CN102646281B - Method and system for rasterizing elliptic arc - Google Patents
Method and system for rasterizing elliptic arc Download PDFInfo
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- CN102646281B CN102646281B CN201110039950.1A CN201110039950A CN102646281B CN 102646281 B CN102646281 B CN 102646281B CN 201110039950 A CN201110039950 A CN 201110039950A CN 102646281 B CN102646281 B CN 102646281B
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Abstract
The invention discloses a method and system for rasterizing an elliptic arc. The method comprises the following steps of: finding out one or more than one pixel square which is intersected with the elliptic arc in a direction of the elliptic arc from a pixel square A0 to a pixel square A7, which are adjacent to a painted pixel square C; and selecting the pixel square which is the nearest to the elliptic arc from one or more than one pixel square as a pixel square to be printed.
Description
Technical field
The present invention relates to computer graphical processing field, relate more specifically to a kind of method and system for carrying out rasterizing to elliptic arc.
Background technology
Rasterizing is a kind of technology in computer graphics, pel scan conversion being become display pixel, is that image conversion vector graphics format represented becomes grating image for the process of the output of display or printer etc.The process of pel being carried out to rasterizing mainly comprises two steps: first, determines on display plane, which pixel is covered by pel; Then, the attribute (color, the degree of depth and texture etc.) of pel is assigned to each pixel covered by this pel.
Current, there are two kinds for carrying out the method for rasterizing to elliptic arc: mid-point method and minimum function value method.Carry out in the process of rasterizing utilizing mid-point method to elliptic arc, with the center of elliptic arc place ellipse for elliptic arc place ellipse is on average divided into eight octant quadrants by benchmark, and in the pixel place quadrant drawn and currently complete mid point between two adjacent pixels of the pixel of drawing according to current having completed in the trend of elliptic arc and judged relative to the absolute value of the functional value of the curvilinear function of elliptic arc place ellipse the pixel which pixel in these two pixels will be selected as the next one and will draw.Carry out in the process of rasterizing utilizing minimum function value method to elliptic arc, any one pixel of elliptic arc tangential direction is regarded the distance of this pixel to elliptic arc as relative to the absolute value of the functional value of the curvilinear function of elliptic arc place ellipse, regard minimum for the current absolute value having completed functional value in the two or more neighbor of the pixel of a drawing neighbor as pixel closest to elliptic arc, and using pixel that pixel minimum for the absolute value of this functional value will be drawn as the next one.
Utilize mid-point method to carry out rasterizing to elliptic arc and there is two problems: 1) because elliptic arc place ellipse has been divided into eight octant quadrants by the method, so need the parameter recalculated for the pixel selecting the next one to draw when being switched to another quadrant from a quadrant, this makes the apparatus structure design realizing mid-point method complicated, and adds computing time; 2) rasterizing that mid-point method has been come elliptic arc cannot when elliptic arc place ellipse is very thin (that is, when oval minor axis is much smaller than the major axis of ellipse), be used.
Utilize minimum function value method to carry out rasterizing to elliptic arc and also there is two problems: 1) because pixel is not the accurate distance of this pixel to elliptic arc relative to the absolute value of the functional value of the curvilinear function of elliptic arc place ellipse, so when elliptic arc place ellipse is very thin, the result that may make mistake; 2) a kind of method for tracing of complexity is needed to follow the trail of along elliptic arc by pixel.
Summary of the invention
In view of above problem, the invention provides a kind of method and system for carrying out rasterizing to elliptic arc of novelty.
Comprising for the method for elliptic arc being carried out to rasterizing according to one aspect of the invention: find out and walk upwards crossing with elliptic arc one or more pixel square with current having completed at elliptic arc in the adjacent pixel square A0 to A7 of the pixel square C that draws; The pixel square that the pixel square that chosen distance elliptic arc is nearest from described one or more pixel square will be drawn as the next one.
Comprising for the system of elliptic arc being carried out to rasterizing according to a further aspect of the invention: intersect pixel acquisition unit, walk upwards with elliptic arc crossing one or more pixel square with current having completed at elliptic arc in the adjacent pixel square A0 to A7 of the pixel square C that draws for finding out; Intersect pixel selection unit, for the pixel square that the pixel square that chosen distance elliptic arc from described one or more pixel square is nearest will be drawn as the next one.
Relative to existing two kinds for carrying out the method for rasterizing to elliptic arc, the present invention can contain all situations, comprises ellipse and is degenerated to flat (that is, major axis is much larger than the situation of the ellipse of minor axis); Secondly, the pixel by pixel track method that the present invention uses is simply effective, and relative to mid-point method, it does not need be divided into 8 quadrants and switch in these quadrants, and relative to minimum function value method, it does not need the gradient vector using arc; Finally, use of the present invention method of carrying out judge crossing with pixel square, want height a bit relative to the precision of minimum function method, the former only needs judgement 1 to 3 pixels, and the latter needs to judge at least 3 pixels.
Accompanying drawing explanation
Below in conjunction with accompanying drawing in the description of the specific embodiment of the present invention, the present invention may be better understood, wherein:
Fig. 1 shows according to an embodiment of the invention for carrying out the block diagram of the system of rasterizing to elliptic arc;
Fig. 2 shows according to an embodiment of the invention for carrying out the process flow diagram of the method for rasterizing to elliptic arc;
Fig. 3 shows elliptic arc and the current foursquare crossing situation of neighbor having completed the pixel square of drawing;
Fig. 4 shows according to another embodiment of the present invention for carrying out the block diagram of the system of rasterizing to elliptic arc; And
Fig. 5 shows elliptic arc and the current crossing situation having completed the square limit of the pixel square of drawing.
Embodiment
The characteristic sum exemplary embodiment of various aspects of the present invention will be described in detail below.Description below covers many details, to provide complete understanding of the present invention.But, it will be apparent to one skilled in the art that the present invention can implement when not needing some details in these details.Below the description of embodiment is only used to by illustrating example of the present invention to provide to the clearer understanding of the present invention.Any concrete configuration that the present invention proposes below being never limited to and algorithm, but cover any amendment of coherent element, parts and algorithm, replacement and improvement under the premise of without departing from the spirit of the present invention.
Here, suppose that the elliptic arc place of carrying out rasterizing oval in x-axis and the mutually orthogonal coordinate system of y-axis centered by (0,0), and its curvilinear equation is:
Ax
2+Bxy+Cy
2＝1。
Wherein,
Wherein, rh is the component of major semi-axis in x-axis of elliptic arc place ellipse, and rv is the component of major semi-axis in y-axis of elliptic arc place ellipse,
the anticlockwise angle of major axis relative to the positive dirction of x-axis of elliptic arc place ellipse.The curvilinear function of elliptic arc place recited above ellipse is:
F(x，y)＝Ax
2+Bxy+Cy
2-1＝0
The gradient of elliptic arc place ellipse is
wherein F
xrepresent the oval gradient in the horizontal direction in elliptic arc place, F
yrepresent the oval gradient in the vertical direction in elliptic arc place.When a pixel is in outside the ellipse of elliptic arc place, this pixel is just relative to the functional value of the curvilinear function of elliptic arc place ellipse.When a pixel is within the ellipse of elliptic arc place, this pixel is negative relative to the functional value of the curvilinear function of elliptic arc place ellipse.
Suppose, current is being just (x in the starting point of the elliptic arc of rasterizing
0, y
0), terminal is (x
1, y
1).It is that the process of the elliptic arc of unit pixel comprises and selecting closest to the pixel of this elliptic arc and the process of drawing these pixels that raster display is drawn camber line width.The degree of closeness of a pixel and elliptic arc can be measured by the distance of this pixel to elliptic arc, but is difficult in practice obtain the distance of pixel to elliptic arc.Therefore existing method is all use a kind of being similar to obtain minor increment.In mid-point method, by calculating the functional value of the mid point of two neighbors in the quadrant that moves towards at elliptic arc, judge that in these two pixels, which is nearest from elliptic arc.In minimum function method, by calculating the functional value of several neighbors of elliptic arc gradient direction, its minimum value is judged as from elliptic arc nearest.
Simply and directly realizing the idea of the rasterizing of elliptic arc is find out a pixel crossing with elliptic arc, the pixel that the pixel that then selection one distance elliptic arc is nearest from the pixel crossing with elliptic arc will carry out drawing as the next one.According to an embodiment of the invention for carrying out the method and system of rasterizing to elliptic arc, regard the current pixel of drawing and the neighbor thereof of having completed as pixel square one by one, and utilize four of pixel square summits to walk upwards with elliptic arc crossing one or more pixel square to find out current having completed at elliptic arc in the neighbor square of the pixel square of drawing relative to the functional value of the curvilinear function of elliptic arc place ellipse, then the pixel square that the pixel square that chosen distance elliptic arc is nearest from one or more pixel square crossing with elliptic arc will be drawn as the next one.
Below in conjunction with Fig. 1 and Fig. 2, describe in detail according to an embodiment of the invention for carrying out the system and method for rasterizing to elliptic arc.Fig. 1 shows according to an embodiment of the invention for carrying out the block diagram of the system of rasterizing to elliptic arc.Fig. 2 shows according to an embodiment of the invention for carrying out the process flow diagram of the method for rasterizing to elliptic arc.
Here for convenience of description, the current pixel square of drawing that completed is designated as pixel square C, by adjacent with pixel square C eight pixel square (namely, the neighbor square of pixel square C) be designated as pixel square A0 to A7, upwards crossing with elliptic arc pixel square will be walked (namely at elliptic arc in pixel square A0 to A7, the pixel square of the pixel square will may drawn as the next one after pixel square C) be designated as pixel square Ai, pixel square Aj, pixel square Ar etc., and by pixel square Ai, Aj, square limit crossing with elliptic arc in Ar etc. is designated as square limit a, square limit b, square limit c etc.It should be appreciated by those skilled in the art that above mark only for illustration of object and should not be understood to any limitation of the invention.
As shown in Figure 1, the system according to an embodiment of the invention for carrying out rasterizing to elliptic arc comprises crossing pixel acquisition unit 102 and crossing pixel selection unit 104.Wherein, intersect pixel acquisition unit 102 and walk upwards with elliptic arc crossing one or more pixel square (that is, perform step S202) with current having completed at elliptic arc in the adjacent pixel square A0 to A7 of the pixel square C that draws for finding out.Intersect the pixel square (that is, performing step S204) that pixel selection unit 104 will be drawn as the next one for the pixel square that chosen distance elliptic arc from one or more pixel square crossing with elliptic arc in pixel square A0 to A7 is nearest.
Fig. 3 shows the crossing situation of elliptic arc and the one or more pixel square in the current neighbor square A0 to A7 having completed the pixel square C drawn (here, suppose that the trend of elliptic arc is for from starting point (x
0, y
0) to terminal (x
1, y
1)):
Fig. 3 a show in the pixel square A0 to A7 adjacent with pixel square C, only have a pixel square Ai at elliptic arc walk upwards crossing with elliptic arc situation.In this case, pixel square Ai is only had to be the pixel that the possible next one will be drawn.Intersecting pixel selection unit 104 can directly using pixel square that pixel square Ai will draw as the next one.
Fig. 3 b show in the pixel square A0 to A7 adjacent with pixel square C, have two pixel square Ai and Aj at elliptic arc walk upwards crossing with elliptic arc situation.In this case, pixel square Ai and Aj is the pixel that the possible next one will be drawn.Particularly in fig 3b, right edge (the object illustrated for convenience of pixel square C, be designated as square limit a) upwards crossing with elliptic arc in walking of elliptic arc, thus with pixel square C share square limit a, the pixel square Ai be on the right side of pixel square C is a pixel that the possible next one will be drawn; Upper side edge (the object illustrated for convenience of pixel square Ai in addition, be called square limit b) upwards crossing with elliptic arc in walking of elliptic arc, and the one other pixel square at b place, square limit is adjacent with pixel square C exactly and be in the top-right pixel square Aj of pixel square C, so the pixel that the pixel square Aj possible next one that is another will be drawn.Intersecting pixel selection unit 104 can chosen distance elliptic arc is nearer from pixel square Ai and Aj a pixel square will drawn as the next one.
(namely the joint that Fig. 3 c shows pixel square C and three pixel square of the upside being in pixel square C in pixel square A0 to A7, right side, upper right side walks upwards crossing with elliptic arc situation at elliptic arc, this joint is on elliptic arc, and the object illustrated for convenience, is designated as summit P by this joint).In this case, the pixel square Ar on the upside of the pixel square Aj of the pixel square Ai on the right side of pixel square C, pixel square C upper right side and pixel square C is the pixel that the possible next one will be drawn.Intersecting pixel selection unit 104 can chosen distance elliptic arc is nearest from pixel square Ai, Aj and Ar a pixel square will drawn as the next one.
Fig. 3 d and 3e shows the situation that elliptic arc and pixel square C exist two point of crossing.In the situation shown in Fig. 3 d, elliptic arc is only crossing with the pixel square Ai on the right side of pixel square C, so only have pixel square Ai to be the pixel that the possible next one will be drawn, intersecting pixel selection unit 104 can directly using pixel square that pixel square Ai will draw as the next one; In the situation shown in Fig. 3 e, elliptic arc is crossing with the pixel square Aj of the pixel square Ai on the right side of pixel square C and upper right side, so pixel square Ai and Aj is the pixel that the possible next one will be drawn, intersects pixel selection unit 104 and can select pixel square Ai and the nearer pixel square will drawn as the next one of Aj middle distance elliptic arc.
Fig. 4 shows according to another embodiment of the present invention for carrying out the block diagram of the system of rasterizing to elliptic arc.As shown in Figure 4, the basic framework of this system is identical with the system shown in Fig. 1, and crossing pixel acquisition unit 102 comprises intersection edges acquisition module 1022 and crossing pixel acquisition module 1024 further.Wherein, intersection edges acquisition module 1022 walks upwards crossing with elliptic arc square limit a for finding out at elliptic arc in pixel square C.Intersect pixel acquisition module 1024 for finding out the pixel square Ai sharing square limit a with pixel square C, and using pixel square Ai as walking upwards crossing with an elliptic arc pixel square (i is integer, and 0≤i≤7) at elliptic arc.
Fig. 5 shows elliptic arc and the current crossing situation having completed the square limit of the pixel square C drawn.Particularly, Fig. 5 a shows and walks at elliptic arc the situation that upwards pixel square C and elliptic arc intersect at a point, and Fig. 5 b and 5c shows and intersect at the situation of 2 at walk upwards pixel square C and the elliptic arc of elliptic arc.
For any one pixel square Q, intersection edges acquisition module 1022 can be found out by following process and walk upwards crossing with elliptic arc square limit at elliptic arc in pixel square Q: judge that whether any two adjacent vertexs (such as, P0 with P1) of pixel square Q are identical relative to the symbol of the functional value of the curvilinear function of elliptic arc place ellipse; If different, then think that the square limit connecting adjacent vertex P0 and P1 is upwards crossing with elliptic arc in walking of elliptic arc; If identical, then judge that whether adjacent vertex P0 with P1 be identical relative to the oval symbol at the functional value of the gradient function of horizontal or vertical direction in elliptic arc place, if different, then think that the square limit connecting adjacent vertex P0 and P1 is upwards crossing with elliptic arc in walking of elliptic arc, if identical, then think that the square limit connecting adjacent vertex P0 and P1 is upwards not crossing with elliptic arc in walking of elliptic arc.
Particularly, if the square limit connecting adjacent vertex P0 and P1 is the horizontal sides of pixel square Q, then according to adjacent vertex P0 and P1 relative to the oval gradient function F in the horizontal direction in elliptic arc place
xthe symbol of the functional value square limit that judges to connect adjacent vertex P1 and P1 whether crossing with elliptic arc (as shown in Figure 5 c) walk upwards at elliptic arc; If the square limit connecting adjacent vertex P0 and P1 is the vertical edges of pixel square Q, then according to adjacent vertex P0 and P1 relative to the oval gradient function F in the vertical direction in elliptic arc place
ythe symbol of the functional value square limit that judges to connect adjacent vertex P1 and P1 whether crossing with elliptic arc (as shown in Figure 5 b) walking upwards at elliptic arc.
If intersection edges acquisition module 1022 judge the such as right edge a of pixel square C elliptic arc walk upwards crossing with elliptic arc time, above-described method also to be utilized to find out and to walk another upwards crossing with elliptic arc square limit b at elliptic arc in the pixel square Ai sharing square limit a with pixel square C.If the pixel square sharing square limit b with pixel square Ai be one of pixel square A0 to A7 (such as, pixel square Aj), then intersect pixel acquisition module 1024 except using pixel square Ai as except the pixel square that the possible next one will be drawn, the pixel square (that is, the situation shown in Fig. 3 b and 3e) also pixel square Aj will drawn as the possible next one.
Crossing pixel acquisition unit 102 find out with current completed in the adjacent pixel square A0 to A7 of the pixel square C that draws elliptic arc walk upwards crossing with elliptic arc one or more pixel square after, intersect the pixel square that pixel square nearest for chosen distance elliptic arc in the one or more pixel square found out from crossing pixel acquisition unit 102 will be drawn as the next one by pixel selection unit 104.
Particularly, if intersect pixel acquisition unit 102 only to have found one walk upwards crossing with elliptic arc pixel square Ai at elliptic arc in the pixel square A0 to A7 adjacent with pixel square C, then intersect the direct pixel square will drawn as the next one by pixel square Ai of pixel selection unit 104; If intersect pixel acquisition unit 102 to have found two or more walk upwards crossing with elliptic arc pixel square at elliptic arc in the pixel square A0 to A7 adjacent with pixel square C, then the pixel square that in the pixel square crossing pixel acquisition unit 102 found out of crossing pixel selection unit 104, a pixel square minimum relative to the absolute value of the functional value of the curvilinear function of elliptic arc place ellipse will be drawn as the next one.
After finding out the pixel square that the next one will draw, the system and method according to an embodiment of the invention for carrying out rasterizing to elliptic arc is drawn to found out pixel square.The parts drawn completed for pixel square can be that independent pixel draws unit (not shown), also can be combined in other unit.
It should be noted that, system and method according to the embodiment of the present invention regards pixel as selection course that pixel square has carried out the pixel will drawn for the next one, thus pixel square mentioned here relative to the curvilinear function of elliptic arc place ellipse functional value, oval relative to elliptic arc place be in fact that pixel is relative to the functional value of the curvilinear function of elliptic arc place ellipse, relative to the oval functional value at the gradient function of horizontal in elliptic arc place at the functional value etc. of the gradient function of horizontal.In addition, above-mentioned drawing pixel square is drawn pixel in fact exactly.
Relative to existing two kinds of methods, the present invention has the following advantages.First, the present invention can contain all situations, comprises ellipse and is degenerated to flat; Secondly, the pixel by pixel track method that the present invention uses is simply effective, and relative to mid-point method, it does not need be divided into 8 quadrants and switch in these quadrants, and relative to minimum function value method, it does not need the gradient vector using arc; Finally, use of the present invention method of carrying out judge crossing with pixel square, want height a bit relative to the precision of minimum function method, the former only needs judgement 1 to 3 pixels, and the latter needs to judge at least 3 pixels.
Below the present invention is described with reference to specific embodiments of the invention, but those skilled in the art all understand, various amendment, combination and change can be carried out to these specific embodiments, and the spirit and scope of the present invention by claims or its equivalents can not be departed from.
Step can be performed as required with hardware or software.Note, without departing from the scope of the invention, the process flow diagram that can provide in this instructions adds step, therefrom removal step or amendment step wherein.In general, process flow diagram is just used to refer to a kind of possible sequence of the basic operation for practical function.
Embodiments of the invention can utilize the universal digital computer of programming, utilize special IC, programmable logic device (PLD), field programmable gate array, light, chemistry, the system of biological, quantum or nanometer engineering, assembly and mechanism realize.In general, function of the present invention can be realized by any means known in the art.Distributed or networked system, assembly and circuit can be used.The communication of data or to transmit can be wired, wireless or by any other means.
Also will recognize, according to the needs of application-specific, one or more in the key element shown in accompanying drawing by be more separated or more integrated mode realizes, or can be removed or to be deactivated even in some cases.The journey logic bomb that realization can be stored in machine readable media performs above-mentioned any method to allow computing machine, also within the spirit and scope of the present invention.
In addition, any signal arrows in accompanying drawing should be considered to be only exemplary, instead of restrictive, indicates unless otherwise specifically.When term be also contemplated as the ability of separation or combination is not known time, the combination of assembly or step also will be considered to describe.
Claims (10)
1., for carrying out a method for rasterizing to elliptic arc, comprising:
Find out and walk upwards crossing with described elliptic arc one or more pixel square with current having completed at elliptic arc in the adjacent pixel square A0 to A7 of the pixel square C that draws;
The pixel square that the pixel square that described in chosen distance, elliptic arc is nearest from described one or more pixel square will be drawn as the next one.
2. the method for carrying out rasterizing to elliptic arc according to claim 1, is characterized in that, the process walking upwards crossing with described elliptic arc one or more pixel square found out at described elliptic arc in described pixel square A0 to A7 comprises:
Find out and walk upwards crossing with described elliptic arc square limit a at described elliptic arc in described pixel square C;
Using the pixel square Ai sharing described square limit a with described pixel square C as walking upwards crossing with a described elliptic arc pixel square at described elliptic arc, wherein i is integer and 0≤i≤7.
3. the method for carrying out rasterizing to elliptic arc according to claim 2, it is characterized in that, when described elliptic arc and described square limit a intersect at the summit P of described pixel square C, using the multiple pixel square sharing described summit P in described pixel square A0 to A7 with described pixel square C as walking upwards crossing with described elliptic arc pixel square at described elliptic arc, or when another the square limit b in described pixel square Ai is upwards crossing with described elliptic arc in walking of described elliptic arc, and pixel square Aj in described pixel square A0 to A7 and described pixel square Ai is when sharing described square limit b, using described pixel square Aj as walking upwards crossing with described elliptic arc one other pixel square at described elliptic arc, wherein j is integer and 0≤j≤7.
4. the method for carrying out rasterizing to elliptic arc according to any one of claim 2 to 3, is characterized in that, the process walking upwards crossing with described elliptic arc square limit found out at described elliptic arc in any one pixel square Q comprises:
Judge that whether any two adjacent vertexs of described pixel square Q are identical relative to the symbol of the functional value of the curvilinear function of described elliptic arc place ellipse;
If different, then conclude that the square limit connecting described two adjacent vertexs is upwards crossing with described elliptic arc in walking of described elliptic arc;
If identical, then judge that whether described two adjacent vertexs are oval relative to described elliptic arc place identical at the symbol of the functional value of the gradient function of horizontal or vertical direction,
If different, then conclude that the square limit connecting described two adjacent vertexs is upwards crossing with described elliptic arc in walking of described elliptic arc,
If identical, then conclude that the square limit connecting described two adjacent vertexs is upwards not crossing with described elliptic arc in walking of described elliptic arc.
5. the method for carrying out rasterizing to elliptic arc according to claim 4, is characterized in that,
When only have in described pixel square A0 to A7 a pixel square Ai described elliptic arc walk upwards crossing with described elliptic arc time, directly using pixel square that described pixel square Ai will draw as the next one;
When have in described pixel square A0 to A7 multiple pixel square described elliptic arc walk upwards crossing with described elliptic arc time, select the pixel square that pixel square minimum relative to the absolute value of the functional value of the curvilinear function of described elliptic arc place ellipse in described multiple pixel square will be drawn as the next one.
6., for carrying out a system for rasterizing to elliptic arc, comprising:
Intersecting pixel acquisition unit, walking upwards with described elliptic arc crossing one or more pixel square with current having completed at elliptic arc in the adjacent pixel square A0 to A7 of the pixel square C that draws for finding out;
Intersect pixel selection unit, for the pixel square that the pixel square that described in chosen distance, elliptic arc is nearest from described one or more pixel square will be drawn as the next one.
7. the system for carrying out rasterizing to elliptic arc according to claim 6, is characterized in that, described crossing pixel acquisition unit comprises:
Intersection edges acquisition module, walks upwards crossing with described elliptic arc square limit a for finding out at described elliptic arc in described pixel square C;
Intersect pixel acquisition module, for using the pixel square Ai sharing described square limit a with described pixel square C as walking upwards crossing with a described elliptic arc pixel square at described elliptic arc, wherein i is integer and 0≤i≤7.
8. the system for carrying out rasterizing to elliptic arc according to claim 7, it is characterized in that, when described elliptic arc and described square limit a intersect at the summit P of described pixel square C, described crossing pixel acquisition unit using the multiple pixel square sharing described summit P in described pixel square A0 to A7 with described pixel square C as walking upwards crossing with described elliptic arc pixel square at described elliptic arc, or another the square limit b in described pixel square Ai is upwards crossing with described elliptic arc in walking of described elliptic arc, and pixel square Aj in described pixel square A0 to A7 and described pixel square Ai is when sharing described square limit b, described crossing pixel acquisition unit using described pixel square Aj as walking upwards crossing with described elliptic arc one other pixel square at described elliptic arc, wherein j is integer and 0≤j≤7.
9. the system for carrying out rasterizing to elliptic arc according to any one of claim 7 to 8, it is characterized in that, described intersection edges acquisition module is found out by following process and is walked upwards crossing with described elliptic arc square limit at described elliptic arc in any one pixel square Q:
Judge that whether any two adjacent vertexs of described pixel square Q are identical relative to the symbol of the functional value of the curvilinear function of described elliptic arc place ellipse;
If different, then conclude that the square limit connecting described two adjacent vertexs is upwards crossing with described elliptic arc in walking of described elliptic arc;
If identical, then judge that whether described two adjacent vertexs are oval relative to described elliptic arc place identical at the symbol of the functional value of the gradient function of horizontal or vertical direction,
If different, then conclude that the square limit connecting described two adjacent vertexs is upwards crossing with described elliptic arc in walking of described elliptic arc,
If identical, then conclude that the square limit connecting described two adjacent vertexs is upwards not crossing with described elliptic arc in walking of described elliptic arc.
10. the system for carrying out rasterizing to elliptic arc according to claim 9, is characterized in that, described crossing pixel selection unit
Only have in described pixel square A0 to A7 a pixel square Ai described elliptic arc walk upwards crossing with described elliptic arc, directly using pixel square that described pixel square Ai will draw as the next one;
Have in described pixel square A0 to A7 multiple pixel square described elliptic arc walk upwards crossing with described elliptic arc, select the pixel square that pixel square minimum relative to the absolute value of the functional value of the curvilinear function of described elliptic arc place ellipse in described multiple pixel square will be drawn as the next one.
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