cloned basic figure is to be rotated 3 times successively 90 ° in a clockwise direction and positioned one behind the other, s. Fig. 1B with the recursions R '(0), R " (0) and R "' (0).

For all integers n> 0, let: [0036] - X (n): = (2Λη -1.0) rotation point; [0037] R '(n-1): = 0 [R (n-1), X (n), 90], [0038] - R " (n-1): = O [R (n-1 ), X (n), 180], [0039] - R " '(n-1): = O [R (n-1), X (n), 270], [0040] - R (n): = R (n-1) U R '(n-1) U R " (n-1) U R' " (n-1).

The first iteration of R based on prototeil R (0) = Q results in R (1) as shown in FIG. 1B can be seen.

It is crucial that cloned (copied) figures partially "behind" the earlier Figu¬ren lie and are precisely overlapped by the preceding figures. For each next iteration " n + 1 " Similarly, the point of rotation is defined analogously at the exact center of the right edge of its figure, derived from the iteration " n " results. In Fig. 1C, the first three iterations of R = Q, R (1), R (2) and R (3) are illustrated in addition to the basic figure Q.

In the two-step IR method according to FIG. 2, the starting figure (= prototype) of the R embodiment is a star-shaped basic figure S, s. Fig. 2A; without limiting the generality, the basic figure S has the side length s = 1 with the center o = (0,0), and the basic figure S is formed from 6 rhombic sub-parts with the side length = 1, which are not invariant upon rotation. For n = 0 set R (0): = p.

In each iteration of the recursion R, the axis of rotation is defined as the east point of the figure to rotate the cloned basic figure clockwise two times and to position each backwards.

For all the integers n> 0, the following applies: [0046] X (n) rotation point = east point of the figure R (n-1): X (n): = 1/2 * (x ( n), y (n) * sqrt (3)) with x (2n) = x (2n-2) + 3Λ (η-1) * 5, y (2n) = y (2n-2) + 3Λ (η-1) and x (2n + 1) = χ (2η-1) + 3Λ (η + 1), y (2n + 1) = y (2n-1) + 3A (n-1 ).

[0050] R '(n-1): = O [R (n-1), X (n), 120].

- R "(n-1): = 0 [R (n-1), X (n), 240].

R (n): = R (n-1) U R '(n-1) U R "(n-1).

In the first iteration, the rotation axis is located at the exact central most easterly point of the output figure S.

FIG. 2B shows how the first iteration of the recursion R results in R (0) = S via R '(0) and R " (0) to R (1) based on the fundamental part.

2C, in addition to the basic figure S (see Fig. 2A) and the first iteration R (1) two further iterations or recursions R (2) and R (3) are shown, in each case in the vorge¬ Step obtained figure, as R (1) or R (2), serves as a new starting figure.

In the five-step IR method is selected as the starting figure (= prototype) of the recursion pure equilateral hexagonal figure H, s. Fig. 3A; without limiting the generality, the figure H should have the side length s = 1 with the center o = (0,0), and it should be formed of six equilateral triangles with the side length = 1, which can change upon rotation. For n = 0, R (0): = H is set.

For each iteration of the recursion R, s. 3B and 3C, the point of rotation is defined as the central easternmost point of the respective output figure in order to rotate the cloned figure clockwise 5 times successively 60 ° and to position each backwards.

For all integers n> 0, let: [0059] X (n): = (2Λη -1.0) rotation axis; [0060] R '(n-1): = O [R (n-1), X (n), 60], [0061] - R "(n-1): = O [R (n-1 ), X (n), 120], [0062] - R "'(n-1): = O [R (n-1), X (n), 180].

[0063] R "" (n-1): = O [R (n-1), X (n), 240].

[0064] - R ..... (n-1): = 0 [R (n-1), X (n), 300].

R (n): = R (n-1) U R '(n-1) UR "(n-1) UR"' (n-1) UR "" (n-1) U R .... (n-1).

According to FIG. 3B, the first iteration of the recursion R, starting with the basic figure H, results in R (1). Starting from this figure R (1), the further iterations, namely recursions R (2) and R (3), are obtained according to FIG. 3C.

The described IR methods generate aperiodic and asymmetric patterns as al partition.

Of importance for the present tissue preparation is the three-step IR method.

Fig. 4 now shows the first three iterations of this three-step IR method based on a prototeil (basic figure) Q, the sub-parts of which are indicated by different arrows, by the orientations of the cloned figures to identify the direction of the arrows better than in Fig. 1C.

This example illustrates the general idea of the three-step IR method throughout an assembly plan for the sub-parts. Despite the simple iteration rule, highly complex, non-repetitive patterns emerge very quickly.

This three-step IR method is advantageously used in a process for producing a fabric, as will now be explained with reference to FIGS. 5 to 7.

In Fig. 5, a sub-element or sub-part (square of side length 1 corresponding to a thread crossing point is illustrated.

In Fig. 6, starting from a basic element (Q in Fig. 1A) with four such sub-parts (marked on the one hand with arrows and on the other hand as in Fig. 5) shown (wherein a part of a fabric with four threads - Cross points is illustrated in accordance with this basic figure.

This basic figure according to FIG. 6 will now be described using the iterations, as shown in FIG. 1B, 1C and Fig. 4 illustrates further developed. In detail, FIG. 7 shows a section of the third iteration R (3), specifically with a network of lines (threads) which cross each other aperi¬odisch below or above.

When using this sample image by identifying the dark lines in the network as textile threads, the aperiodic and asymmetric cross over each other in the network above and below, fabric or textile materials can be produced by computer-controlled weaving machines.

The textile materials thus woven according to the three-step IR method give inhomogeneous materials. Aperiodic differences in web density lead to corresponding aperiodic textile concentrations. The permanent oscillation of loose and dense weaving in an aperiodic order causes an inhomogeneous material which can not be easily torn apart with a crack, as is known from silk. This property is to be compared with the aperiodic effect of the anti-lock braking system (ABS) in motor vehicles when decelerating. In addition, the network of the background pattern - the second, concealed resulting pattern - can be additionally combined and used as a second layer of material for strengthening.

Claims (4)

1. A method for producing a tissue with the aid of a computer-controlled Webma¬ machine, wherein a tissue pattern with a square basic figure, which corresponds to a Kreu¬zungspunkt of threads, is arranged multiple times in the tissue, characterized ge indicates that the computer Control is carried out in such a way that at a quadratic output figure, which is composed of a plurality of square basic figures, that is to say a plurality of crossing points of threads, an edge-side rotation point is defined in a side center in order to successively successively round the three copies of this initial figure by 90 °, Rotated 180 ° and 270 ° and positioned in a fan-like manner in order to obtain a composite figure, which is then set as the starting figure for a corresponding nach¬folgende fan-like composition of their successively rotated copies by 90 °, 180 ° and 270 ° so iteratively arbitrarily large figures from crossing points of threads corresponding to the tissue In the tissue, the threads intersect each other aperiodically and asymmetrically above and below. A method according to claim 1, characterized in that the output figures of each iteration are rotated clockwise. 3. The method according to claim 1 or 2, characterized in that the central eastern, i. rightmost point of the starting characters is set as a rotation point. For this 4 sheets drawings