WO2006005852A1

WO2006005852A1 - Method and device for filling a geometrical shape

Info

Publication number: WO2006005852A1
Application number: PCT/FR2005/001527
Authority: WO
Inventors: Raphaël LEMOINE
Original assignee: Lemoine Raphael
Priority date: 2004-06-17
Filing date: 2005-06-17
Publication date: 2006-01-19
Also published as: FR2865563B1; FR2865563A1

Abstract

The inventive method for filling a geometrical shape consists in decomposing a geometrical shape into primary simple graphical elements called fragments (1504) and in calculating, at least once, an intersection area (1505) between each fragment and a filter whose surface is greater than a pixel surface. For example said method involves at least one stage for decomposing the base of at least one filter into primary simple graphical elements (1501) called portions , at least one stage for calculating the intersection areas between each fragment and each portion (1505) and, for each pixel, at least one stage for digitally calculating an intersection area function which forms the shape of the filter applied to the pixel (1506) and gives at least one colour element to the pixel to which said filter is applied.

Description

METHOD AND DEVICE FOR FILLING A GEOMETRIC FORM

The present invention aims a new method of filling a geometric shape offering a simple and effective solution to problems of quality and / or speed, inherent in all current methods.

A digital image consists of a finite number of elementary units, called pixels, which each represent a portion of the image in its horizontal and vertical spatial dimensions. Each pixel is characterized at least by a uniform color, and may contain other information (depth, opacity, etc.). In the remainder of this document, each pixel is considered to be of square shape, of unitary edge. Digital images can be acquired by devices such as scanners, digital cameras or camcorders, but can also be created directly by computer programs, for example from geometric information entered by the user, or generated automatically. A mandatory step is the passage of information stored in vector form (continuous) to its digital representation (discrete). This step, implemented in a camera in the form of an analog / digital converter or ADC, is commonly called rasterization in the case of the synthesis of a digital image by a computer. Rasterization simply consists of displaying (filling out) at least one geometric shape in a digital image.

Any method of rasterization of a geometric shape can be decomposed into two distinct steps, repeated at least once for each pixel considered in the digital image: 1 - at least one step of computing at least one piece of information thanks to the geometric data continuous. In the remainder of this document, this step is called "READ". 2 - at least one step of using this information to, optionally, calculate at least one color and write each color information in at least one pixel. In the rest of this document, this step is called "WRITING". The rasterization technique used by the first algorithms for filling geometric primitives (circles, polygons, etc.), often referred to as "Uniform Point Sampling" (or "Uniform Point Sampling") can be decomposed in the same way next :

For each pixel characterized by its coordinates (X, Y) considered,

- READING: One tests if the point with the coordinates (X + 0,5, Y + 0,5) (corresponding to the center of the pixel) is inside or outside the geometrical form. We compute information of Boolean type, with 2 possible values: "inside" or "outside";

- WRITE: If the point is included in the geometric form (the previously calculated information is "in"), the color of the pixel at the coordinates (X, Y) is set to the color of the geometric shape.

It is considered above that a pixel is a discrete point, and not a square of edge and unit area. In fact, a sampling of the continuous function defining the geometric shape at a frequency of 1 per pixel is performed, followed by an unweighted reconstruction of the samples. The images synthesized by this technique suffer from many visible defects such as staircase effects, and unwanted frames.

The ideal rasterization of a geometric shape can be mathematically defined as the sampling at an infinite frequency of a continuous function (step of

READING), followed by the reconstruction of this function by convolution of the samples calculated with a filter defined by the "sin (x) / x" function and of size also infinite (WRITE step). This theoretical approach to rasterization was first described by F. Crow in his article "The Problem Aliasing in Computer-Generated Images Shaded (Communications of the ACM, November 1977, Vol. 20, N ⁰ 11, Pages 799-805 Methods using this sampling / reconstruction approach are commonly referred to as "Weighted Area Sampling", in practice it is impossible to sample a function at an infinite frequency, just as it is It is impossible to apply an infinite-size filter to calculated samples Usually, defects created by implementations of this rasterization method are classified into two broad categories, depending on their cause:

- Sampling at a frequency too low (not infinite). The visible defects due to a sampling frequency that is too low are in the following of this document called ALIASING. These defects are also sometimes called PRE-ALIASING. - Size of the convolution filter too small (not infinite) or function of the convolution filter not adapted. Visible defects due to a convolutional filter size that is too small, or to an inadequate convolution filter function, are hereafter referred to as RASTERlNG. These defects are also sometimes called POST-ALIASING.

The defects of ALIASING (or PRE-ALIASING) can be mitigated, for example by oversampling and / or the use of stochastic techniques, and the defects of RASTERING (or POST-ALIASING) can also be attenuated for example by the use of particular forms of filters (triangular filter, Gaussian, t-sinc, etc.), and / or by using a larger convolution filter size. In the remainder of this document, we consider that a filter is characterized by its BASE and its FORM. For example, a pyramidal filter (in English "tent filter") has a square BASE plane and a vertex outside the plane of the base. Starting from the remark that the sampling of a function at an infinite frequency corresponds in fact to the integration of this function, E. Catmull proposed in his article "A Hidden Algorithm With Anti-Aliasing" (Proceeding of SIGGRAPH 78, Atlanta, Georgia, August 23-25, 1978) a rasterization method wrongly referred to as "Unweighted Area Sampling" (or "Unweighted Surface Sampling"). This consists of breaking down the geometric shape into simple primitives included in one and only one pixel, calculating the area of overlap of all the primitives included in each pixel, then writing the color value multiplied by the ratio between the coverage area and the total area of one pixel. This technique can be broken down as follows:

For each pixel characterized by its coordinates (X, Y) considered: - READ: One calculates the total area of intersection between the square of coordinates (X, Y), (X + 1, Y + 1) and the geometrical form . This is easily done by a prior decomposition of the geometric shape into simple primitives such as triangles, trapezoids and rectangles, all included in the pixel under consideration, decomposition carried out thanks, for example, to the use of an algorithm of " Scanning Line "(Scanline); - WRITE: If this area is non-zero, the pixel color at the coordinates (X, Y) is set to the color of the geometric shape multiplied by the ratio between the intersection area and the total area of a pixel .

This method does not suffer from any ALIASING (or PRE-ALIASING), the READING step consisting of an integration and not a sampling. However, since the WRITE step is unweighted (no operation equivalent to convolution by a filter), the so-called unweighted surface sampling method suffers, in contrast to the weighted surface sampling methods, very strong and very visible effects of type RASTERING.

According to a first aspect, the present invention aims a method of filling a geometric shape, characterized in that it comprises:

at least one step of decomposing the geometric form into simple graphic primitives, called "fragments" and

at least one step of calculating the area of intersection between each fragment and a filter whose surface is greater than the surface of a pixel. This process, which may be termed "Weighted Pixel Integration", is the first to possess the combined advantages of the two main current techniques, namely: - like unweighted surface sampling, there is no creation of defaults of ALIASING and

- like weighted surface sampling, RASTERING defects are attenuated, depending on the shape and size of the filter.

It is important to note that this method is also the first weighted rasterization method (with the possibility of using a filter of any base and shape), but without sampling, since it is based on exact geometric operations such as intersection , union, addition and integration.

According to particular features, the method as succinctly set forth above comprises: at least one step of decomposing the base of at least one filter into simple graphic primitives, called "portions";

at least one step of calculating the areas of intersection between each fragment and each portion and

for each pixel, at least one step of numerical calculation of a function of the intersection areas comprising the shape of the filter applied to the pixel, said function giving at least one color element for said pixel to which said filter is applied.

According to particular features, during the step of decomposing the base into portions, each portion is included in one and only one pixel.

According to particular features, during the step of decomposing the geometric shape into fragments, each fragment is included in one and only one pixel.

According to particular characteristics, during the step of decomposing the base of at least one filter, the intersections of the portions are empty and their meeting is equal to said base.

According to particular features, during the step of decomposing the geometric shape, the intersections of the fragments are empty and their meeting is equal to said geometric shape.

According to particular characteristics, during the numerical calculation step, a weighting step of the different areas is carried out.

According to particular characteristics, during the weighting step, each area is weighted according to a function whose value depends on the distance from said intersection to the center of the pixel to which said filter is applied. For example, the decreasing function is an inverse function, that is, f (d) = z * (dmax - d), where "d" is the distance considered, "z" is any constant, and "dmax" the maximum value that d. According to particular characteristics, during the numerical calculation step, a summation or addition of the possibly weighted intersection areas is performed, which forms the shape of the filter applied to the pixel. With each of these provisions, the numerical calculation step is easy and quick to implement.

According to particular features, the numerical calculation step comprises a step of multiplication by the ratio between the area of the pixel and the total area of the filter. According to particular features, during the step of decomposing the base of a filter, said filter has a rectangular base, each side of which is a multiple of the corresponding side of a pixel. . ^•

Thanks to these provisions, the different process steps can be easier and quick to implement. According to particular characteristics, during the step of calculating the intersection areas, at least one first intersection area is calculated by implementing at least one fragment and at least one portion and at least one other area is calculated. intersection, for another pixel to which the same filter is applied, by implementing said first intersection area. Indeed, the inventor discovered that for the rectangular shapes described above, there were relationships between the intersection areas. For example, for a rectangular base that corresponds to four pixels (2 x 2) spanning nine pixels around the pixel to which the filter is applied, for each column or each line, the sums of the extreme areas are equal to central area (the calculation of 4 areas allows the calculation of 9 areas). For example, for a rectangular base that corresponds to nine pixels (3 x 3) extending over nine pixels around the pixel to which the filter is applied, for each column or each line, the end areas are each equal to the central area.

According to particular characteristics, during the numerical calculation step, the color is weighted by a filter. It is observed that said filter may be, for example, Gaussian, sinusoidal, etc. For this purpose, it is sufficient to calculate the center of gravity of the intersection between each fragment and each portion, then the distance between this center of gravity and the center of the pixel to which the filter is applied.

According to particular characteristics, the shape of the filter is an integral of a polygonal shape.

According to particular features, the method as succinctly described above is carried out successively for successive pixels on the same line, by successively treating the successive lines of the image to constitute. This so-called Scanline technique (or "Scanning Line") makes it possible to reduce the number of calculations necessary to implement the method that is the subject of the present invention since the calculations of portions, fragments or intersection areas made for a pixel can at least partially reused for at least one pixel located near the pixel in question. According to a second aspect, the present invention aims at a rasterization device of a geometrical shape, characterized in that it comprises: at least one means of decomposing the geometric form into simple graphic primitives, called "fragments" and

at least one means for calculating the area of intersection between each fragment and a filter whose area is greater than the area of a pixel. Since the advantages, aims and features of the second aspect of the present invention are similar to those of the first aspect of the present invention, they are not recalled here.

Other advantages, aims and features of the present invention will emerge from the description which follows, made for explanatory and non-limiting purposes with reference to the accompanying drawings in which:

FIG. 1 represents a device according to one aspect of the present invention,

FIG. 2 represents a succession of steps implemented in a particular embodiment of the method that is the subject of the present invention,

FIG. 3 represents a succession of steps carrying out one of the steps illustrated in FIG. 2,

- ^'Figure 4 shows a succession of steps providing any of the steps illustrated in Figure 2,

FIG. 5 represents a succession of steps carrying out one of the steps illustrated in FIG. 2; FIGS. 6A, 6B and 6C represent a succession of steps carrying out one of the steps illustrated in FIG. 2;

FIG. 7 represents a particular polygon,

FIG. 8 represents pixel coordinates and a decomposition of a geometric shape into fragments in a particular embodiment of the method that is the subject of the present invention,

FIG. 9 represents nine particular pixels represented in FIG. 8;

FIG. 10 shows the portions of a square-size filter of two-by-two pixel size applied to the central pixel illustrated in FIG. 8 as well as a part of the geometrical shape considered corresponding to said filter; FIG. trapezoidal fragment of the central pixel illustrated in FIG. 9, the intersection areas of the nine filter portions extending on the central pixel illustrated in FIG. 9 with this trapezium-shaped fragment with the convention which has been represented at the top left, the intersection with the lower right portion,

FIG. 12 represents, for a rectangle-shaped fragment of the central pixel illustrated in FIG. 9, the intersection areas of the nine filter portions extending on the central pixel illustrated in FIG. 8 with this rectangle-shaped fragment with the same convention as for Figure 10, FIG. 13 represents the addition of the areas represented in FIGS. 11 and 12,

FIG. 14 represents, for each pixel whose applied filter extends over the central pixel illustrated in FIG. 8, the various non-empty intersection areas of the fragments and portions that extend on said central pixel; FIG. 15 represents nine intersection areas of the filter portions illustrated in FIG. 9 and the geometrical shape considered for synthesizing the color of the central pixel illustrated in FIG. 8,

FIG. 16 represents a logic diagram of steps implemented in a particular embodiment of the method that is the subject of the present invention; and FIG. 17 represents, schematically, the constitution of a particular filter.

Throughout the description, the following definitions are used:

- "simple polygon": a polygon defined by a list of vertices and having no intersection between the segments connecting these vertices;

- "composite polygon": a polygon defined by at least one list of vertices and having no intersection between the segments connecting these vertices;

- "arbitrary polygon": a polygon defined by at least one list of vertices and possibly having intersections between the segments connecting these vertices.

In the description, only the processing of single polygons and composite polygons is described, it being understood that the present invention is not limited to these particular types of polygons.

In the description, at least one particular embodiment of a method and a device for decomposing a geometric shape that combines favorably with the present invention (FIGS. 1 to 7) and then a particular embodiment of the invention are described first. process of the present invention (Figures 8 to 16) before describing advantageous combinations of different methods.

To define a synthetic image, this image is traditionally broken down into polygons. In the remainder of the description, the filling of one of these polygons is described, the other polygons being treated in the same way as described below or in another way, according to their defined complexity, for example, by Ie. number of vertices (the method described below is employed when the number of vertices is greater than a predetermined number.

A polygon is defined by a list of vertices through which the perimeter passes successively. On this perimeter, the summit preceding the first summit of the list is the last top of the list. Each vertex is defined by an abscissa "x" and an ordinate "y". Traditionally, the origin of the abscissa and the ordinate are at the bottom left corner of the image (or display).

Throughout the description, a "monotone" polygon is called a monotone polygon in its vertical dimension, "y".

A monotonic section is defined as a path passing through successive vertices of the polygon between a "lowest" vertex (a vertex whose neighboring vertex not in the monotonic section has an ordinate "y" greater than or equal to its own and, in case of equality, the next vertex has an ordinate "y" greater than or equal to its own, and so on) and a highest vertex (vertex whose neighboring vertex is not in the monotonic section has an ordinate "y" inferior or equal to its own and, in case of equality, the next vertex has an ordinate "y" inferior or equal to its own, and so on). The next term, vertex A is "below" vertex B, signifies that the ordinate of vertex A is strictly less than the ordinate of vertex B. Respectively, the term "above" means that the ordinate of the first is strictly greater than the ordinate of the second.

One defines a direction of course of the perimeter of the polygon, positive or negative, corresponding, in the technical literature to the terms "in the direction of the clockwise" ¹ (in English clockwise or CW) and "in the opposite direction of the needles of a watch "(in English conterclockwise or CCW).

FIG. 1 shows a computer 50 comprising a volatile memory 51, a non-volatile memory 52 | a processor 53, a display screen 54, a keyboard 55, a pointing device 56, an image memory 57 and a data output means 58.

The computer 50 is of known type, for example a PC (for "personal computer" or personal computer). The non-volatile memory 52 retains a computer program allowing the processor 53 to implement the process steps illustrated in FIGS. 2A, 2B and 3. The image memory 57 keeps a point-by-point representation of the image to be displayed on the screen. the display screen 54 or to be transmitted by the data output means 58. The data output means may be an interface for remote transmission, for example a modem, a network card or a non-volatile data carrier, for example a digital compact.

The processor 53, the nonvolatile memory 52, the volatile memory 51, the data output means 58 and the image memory 57 together constitute the characteristic means of the image display device according to the present invention comprising a means for outputting a signal representative of an image and suitable processing means for decomposing a geometric shape defined by at least one ordered and cyclic list of vertices, to perform: at least one step of searching for monotonic sections on the succession of vertices defined by each said ordered list and the boundaries of these sections, according to at least one dimension and a direction; at least one step of grouping the two-by-two monotonic sections to define regions of said geometric form;

at least one step of classifying said regions into "internal" regions for which the inside of the shape is inside the region in question, and into "external" regions for which the inside of the shape is at outside the region;

a step of sorting the outer regions according to their coordinates in a dimension and a direction; . ^••

a step of decomposing the geometrical shape into simple internal geometrical shapes, decomposition using the internal and external regions. FIG. 2 shows steps implemented in a particular embodiment of the method that is the subject of the present invention.

During a step 200, a direction and direction of polygon filling is defined, for example, by default or implicitly, from bottom to top, ie horizontal line by horizontal line, in the direction of the polygons. orderly increasing. During a step 205, determining a start vertex, as shown in Figure 3, ^'which is described below.

For the brevity of the description, for the description of FIG. 3, the following notations are used:

- "SC" désigrieje ^current peak, - "SD" refers to the departure node which is determined according to the logic diagram illustrated in Figure 3,

- "SX. Y" designates the ordinate of the vertex SX (X taking all possible numerical values to define the vertices of the list of vertices which define the polygon),

- "#SS (SX)" means the vertex following the vertex "SX" and - #ROUTE (SMIN, SMAX ₁ SENS) creates a monotonic section with SMIN and SMAX as monotonic section ends and SENS as sense.

During a step 305, the current vertex "SC" is defined as the first vertex named SO in the list of vertices defining the polygon, and the current vertex SC is defined as the provisional start vertex SD. During a step 310, the new current vertex is defined as the vertex following the previous current vertex. During a step 315, it is determined whether the current vertex is the vertex SO, that is to say the first vertex of the list of vertices defining the polygon and also the vertex following the last vertex of this list.

If the result of step 315 is negative, during a step 320, it is determined whether the ordinate of the current vertex is less than or equal to the ordinate of the provisional starting vertex. If the result of step 320 is negative, step 310 and the following steps are repeated. If the result of step 320 is positive, during a step 325, it defines as a new provisional starting summit, the current vertex and repeating step 310 and the following ones.

If the result of step 315 is positive, that is to say if the current vertex is the peak SO, during a step 330, the current starting vertex is defined as the current vertex. Then, during a step 335, defining as new current vertex the vertex following the previous current vertex in the list of vertices defining the polygon. During a step 340, it is determined whether the ordinate of the current vertex is equal to the ordinate of the provisional start vertex. If so, during a step 345, the new current vertex is defined as the current vertex and step 335 and the following ones are repeated. When the result of step 340 is negative, proceed to step 210, FIG.

It is observed that following step 205, we found a starting vertex which is one of the lowest vertices of the polygon and whose next vertex has an ordinate strictly greater than that of the starting vertex.

During a step 210, all the monotonic sections of the polygon are determined according to the logic diagram illustrated in FIG. 4. For the description of FIG. 4, the following notations are used:

- "SD" means the starting vertex,

- "SMIN" refers to a beginning vertex of monotonic section.

- "SMAX" means a thin vertex of monotonic section, - "#SS (SX)" means the vertex following the "SX" vertex,

- "SENS" means the current direction (the direction is positive, +1, when it corresponds to a growth of ordinates and negative, -1, when it corresponds to a decrease of the ordinates),

"SS" refers to the next vertex and "SC" refers to the current vertex.

FIG. 4 shows a step 405 during which the starting vertex is defined as the beginning vertex of the monotonic section, as the vertex following the starting vertex, and as the current direction, the positive direction.

During a step 410, the following vertex is defined as the current vertex, and as a new vertex following the vertex that follows the preceding preceding vertex, in the circular list of vertices defining the polygon.

During a step 415, it is determined whether the current direction is the positive direction or the negative direction. If the current direction is the positive direction, during a step 420, it is determined whether the ordinate of the next vertex is strictly less than the ordinate of the current vertex. If so, during a step 425, a monotonic section is created in an array of monotonic sections and given the following attributes: SMIN, SMAX and SENS. Then, during a step 430, the current direction in the negative direction is passed, the SMIN to SS and the SMAX to SC, then repeating step 410 and the following. If the result of step 420 is negative, during a step 435, it is determined whether the ordinate of the next vertex is strictly greater than the ordinate of the current vertex. If no, repeat step 410 and the following. If so, during a step 440, SMAX is defined as the next vertex and step 410 and the following are repeated.

If during step 415, it is determined that the current direction is the negative direction, during a step 445, it is determined whether the ordinate of the next vertex is strictly greater than the ordinate of the current vertex. If so, during a step 450, a monotonic section is created in an array of monotonic sections and given the following attributes: SMIN, SMAX and SENS. Then, during a step 455, it is determined whether the vertex is the starting vertex. If not, during a step 460, we pass the current direction in the positive direction, the SMIN to SC and the SMAX to SS, then repeating step 410 and following. If the result of step 455 is positive, go to step 215 (see FIG. 2).

If the result of step 445 is negative, during a step 465, it is determined whether the ordinate of the next vertex is strictly less than the ordinate of the current vertex. If no, repeat step 410 and the following. If so, in a step 470, SMIN is defined as the next vertex and step 410 and the following are repeated.

It is observed that following step 205, all the monotonic sections of the polygon have been found and entered in the table of monotonic sections, which comprises, for each monotonic section, the following information:

- beginning summit of monotonic section "SMIN",

- top end of monotonic section "SMAX",

- "YCUR", the current ordinate,

- "XCUR", the current abscissa, - "SENS", the direction of travel (positive, if the lowest vertex is before the highest vertex in the list of vertices that define the polygon, if not negative),

- pointer to the next monotonic section ^* "NEXT",

- pointer to the monotonic section "PREV" and

- "DONE" flag (set to "false" default, which indicates if the monotonic section has already been fully exploited for the decomposition and possibly the filling of the polygon (see below).

For example, for the polygon illustrated in FIG. 7, the monotonic section table comprises the following monotonic sections:

n noo .. d dddddd dd ffinn d ee dd sense dee next section previous section section section section

0 5 6 positive 1 5 1 7 6 negative 2 0

2 7 10 positive 3 1

3 12 11 negative 4 2

4 13 14 positive 5 3

5 4 14 negative 0 4

In step 215, the direction of the polygon is determined (see steps 505 and 510, FIG. 5). ^•;

During a step 220, the regions are determined and classified into internal regions, for which the interior of the polygon is between the two monotonic sections defining the region, and outer regions, for which the interior of the polygon is the outside of the two monotonic sections defining the region, according to the logic diagram illustrated in FIG. 5, starting from the end of step 510. For the description of FIG. 5, the following notations are used:

- "#SECSORDER (Param1, Param2)" is a function that returns the value "1" if the first 1.5 monotonic section (Param 1) is to the left of the second monotonic section

(Param2) and returns the value "0" if the first monotonic section (Param 1) is to the right of the second monotonic section (Param2);

- "#NEWINTERNAL (Param1, Param2)" is a function that adds a region to the list of internal regions, with the first parameter (Param 1) as the left monotonic section 0 and the second parameter (Param2) as the right monotonic section;

- "#NEWEXTERNAL (Param1, Param2)" is a function that adds an external region to the list of external regions, with the first parameter (Parami) as the left monotonic section and the second parameter (Param2) as the right monotonic section; 5 - "#NEXT (Param)" is a function that returns the next monotonic section of the monotonic section passed as parameter (Param);

- "# NEXT2SECS (Param)" is a function that returns the two monotonic sections following the Param section, in SECO and SEC1 values and increments the value of PTRSEC by two (takes the next one from the next); 0 - "PTRBASE" is a pointer to a monotonic section;

- "PTRSEC" is a pointer to a monotonic section, initially pointing to the last monotonic section created in step 210 and

"ORDERBASE" and "ORDER" are variables taking the numerical values "0" OR ¹ T. 5 FIG. 5 shows a step 505 in which PTRBASE is assigned the value PTRSEC, the function # NEXT2SECS is carried out (PTRSEC) and ORDERBASE is assigned the value from the #SECSORDER function (SEC0, SEC1). During in a step 510, it is determined whether ORDERBASE is "1". If so, during a step 515, the function #NEW! NTERNAL (SECO, SEC1) is performed. Otherwise, during a step 520, the function (#NEWINTERNAL (SEC1, SECO) is performed.

It is observed that step 510 amounts to determining the direction of the polygon: if ORDERBASE is "1", the direction of the polygon is in the opposite direction of clockwise;

- if ORDERBASE is "0", the direction of the polygon is in a clockwise direction.

Following either of the steps 515 and 520, in a step 525, it is determined whether PTRSEC is PRTBASE. If yes, step 220 is completed. Otherwise, during a step 530, the function # NEXT2SECS (PTRSEC) is performed and the variable ORDER is assigned the value of the function #SECSORDER (SEC0, SEC1). Then, during a step 535, it is determined whether the variable ORDER takes the value of ORDERBASE. If yes, during a step 540, it is determined whether the variable ORDER takes the value "1". If yes, during a step 545, the function #NEWI NTERNAL (SECO, SEC1) is carried out and return to step 525. Otherwise, during a step 550, the function #NEWINTERNAL (SEC1 is performed , SECO) and return to step 525.

If the result of step 535 is negative, during a step 555, it is determined whether the variable ORDER takes the value "1". If so, during a step 560, the function #NEWEXTERNAL (SECO, SEC1) is carried out and we return to step 525. Otherwise, during a step 565, the function #NE WEXTE RN AL is performed. (SECI, SECO) and return to step 525.

Following step 220, the table of internal regions is available, which contains for each region the following information:

- left mononotic section, - right monotonic section,

- order of departure from the region; and the external region table, which contains for each region the following information:

- left mononotic section,

- right monotonic section, - ordered departure from the region;

For example, for the polygon illustrated in FIG. 7, the 6 monotonic sections determine 3 regions, of which 2 are internal regions and 1 is an external region. The 2 internal regions created have the following pairs of monotonic sections: no. of region left section right section 0 0 5

1 2 1

The external region created has the following pairs of monotonic sections: no. of region section left section right

0 3 4

During a step 225, the outer regions are sorted in order of increasing ordinates. Alternatively, during this sorting step, the internal regions are also sorted to save time in their use.

During a step 230, the polygon is decomposed into y-monotone polygons, and, optionally, the polygon is filled. For this purpose, the logic diagram shown in FIGS. 6A to 6C is implemented. For the description of FIGS. 6A to 6C, the following notations are used:

- "NSTART" means the number of internal regions remaining to be processed,

- "NSPLIT" means the number of external regions remaining to be processed,

- "NTEMP" means the number of pointers in a temporary stack called "TEMP", LIFO type, pointers to y-monotone polygons, - "YM" means a pointer to a y-monotone polygon defined by YMIN, its minimum ordinate (or start), YMAX, its maximum (or end) ordinate, a left monotonic section RG and a straight monotonic section RD,

- "RG" means a left monotonic section (the points immediately to the left of this monotonic section are outside the polygon and the points immediately to the right of this monotonic section are in the polygon),

- "RD" means a straight monotonic section (the points immediately to the right of this monotonic section are outside the polygon and the points immediately to the left of this monotonic section are in the polygon),

- "RM" a temporary pointer of monotonic section used for the fusion tests, - "RG.SMAX.Y" the ordinate of SMAX for the left monotonic section,

- "RD.SMAX.Y" the ordinate of SMAX for the straight monotonic section,

- "DG" is a flag (linked to the left monotonic section),

- "DD" is a flag (linked to the right monotonic section),

- "GSPLIT" is a pointer to the current external region, - "# GS1 (Y, YMAX)" is the first outer region whose ordinate is greater than or equal to the current ordinate Y on the left and right monotonic sections and whose ordinate is strictly inferior to the current YMAX,

- "#GSN (GSPLIT, YMAX)" is the outer region following the current external region GSPLIT whose ordinate is greater than or equal to the ordinate ordinate on the left and right monotonic sections and whose ordinate is strictly lower than the YMAX current,

- "#GST (RG, RD, GSPLIT)" is the result of a test if the current external region GSPLIT cuts, that is to say, lies between, the right and left monotonic sections for the current ordinate, this result taking the value zero if it is negative and the value 1 if it is positive,

- "#RU (RG, RD, Y)" means the function of updating the left and right monotonic sections for a given Y-ordinate, that is, sets YCUR to the current ordinate and calculates the abscissa corresponding for XCUR to take this calculated value,

- "#PUSH (RG, RD)" means the function of creating a new y-monotone polygon with as RG attributes as left monotonic section and RD as right monotonic section, and storing a pointer on this polygon in the TEMP stack, - "#POP ()" is the function that removes the most recent pointer from the stack

TEMP and

- "#GSR (GSPLIT)" is the function that removes the outer region from the list of external regions.

During a step 605 (FIG. 6A), NTEMP is defined as zero, NSPLIT is the number of external regions, and NSTART is the value of the number of internal regions. During a step 610, it is determined if NTEMP is strictly greater than zero. If yes, during a step 615, YM is defined as the content of the stack TEMP, NTEMP is decremented, the function #POP () is performed and step 630 is proceeded to. If the result of the step 610 is negative, during a step 620, it is determined whether the number NSTART is strictly greater than zero. Otherwise, the process is complete. If yes, during a step 625, a y-monotone polygon is created in an array of y-monotone polygons and assigned YMIN, which is the ordinate ordinate as the starting ordinate, and the left and right monotonic sections of Ia. next internal region in the list of internal regions, the pointer YM is set to the value of a pointer pointing to this internal region, NSTART is decremented and then step 630 is performed during which, for the y-monotone polygon, RG takes the value of a pointer to the left monotonic section of the inner region and RD takes the value of a pointer to the right monotonic section of the inner region.

During a test 635, the value of RG.SMAX.Y-RD.SMAX.Y is determined, the first term designating the SMAX ordinate for the left monotonic section and the second term designating the SMAX ordinate for the right monotonic section. If this value is strictly negative, step 640 is carried out. If it is zero, step 645 is carried out. If it is strictly positive, step 650 is carried out.

In step 640, the left flag DG is set to 1, the right flag DD to zero, and YMAX is set to RG.SMAX.Y. In step 645, the left flag DG is set to 1, the right flag DD is set to 1 and YMAX is set to RG.SMAX.Y. During step 650, the left flag DG is set to zero, the DD right flag at the value 1 and YMAX takes the RD value. SMAX. Y.

Following any of steps 640, 645 and 650, in step 655, it is determined whether the number of NSPL1T of external regions remaining to be processed is strictly positive. Otherwise, during a step 660, GSPLIT is set to zero, which means there is no more split to process. If the result of step 655 is positive, during a step 665, GSPLIT is set to # GS1 (Y ₁ YMAX), which can take the value "0" if there is no external region meeting the search criterion.

During a step 670 (FIG. 6B), it is determined whether GSPLIT is different from zero. If so, during a step 675, the left and right monotonic sections are updated with the ordinate of GSPLIT. Then, in a step 680, it is determined whether #GST (RG, RD GSPLIT) is 1, that is, whether the outer region GSPLIT is between the monotonic sections RG and RD. If not, during a step 685, GSPLIT takes the value #GSN (GSPLIT, YMAX) and then repeats step 670 and following. If the result of step 680 is positive, during a step 690, two new y-monotone polygons are created with, respectively RG and the left monotonic section of GSPLIT, on the one hand and the right monotonic section of GSPLIT. and RD, on the other hand, and store in the stack TEMP, two pointers on these polygons, increment two NTEMP, remove the outer region GSPLIT from the list of external regions and close the y-monotone polygon YM current , that is to say that its variable YMAX is assigned the current ordinate, and then repeats step 610 and the following ones.

If the result of step 670 is negative, during a step 695, the left and right monotonic sections are updated with the YMAX ordinate. During a step 700, it is determined whether the left flag is equal to 1. If yes, during a step 705, the pointer of the left monotonic section of the current y-monotone polygon is set to the value of the pointer on the current y-monotone polygon, the DG flag of the left monotonic section is set to "1". Following step 705 or if the result of step 700 is negative, during a step 710, it is determined whether the right flag is equal to 1. If yes, during a step 715, the pointer of the right monotonic section of the current y-monotone polygon is set to the value of the pointer on the current y-monotone polygon, the flag DD of the right monotonic section is set to "1".

Following step 715 or if the result of step 710 is negative, during a step 720 (FIG. 6C), it is determined whether the left flag DG is equal to 1.

If yes, during a step 725, it is determined whether the direction of the left monotonic section RG. SENS is positive. If so, during a step 730, the variable RM, monotonic melting section, is set to the RG.NEXT value, that is to say the value of the pointer on the monotonic section following the left monotonic section. Otherwise, during a step 735, the variable RM, monotonic melting section, is set to the value RG. PREV, that is, say the value of the pointer on the monotonic section preceding the left monotonic section. Following one of the steps 730 or 735, during a step 740, the y-monotone polygon is closed, defining its YMAX. Then, during a step 745, it is determined whether the variable RM is equal to the right monotonic section. If yes, repeat step 610 and the following steps. Otherwise, during a step 750, it is determined whether the flag DONE of the monotonic section RM is equal to 1. If yes, during a step 755, a new y-monotone polygon is created and attributed to it as left monotonic section, the left monotonic section of the polygon pointed to by the monotonic fusion section, RM. YM. RG, and, as straight monotonic section the current straight monotonic section RD and the NTEMP counter is incremented.

Following step 755 or if the result of step 750 is negative, step 610 and the following steps are repeated.

If the result of step 720 is negative, during a step 760, it is determined whether the direction of the straight monotonic section RD. SENS is positive. If yes, during a step 765, the variable RM, monotonic melting section, is set to the value RD. NEXT, that is, the value of the pointer on the monotonic section following the right monotonic section. Otherwise, during a step 770, the variable RM, monotonic merge section, is set to the value RD. PREV, that is, the value of the pointer on the monotonic section preceding the right monotonic section. Following one of the steps 765 or 770, during a step 775, the y-monotone polygon is closed, defining its YMAX. Then, during a step 780, it is determined whether the variable RM is equal to the left monotonic section. If yes, repeat step 610 and the following steps. Otherwise, during a step 785, it is determined whether the flag DONE of the monotonic section RM is equal to 1. If yes, during a step 790, a new y-monotone polygon is created and attributed to it as left monotonic section, the current left monotonic section and as straight monotonic section, the right monotonic section of the polygon pointed by the monotonic melting section, RM.YM.RD and the NTEMP counter is incremented.

Following step 790 or if the result of step 785 is negative, step 610 and the following steps are repeated. By implementing the logic diagram illustrated in FIGS. 2 to 6C, the initial polygon is decomposed into y-monotone polygons, each y-monotone polygon being defined by a left monotonic section, a right monotonic section, a minimum ordinate and an ordinate. Max.

A complex geometric shape is thus decomposed into an ordered graph of simpler geometric shapes (here, y-monotone). In variants, a decomposition into triangles or trapezoids is performed.

It is observed that the number of "y-monotone" polygons created is at most equal to one less than twice the sum of the number of internal regions and the number of external regions.

It is observed that certain "y-monotone" polygons created as indicated above have a zero height but that they have, at most, two predecessors (that is to say that their lower side touches at most two other polygons " y-monotones "in the processed polygon) and two successors (that is, their upper side touches at most two other" y-monotone "polygons in the processed polygon).

Alternatively, the filling of the polygon is performed during each of the steps 675 and 695. It is observed that the processing time of steps 200 to 220 is substantially proportional to the numbers of the vertices of the polygon to be broken down.

In contrast, the duration of step 225 is on average proportional to the number of external regions multiplied by the logarithm of this number, and the duration of step 230 is, in practice, substantially a function of the number of split vertices. As a variant, to reduce the total processing time, if the number of split vertices is greater than a predetermined number by the number of starts, or if the number of split vertices is a predetermined number of times greater than the number of vertex starts, it is treated the polygon from top to bottom (filling the "y-monotone" polygons by decreasing ordinates) and not, as indicated above, from bottom to top (filling of the "y-monotone" polygons in order of increasing ordinates).

In a preferred embodiment, during the determination of the monotonic sections, the bounding boxes of each monotonic section are created and, in the course of the steps 665 and 685, only the external regions whose two abscissas are between the extreme abscissae of the bounding boxes of the two monotonic sections considered.

In the case of a so-called "outer" polygon surrounding at least one other polygon, called "internal", the same steps of determination of the internal regions and of the external regions are carried out as explained above and before carrying out the In step 225, the outer regions of each inner polygon are considered internal regions of the outer polygon and the inner regions of each inner polygon are considered as outer regions of the outer polygon.

The table below gives a comparison of the decomposition time and filling (in milliseconds) of "massively" concave polygons for the method described in the document Gordon cited in preamble and for the method object of the present invention, on the same computer. : number of points duration "Gordon" duration present invention gain ratio

4000 420 330 1, 3 5000 720 390 1.8

6000 1300 460 2.8

7000 1800 550 3.3

8000 2500 630 4.0

9000 3900 760 5.1

10000 5300 890 6.0

15000 16000. 1800 8.9

20000 33000 3300 10.0

25000 60000 5200 11.5

30000 96000 7900 12.2

35000 140000 11000 12.7

40000 205000 14000 14.6

It is observed that the more the massively concave polygon has vertices, the more time is saved. This is partly due to the fact that the only sorting operation required only takes place on the outer regions. The internal regions are processed in any order during step 230, which avoids any sorting of the internal regions ...

Moreover, unlike the Scanline type decomposition methods, the decomposition of the geometric form into simple (y-monotone) forms is performed once during a first phase and the filling is performed during a second phase. , which saves processing time.

Before describing a particular embodiment of the method that is the subject of the present invention, with reference to FIGS. 8 to 16, it is pointed out that it has been considered in this description that the pixels of the image to be synthesized are square that the the basis of the filter applied to each pixel is square with a side equal to an integer multiple of the pixel side, the latter side being considered unitary, for simplification of the description. Each pixel is marked by the abscissa and ordered from its lower left corner, the lowest and the leftmost pixel has coordinates (0,0), the next one, on the right, on the same line has for coordinates (1, 0), the next, above the pixel (0,0) has for coordinates (0,1) and so on. In this description, it is shown that a black geometrical shape on a white background (in FIGS. 8 and 9, only the contours of this shape and its fragments are represented), the present invention applying, in the same manner for geometric shapes having shades or colors, for example represented in red, green and blue with possibly variations of these colors on the extent of each geometric shape.

FIGS. 8 to 16 describe a particular embodiment of the method that is the subject of the present invention, the characteristics of which advantageously combine with characteristics of the decomposition method illustrated, by way of example, in FIGS. 1 to 7, and which concerns a method of filling a geometric shape which comprises:

at least one step of decomposing the geometric shape into simple graphical primitives, called "fragments", and at least one step of calculating the intersection area between each fragment and a filter whose surface is greater than the surface of a pixel.

In the embodiment. particular described and shown; filter portions which are each in a single pixel are implemented. In variant not shown, it does not implement a portion but a filter of a surface greater than that of a pixel, as indicated in the general definition of the method object of the invention mentioned above.

FIG. 8 shows the coordinates of the 36 lowest and most left pixels of an image, assuming that a geometric star shape 800 with straight sides, the image of which must be synthesized, was entirely there included. The star geometrical shape 800 is, in FIG. 8, decomposed into simple primitives, or "fragments", each fragment being entirely included in a pixel, having a number of sides less than or equal to four and at least one vertical or horizontal side: triangles or quadrilaterals (rectangles, trapezes, ...).

FIG. 9 shows the pixel of coordinates (2,4) and the eight pixels which are closest to it, with coordinates (1,5) to (3,5), (1,4), (3) , 4) and (1,3) to (3,3). For a better reading of FIG. 9 and the following figures, the various pixels were slightly separated, the separation interval not being considered in the various steps of the method that is the subject of the present invention.

It can be seen in FIG. 9 that the coordinate pixel (2, 4) comprises two fragments 901 and 902, the first one, at the top, of trapezoidal shape and the second, at the bottom, of rectangular shape.

FIG. 10 shows a square base filter, which will apply to the coordinate pixel (2,4), which is centered on the center of the coordinate pixel (2,4) and whose side is equal to twice on the side of a unit pixel. FIG. 10 also shows the nine portions 1001 to 1009 which form a decomposition of the filter base, each portion being entirely included in a pixel and each pixel comprising at most one portion. The central portion 1005 is square and covers the coordinate pixel (2,4), the portions 1001, 1003, 1007 and 1009 are square and cover the nearest quarter of the coordinate pixel (2,4) of the respective coordinate pixels. (1, 5), (3,5), (1,3) and (3,3). Portions 1002, 1004, 1006, and 1008 are rectangles that overlap the nearest half of the coordinate pixel (2,4) of the respective coordinate pixels ((2,5), (1,4), (3,4 ) and 2,3).

For the fragment 901, we can see the nine areas of intersection of this fragment with the filter portions included in the coordinate pixel (2,4) of the filters applied to the nine coordinate pixels (1, 5) to (3,3) shown in FIG. 9. By convention, there is shown at the top left, the intersection area of the fragment considered with the portion of the filter applied to the pixel at the bottom right, with coordinates (3,3), in the middle on the left, the intersection area of the fragment considered with the portion of the filter applied to the pixel in the middle right, coordinates (3,4) and so on.

FIG. 12 shows, for the fragment 902, the nine areas of intersection of this fragment with the filter portions included in the coordinate pixel (2,4) of the filters applied to the nine coordinate pixels (1, 5) to (3,3) shown in FIG. 9. The same representation convention as in FIG. 11 was used.

FIG. 13 shows the sums of intersection areas illustrated in FIGS. 11 and 12, of the geometrical shape with the filter portions included in the coordinate pixel (2,4) of the filters applied to the nine coordinate pixels ( 1, 5) to (3.3) shown in FIG. 9. The same representation convention as for FIG.

FIG. 14 shows a matrix representation in which each line represents the different intersection areas, in the pixel whose coordinates are given at the beginning of the line, fragments and portions that are used to synthesize the pixel of coordinates ( 2.4). For the sake of simplicity, pixels that contain no fragments or pixels that do not contain any portion of the filter are not represented.

The color of the pixel (2,4) is, in a particular mode of filter having the base illustrated in FIG. 9, a filter taking only the value "1" over its entire base, without weighting (it is commonly referred to as " box filter "), the sum of the intersection areas shown in FIG. 14 divided by the surface of the filter base, here four times the unit area (see FIG. 10) and multiplied by the area of the pixel (2.4) ( here unitary surface). Fig. 15 shows the summed area of intersection areas considered for the coordinate pixel (2,4) in the total area of the filter base. The color of the synthesized image in the coordinate pixel (2,4) is equal to the ratio of the black surface shown in FIG. 15, over the total area of the filter. For example, if black is represented by the value 0 and white as 255, the gray level of the pixel (2,4) is about 184.

FIG. 16 shows different steps implemented in a particular embodiment of the method that is the subject of the present invention.

During a step 1500, the method is initialized by zeroing the value of its various parameters (in particular x and y), determining at least one geometrical shape to be represented on an image to be synthesized, the number of pixels of the image to be synthesized and a filter to be applied to each pixel of the image to be synthesized. By convention, applied filters pixels at the edge or corner of the image are constituted by truncation of the base of the current filter. In the following description of Figure 16, we consider the filter whose base is illustrated in Figure 10 and whose value is "1" on the entire base.

During a step 1501, the portions of the base of the current filter are determined. In the embodiment shown, the decomposition of the filter base into portions is such that each portion is included in a single pixel.

During a step 1503, consider the pixel whose coordinates are (x, y). During a step 1504, the fragments of each geometric shape are determined for the coordinate pixel (x, y) and for the eight pixels surrounding this pixel, if they exist. Fragmenting is done in such a way that each created fragment is included in one and only one pixel. These fragments are stored in memory as a linked list of fragments per pixel. Thus, each pixel has the list of all the fragments included in itself. When a fragment has already been determined during a previous step 1504, it is read in memory and not determined again, to reduce the processing times.

During a step 1505, for each fragment determined during step 1504, the intersection area between the fragment considered and each portion of the filter is calculated and this area is memorized with respect to the pixel whose filter comprises this portion of filter.

It is observed that the calculations of the different areas are simplified in many cases in which there are relations between the intersection areas, especially when the filter bases are multiples of the pixel. For example, for a rectangular base that corresponds to four pixels (2 x 2) spanning nine pixels around the pixel to which the filter is applied, for each column or each line, the sums of the extreme areas are equal to the area central (the calculation of 4 areas allows the calculation of 9 areas). Similarly, for a rectangular base that corresponds to nine pixels (3 x 3) extending over nine pixels around the pixel to which the filter is applied, for each column or each line, the extreme areas are each equal to the central area. .

During a step 1506, for the pixel of coordinates (x, y), the total intersection area between the geometrical shape and the base of the filter is calculated by adding together all the intersection areas of the portions of the filter applied to the coordinate pixel (x, y) with the different fragments of each geometric shape. Then we multiply this surface by the color of this geometric shape and add the results. Then, we multiply the result of this addition by the ratio between the area of a pixel and the area of the filter, namely in this case% or 0.25. During a step 1507, the result of step 1506 is written in a final image memory, for the coordinate pixel (x, y).

During a step 1508, it is determined if x corresponds to the last pixel of a line. If not, the value of x is incremented, step 1509 and return to step 1504. If the result of step 1508 is positive, during a step 1510, it is determined whether y is the last line of the image to be synthesized. If no, the value of y is incremented and the value of x is reset to 0, step 1511, and step 1504 is returned. If the result of step 1510 is positive, the synthesis of the image is complete. .

As a variant, a statistical perturbation, for example of the "Poisson distribution" type, is applied to the coordinates of the various geometrical elements, namely the BASE of the filter, and / or the PORTIONS of the filter, and / or the fragments of the form. geometrical to rasterize. Indeed, as recalled by R. Cook in his article "Stochastic Sampling in

Computer Graphics "(ACM Transactions on Graphics, Vol 5, No. 1, January 1986, Pages 51-72), outside the fovea (retinal region located in the macula, near the optical axis of the eye), the distribution of the photosensitive cells is non-uniform, of "Poisson's disc" type, reason why the human eye does not create aliasing, in spite of the fact that these photosensitive cells are in limited number: the The human visual system is much more sensitive to stair effects and frames than to pseudo-random noise introduced by a statistical distribution of photosensitive cells.

FIG. 17 represents, schematically, the constitution of a particular filter, the shape of which is an integral of a polygonal shape. The right part of FIG. 17 indicates the correspondence of the polygonal shape, here pyramidal, with pixels and then the section of the shape of the corresponding filter defined as the integral of the polygonal shape when the top of the pyramid travels the pixel.

The left part of FIG. 17 indicates the correspondence of the polygonal shape, here cubic, with pixels and then the section of the shape of the corresponding filter defined as the integral of the polygonal shape.

Claims

1 - A method of filling a geometric shape, characterized in that it comprises:

at least one step of decomposing the geometric form into simple graphic primitives, called "fragments" (1504, FIG.

at least one step of calculating the intersection area (1505, FIGS. 11 and 12) between each fragment and a filter whose surface is greater than the area of a pixel.

2 - Process according to claim 1, characterized in that it comprises:

at least one step of decomposing the base of at least one filter into simple graphic primitives (1501, FIG. 10), called "portions";

at least one step of calculating the intersection areas between each fragment and each portion (1505, FIGS. 11 and 12) and

for each pixel, at least one step of numerical calculation of a function of the intersection areas composing the form of the filter applied to the pixel (1506, FIGS. 13 and 14), said function giving at least one color element for said pixel to which said filter is applied.

3 - Process according to claim 2, characterized in that during the step of decomposing the base portions (1501), each portion is included in one and a single pixel. 4 - Process according to any one of claims 2 or 3, characterized in that during the step of decomposing the base of at least one filter (1501), the intersections of the portions are empty and their meeting is equal at said base.

5 - Process according to any one of claims 2 to 4, characterized in that during the decomposition step of the base of a filter (1501), said filter has a rectangular base each side of which is a multiple of corresponding side of a pixel.

6 - Process according to any one of claims 2 to 5, characterized in that during the numerical calculation step (1506), a weighting step of the different areas is carried out.

7 - Process according to claim 6, characterized in that during the weighting step, each area is weighted according to a function whose value depends on the distance from said intersection to the center of the pixel to which said filter is applied.

8 - Process according to any one of claims 2 to 7, characterized in that during the numerical calculation step (1506), a summation or addition of the intersection areas, possibly weighted, composing the shape of the filter applied to the pixel. 9 - Process according to any one of claims 2 to 8, characterized in that during the step of calculating the intersection areas (1505), is calculated at least a first intersection area by implementing at least one fragment and at least one portion and one calculates at least one other intersection area, for another pixel to which the same filter is applied, by implementing said first intersection area.

10 - Process according to any one of claims 1 to 9, characterized in that during the step of decomposing the geometric form into fragments (1504), each fragment is included in one and a single pixel.

11 - Process according to any one of claims 1 to 10, characterized in that during the decomposition step of the geometric shape (1504), ^{'intersections} fragments are empty and their union is equal to said geometrical shape .

12 - Process according to any one of claims 1 to 11, characterized in that the numerical calculation step (1506) comprises a step of multiplication by the ratio between the area of the pixel and the total area of the filter.

13 - Process according to any one of claims 1 to 12, characterized in that during the numerical calculation step (1506), the color is weighted by a filter.

14 - Process according to any one of claims 1 to 13, characterized in that the shape of the filter is an integral of a polygonal shape (Figure 17).

15 - Process according to any one of claims 1 to 14, characterized in that it is performed successively for successive pixels on the same line, by successively treating the successive lines of the image to constitute.

16 - Device for rasterizing a geometric shape, characterized in that it comprises: at least one means for decomposing the geometrical shape into simple graphic primitives, called "fragments" (50, 53) and

at least one means for calculating the area of intersection between each fragment and a filter whose area is greater than the area of one pixel (50, 53).