CN102819854B - Method and system for describing elliptic arc on raster display - Google Patents
Method and system for describing elliptic arc on raster display Download PDFInfo
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- CN102819854B CN102819854B CN201110162429.7A CN201110162429A CN102819854B CN 102819854 B CN102819854 B CN 102819854B CN 201110162429 A CN201110162429 A CN 201110162429A CN 102819854 B CN102819854 B CN 102819854B
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Abstract
The invention discloses a method and a system for describing an elliptic arc on a raster display. The method provided by the invention comprises the steps of dividing an adjacent pixel of the current pixel into two pixel groups by connecting a line of the current pixel and the elliptic arc in the center of an ellipse, selecting next pixel to be rendered in the pixel group which is positioned the trend side of the elliptic arc and rending the selected pixel, wherein the current pixel which is just rendered during the process of describing the elliptic arc. According to the invention, description for elliptic arcs on ellipses in different shapes can be simply realized.
Description
Technical field
The present invention relates to field of Computer Graphics, relate more specifically to a kind of for draw the method and system of elliptic arc on raster display.
Background technology
The process of briefly, drawing elliptic arc on raster display is exactly on raster display, to select the process that approaches the pixel of elliptic arc most and these pixels are played up.This process normally completes by following the trail of pixel along elliptic arc.
Exist at present two kinds popular for draw the method for elliptic arc on raster display: mid-point method and minimum function value method.The pixel that they all use gradient vector and 8 octant quadrants to judge that the next one is drawn is to follow square mobile (Δ x=± 1 or Δ y=± 1) still to follow diagonal line and move (Δ x=± 1 and Δ y=± 1).Wherein, when elliptic arc is that while being positioned at major axis much larger than elliptic arc on the ellipse (referred to as very thin ellipse) of minor axis, the above mid-point method lost efficacy.And minimum function value method judges with elliptic arc and pixel square limit crossing the pixel that should select which pixel will draw as the next one in 8 neighbors around current pixel of having drawn.In minimum function value method, all crossing situations are summarized in the independent definition of neither one, so it is remarkable to realize situation.
Summary of the invention
Problem in view of the above, the invention provides a kind of novelty for draw the method and system of elliptic arc on raster display.
According to the embodiment of the present invention for draw the method for elliptic arc on raster display, comprise: utilize the straight line at the center that connects current pixel and elliptic arc place ellipse that the neighbor of current pixel is divided in two pixel groups, wherein current pixel is in the process of drawing elliptic arc, just to have completed the pixel of playing up; And from the pixel groups moving towards side in elliptic arc, select the next pixel that will play up, and selected pixel is played up.
According to the embodiment of the present invention for draw the system of elliptic arc on raster display, comprise: group pixels unit, for the straight line that utilizes the center that connects current pixel and elliptic arc place ellipse, the neighbor of current pixel is divided into two pixel groups, wherein current pixel is in the process of drawing elliptic arc, just to have completed the pixel of playing up; Pixel rendering unit, for selecting the next pixel that will play up from the pixel groups moving towards side in elliptic arc, and plays up selected pixel.
By the present invention, can not need compute gradient value, do not need to consider various crossing situations, and need between 8 cyclotomy quadrants, not switch, and realize simply drawing for the elliptic arc on the ellipse of various shapes.
Brief description of the drawings
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 show according to the embodiment of the present invention for draw the process flow diagram of method of elliptic arc on raster display;
Fig. 2 show according to the embodiment of the present invention for draw the block diagram of system of elliptic arc on raster display;
Fig. 3 shows the example of one group of pixel that the optimal approximation to elliptic arc is provided;
Fig. 4 shows current pixel on elliptic arc, enters pixel and go out the example of pixel;
Fig. 5 shows the processing example of selecting the next pixel that will play up in the process of drawing elliptic arc.
Embodiment
Feature and the exemplary embodiment of various aspects of the present invention will be described in detail below.Many details have been contained in description below, to 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 some details in these details in the case of not needing.Below the description of embodiment is only used to by illustrating that example of the present invention provides the clearer understanding to the present invention.The present invention is never limited to any concrete configuration and the algorithm that propose below, but has covered under the premise of without departing from the spirit of the present invention any amendment, replacement and the improvement of coherent element, parts and algorithm.
The invention provides a kind of novelty for draw the method and system of elliptic arc on raster display.According to the embodiment of the present invention for draw the method and system of elliptic arc on raster display, (the straight line that utilizes the center that connects current pixel and elliptic arc place ellipse is divided into current pixel of drawing 8 neighbors around in two planes, be divided into two pixel groups), the pixel of then selecting the next one to draw from move towards a plane of side in elliptic arc.According to the elliptic arc on the ellipse that is applicable to any shape for draw the method and system of elliptic arc on raster display of the embodiment of the present invention, and be easy to realize.
Below in conjunction with accompanying drawing, describe in detail according to the embodiment of the present invention for draw the method and system of elliptic arc on raster display.Fig. 1 show according to the embodiment of the present invention for draw the process flow diagram of method of elliptic arc on raster display.Fig. 2 show according to the embodiment of the present invention for draw the block diagram of system of elliptic arc on raster display.
As shown in Figure 1, comprise according to the method for draw elliptic arc on raster display of the embodiment of the present invention: S102, utilize the straight line at the center that connects current pixel and elliptic arc place ellipse that the neighbor of current pixel is divided in two pixel groups, wherein current pixel is in the process of drawing elliptic arc, just to have completed the pixel of playing up; And S104, from the pixel groups moving towards side in elliptic arc, select the next pixel that will play up, and selected pixel is played up.
As shown in Figure 2, comprise group pixels unit 202 and pixel rendering unit 204 according to the embodiment of the present invention for draw the system of elliptic arc on raster display.Wherein, (the straight line that group pixels unit 202 utilizes the center that connects current pixels and elliptic arc place ellipse is divided into the neighbor of current pixel in two pixel groups, execution step S102), pixel rendering unit 204 is selected the next pixel that will play up and selected pixel is played up to (, execution step S104) from the pixel groups moving towards side in elliptic arc.
Below in conjunction with example, describing in detail is how to complete drawing of elliptic arc according to the embodiment of the present invention for draw the method and system of elliptic arc on raster display.
Here, the ellipse of supposing the elliptic arc place that need to draw is the ellipse centered by coordinate points (0,0), and its implicit function is:
F(x，y)＝Ax
2+Bxy+Cy
2-1＝0
Wherein, rh represents oval horizontal radius, and rv represents oval vertical radius,
represent the counterclockwise angle of oval horizontal radius with respect to x axle.The starting point of supposing elliptic arc is (x
0, y
0), terminating point is (x
1, y
1).
Outside the ellipse at the elliptic arc place that a pixel on raster display is drawn in needs time, this pixel with respect to the functional value of oval implicit function for just; Otherwise within the ellipse at the elliptic arc place that a pixel on raster display is drawn in needs time, this pixel is negative with respect to the functional value of oval implicit function.
On raster display, draw there is no the camber line of the thickness process of (that is, width or fineness are the camber line of a pixel unit), find out the process that approaches the pixel of this camber line most and these pixels are played up.The direct estimation of the degree of closeness of pixel and camber line is the distance between this pixel and camber line.But, be difficult in practice accurately draw the distance between pixel and camber line, so need a kind of approximation method to draw roughly the distance between pixel and camber line.
In the process of elliptic arc of drawing a pixel unit width, be to be provided by one group of such pixel to the optimal approximation of elliptic arc: in this group pixel, do not have three pixels adjacent with same pixel.Fig. 3 shows the example of one group of pixel that the optimal approximation to elliptic arc is provided.As shown in Figure 3, be not that all pixels (or pixel square) crossing with elliptic arc all should be played up.Here for convenience of description, on raster display, drawing in the process of elliptic arc, is benchmark with current pixel (, the current pixel of drawing that just completed), previous pixel of having drawn is called into pixel, and the pixel that the next one will be drawn is called pixel.
Fig. 4 shows current pixel on elliptic arc, enters pixel and go out the example of pixel.As shown in Figure 4, the pixel that is positioned at current pixel left side is into pixel, and the pixel that is positioned at current pixel upper right side is pixel.Can find out according to the situation shown in Fig. 3 and Fig. 4, with respect to current pixel, only exist one to enter pixel, and only exist one to go out pixel.In some cases, entering pixel and go out pixel can be same pixel.In some cases, entering pixel, current pixel and go out pixel can be same pixel.
In the example depicted in fig. 4, in the neighbor of current pixel, exist two to move towards side (counterclockwise at elliptic arc, i.e. direction from point A to point B) pixel crossing with elliptic arc is (, exist two will be after current pixel coloured candidate pixel), one is positioned at the upside of current pixel, and another is positioned at the upper right side of current pixel.Can know according to the optimal approximation rule to elliptic arc of describing with reference to figure 1 above, the pixel that pixel rendering unit 204 should select the pixel that is positioned at current pixel upper right side will draw as the next one, and the pixel that should not select the pixel that is positioned at current pixel upside will draw as the next one.
Because center and the current pixel of elliptic arc place ellipse are all known, so be easy to utilize the center of connection elliptic arc place ellipse and the straight line of current pixel that 8 neighbors of current pixel are divided in two pixel groups.Wherein, the neighbor in a pixel groups is different from neighbor in the one other pixel group symbol with respect to the limit equation value of this straight line with respect to the symbol of limit equation value that connects the center of elliptic arc place ellipse and the straight line of current pixel.
In an embodiment of the present invention, for any one neighbor P of current pixel, group pixels unit 202 judges with respect to the limit equation value of the limit equation of the straight line at the center of connection current pixel and elliptic arc place ellipse whether neighbor P belongs to the pixel groups moving towards side in elliptic arc according to neighbor P.Particularly, if (neighbor P is greater than 0 with respect to the limit equation value of the limit equation of the straight line at the center of connection current pixel and elliptic arc place ellipse, the symbol of limit equation value is for just), group pixels unit 202 thinks that neighbor P belongs to the pixel groups moving towards side in elliptic arc; Otherwise, group pixels unit 202 think neighbor P belong in elliptic arc with move towards the rightabout pixel groups of side.
Fig. 5 shows the processing example of selecting the next pixel that will play up in the process of drawing elliptic arc.As shown in Figure 5, the trend of elliptic arc place ellipse (, the trend of elliptic arc) be counterclockwise, utilize in each pixel groups that the straight line at the center that connects current pixels and elliptic arc place ellipse marks off in group pixels unit 202, there are at most 4 neighbors.At this moment, the pixel that neighbor will be played up as the next one that approaches elliptic arc most in the pixel groups moving towards side in elliptic arc that group pixels unit 202 marks off is selected in pixel rendering unit 204.For example, in Fig. 5, the trend of elliptic arc is counterclockwise, is the pixel that one of positive pixel will be drawn as the next one so the symbol of limit equation value of straight line with respect to the center that connects current pixel and elliptic arc place ellipse in the neighbor of current pixel is selected in pixel rendering unit 204.If the trend of elliptic arc is clockwise, to select the symbol of limit equation value of straight line with respect to the center that connects current pixel and elliptic arc place ellipse in the neighbor of current pixel be the pixel that one of negative pixel will be drawn as the next one in pixel rendering unit 204.Particularly, pixel rendering unit 204 using the neighbor in the pixel groups moving towards side in elliptic arc with respect to the functional value of the implicit function of elliptic arc place ellipse the distance between this neighbor and elliptic arc, and the pixel that a neighbor of distance minimum between selection and elliptic arc will be played up as the next one is played up.
Here hypothesis, the coordinate at the center of elliptic arc place ellipse is (cx, cy), and the coordinate of current pixel is (x
d, y
d), the limit equation that connects the center of elliptic arc place ellipse and the straight line of current pixel is f (x, y)=ax+by+c, wherein a=cy-y
d, b=x
d-cx, c=cxy
d-x
dcy.Owing to only need to judging that the neighbor of current pixel is with respect to the limit equation value of the limit equation of the straight line at the center of connection current pixel and elliptic arc place ellipse, so there is x=x
d+ dx, y=y
d+ dy, dx and dy are ± 1 or 0.By a=cy-y
d, b=x
d-cx, c=cxy
d-x
dcy, x=x
d+ dx, y=y
d+ dy substitution f (x, y)=ax+by+c, can draw f by following derivation
d=adx+bdy.
f
d＝f(x
d+dx，y
d+dy)
＝a(x
d+dx)+b(y
d+dy)+c
＝(cy-y
d)(x
d+dx)+(x
d-cx)(y
d+dy)+cx·y
d-x
d·cy
＝cy·x
d+cy·dx-y
dx
d-y
ddx+x
dy
d+x
ddy-y
dcx-cx·dy+cx·y
d-x
d·cy
＝x
dcy-x
dcy+y
dcx-y
dcx+x
dy
d-x
dy
d+(cy·dx-y
ddx)+(x
ddy-cx·dy)
＝(cy-y
d)dx+(x
d-cx)dy
＝a·dx+b·dy
Eight neighbors of current pixel are respectively with respect to the limit equation value of the limit equation that connects the center of elliptic arc place ellipse and the straight line of current pixel:
f
d0＝-a-b，(dx＝-1，dy＝-1)；
f
d1＝-b，(dx＝0，dy＝-1)；
f
d2＝a-b，(dx＝1，dy＝-1)；
f
d3＝a，(dx＝1，dy＝0)；
f
d4＝a+b，(dx＝1，dy＝1)；
f
d5＝b，(dx＝0，dy＝1)；
f
d6＝-a+b，(dx＝-1，dy＝1)；
f
d7＝-a，(dx＝-1，dy＝0)；
In the time that current pixel moves to the pixel that the next one will play up, will there is x
d=x
d+ dx, y
d=y
d+ dy, wherein dx and dy are ± 1.Only need to upgrade neighbor that a and b can draw each current pixel with respect to the limit equation value of straight line that is connected current pixel and elliptical center.
In order to calculate the functional value of the neighbor of current pixel with respect to the implicit function of elliptic arc place ellipse, can use in one embodiment of the invention forward-difference method.For example, for the ellipse centered by (0,0), its implicit function is F (x, y)=Ax
2+ Bxy+Cy
2-1=0.
The first order difference of the implicit function of elliptic arc place ellipse is:
The second order difference of the implicit function of elliptic arc place ellipse is:
Δ
2F
x＝ΔF
x(x±1，y)-ΔF
x(x，y)＝±2A，
Δ
2F
y＝ΔF
y(x，y±1)-ΔF
y(x，y)＝±2C，
Δ
2F
xy＝ΔF
xy(x±1，y±1)-ΔF
xy(x，y)＝±2(A+B+C)
Here the coordinate of supposing the pixel of the starting point that approaches elliptic arc is most (x
s, y
s), this pixel is F (x with respect to the functional value of the implicit function of elliptic arc place ellipse
s, y
s), and the first order difference value at this pixel place is Δ F
x(x
s, y
s), Δ F
y(x
s, y
s), Δ F
xy(x
s, y
s).If selection coordinate is (x
s+ 1, y
s) pixel as the next pixel that will judge, this pixel can be by by F (x with respect to the functional value of the implicit function of elliptic arc place ellipse
s, y
s) and Δ F
x(x
s, y
s) be added draw.The like, only need according to relevant (x
s, y
s) initial value, can show that all pixels of judgement that need are with respect to the functional value of the implicit function of elliptic arc place ellipse by addition calculation.
From above description, can not need compute gradient value by the present invention, do not need to consider various crossing situations, and need between 8 cyclotomy quadrants, not switch, and realize simply drawing for the elliptic arc on the ellipse of various shapes.
Below with reference to specific embodiments of the invention, the present invention has been described, but those skilled in the art all understand, can carry out various amendments, combination and change to these specific embodiments, and can not depart from the spirit and scope of the present invention that limited by claims or its equivalent.
Can perform step with hardware or software as required.Note, without departing from the scope of the invention, can add step, therefrom remove step or amendment step wherein to the process flow diagram providing in this instructions.In general, process flow diagram is just used to refer to a kind of possible sequence for the basic operation of practical function.
Embodiments of the invention can utilize programming universal digital computer, utilize special IC, programmable logic device (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 by any other means.
Also will recognize, according to the needs of application-specific, one or more can, by more separating or more integrated mode realizes, or being removed even in some cases or being deactivated in the key element shown in accompanying drawing.The journey logic bomb that realization can be stored in machine readable media is carried out above-mentioned any method with permission computing machine, also within the spirit and scope of the present invention.
In addition, it is only exemplary that any signal arrows in accompanying drawing should be considered to, instead of restrictive, unless separately there is concrete instruction.Make to separate or the ability of combination while not knowing when term is also contemplated as, the combination of assembly or step also will be considered to record.
Claims (8)
1. for draw a method for elliptic arc on raster display, comprising:
Utilize the straight line at the center that connects current pixel and elliptic arc place ellipse that the neighbor of described current pixel is divided in two pixel groups, wherein said current pixel is in the process of drawing described elliptic arc, just to have completed the pixel of playing up; And
From the pixel groups moving towards side in described elliptic arc, select the next pixel that will play up, and selected pixel is played up, wherein
For any one neighbor P of described current pixel, judge with respect to the limit equation value of the limit equation of the straight line at the center of the described current pixel of connection and described elliptic arc place ellipse whether described neighbor P belongs to the pixel groups moving towards side in described elliptic arc according to described neighbor P.
2. method according to claim 1, is characterized in that, selects a nearest pixel that neighbor will be played up as the described next one of elliptic arc described in the distance in a pixel groups moving towards side in described elliptic arc.
3. method according to claim 2, it is characterized in that, using each neighbor in the pixel groups moving towards side in described elliptic arc with respect to the functional value of the implicit function of described elliptic arc place ellipse the distance between described each neighbor and described elliptic arc.
4. method according to claim 3, is characterized in that, utilizes forward-difference method to calculate each neighbor in the pixel groups moving towards side in described elliptic arc functional value with respect to the implicit function of described elliptic arc place ellipse.
5. for draw a system for elliptic arc on raster display, comprising:
Group pixels unit, for the straight line that utilizes the center that connects current pixel and elliptic arc place ellipse, the neighbor of described current pixel is divided into two pixel groups, wherein said current pixel is in the process of drawing described elliptic arc, just to have completed the pixel of playing up;
Pixel rendering unit, for selecting the next pixel that will play up from the pixel groups moving towards side in described elliptic arc, and plays up selected pixel, wherein
For any one neighbor P of described current pixel, described group pixels unit judges with respect to the limit equation value of the limit equation of the straight line at the center of the described current pixel of connection and described elliptic arc place ellipse whether described neighbor P belongs to the pixel groups moving towards side in described elliptic arc according to described neighbor P.
6. system according to claim 5, is characterized in that, a nearest pixel that neighbor will be played up as the described next one of elliptic arc described in the distance in the pixel groups moving towards side in described elliptic arc is selected in described pixel rendering unit.
7. system according to claim 6, it is characterized in that, described pixel rendering unit using each neighbor in the pixel groups moving towards side in described elliptic arc with respect to the functional value of the implicit function of described elliptic arc place ellipse the distance between described each neighbor and described elliptic arc.
8. system according to claim 7, it is characterized in that, described pixel rendering unit by using forward-difference method is calculated each neighbor in the pixel groups moving towards side in described elliptic arc functional value with respect to the implicit function of described elliptic arc place ellipse.
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| CN101901488A (en) * | 2009-05-25 | 2010-12-01 | 富士通株式会社 | Method and device for curve approximation and method and device for controlling graphics display |
| CN102646281A (en) * | 2011-02-16 | 2012-08-22 | 富士通株式会社 | Method and system for rasterizing elliptic arc |
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| CN101901488A (en) * | 2009-05-25 | 2010-12-01 | 富士通株式会社 | Method and device for curve approximation and method and device for controlling graphics display |
| CN102646281A (en) * | 2011-02-16 | 2012-08-22 | 富士通株式会社 | Method and system for rasterizing elliptic arc |
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