CN102646281A - Method and system for rasterizing elliptic arc - Google Patents
Method and system for rasterizing elliptic arc Download PDFInfo
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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 the computer graphical process field, relate more specifically to a kind of method and system that is used for elliptic arc is carried out rasterizing.
Background technology
Rasterizing is a kind of technology that in the computer graphics pel scan conversion is become display pixel, is the image transformation that vector graphics format is represented is become the process of grating image with the output that is used for display or printer etc.The process of pel being carried out rasterizing mainly comprises two steps: at first, confirm which pixel is covered by pel on the display plane; Then, the attribute (color, the degree of depth and texture etc.) of pel is composed each pixel of giving by this pel covering.
Current, there are two kinds of methods that are used for elliptic arc is carried out rasterizing: mid-point method and minimum function value method.Elliptic arc is carried out in the process of rasterizing utilizing mid-point method; With oval center, elliptic arc place is that benchmark belongs to ellipse with elliptic arc and on average is divided into eight octant quadrants, and has accomplished the absolute value of having accomplished the functional value of mid point between two adjacent pixels of the pixel of the drawing curvilinear function oval with respect to the elliptic arc place in the pixel place quadrant of drawing and current and judge that which pixel in these two pixels will be selected the pixel that will draw as the next one according to current on the trend of elliptic arc.Elliptic arc is carried out in the process of rasterizing utilizing minimum function value method; The absolute value of the functional value of the curvilinear function that any pixel of elliptic arc tangential direction is oval with respect to the elliptic arc place is regarded the distance of this pixel to elliptic arc as; Regard a minimum neighbor of absolute value of functional value in current two above neighbors having accomplished the pixel of drawing as pixel near elliptic arc, and the pixel that will draw as the next one of the pixel that the absolute value of this functional value is minimum.
Utilize mid-point method that elliptic arc is carried out rasterizing and have two problems: 1) be divided into eight octant quadrants owing to this method belongs to ellipse with elliptic arc; So when when a quadrant switches to another quadrant, recomputating the parameter that is used to select the pixel that the next one will draw; This feasible apparatus structure complex design that realizes mid-point method, and increased computing time; 2) when elliptic arc place ellipse is very thin (, oval minor axis much smaller than long axis of ellipse time) can't use mid-point method to accomplish the rasterizing to elliptic arc.
Utilize minimum function value method that elliptic arc is carried out rasterizing and also have two problems: 1) because pixel is not the accurate distance of this pixel to elliptic arc with respect to the absolute value that elliptic arc belongs to the functional value of oval curvilinear function; So when elliptic arc place ellipse is very thin, the result that may make mistake; 2) need a kind of method for tracing of complicacy to come to follow the trail of by pixel ground along elliptic arc.
Summary of the invention
In view of above problem, the invention provides a kind of method and system that is used for elliptic arc is carried out rasterizing of novelty.
The method that is used for elliptic arc being carried out rasterizing according to one aspect of the invention comprises: find out and the current one or more pixels squares that intersect with elliptic arc of walking upwards of having accomplished the pixel square C adjacent pixels square A0 to A7 that draws at elliptic arc; The pixel square that the nearest pixel square of chosen distance elliptic arc will be drawn as the next one from said one or more pixel squares.
Being used for according to a further aspect of the invention carried out rasterizing to elliptic arc system comprises: intersect pixel acquisition unit, be used for finding out and the current one or more pixels squares that intersect with elliptic arc of walking upwards of having accomplished the pixel square C adjacent pixels square A0 to A7 that draws at elliptic arc; Intersect the pixel selection unit, be used for the pixel square that to draw as the next one from the nearest pixel square of said one or more pixel square chosen distance elliptic arcs.
Be used for concerning elliptic arc carries out the method for rasterizing with respect to existing two kinds, the present invention can be contained all situations, comprises that ellipse is degenerated to flat (that is, major axis is much larger than the situation of the ellipse of minor axis); Secondly, the pointwise tracking that the present invention uses is simply effective, and it need not be divided into 8 quadrants and in these quadrants, switch with respect to mid-point method, and it need not use the gradient vector of arc with respect to minimum function value method; At last, use of the present invention and pixel square intersect the method for judging, want height a bit with respect to the precision of minimum function method, and the former only needs to judge 1 to 3 pixel, and the latter need judge at least 3 pixels.
Description of drawings
From below in conjunction with understanding the present invention better the description of accompanying drawing specific embodiments of the invention, wherein:
Fig. 1 shows the block diagram that is used for elliptic arc is carried out the system of rasterizing according to an embodiment of the invention;
Fig. 2 shows the process flow diagram that is used for elliptic arc is carried out the method for rasterizing according to an embodiment of the invention;
Fig. 3 shows elliptic arc and the current foursquare crossing situation of the foursquare neighbor of the pixel of drawing of having accomplished;
Fig. 4 shows the block diagram that is used for elliptic arc is carried out the system of rasterizing according to another embodiment of the present invention; And
Fig. 5 shows elliptic arc and the current crossing situation of having accomplished the foursquare square limit of pixel of drawing.
Embodiment
To describe the characteristic and the exemplary embodiment of various aspects of the present invention below in detail.Many details have been contained in following description, so that complete understanding of the present invention is provided.But, it will be apparent to one skilled in the art that the present invention can implement under the situation of some details in not needing these details.Description in the face of embodiment only is in order through example of the present invention is shown the clearer understanding to the present invention to be provided down.Any concrete configuration and the algorithm that are proposed below the present invention never is limited to, but any modification, replacement and the improvement that under the prerequisite that does not break away from spirit of the present invention, have covered coherent element, parts and algorithm.
Here, supposing to carry out the elliptic arc place of rasterizing oval is the center with (0,0) in the mutually orthogonal coordinate system of x axle and y axle, and its curvilinear equation is:
Ax
2+Bxy+Cy
2＝1。
Wherein,
Wherein, Rh is the oval component of major semi-axis on the x axle in elliptic arc place; Rv is the oval component of major semi-axis on the y axle in elliptic arc place,
be the anticlockwise angle of elliptic arc place long axis of ellipse with respect to the positive dirction of x axle.The oval curvilinear function in elliptic arc recited above place is:
F(x，y)＝Ax
2+Bxy+Cy
2-1＝0
The oval gradient in elliptic arc place does
F wherein
xThe oval gradient in the horizontal direction in expression elliptic arc place, F
yThe oval gradient in expression elliptic arc place in vertical direction.In the time of outside a pixel is in elliptic arc place ellipse, the functional value of the curvilinear function that this pixel is oval with respect to the elliptic arc place is for just.In the time of within a pixel is in elliptic arc place ellipse, the functional value of the curvilinear function that this pixel is oval with respect to the elliptic arc place is for negative.
Suppose that current is being (x in the starting point of the elliptic arc of rasterizing just
0, y
0), terminal point is (x
1, y
1).The processing of on raster display, drawing the camber line width and be the elliptic arc of unit picture element comprises that selection is near the pixel of this elliptic arc and the process that these pixels are drawn.The degree of closeness of pixel and elliptic arc can be measured to the distance of elliptic arc by this pixel, yet is difficult to obtain the distance of pixel to elliptic arc in practice.Therefore existing method all is to use a kind of being similar to obtain minor increment.In mid-point method,, judge that which is nearest from elliptic arc in these two pixels through in the quadrant of elliptic arc trend, calculating the functional value of the mid point of two neighbors.In the minimum function method, the functional value of the several neighbors through calculating the elliptic arc gradient direction, its minimum value is judged as from elliptic arc nearest.
A kind of simple and realize that directly idea to the rasterizing of elliptic arc is to find out and pixel that elliptic arc intersects, from the pixel that intersects with elliptic arc, select the pixel that the pixel nearest apart from elliptic arc will be drawn as the next one then.Be used for elliptic arc is carried out the method and system of rasterizing according to an embodiment of the invention; Regard current pixel and the neighbor thereof drawn accomplished as one by one pixel square; And the functional value that utilizes foursquare four summits of the pixel curvilinear function oval with respect to elliptic arc place finds out the current one or more pixels squares of having accomplished in the foursquare neighbor square of the pixel of drawing at elliptic arc that intersect with elliptic arc of walking upwards, the pixel square that a nearest pixel square of chosen distance elliptic arc will be drawn as the next one from the one or more pixel squares that intersect with elliptic arc then.
Below in conjunction with Fig. 1 and Fig. 2, specify the system and method that is used for elliptic arc is carried out rasterizing according to an embodiment of the invention.Fig. 1 shows the block diagram that is used for elliptic arc is carried out the system of rasterizing according to an embodiment of the invention.Fig. 2 shows the process flow diagram that is used for elliptic arc is carried out the method for rasterizing according to an embodiment of the invention.
Here explanation for ease; The current pixel square of drawing of having accomplished is designated as pixel square C; Eight pixel squares that will be adjacent with pixel square C (promptly; The neighbor square of pixel square C) is designated as pixel square A0 to A7; With the pixel square that intersects with elliptic arc in walking upwards of elliptic arc among the pixel square A0 to A7 (promptly; Maybe be square as the foursquare pixel of the next pixel that will draw after pixel square C) be designated as pixel square Ai, pixel square Aj, pixel square Ar etc., and with being designated as square limit a, square limit b, square limit c etc. with the crossing square limit of elliptic arc among pixel square Ai, Aj, the Ar etc.It should be appreciated by those skilled in the art that above mark only is used for illustrative purposes and should be understood that any restriction of the present invention.
As shown in Figure 1, be used for according to an embodiment of the invention the system that elliptic arc carries out rasterizing comprised and intersect pixel acquisition unit 102 and crossing pixel selection unit 104.Wherein, intersecting pixel acquisition unit 102 is used for finding out and the current one or more pixels squares (that is execution in step S202) that intersect with elliptic arc of walking upwards of having accomplished the pixel square C adjacent pixels square A0 to A7 that draws at elliptic arc.Intersect pixel selection unit 104 and be used for the pixel square (that is execution in step S204) that the nearest pixel square of chosen distance elliptic arc will be drawn as the next one from the one or more pixel squares that intersect with elliptic arc of pixel square A0 to A7.
Fig. 3 shows elliptic arc and current and has accomplished the foursquare crossing situation of one or more pixels among the neighbor square A0 to A7 of the pixel square C that draws (trend of suppose elliptic arc here, is from starting point (x
0, y
0) (x breasts the tape
1, y
1)):
Fig. 3 a show with pixel square C adjacent pixels square A0 to A7 in have only walk the upwards situation that with elliptic arc intersect of a pixel square Ai at elliptic arc.In this situation, having only pixel square Ai is the pixel that the possible next one will be drawn.Intersect the pixel square that pixel selection unit 104 can directly will be drawn pixel square Ai as the next one.
Fig. 3 b show with pixel square C adjacent pixels square A0 to A7 in two pixels square Ai and Aj walking upwards and the crossing situation of elliptic arc at elliptic arc arranged.In this case, pixel square Ai and Aj are the pixels that the possible next one will be drawn.Particularly in Fig. 3 b; The right edge of pixel square C (illustrative purposes for convenience; Be designated as square limit and a) intersect in walking upwards of elliptic arc with elliptic arc, thus with the pixel square Ai shared square limit a of pixel square C, that be in pixel square C right side be a pixel that the possible next one will be drawn; The upper side edge of pixel square Ai (illustrative purposes for convenience in addition; Be called square limit b) intersect with elliptic arc in walking upwards of elliptic arc; And the one other pixel square at square limit b place is adjacent with pixel square C exactly and be in the top-right pixel square of pixel square C Aj, so pixel square Aj is the pixel that another possible next one will be drawn.Intersecting pixel selection unit 104 can be square from the pixel that chosen distance elliptic arc pixel square Ai and the Aj nearer will be drawn as the next one.
Three foursquare joints of pixel that Fig. 3 c shows the upside that is in pixel square C among pixel square C and the pixel square A0 to A7, right side, upper right side elliptic arc walk upwards with the crossing situation of elliptic arc (promptly; This joint is on the elliptic arc; And illustrative purposes is designated as summit P with this joint for convenience).In this case, the pixel square Ar of the pixel square Aj of the pixel square Ai on pixel square C right side, pixel square C upper right side and pixel square C upside is the pixel that the possible next one will be drawn.Intersect pixel selection unit 104 can be from pixel square Ai, Aj and Ar the nearest pixel square that will draw as the next one of chosen distance elliptic arc.
Fig. 3 d and 3e show the situation of elliptic arc and two point of crossing of pixel square C existence.In the situation shown in Fig. 3 d; Elliptic arc is only crossing with the pixel square Ai on pixel square C right side; So having only pixel square Ai is the pixel that the possible next one will be drawn, intersect the pixel square that pixel selection unit 104 can directly will be drawn pixel square Ai as the next one; In the situation shown in Fig. 3 e; The pixel square Ai on elliptic arc and pixel square C right side and the pixel square Aj of upper right side intersect; So pixel square Ai and Aj are the pixels that the possible next one will be drawn, intersect pixel selection unit 104 and can select a pixel square Ai and the nearer pixel square that will draw as the next one of Aj middle distance elliptic arc.
Fig. 4 shows the block diagram that is used for elliptic arc is carried out the system of rasterizing according to another embodiment of the present invention.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 further comprises intersection edges acquisition module 1022 and crossing pixel acquisition module 1024.Wherein, intersection edges acquisition module 1022 is used for finding out walk the upwards square limit a that with elliptic arc intersect of pixel square C at elliptic arc.Intersect pixel acquisition module 1024 and be used to find out the pixel square Ai with the shared square limit a of pixel square C, and with pixel square Ai as walking upwards and the crossing pixel square (i is an integer, and 0≤i≤7) of elliptic arc at elliptic arc.
Fig. 5 shows elliptic arc and the current crossing situation of having accomplished the square limit of the pixel square C that draws.Particularly, Fig. 5 a shows the situation that upwards pixel square C and elliptic arc intersect at a point of walking at elliptic arc, and Fig. 5 b and 5c show the situation that intersects at walk the to make progress square C of pixel and the elliptic arc of elliptic arc at 2.
For any pixel square Q; Intersection edges acquisition module 1022 can be found out among the pixel square Q the square limit of intersecting with elliptic arc of walking upwards at elliptic arc through following processing: whether the symbol of functional value of judging the curvilinear function that any two adjacent vertexs (for example, P0 and P1) of pixel square Q are oval with respect to the elliptic arc place is identical; If different, think that then the square limit that connects adjacent vertex P0 and P1 is upwards crossing with elliptic arc in walking of elliptic arc; If it is identical; Judge then whether adjacent vertex P0 is identical at the symbol of the functional value of the gradient function of level or vertical direction with respect to elliptic arc place ellipse with P1; If it is different; Think that then the square limit that connects adjacent vertex P0 and P1 is upwards crossing with elliptic arc in walking of elliptic arc,, think that then the square limit that connects adjacent vertex P0 and P1 is upwards crossing with elliptic arc in walking of elliptic arc if identical.
Particularly, if connect the horizontal sides that the square limit of adjacent vertex P0 and P1 is pixel square Q, then belong to oval gradient function F in the horizontal direction with respect to elliptic arc according to adjacent vertex P0 and P1
xThe symbol of functional value judge the square limit that connects adjacent vertex P1 and P1 whether walking upwards and elliptic arc crossing (shown in Fig. 5 c) at elliptic arc; If connect the square limit of adjacent vertex P0 and P1 is the vertical edges of pixel square Q, then belongs to oval gradient function F in vertical direction according to adjacent vertex P0 and P1 with respect to elliptic arc
yThe symbol of functional value judge the square limit that connects adjacent vertex P1 and P1 whether walking upwards and elliptic arc crossing (shown in Fig. 5 b) at elliptic arc.
When if intersection edges acquisition module 1022 is judged the for example right edge a of pixel square C and upwards intersected with elliptic arc in walking of elliptic arc, also to utilize above-described method to find out another the square limit b that intersects with elliptic arc that walks upwards among the pixel square Ai with the shared square limit a of pixel square C at elliptic arc.If with the pixel square of the shared square limit b of pixel square Ai be one of pixel square A0 to A7 (for example; Pixel square Aj); Then intersect pixel acquisition module 1024 except the pixel square that pixel square Ai will be drawn as the possible next one; The pixel square (that is the situation shown in Fig. 3 b and the 3e) that also pixel square Aj will be drawn as the possible next one.
Intersect pixel acquisition unit 102 find out with current accomplished among the pixel square C adjacent pixels square A0 to A7 that draws in the walking upwards after the one or more pixel squares that intersect with elliptic arc of elliptic arc, intersect the pixel square that pixel selection unit 104 will the nearest pixel square of chosen distance elliptic arc will be drawn as the next one from intersect one or more pixel squares that pixel acquisition unit 102 finds out.
Particularly; If intersect pixel acquisition unit 102 with pixel square C adjacent pixels square A0 to A7 in only found out a pixel square Ai who intersects with elliptic arc that walks upwards at elliptic arc, then intersect the pixel square that pixel selection unit 104 directly will be drawn pixel square Ai as the next one; If intersect pixel acquisition unit 102 with pixel square C adjacent pixels square A0 to A7 in found out two or more pixel squares that intersects with elliptic arc of walking upwards at elliptic arc, then intersect pixel selection unit 104 and will intersect the pixel square that the minimum pixel square of absolute value of the functional value of curvilinear function oval with respect to the elliptic arc place in the pixel square that pixel acquisition unit 102 finds out will be drawn as the next one.
After finding out the pixel square that the next one will draw, the system and method that is used for elliptic arc is carried out rasterizing according to an embodiment of the invention will be drawn the pixel square of being found out.Completion can be that individual pixels is drawn the unit (not shown) for the foursquare parts of drawing of pixel, also can be combined in other unit.
Need to prove; System and method according to the embodiment of the invention is regarded pixel as selection course that the pixel square is accomplished the pixel that will draw for the next one, thus the functional value of the pixel square of being mentioned the here curvilinear function oval with respect to elliptic arc place, with respect to the functional value of the oval gradient function in horizontal/in elliptic arc place etc. come down to the functional value of the pixel curvilinear function oval with respect to the elliptic arc place, with respect to the functional value of the oval gradient function in horizontal/in elliptic arc place.In addition, the above-mentioned pixel square is drawn in fact exactly drawn pixel.
With respect to existing two kinds of methods, the present invention has following advantage.At first, the present invention can be contained all situations, comprises that ellipse is degenerated to flat; Secondly, the pointwise tracking that the present invention uses is simply effective, and it need not be divided into 8 quadrants and in these quadrants, switch with respect to mid-point method, and it need not use the gradient vector of arc with respect to minimum function value method; At last, use of the present invention and pixel square intersect the method for judging, want height a bit with respect to the precision of minimum function method, and the former only needs to judge 1 to 3 pixel, and the latter need judge at least 3 pixels.
Below the present invention has been described with reference to specific embodiment of the present invention; But those skilled in the art all understand; Can carry out various modifications, combination and change to these specific embodiments, and can not break away from the spirit and scope of the present invention that limit accompanying claims or its equivalent.
Can come execution in step with hardware or software as required.Notice that without departing from the scope of the invention, the process flow diagram that can in this instructions, provide adds step, therefrom removes step or revise step wherein.In general, process flow diagram just is used for indicating a kind of possible sequence of the basic operation that is used to realize function.
The universal digital computer of embodiments of the invention programming capable of using, utilize special IC, PLD, field programmable gate array, light, chemistry, biological, system quantum or nanometer engineering, assembly and mechanism to realize.In general, function of the present invention can be realized by any means known in the art.Can use distributed or networked system, assembly and circuit.The communication of data or to transmit can be wired, wireless or through any other means.
Also will recognize, according to the needs of application-specific, one or more can perhaps even in some cases being removed or being deactivated in the key element shown in the accompanying drawing by more separating or more integrated mode realizes.Program or code that realization can be stored in the machine readable media are carried out above-mentioned any method to allow computing machine, also within the spirit and scope of the present invention.
In addition, it only is exemplary that any signal arrows in the accompanying drawing should be considered to, rather than restrictive, only if concrete indication is arranged in addition.Separate or the ability of combination when not knowing when term is also contemplated as to make, the combination of assembly or step also will be considered to put down in writing.
Claims (10)
1. method that is used for elliptic arc is carried out rasterizing comprises:
Find out and the current one or more pixels squares of having accomplished among the pixel square C adjacent pixels square A0 to A7 that draws at elliptic arc that intersect with said elliptic arc of walking upwards;
The pixel square that the nearest pixel square of the said elliptic arc of chosen distance will be drawn as the next one from said one or more pixel squares.
2. the method that is used for elliptic arc is carried out rasterizing according to claim 1 is characterized in that, finds out among the said pixel square A0 to A7 to comprise with the crossing foursquare processing of one or more pixels of said elliptic arc in walking upwards of said elliptic arc:
The square limit a that intersects with said elliptic arc that walks upwards that finds out among the said pixel square C at said elliptic arc;
Will with the pixel square Ai of the shared said square limit a of said pixel square C as the pixel square that intersects with said elliptic arc of walking upwards at said elliptic arc, wherein i is integer and 0≤i≤7.
3. the method that is used for elliptic arc is carried out rasterizing according to claim 2; It is characterized in that; When said elliptic arc and said square limit a intersect at the summit P of said pixel square C; With among the said pixel square A0 to A7 with a plurality of pixels squares of the shared said summit P of said pixel square C as said elliptic arc to walk upwards the pixel that intersects with said elliptic arc square; Perhaps another the square limit b in said pixel square Ai intersects with said elliptic arc in walking upwards of said elliptic arc; And during the shared said square limit b of the pixel square Aj among the said pixel square A0 to A7 and said pixel square Ai, with said pixel square Aj as square in walking upwards of said elliptic arc with the crossing one other pixel of said elliptic arc.
4. according to each described method that is used for elliptic arc is carried out rasterizing in the claim 2 to 3, it is characterized in that the processing of finding out among any pixel square Q at said elliptic arc of walking upwards the square limit of intersecting with said elliptic arc comprises:
Whether any two adjacent vertexs of judging said pixel square Q are identical with respect to the symbol of the functional value of the curvilinear function of said elliptic arc place ellipse;
If different, conclude that then the square limit that connects said two adjacent vertexs is upwards crossing with said elliptic arc in walking of said elliptic arc;
If identical, judge then whether said two adjacent vertexs are identical at the symbol of the functional value of the gradient function of level or vertical direction with respect to said elliptic arc place ellipse,
If different, conclude that then the square limit that connects said two adjacent vertexs is upwards crossing with said elliptic arc in walking of said elliptic arc,
If identical, conclude that then the square limit that connects said two adjacent vertexs is upwards crossing with said elliptic arc in walking of said elliptic arc.
5. the method that is used for elliptic arc is carried out rasterizing according to claim 4 is characterized in that,
When having only a pixel square Ai upwards to intersect among the said pixel square A0 to A7 with said elliptic arc in walking of said elliptic arc, the pixel square that directly said pixel square Ai will be drawn as the next one;
When having a plurality of pixel squares upwards to intersect among the said pixel square A0 to A7 with said elliptic arc in walking of said elliptic arc, the pixel square of selecting the minimum pixel square of absolute value of the functional value of curvilinear function oval in said a plurality of pixel square will draw as the next one with respect to said elliptic arc place.
6. system that is used for elliptic arc is carried out rasterizing comprises:
Intersect pixel acquisition unit, be used for finding out and the current one or more pixels squares that intersect with said elliptic arc of walking upwards of having accomplished the pixel square C adjacent pixels square A0 to A7 that draws at elliptic arc;
Intersect the pixel selection unit, be used for the pixel square that to draw as the next one from the nearest pixel square of the said elliptic arc of said one or more pixel square chosen distances.
7. the system that is used for elliptic arc is carried out rasterizing according to claim 6 is characterized in that, said crossing pixel acquisition unit comprises:
The intersection edges acquisition module is used for finding out walk the upwards square limit a that with said elliptic arc intersect of said pixel square C at said elliptic arc;
Intersect the pixel acquisition module, be used for with the pixel square Ai of the shared said square limit a of said pixel square C as in the walking upwards and a crossing pixel square of said elliptic arc of said elliptic arc, wherein i is integer and 0≤i≤7.
8. the system that is used for elliptic arc is carried out rasterizing according to claim 7; It is characterized in that; Intersect at said elliptic arc and said square limit a under the situation of summit P of said pixel square C; Said crossing pixel acquisition unit with among the said pixel square A0 to A7 with a plurality of pixels squares of the shared said summit P of said pixel square C as said elliptic arc to walk upwards the pixel that intersects with said elliptic arc square; Perhaps another the square limit b in said pixel square Ai intersects with said elliptic arc in walking upwards of said elliptic arc; And under the pixel square Aj among the said pixel square A0 to A7 and the situation of the shared said square limit b of said pixel square Ai, said crossing pixel acquisition unit with said pixel square Aj as square in walking upwards of said elliptic arc with the crossing one other pixel of said elliptic arc.
9. according to each described system that is used for elliptic arc is carried out rasterizing in the claim 7 to 8; It is characterized in that said intersection edges acquisition module is found out among any pixel square Q the square limit of intersecting with said elliptic arc of walking upwards at said elliptic arc through following processing:
Whether any two adjacent vertexs of judging said pixel square Q are identical with respect to the symbol of the functional value of the curvilinear function of said elliptic arc place ellipse;
If different, conclude that then the square limit that connects said two adjacent vertexs is upwards crossing with said elliptic arc in walking of said elliptic arc;
If identical, judge then whether said two adjacent vertexs are identical at the symbol of the functional value of the gradient function of level or vertical direction with respect to said elliptic arc place ellipse,
If different, conclude that then the square limit that connects said two adjacent vertexs is upwards crossing with said elliptic arc in walking of said elliptic arc,
If identical, conclude that then the square limit that connects said two adjacent vertexs is upwards crossing with said elliptic arc in walking of said elliptic arc.
10. the system that is used for elliptic arc is carried out rasterizing according to claim 9 is characterized in that, said crossing pixel selection unit
In said pixel square A0 to A7, have only a pixel square Ai to walk upwards under the situation about intersecting the pixel square that directly said pixel square Ai will be drawn as the next one with said elliptic arc at said elliptic arc;
A plurality of pixel squares are arranged in the walking upwards under the situation about intersecting of said elliptic arc in said pixel square A0 to A7, the pixel square of selecting the minimum pixel square of absolute value of the functional value of curvilinear function oval in said a plurality of pixel square will draw as the next one with respect to said elliptic arc place with said elliptic arc.
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| CN102819854A (en) * | 2011-06-10 | 2012-12-12 | 富士通株式会社 | Method and system for describing elliptic arc on raster display |
| CN102819854B (en) * | 2011-06-10 | 2014-11-12 | 富士通株式会社 | Method and system for describing elliptic arc on raster display |
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