EP2183604A1

EP2183604A1 - Method and device for displaying lines between scanned measurement values

Info

Publication number: EP2183604A1
Application number: EP08759242A
Authority: EP
Inventors: Michael Reinhold; Markus Freidhof
Original assignee: Rohde and Schwarz GmbH and Co KG
Current assignee: Rohde and Schwarz GmbH and Co KG
Priority date: 2007-09-06
Filing date: 2008-06-13
Publication date: 2010-05-12
Also published as: DE102007042323A1; US8497864B2; US20110267349A1; WO2009033513A1

Abstract

Measurement points (63, 64, 65, 66, 67, 68) for display on a two-dimensional pixel-based display device are formed by scanned and digitized measurement values. To this end, the resolution of each measurement point (63, 64, 65, 66, 67, 68) according to time and/or value is higher than the resolution of the two-dimensional pixel-based display device. The measurement points (63, 64, 65, 66, 67, 68) are connected into a continuous measurement point curve (60, 61, 62) if they are not located on directly adjoining pixels. In order to determine the pixels to be depicted of the continuous measurement point curve (60, 61, 62) between two measurement points (63, 64, 65, 66, 67, 68) not located on directly adjoining pixels, the positions of the adjoining measurement points (63, 64, 65, 66, 67, 68) within the associated pixels are taken into consideration.

Description

Method and apparatus for displaying lines between sampled readings

The invention relates to a method and a device for displaying digital measured values on pixel-based display devices, in particular display devices in measuring devices.

Traditionally, to display digital readings on pixel-based displays, the readings are mapped as accurately as possible to individual pixels. However, if the measured values are far apart, the result is an image that is difficult to read, consisting only of individual points. For this reason, conventionally, interpolation is performed between the measured values. This creates a more readable image, but requires a lot of computational effort. However, if the sampling times of the digital signal are not synchronized with the image change of the display, this process also results in a restless image since different measurement curves are produced by the different interpolation nodes.

Thus, EP 0 919 818 B1 discloses a method and an apparatus for displaying waveforms. This method applies an interpolation of displayed points between readings. On the one hand, this requires a high computational effort. On the other hand, a smooth image is not always generated because, due to the lack of synchronicity of the sampling times with the image structure, the position of the nodes of the interpolation varies. The invention is based on the object to provide a method and a device that represent digital readings on a display with a quiet picture, good readability and low computational effort.

The object is achieved by the features of independent claim 1 for the method and by the features of independent claim 7 for the device. Advantageous developments are the subject of the dependent claims.

To display measured values on a two-dimensional pixel-based display device, measuring points are formed from sampled and digitized measured values in a two-dimensional coordinate system. The resolution by time and / or value of each measurement point is higher than the resolution of the two-dimensional pixel-based display device. The measurement points are connected to a continuous measurement point curve if they are not on directly adjacent pixels. to

Determining the pixels of the continuous measuring point curve to be displayed between two measuring points which are not located on directly adjacent pixels, takes into account the position of the adjacent measuring points within the associated pixels. The illustrated continuous measuring point curve is thus sharper and more stable over the course of the measurement with a constant signal than with conventional display methods.

In order to determine the pixels to be displayed of the continuous measuring point curve between two adjacent measuring points, which are offset horizontally by exactly one pixel, preferably one or more transition points of the continuous measuring point curve are transposed over the boundaries between calculates the pixel lines. Advantageously, the continuous measurement point curve is displayed from the first of the two adjacent measurement points to the first transition point in the pixel line of the first measurement point. Advantageously, the continuous measurement point curve is displayed from the first transition point to the last transition point in the redrawn pixel line. Advantageously, the continuous measurement point curve is displayed from the last transition point to the second of the two adjacent measurement points in the pixel line of the second measurement point.

In order to determine the pixels to be displayed of the continuous measuring point curve between two adjacent measuring points which are vertically offset, it is preferred to enter

Transition point of the continuous measurement point curve calculated over the boundaries between the pixel columns. Advantageously, the continuous measurement point curve is displayed from the first of the two adjacent measurement points to the first transition point in the pixel column of the first measurement point. Advantageously, the continuous measurement point curve is displayed from the first transition point to the last transition point in each case in the swept pixel column. Advantageously, the continuous measurement point curve is displayed from the last transition point to the second of the two adjacent measurement points in the pixel column of the second measurement point. This clearly defines how the measuring point curve should be displayed. This results in a clear, sharp and at the same time stable curve that largely corresponds to the course of the analog measured value.

The transition point (s) are preferably selected from the proportions of the pixels in the columns or pixel lines running length of a direct connecting line of the two measuring points calculated. The curve thus obtained can further increase the proximity to the analog measured values.

Advantageously, the two adjacent measuring points to be connected to a continuous measuring point curve are offset horizontally or vertically by exactly one pixel column or pixel row.

Alternatively, all pixels exceeded by a direct connecting line of the two measuring points to be connected are displayed as part of the continuous measuring point curve. By this alternative method, a sufficiently stable and sharp curve is achieved with very little computational effort.

The invention will be described by way of example with reference to the drawing, in which an advantageous embodiment of the invention is shown. In the drawing show:

Fig. 1 shows the course of a first exemplary analog

Signal and the associated sampled signal;

FIG. 2 shows the course of a second exemplary analog signal and the associated sampled signal in a plurality of sampling passes; FIG.

Fig. 3 exemplary connection possibilities of

Measuring points on a two-dimensional display device; Fig. 4 exemplary connection possibilities of

Measuring points on a two-dimensional display device with superimposed possible associated analog waveforms.

5 shows a first exemplary analog signal superimposed on associated measurement points of a plurality of scanning passes on a two-dimensional display device;

FIG. 6 shows a first exemplary output of a two-dimensional display device resulting from the signal from FIG. 5; FIG.

7 shows exemplary signals with connections according to the invention of measuring points on a two-dimensional display device;

8 shows a second exemplary analog signal superimposed on associated measurement points of a plurality of scanning passes on a two-dimensional display device;

FIG. 9 shows a second exemplary output of a two-dimensional display device here resulting from the signal from FIG. 8, and FIG

10 is a block diagram of an exemplary embodiment of the device according to the invention.

First, the problem and the occurring signals will be explained with reference to FIGS. 1-6. By means of Fig. 7 and 9, the operation of an embodiment of the inventive method illustrated. The operation of the device according to the invention is illustrated with reference to FIG. Identical elements have not been repeatedly shown and described in similar figures.

The following table summarizes the symbols used below:

In Fig. 1, the course of a first exemplary analog and sampled signal is shown. Given an analog trace 12. This can initially run horizontally, then rise, and then again horizontally run. To record this trace 12, a trigger threshold is defined. The time T _Tπgger 10 at which the analog measurement curve 12 exceeds the trigger threshold 11 will be chosen below as a reference point for the representation. The representation is made on a two-dimensional pixel-based display device, which is divided into pixel columns 14 and pixel lines 15. The measuring curve 12 is scanned. The sampling points 17 are shown on the measurement curve 12. To simplify the following description, it is assumed that the measurement curve 12 is to be displayed on the screen only starting from this trigger time T _Tengger 10. For this purpose, a new time axis is defined, with the trigger time 10 representing the zero point. In general, the image display could also begin at any time before or after the trigger time ^τ m _gger 10.

Since triggering and sampling are, independently, is usually the first sample is not exactly on the trigger point, but is offset in time to the trigger offset T _τo sixteenth

Let f _{a be} the sampling rate, then

T _s = \ lf _β (D

the distance between two samples 13. Then, the first sample 13 happens to be in the range after the trigger event

o <r _ro <r _s. (2) If this first sample value 13 has the index k = 0, the * th sample value 13 is also present at the time t _s (k)

t _s (k) = kT _s + T _T0 . (3)

Become a time on the entire screen

^• * Display '^'

shown at N _PX pixel columns 14 calculates a time T _px per pixel column 14 with it

T _PX = T _Dplay IN _PX . (5)

A sample x _s {k) is displayed in the m-th pixel column 14 when

mT _PX <k -T _s (k) + T _τo <(m + \) T _px with 0≤m≤N _px -l (6)

applies. This equation can also be formulated as follows:

k- T _s {k) + T _n

S _px (Jt) = floor (7)

where S _px (k) indicates the pixel column 14 to which the £ th sample is assigned. The floor function rounds off the argument. This results in an average number of samples N _{5 px} per column

_N. - ^r ° "^. ( ₈ )

- ¹ TS- ^J N ^y pχ

An example: Be X _a = IGHz, (9)

follows from it

r _s = l // _a = lnsec. (10)

Have the screen Columns and _display a time of T _Display = 20ßjs, the result is:

T _px = T _Dis≠yy IN _px = 20 // sec / 1000 = 2 «sec (11)

and further

N _{S PX} = ^2QμSQC = 2. (12)

^S - ^PX In sec-1000

Analogous to

f _a = 0.5 GHz, (13)

applies

20ji.ec ₌ S- ^PX In sec-1000

FIG. 2 shows the course of a second exemplary analog and sampled signal 20 in a plurality of sampling passes. The sampling points 21, 22, 23 correspond to three different sampling passages. The distance between sampling points 21, 22, 23 of the same sampling pass is greater than the distance between the pixel lines. Consequently, between the sampling points are pixels in which no sampling point comes to lie. The simplest display mode is the so-called point mode: on the screen only the samples are displayed as dots. If you have only one trace and a small N _{s px} , ie few points per pixel column, you will only see single points on the screen. To see a closed curve on the screen during the point mode, you have to:

either choose N _{5 px} sufficiently large, which is not always possible, or superimpose multiple traces on a periodic signal. Since the trigger offset varies randomly, the result is a closed curve.

In general, the brightness of a pixel on the screen is proportional to the number of times this pixel has been "hit".

Another mode is the line mode; In this case, two temporally successive samples k and k + l are connected by a line in the screen display. If these two points are not in the same screen column, current measuring instruments use three different line-visualization methods. FIG. 3 shows exemplary connection possibilities of measuring points on a two-dimensional display device. A first option is that the line 30 runs completely in the column of the measuring point k 33. Another option is that line 31 is completely in the column of

Measuring point k + l 34 runs. One last option is that in each case half of the line 32 runs in the column of the measuring point k 33 and the measuring point 34 k + l. Disadvantages of these methods shown are that the line does not reflect the actual course of the measurement curve. This is especially true if the line is drawn completely in the column of the measuring point k 33 or the measuring point k + \ 34.

FIG. 4 shows these exemplary connection possibilities of measuring points on a two-dimensional display device with superimposed possibly associated analog signal waveforms. Thus, line 30 is shown completely in the column of the measuring point 33. This reflects well the possible course 40 of the analog signal. As with the measuring points 33 and 34, however, analog signals 41 and 42 are mapped poorly. Artefacts arise. Pixels are displayed that are not passed by the actual analog signal. Similar considerations apply to the line 31 and the possible analog signals 44, 45, 46. The line curve 32 gives better results with the possible analog signals 46, 47, 48, but also does not represent an optimum for all possible analog signals.

In Fig. 5, a first exemplary analog signal 53 is shown superimposed over associated measurement points 50, 51, 52 of several scanning passes on a two-dimensional display device. A measurement curve 53 has a slope of five pixel rows 15 per pixel column 14 and is scanned once per pixel column 14, ie N _s . This periodic trace 53 is scanned and recorded five times, each time slightly offset in time. These sampling points 50, 51, 52 are marked X in the figure, those of the first sample are marked with a circle. Here, the connecting line is drawn completely in the column of the measuring point k 33. The connection to the following measuring point of the same scanning pass is drawn at each measuring point.

FIG. 6 shows a first exemplary output of a two-dimensional display device resulting from the signal from FIG. 5. The artifacts explained with reference to FIG. 4 are shown here. If the pixel frequencies are represented as brightnesses 54, 55, 56, 57, 58 on the screen, the drawing smears on the screen due to the line drawing.

FIG. 7 shows exemplary signals with connections according to the invention of measuring points on a two-dimensional display device. Let N _Lme (k) be the length of the line between the k-th point 63, 66, 68 falling within the pixel column S _PX (k) = m 14 and the A + l-th point 64, 65 , 67, which falls into the pixel column _Spx (k + l) = m + l 14. Then the line 60, 61, 62 is pulled over two columns. For the division of the line 60, 61, 62 in the two columns applies, where N _üπιei (k) the length of the line 60, 61, 62 in the column m and N _Lιme2 (k) the length of the line 60, 61, 62nd in column m + 1 is:

Equation (15) can also be formulated differently: the distance between the i-th and the t + 1-th point is T _s according to Equation (10). With At _t (k) = S _PX (m + 1) T _PX - kt _s (k) ^■

At ₂ (k) = (k + 1) t _s (k + 1) - S _px (m + \) T _PX (16) with T _s = At _t (k) + At ₂ (k)

At _{ (k) is the time interval of the k-th point 63, 66, 68 to the beginning of the next image column m + 1, while At ₂ (k) indicates how far the & + l-th point 64, 65, 67 already in the column m + \ lies. Reformulation of Equation (15) by Equation (16) yields

N _Lm , _e, m = ^ - N _Ume (k) in S _PX (m)

¹ PX

N _Lm eΛ ^k) = ^ _n ^ -Nu) ώ S _PX (m + \) (17)

¹ PX with N _Lιme (k) = N _LιmeΛ (k) ₊ N _Lιmet2 (k)

It can thus be seen that at the measuring points 63 and 64, which both lie at the left edge of their respective pixel column 14, the connecting line 60 runs completely in the pixel column 14 of the measuring point 63. With measuring points 65, 66 arranged centrally in the pixels, the connecting line 61 runs in equal parts in the pixel columns 14 of the measuring points 65, 66. The measuring points 67, 68 are both located at the right edge of their respective pixel column 14. The connecting line thus runs 62 completely in the pixel column 14 of the measuring point 67. Thus, the curve of the curve is reproduced optimally for each measuring point distribution within the pixels. Likewise, the artifacts, as can be seen in the example of FIG. 6, are eliminated.

8 shows a second exemplary analog signal 73 superimposed over associated measurement points 70, 71, 72 of several scanning passes on a two-dimensional display device with pixel columns 14 and pixel lines 15. In contrast to FIG. 5, the connecting lines of the measuring points 70 are , 71, 72 are much stronger here History of the analog signal 73 oriented. Only pixels from the connecting lines which are exceeded by the analogue signal 73 are touched.

In Fig. 9, a second exemplary output 74 of a two-dimensional display device is shown here as a result of the signal 73 of Fig. 8. Since the frequency of crossing each of the pixels touching the connecting lines of the measuring points 70, 71, 72 is identical, there is no smearing of the resulting curve. The curve 74 is continuous, sharp, and optimally adapted to the analog signal 73.

Thus, no artifacts occur in the inventive method. In a conventional linear

Interpolation with N ₃₁₁₁₀ nodes can _cause artifacts:

Is the number of sampling points N _Slät2 in relation to the current line length N (k) _üme too low selected, for example, 10 sampling points, while the vertical distance between two pixels is 200 lines, only one point in every 20th line is either set. If you connect these 10 nodes, artefacts appear again. - If the number of nodes N _smt2 large, for example, 100 nodes while the vertical distance between two pixels is 10 lines, so there is considerable unnecessary computational effort. In addition, a further artifact occurs at a fixed number of N _Sιaa support points: If, for example, N _a0 = I00, then each line point at N (k) _Lmιe = 10 is set a total of 10 times and appears considerably brighter than if the line had a length of N (k) _Lιme = 100, with each pixel being set once. FIG. 10 shows a block diagram of an exemplary embodiment of the device according to the invention. The sampled digitized measurements 104 are transmitted to a scaling device 100. This scales the measured values 104 such that they can be displayed on the display device 103. The scaled measurements 105 are forwarded to the pixel mapper 101. This assigns the measured values to pixels on the display device 103. The pixel connection device 102 generates the continuous measurement point curve if the pixels assigned by the pixel allocation device 101 are not directly adjacent. The display device 103 displays the continuous measurement curve generated by the pixel connection device 102.

The invention is not limited to the illustrated embodiment. As already mentioned, both horizontal and vertical transitions of the measurement point curve can be processed over the pixel rows or columns. Likewise, the application of the method in three-dimensional pixel-based displays is conceivable. All features described above or features shown in the figures can be combined with each other in the invention as desired.

Claims

claims

Method for displaying measured values on a two-dimensional pixel-based display device (103) of a measuring device, wherein the measured values are scanned and digitized, wherein the scanned and digitized measured values comprise measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) in a two-dimensional coordinate system, the resolution being calculated according to time and / or value of each measuring point (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) is higher than the resolution of the two-dimensional pixel-based display device (103), the measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) on the two-dimensional pixel-based display device (103) to a continuous measurement point curve (30 , 31, 32, 60, 61, 62) when the measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) are not located on directly adjacent pixels, thereby geken indicates that in order to determine the pixels to be displayed, the continuous measuring point curve (30, 31, 32, 60, 61, 62) between two measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) the position of the adjacent measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) within the associated pixels, when the measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75 , 76, 77) are not located on directly adjacent pixels.

2. The method according to claim 1, characterized in that for determining the pixels to be displayed, the continuous measuring point curve (30, 31, 32, 60, 61, 62) between two adjacent measuring points (13, 21, 22, 23, 33, 34 , 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) which are offset horizontally one or more transition points of the continuous measuring point curve (30, 31, 32, 60, 61, 62) over the boundaries between the pixel lines (15), that the continuous measuring point curve (30, 31, 32, 60, 61, 62) of the first of the two adjacent measuring points (13, 21, 22, 23 , 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) to the first transition point in the pixel line (15) of the first measuring point (13, 21, 22 , 23, 33, 34,

50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) is indicated that the continuous measuring point curve (30, 31, 32, 60, 61, 62) from the first transition point until the last one

Transition point in each exceeded pixel line

(15) is displayed, and that the continuous measuring point curve (30, 31, 32, 60, 61,

62) from the last transition point to the second of the two adjacent measuring points (13, 21, 22, 23, 33, 34, 50,

51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) in the pixel line (15) of the second measuring point (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) is displayed.

3. The method according to claim 1 or 2, characterized in that for determining the pixels to be displayed, the continuous measuring point curve (30, 31, 32, 60, 61, 62) between two adjacent measuring points (13, 21, 22, 23,

33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) which are vertically offset one or more transition points of the continuous measuring point curve (30, 31, 32, 60 , 61, 62) over the boundaries between the pixel columns (14) that the continuous measuring point curve (30, 31, 32, 60, 61, 62) of the first of the two adjacent measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) to the first transition point in the pixel

Column (14) of the first measuring point (13, 21, 22, 23, 33, 34,

Transition point in the respective exceeded pixel column

(14) is displayed, and that the continuous measuring point curve (30, 31, 32, 60, 61,

51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) in the pixel column (14) of the second measuring point (13, 21, 22, 23, 33,

34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77).

4. The method according to claim 2 or 3, characterized in that the transition point or the transition points from the proportions of in the pixel columns (14) and pixel rows (15) extending length of a direct connecting line of the two measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77).

5. The method according to any one of claims 1 to 4, characterized in that the two adjacent measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63) to be connected to a continuous measuring point curve (30, 31, 32, 60, 61, 62) 64, 65, 66, 67, 68, 75, 76, 77) are offset horizontally or vertically by exactly one pixel column (14) or pixel row (15).

6. The method according to any one of claims 1 to 5, characterized in that all, of a direct connection line of the two measuring points to be connected (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65 , 66, 67, 68, 75, 76, 77) are displayed as part of the continuous measuring point curve (30, 31, 32, 60, 61, 62).

7. A device for displaying measured values on a two-dimensional pixel-based display device (103), comprising a scaling device (100), a pixel allocation device (101) and a pixel connection device, wherein the scaling device ( 100) the sampled and digitized measured values of the two-dimensional pixel-based display device (103) corresponding to measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77), wherein the resolution is scaled by the time and / or value of each measuring point (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) is higher than the resolution of the two-dimensional pixel-based display device (103), wherein pixel allocation device (101) controls the measurement points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) assigns pixels to the two-dimensional pixel-based display device (103), the pixel connection device (102) comprising the measurement points (13, 21, 22, 23, 33, 34, 50, 51, 52 , 63, 64, 65, 66, 67, 68, 75, 76, 77) to a continuous

Measuring point curve (30, 31, 32, 60, 61, 62) connects when the measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63,

64, 65, 66, 67, 68, 75, 76, 77) are not located on directly adjacent pixels, and wherein the pixel connection means (102) comprises the continuous measurement point curve (30, 31, 32, 60, 61, 62) to the display device (103), characterized in that the pixel connection device (102) for determining the pixels to be displayed, the continuous measuring point curve (30, 31, 32, 60, 61, 62) between two Measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64,

65, 66, 67, 68, 75, 76, 77) the position of the adjacent measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) within the associated

Pixels taken into account when the measurement points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) are not on directly adjacent pixels.

8. The device according to claim 7, characterized in that the pixel connection device (102) for determining the pixels to be displayed the continuous measuring point curve (30, 31, 32, 60, 61, 62) between two adjacent measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) which are offset horizontally, one or more transition points of the continuous measuring point curve ( 30, 31, 32, 60, 61, 62) across the boundaries between the pixel lines (15), in that the pixel connection device (102) determines the continuous measuring point curve (30, 31, 32, 60, 61, 62) from the first of the two adjacent measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) to the first transition point in the pixel line (15) of the first measuring point (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) determines that the pixel connection device (102) determines the continuous measurement point curve (30, 31, 32, 60, 61, 62) from the first transition point to the last one

Transition point in each exceeded pixel line (15) sets, and that the pixel connection device (102) the continuous measuring point curve (30, 31, 32, 60, 61, 62) from the last transition point to the second of the two adjacent measurement points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) in the pixel row (15) of the second Measuring points (13, 21, 22, 23, 33, 34, 50,

51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77).

9. Apparatus according to claim 7 or 8, characterized in that the pixel connection device (102) for determining the pixels to be represented the continuous measuring point curve (30, 31, 32, 60, 61, 62) between two adjacent measuring points ( 13, 21, 22, 23, 33, 34, 50, 51,

52, 63, 64, 65, 66, 67, 68, 75, 76, 77) which are vertically offset, one or more transition points of the continuous measuring point curve (30, 31, 32, 60, 61, 62) over the Boundaries between the pixel columns (14) calculates that the pixel connection device (102) determines the continuous measurement point curve (30, 31, 32, 60, 61, 62) from the first of the two adjacent measurement points (13, 21 , 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76,

77) to the first transition point in the pixel column (14) of the first measuring point (13, 21, 22, 23, 33, 34, 50, 51, 52,

63, 64, 65, 66, 67, 68, 75, 76, 77) determines that the pixel connection means (102) detects the continuous measurement point curve (30, 31, 32, 60, 61, 62) of the first transition point to the last transition point in the respective exceeded pixel column (14) defines, and that the pixel connection device (102) the continuous measuring point curve (30, 31, 32, 60, 61, 62) of the last transition point to the second of the two adjacent measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) in the pixel Column (14) of the second measuring point (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) determines.

10. Apparatus according to claim 8 or 9, characterized in that the pixel connection device (102) the transition point or the transition points from the proportions of the pixel columns (14) and pixel rows (15) extending length a direct connecting line of the two measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63,

64, 65, 66, 67, 68, 75, 76, 77).

11. Device according to one of claims 7 to 10, characterized in that the two, to a continuous measuring point curve (30, 31, 32, 60, 61, 62) to be connected adjacent measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64,

65, 66, 67, 68, 75, 76, 77) horizontally or vertically exactly one pixel column (14) or pixel row (15) are offset.

12. Device according to one of claims 7 to 11, characterized in that the pixel connection device (102) all, from a direct connection line of the two to be connected measuring points (13, 21, 22, 23, 33, 34, 50, 51, 52, 63, 64, 65, 66, 67, 68, 75, 76, 77) defined pixels as part of the continuous measurement point curve (30, 31, 32, 60, 61, 62).