EP0037320A1 - Method of representing graphics on a television screen - Google Patents

Abstract

The invention relates to a method for smoothing generated curves for a television scan. This method consists in using, to draw the above-mentioned curves, patterns composed of at least two pixels, the barycenter of which is positioned on the curve to be traced. The generation of the curves can be carried out according to the principle of the algorithm of Bresenham. The invention applies in particular to display devices.

Description

The present invention relates to a method for smoothing the curves generated by black and white or color television scanning.

Generally, we note that, on a television tube, as soon as a line is no longer neither horizontal nor vertical, stair steps appear on the path, the more visible the closer the line horizontal or vertical.

The number of steps and their length depend on the slope and the definition of the image.

It is recalled that the screen of a television tube can be divided into a plurality of fictitious squares, generally designated by the name of image points or pixels (picture elements) defined by the coordinates of their center.

The reproduction or even the production of an image can therefore be obtained by causing, by scanning, the illumination of a corresponding number of image points affected by a determined luminance and possibly a chrominance.

The invention relates more particularly, but not exclusively, to a method of smoothing curves generated by a television scan, according to which the calculation of the points of the screen to be switched on can be carried out using additions and offsets.

We know that it is easy to make a vector originating from the center (XY _o of a pixel and, at the end, the center (XY) of another pixel.

• - à allumer le pixel de coordonnées X_o Y_o,
• - à incrémenter X d'une unité, X passant alors à X₁,
• - à déterminer la valeur de l'écart e (signé) entre le vecteur et le centre du pixel de coordonnées X₁ Y_o,
• - à comparer cette valeur e à une valeur hégale à 2 moitié de la hauteur d'un pixel (0,5 si cette hauteur est égale à l'unité),
• - à incrémenter Y, qui passe à Y₁, si e est supérieur
• - à conberver la valeur Y si e est inférieur à
  
• - à allumer selon le cas le pixel de coordonnées X₁ Y₁ ou X₁ Y₀,
• - à incrémenter à nouveau X d'une unité (X passant à X₂) et à répéter le processus jusqu'à atteindre le pixel de coordonnées X Y .

The generation of this vector can be. performed according to the Bresenham algorithm which consists, in the case where the vector passes through the first quadrant and has a slope less than 45:

• - switch on the pixel with coordinates X _o Y _o ,
• - to increment X by a unit, X then passing to X ₁ ,
• to determine the value of the difference e (signed) between the vector and the center of the pixel with coordinates X ₁ Y _o ,
• - to compare this value e to a value equal to 2 half the height of a pixel (0.5 if this height is equal to unity),
• - to increment Y, which goes to Y ₁ , if e is greater
• - to keep the value Y if e is less than
  
• - to switch on the pixel with coordinates X ₁ Y ₁ or X ₁ Y _{0 as appropriate} ,
• - to increment X again by one unit (X passing to X ₂ ) and to repeat the process until reaching the pixel with coordinates XY.

• - valeur de pente supérieure à 45° X
  
  Y,
• - vecteur dans le deuxième quadrant X → - X,
• - vecteur dans le troisième quadrant X → - X, Y → -Y,
• - vecteur dans le quatrième quadrant Y → -Y.

It is clear that all the other cases can be deduced from this algorithm by various symmetries:

• - slope value greater than 45 ° X
  
  Y,
• - vector in the second quadrant X → - X,
• - vector in the third quadrant X → - X, Y → -Y,
• - vector in the fourth quadrant Y → -Y.

It therefore appears that, according to this generation mode, all the vectors generated in the first octant are formed by a series of horizontal segments, offset from one another, in the form of stair treads.

To eliminate this drawback, it is therefore necessary to carry out a smoothing by proceeding to a local decrease in the contrast between the line and the background and by artificially increasing the definition of the image, the eye of the observer filtering the whole and not perceiving the staircase more distinctly.

To this end, according to a known technique similar to the printing technique, a set of patterns is used, the repeated printing of which gives a more or less dark gray effect.

However, it has been found that by using patterns according to a two-level technique, which has the advantage of using only one bit to code each pixel, the smoothing effect decreases sharply for lower slopes. at 10 °, so that no convincing result could be obtained. This technique is only of interest for high resolution tubes and large screen memory and whose figuration does not require high quality smoothing.

To eliminate this drawback, the invention therefore proposes to use patterns composed of several pixels, the barycenter of which, taking the coefficient, for example in the case of a white on black image, the luminance, is positioned on the line to be traced. We thus make the place of visual perception coincide with the line to be traced, which makes it possible to obtain an impression of continuity.

Furthermore, the use of this principle makes it possible to locally decrease the contrast between the line and the background and to increase the definition of the image in an articulated manner. Its implementation is easy using the value of e of the Bresenham algorithm.

For this purpose, instead of lighting up, for each of the values of e, a single pixel, as in the algorithm described above, a pattern is formed consisting of at least a pair of adjacent pixels arranged on the same column and whose luminance L 'is chosen so that the barycenter is located on the curve to be plotted, so that, for the homogeneity of the trace, all the patterns have approximately the same luminance value.

The application to the method described above for smoothing a color image requires the definition of several intermediate colors C ₁ C _n-1 between the color of the line C _n and that of the background C ₀ ,

According to another characteristic of the invention, so as to present the least contrast between them and between C ₀ and C _n , these intermediate colors are taken on the segment C _n C ₀ traced in a space of substantially uniform colors, for example, space (U, V, Y). The value of the luminances (values Y ' ₁ ' Y '_2' ... Y ' _n-1 in the space X, Y, Z) of these intermediate colors C ₁ , C ₂ ... C _n-1 , thus that their chrominance (for example calculation in the plane U, V or even in the space L *, U *, V * defined in 1976 by the International Commission of Lighting) are therefore intermediate.

Furthermore, the color differences between C ₀ and C ₁ , C ₁ and C ₂ , C _n-1 and C _n , are taken to be substantially equal.

According to another characteristic of the invention, in order to draw the above-mentioned curves, a determined number n of patterns is used a ₀ , a ₁ , a ₂ ... a _n each composed of at least one pair of adjacent pixels located on the same column, the position of the barycenter of the pattern a ₀ being central, while the positions of the barycenters of the other patterns are offset relative to said central position in an increasing and alternating fashion. In this case, the choice of patterns (a ₀ ... a _n ) to be applied is determined as a function of the position of the above value e with respect to a series of values h ₁ ... h _n established in advance. .

• - La figure 1 est une représentation partielle schématique d'un vecteur que l'on désire tracer sur un écran de télévision dont on a représenté les pixels ;
• - La figure 2 représente un organigramme simplifié de l'algorithme de Bresenham pour la génération d'un vecteur de pente inférieure à 45° dans le premier quadrant (premier octant) ;
• - La figure 3 est un tableau dans lequel on a numéroté la luminance L pour une échelle de gris (allant du noir au blanc) ;
• - Les figures 4 et 5 représentent un ensemble de motifs pouvant être utilisés pour générer un trait fin (motifs a, b, c, (figure 4) et pour'générer un trait moyen (motifs d, à g (figure 5);

Embodiments of the invention will be described below by way of nonlimiting example, with reference to the appended drawings in which:

• - Figure 1 is a partial schematic representation of a vector that one wishes to trace on a television screen whose pixels have been represented;
• - Figure 2 shows a simplified flowchart of the Bresenham algorithm for the generation of a vector with a slope less than 45 ° in the first quadrant (first octant);
• - Figure 3 is a table in which the luminance L has been numbered for a gray scale (going from black to white);
• - Figures 4 and 5 represent a set of patterns that can be used to generate a fine line (patterns a, b, c, (Figure 4) and to generate a medium line (patterns d, to g (Figure 5);

Figure 6 is a U, V, Y diagram, used in this example for the determination of intermediate colors.

With reference to FIG. 1, the television screen has been partially represented in the form of a grid in which each square, with sides equal to unity, represents a pixel defined by the X, Y coordinates of its center. In this screen, the vector A, B to be traced originates from the center of the pixel with coordinates X, Y and for its end the center from the pixel with coordinates X, Y. We have also shown in each of the pixels crossed by the vector, the differences e ₁ .... e _n-1 between the center of the pixels and said vector, these differences serving, as previously mentioned, to plot the vector using l Bresenham algorithm.

According to this algorithm, and in accordance with the flowchart represented in FIG. 2, in a first phase, the pixel with coordinates X ₀ Y ₁ is turned on (block 11). Then (block 12) X is incremented by one unit (X _o → X ₁ ), then calculate the difference e ₁ . It is then determined, for example by comparing it with a value 0.5, whether the value e is positive or negative (block 13).

e> O signifying that the vector passes below the center of the pixel.

e <0 signifying that the vector passes above the center of the pixel.

If e is positive, which is the case for e ₁ , Y is incremented by one unit (block 14), and the pixel with coordinates X ₁ Y is then lit (block 15). The system then verifies that X ₁ is less than X _n (block 16) and orders a new incrementation of X which passes to X for the following sequence.

If e is equal to 0.5, which is the case for e ₂ , Y ₁ is not incremented (block 17). In this case, the pixel with coordinates X ₂ Y ₁ is lit.

Similarly, if e is negative, which is the case for e ₃ , Y ₁ is still not incremented and, in this case, the pixel with coordinates X ₃ Y ₁ is lit.

This process continues until the value of X becomes equal to the value X.

We therefore obtain the staircase curve shown in gray in Figure 1.

To eliminate this drawback, the invention proposes a smoothing method consisting in causing, at the end of each of the sequences, the illumination of at least two pixels (at the lim of one) of luminance such as their barycenter (taking as coefficient the luminance), is located on the vector to be plotted.

Indeed, if we realize for example two patterns a and b of which one, the pattern a, is uniformly white and the other, the pattern b is half gray and half white, an observer sufficiently distant will perceive them like dots of different colors and above all positioned differently.

The invention therefore uses this feature to bring the place of visual perception to coincide with the curve to be drawn.

The table shown in Figure 3 provides a numbering of the four luminance values 'L' supplied by a conventional television tube (these values being substantially linear).

• - une image a comprenant deux pixels de coloration 2 (gris clair) et dont la position du barycentre se situe sur un axe médian de référence (position 0) ;
• - une imago b comprenant deux pixels, à savoir : un pixel supérieur de luminance 1 (gris foncé) et un pixel inférieur de luminance 3 (blanc), la position du barycentre étant située à -0,25 (par rapport à l'axe de référence) ;
• - une image c comprenant un pixel supérieur de luminance 3 (blanc) et un pixel inférieur de luminance 1, la position du barycentre étant située à 0,25, par rapport à l'axe de référence.

Thus, the realization of a thin line can be obtained by means of three types of images constituted by at least two adjacent pixels and arranged on the same column, namely (FIG. 4):

• - an image a comprising two pixels of coloration 2 (light gray) and whose position of the barycenter is located on a reference median axis (position 0);
• - an imago b comprising two pixels, namely: an upper pixel of luminance 1 (dark gray) and a lower pixel of luminance 3 (white), the position of the barycenter being located at -0.25 (relative to the axis reference) ;
• an image c comprising an upper pixel of luminance 3 (white) and a lower pixel of luminance 1, the position of the barycenter being located at 0.25, relative to the reference axis.

The choice of the luminances of each of the patterns is chosen in such a way that the sum of the luminances of the two pixels which compose it is constant. In the example shown in Figure 4 it is equal to 4.

In this example

In the case of a vector with a negative slope, the images b and c must be inverted.

To make a line of average thickness, we use the images d, e, f and g with two or three pixels represented in FIG. 5. It will be noted that in these the sum of the luminances of the two or three pixels is constant and equal to 6, with the exception of image g, the sum of the luminances of which is equal to 5. The use of image g will therefore give an impression of discontinuity.

Thus, when generating a curve:

In a similar way to the previous one, when the slope of the vector is negative, it suffices to reverse the columns a and f

In the case where the lines to be produced are very thick, it suffices to apply the fine line algorithm to the edges of this line.

It can be seen that the method described above, whether it is a fine line, a medium line or even a thick line, makes it possible to obtain a smoothing effect by coding the grays on only two bits.

Furthermore, in any case, the number of intermediate grays necessary for obtaining a given quality of smoothing increases with the luminance delivered for the white. Indeed, the perception of a border between two grays depends on the difference in their luminances. The greater this difference, the poorer the quality of the smoothing.

The principle of smoothing a white on black curve previously described can be used for smoothing in color. It requires the definition of several intermediate colors between the color of the line and that of the background. The quality of the imago increases with the number of intermediate colors used.

With reference to FIG. 6, the colors of the line and of the background are represented by two points C ₃ and C ₀ in the color space (U, V, Y). The intermediate colors C and C ₂ are taken on the segment C ₃ C ₀ so as to present the least contrast between them and between C ₀ and C _3.

C ₁ and C ₂ are therefore intermediate in luminance (value of Y) and in chrominance (calculation in the u, v plane).

The differences in luminance between C ₀ and C ₁ , C and C ₂ , C ₂ and C ₃ are taken equal.

• Y₁ étant la luminance an point C₁
• Y₂ étant la luminance au point C₂
• Y₃ étant la luminance au point C₃
• Y_o étant la luminance au point C₀,

So they are written "

• Y ₁ being the luminance at point C ₁
• Y ₂ being the luminance at point C ₂
• Y ₃ being the luminance at point C ₃
• Y _o being the luminance at point C ₀ ,

The chrominance differences between C and C ₁ , C ₁ and C ₂ , C ₂ and C ₃ are taken equal.

u₀, u₁, u₂, u₃ et v₀, v₁,v₂, v₃ étant les coordonnées respectives des points C₀, C₁, C₂, C₃ dans le plan u, v.In the plane u, v this is therefore written:

u ₀ , u ₁ , u ₂ , u ₃ and v ₀ , v ₁ , v ₂ , v ₃ being the respective coordinates of the points C ₀ , C ₁ , C ₂ , C ₃ in the plane u, v.

avec

relations dans lesquelles : (X, Y, Z) sont les composantes dans l'espace (X,Y,Z) 1931 l'indice n réfère à l'illuminant de référence A ou D65.. 1* est appelé clarté psychométrique CIE 1976Of course the determination of the intermediate colors can be carried out by using instead of the space u, v, y, the space (1 ^* , u *, v ^* ) defined by the following relationships:

with

relations in which: (X, Y, Z) are the components in space (X, Y, Z) 1931 the index n refers to the reference illuminant A or D65 .. 1 * is called psychometric clarity CIE 1976

• 

According to this space the difference between two colors is then defined by:

• 

The patterns used for producing color curves can be substantially the same as those described with reference to FIGS. 3 and 4, with the difference that the color black is replaced by the background color C ₀ , for example green, gray dark is replaced by the intermediate color C ₁ (close to C ₀ ), gray. clear is replaced by the intermediate color C ₂ close to that of the line, white is replaced by the color of the line, for example red.

Of course, due to the limits of the electronic tubes used, it is not always possible to produce exactly colors having values calculated in the manner previously described.

The values used are then obtained by trying to respect the chrominancs (proucentage of R, G, B) and to approach the luminances calculated while approaching the luminance of the line, for C, and that of the background, for C ₁ ,

It therefore appears that color smoothing is relatively more delicate than black and white smoothing, because there are two parameters, to be controlled instead of just one and the fact that the eye does not always respond equally to colorful light excitement.

Smoothing is nevertheless obtained by using patterns of the kind developed for black and white smoothing, as a function of the value e of the Bresenham algorithm, the intermediate colors being able to be determined by calculation using a uniform color space.

Claims (10)

1.- Method for smoothing the curves generated by a television scan, characterized in that it consists in using, to carry out the tracing of the above-mentioned curves, patterns composed of at least two pixels whose barycenter is positioned on the curve to draw. 2. A smoothing method according to claim 1, characterized in that the generation of the above curves is carried out according to the principle of the Bresenham algorithm in which for each of the values of e (differences between the curve and the centers of the pixels crossed by the curve) a pattern is formed consisting of at least a couple of adjacent pixels arranged on the same column and whose luminance L 'is chosen so that the barycenter is located on the curve to be traced, making sure that, for the homogeneity of the line, all the patterns have roughly the same luminance value. 3.- Method according to one of the preceding claims, characterized in that a predetermined number of patterns of constant luminance are used and whose barycenters are staggered, and in that for each of the values of e the pattern is chosen whose the barycenter is closest to the vector to be traced. 4.- Method according to one of the preceding claims, characterized in that, to perform the drawing of the above curves, using a determined number n of patterns a _{0 '} a _1' a ₂ ... a _n each composed of at least one pair of adjacent pixels located on the same column, the position of the barycenter of the pattern a ₀ being central while the positions of the barycenters of the other patterns are shifted with respect to said central position in an increasing and alternating manner and in that the choice of the patterns (a .... a) to be applied is determined as a function of the position of the value e with respect to a series of values h ₁ .., h _n established in advance. 5.- Method according to one of the preceding claims, characterized in that in particular in the case where it is desired to draw a fine line three patterns a, b, c, compo are used each of a pair of adjacent plxels situated on the same column, the position of the barycenter of a being central (for example equal to O) while the position of b and of c is offset with respect to said central position (for example -0.25 for b and +0.25 for c) and in that the pattern a is applied when the value e satisfies the relations (h ₁ <e <h ₂ ) and (h ₃ <e <h ₄ ) the motif b is applied when the value of e satisfies the relation (O <e≤h ₃ ) and the motif c is applied when the value e satisfies the relation (h ₂ ≤ e ≤0), h ₁ , h ₂ , ^h ₃ and ^h ₄ being values which can be equal to: -

6.- Method according to one of claims 1 to 4, characterized in that, in particular in the case where it is desired to draw a thick line, four patterns d, e, f, g are used, each consisting of three pixels arranged on the same column, the position of the barycenter of d being central (for example equal to O) the positions of the barycenter of e and f being intermediate (for example respectively equal to +0.33 and -0.33) and the position of the barycenter of g, being extreme, for example equal to 0.5 (these positions being taken with respect to a reference axis common to the two lower pixels) and in that the pattern d is applied when the value of e satisfies the relations (h ₅ ≤e <h ₆ and ( ^h <e≤h ₈ ), the pattern f is applied when the value of e satisfies the relation (h ₉ ≤e <h ₅ ) the pattern e is applied when the value of e satisfies the relation (h ₈ <e≤h ₉ ) and the pattern g is applied when the value of e satisfies the relation (h ₁₀ <e <h ₉ ), relations in which the values urs of h can be equal to:

7.- Method according to one of the preceding claims, characterized in that, in the case of color, several intermediate colors C ₁ and C _n-1 are defined between the color of the line C ₁ and that of the background C ₀ . 8.- Method according to claim 7, characterized in that the intermediate colors C and C _n-1 are taken on the segment C _n , C ₀ traced in a space of substantially uniform colors. 9.- Method according to one of claims 7 and 8, characterized in that the value of the luminances (values Y ' ₁ and Y' ₂ in the space X, Y, Z) of these intermediate colors C ₁ and C ₂ as well as their chroma, are intermediate. 10.- Method according to one of claims 7, 8 and 9, characterized in that the color differences between C ₀ and C ₁ , C ₁ and C ₂ , C ₂ and C ₃ , C _n-1 and C _n are taken substantially equal.

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