CN104217450B - Quick drawing method of any-angle circular arc - Google Patents
Quick drawing method of any-angle circular arc Download PDFInfo
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- CN104217450B CN104217450B CN201410457445.2A CN201410457445A CN104217450B CN 104217450 B CN104217450 B CN 104217450B CN 201410457445 A CN201410457445 A CN 201410457445A CN 104217450 B CN104217450 B CN 104217450B
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Abstract
The invention discloses a quick drawing method of any-angle circular arc, and belongs to the technical field of graphical display. The invention is improved by aiming at problems that a traditional circular arc drawing method needs a great quantity of (inverse) trigonometric function calculation and drawing time is long, and the any-angle circular arc is drawn according to an anticlockwise direction. The quick drawing method comprises the following steps: firstly, according to a circular arc starting angle and end angle, determining a circular arc drawing starting interval and termination interval; then, successively mapping point coordinate values on 1/8 circular arc into all intervals from the starting interval to the termination interval according to the anticlockwise direction; comparing the point coordinates with a circular arc starting point coordinate value and the end point coordinate value in the starting interval and the termination interval to judge whether the point is within a drawing range, wherein the point coordinate value of a middle interval is directly effective without judgment; and displaying and outputting a point endowment gray value corresponding to an effective coordinate value to obtain an integral circular arc. The method does not need to carry out a great quantity of (inverse) trigonometric function calculation, hardware realization method is effectively shortened, and display instantaneity is improved.
Description
Technical field
The present invention relates to a kind of fast drawing method of circular arcs with arbitrary angles, belong to graphical display technicss field.
Background technology
Circular arc is one of composition most basic element of computer graphical, needs to draw arbitrarily angled in a lot of display systems
Circular arc.But most of research to arc drafting at present, is limited only to for doing basis for improving picture circle effect, and does not have
There is the method for drafting considering circular arcs with arbitrary angles.
In airborne display system, need to draw plurality of lines figure, when the drafting of wherein circular arc needs to take substantial amounts of
Between and resource.How to reduce circular arcs with arbitrary angles and draw the time, improve the real-time of figure shows, reduce (anti-) triangle letter simultaneously
The access times of number, save logical resource, become important research contents.
Conventional circular arcs with arbitrary angles method for drafting has method of polar coordinates and angle diagnostic method etc..
Method of polar coordinates (list of references [computer graphicss, He En (Donald Hearn), Bark (M.Pauline
Baker), Electronic Industry Press, the third edition, 80-81]) represent point on circular arc with parameter polar form, in known circular arc
When start angle and termination point, for obtaining more continuous output point, Δ θ takes the inverse of arc radius, is calculated with Δ θ for stepping
Point coordinates value in circular arc.The method advantage is to judge that step is few, and shortcoming is arc radius and circular arc span is bigger, needs to calculate
Trigonometric function quantity sharply increase, hardware is realized difficult.
Angle diagnostic method (list of references [Airborne Video System based on FPGA is processed and Grafmaster design and realization,
Dawn swallow, 41-42]) circle draw on the basis of add angle judge operation, calculate 1/8th circular arcs on every corresponding anyway
Cut value, and be mapped to entirely justify on, the angle of every is contrasted with arc angle scope, in the range of then draw, do not exist
In the range of then do not draw.The method advantage is to be easily achieved on the basis of circle is drawn, and shortcoming is to draw the time of one section of circular arc
Than entirely, the round time is long, and each coordinate is judged with arctangent computation angle value, significantly wastes logical resource.
Content of the invention
The technical problem to be solved is to overcome angle diagnostic method to draw the time that circular arcs with arbitrary angles needs
Deficiency that is longer than the time entirely justified and wasting logical resource, provides a kind of Fast Drawing side being applied to circular arcs with arbitrary angles
Method, can effectively reduce the calculating of (anti-) trigonometric function, improve arc drafting speed, significantly increase the real-time of figure shows.
The present invention employs the following technical solutions：
Whether a kind of fast drawing method of circular arcs with arbitrary angles, can fast and effeciently judge pixel in arc drafting
In angular range, in the range of drawing, then draw, otherwise abandon：
Indicator screen is divided into interval 1～interval 8 according to symmetry, circular arc initial angle θs(0°≤θs≤ 360 °) and
End angle θe(0°≤θe≤ 360 °) place interval is referred to as initial interval a and terminates interval b, and whether pixel is painted in circular arc
Judgement in the range of system is as follows：
If θs≤θe, then
If θs＞ θe, then
In formula, en indicates whether to draw this pixel, and 1 represents drafting, and 0 expression is not drawn；C represents currently pixel to be judged
Interval, then 1≤c≤8 that point is located；En ' represents in initial interval a and terminates needing in interval b to further determine whether to draw.
Pixel in initial interval a or terminates needing to further determine whether, in the range of arc drafting, painting in interval b
In the range of system, then draw, otherwise abandon；Circular arc initial angle θsWith end angle θeCorresponding rectangular coordinate is (xs, ys) and (xe,
ye), pixel rectangular coordinate currently to be judged is (x, y), then in initial interval a pixel whether in arc drafting scope
Interior judgement is as follows：
In terminating interval b, the judgement in the range of arc drafting is as follows for pixel：
All circular arcs all using the technique of painting counterclockwise, then exchange initial angle and end angle for clockwise arc, are continuing with
The technique of painting counterclockwise.
The fast drawing method of circular arcs with arbitrary angles as mentioned above, if θs≤θe, then described circular arcs with arbitrary angles is without x
Positive axis；The described circular arc without x positive axis is drawn, specifically includes following steps：
Step 1, indicator screen interval is adopted it is divided into 8 intervals with the following method：Interval 1 corresponding angle [0 °,
45°]；Interval 2 corresponding angles (45 °, 90 °]；Interval 3 corresponding angles (90 °, 135 °]；Interval 4 corresponding angles (135 °, 180 °]；
Interval 5 corresponding angles (180 °, 225 °]；Interval 6 corresponding angles (225 °, 270 °]；Interval 7 corresponding angles (270 °, 315 °]；Area
Between 8 corresponding angles (315 °, 360 °]；Circular arc intercept in a circle one section wherein a line and display pixel column/as
Element row are parallelCircular arc, obtains remaining corresponding pixel point coordinates in 7 intervals using symmetry.
Step 2, judge pixel whether in arc drafting angular range, in the range of drawing, then draw, otherwise lose
Abandon：
In formula, en indicates whether to draw this pixel, and 1 represents drafting, and 0 expression is not drawn；C represents currently pixel to be judged
Interval, then 1≤c≤8 that point is located；En ' represents in initial interval a and terminates needing in interval b to further determine whether to draw.
Step 3, circular arc initial angle θsWith end angle θeCorresponding rectangular coordinate is (xs, ys) and (xe, ye), if arc radius are r,
In units of pixel, then：Circular arc starting point rectangular coordinate isTerminating point rectangular coordinate is
Wherein [] represents round.
Pixel in initial interval a or terminates needing to further determine whether in the range of arc drafting in interval b：Rising
The judgement whether in the range of arc drafting of pixel in interval a of beginning is as follows：
In terminating interval b, the judgement in the range of arc drafting is as follows for pixel：
The fast drawing method of circular arcs with arbitrary angles as mentioned above, if θs＞ θe, then described circular arcs with arbitrary angles is being through x just
Semiaxis；The described circular arc through x positive axis is drawn, specifically includes following steps：
Step 1, indicator screen interval is adopted it is divided into 8 intervals with the following method：Interval 1 corresponding angle [0 °,
45°]；Interval 2 corresponding angles (45 °, 90 °]；Interval 3 corresponding angles (90 °, 135 °]；Interval 4 corresponding angles (135 °, 180 °]；
Interval 5 corresponding angles (180 °, 225 °]；Interval 6 corresponding angles (225 °, 270 °]；Interval 7 corresponding angles (270 °, 315 °]；Area
Between 8 corresponding angles (315 °, 360 °]；Circular arc intercept in a circle one section wherein a line and display pixel column/as
Element row are parallelCircular arc, obtains remaining corresponding pixel point coordinates in 7 intervals using symmetry.
Step 2, judge pixel whether in arc drafting angular range, in the range of drawing, then show, otherwise lose
Abandon：
In formula, en indicates whether to draw this pixel, and 1 represents drafting, and 0 expression is not drawn；C represents currently pixel to be judged
Interval, then 1≤c≤8 that point is located；En ' represents in initial interval a and terminates needing in interval b to further determine whether to draw；
Step 3, circular arc initial angle θsWith end angle θeCorresponding rectangular coordinate is (xs, ys) and (xe, ye), if arc radius are r,
In units of pixel, then：Circular arc starting point rectangular coordinate isTerminating point rectangular coordinate is
Wherein, [] represents round.
Pixel in initial interval a or terminates needing to further determine whether in the range of arc drafting in interval b：Rising
The judgement whether in the range of arc drafting of pixel in interval a of beginning is as follows：
In terminating interval b, the judgement in the range of arc drafting is as follows for pixel：
Compared to existing technology, the invention has the advantages that：
(1) the inventive method can realize the Fast Drawing of circular arcs with arbitrary angles, and practicality is higher；
(2) compared with angle diagnostic method, angle diagnostic method calculates corresponding to each pixel to be judged the inventive method
Angle, is contrasted with circular arc initial angle and end angle；And the present invention calculates circular arc initial angle and the corresponding coordinate figure of end angle
Contrasted with pixel point coordinates to be judged, (anti-) trigonometric function amount of calculation significantly reduces；(anti-) trigonometric function of two methods
Amount of calculation is compared as follows shown in table, and when arc radius r (in units of pixel) is bigger, the inventive method advantage is more obvious, favorably
Use in reducing logical resource；
(3) the inventive method compared with angle diagnostic method, add angle on the basis of circle is drawn and judge by angle diagnostic method
Operation, needs the point interval to 8 to carry out angle judgement successively, spends the unnecessary time；And the present invention can quickly judge
In addition to whole story interval, whether other interval point are drawn it is only necessary to determine whether to point initial interval and that termination is interval, make
Obtain the drafting time that the arc drafting time is less than circle, improve arc drafting speed, significantly increase the real-time of figure shows.
Brief description
Fig. 1 is the interval division schematic diagram of plane right-angle coordinate；
Fig. 2 is θs≤θeCircular arc judge schematic diagram whether in the range of drawing for the pixel；
Fig. 3 is that embodiment one draws θs≤θeCircular arc instantiation schematic diagram；
Fig. 4 is the hard-wired Showing Effectiveness On Screen figure of the corresponding circular arc of Fig. 3；
Fig. 5 is θs＞ θeCircular arc judge schematic diagram whether in the range of drawing for the pixel；
Fig. 6 is that embodiment two draws θs＞ θeCircular arc instantiation schematic diagram；
Fig. 7 is the hard-wired Showing Effectiveness On Screen figure of the corresponding circular arc of Fig. 6.
Specific embodiment
Below in conjunction with the accompanying drawings technical scheme is described in detail：
The thinking of the present invention is to be improved based on the arc drafting method of angle diagnostic method to existing, changes judgement side
Formula, reduces the calculating of (anti-) trigonometric function, thus reduce logical resource using；Determined according to circular arc start angle and termination point
Interval that circular arc is located, judges to point coordinates value, the interval coordinate figure in centre directly exports in initial interval and termination interval,
Do not need to judge, thus improving the speed of circular arcs with arbitrary angles drafting.
The inventive method is applied to the drafting of circular arcs with arbitrary angles.For the ease of public understanding technical solution of the present invention, under
Face is respectively with θs≤θeCircular arc and θs＞ θeCircular arc as a example illustrating, wherein θsFor circular arc initial angle, θeFor circular arc eventually
Angle till.
Embodiment one,
In the present embodiment, Ideal graph to be drawn is θs≤θeCircular arc, then described circular arc is without x positive axis.
Fig. 1 is the interval division schematic diagram of plane right-angle coordinate, the x-axis of this plane right-angle coordinate, y-axis respectively with aobvious
Show that pixel column, the pixel column of device are parallel, screen is symmetrically divided into 8 intervals.Intercept one section wherein one in circular arc in a circle
Bar side is parallel with the pixel column/pixel column of displayCircular arc, obtains remaining corresponding pixel in 7 intervals using symmetry
Coordinate.
Fig. 2 is θs≤θeCircular arc judge schematic diagram whether in the range of drawing for the pixel, in the range of drawing, then paint
System, otherwise abandons：
In formula, en indicates whether to draw this pixel, and 1 represents drafting, and 0 expression is not drawn；C represents currently pixel to be judged
Interval, then 1≤c≤8 that point is located；En ' represents in initial interval a and terminates needing in interval b to further determine whether to draw.?
In initial interval a, the judgement in the range of arc drafting is as follows for pixel：
In terminating interval b, the judgement in the range of arc drafting is as follows for pixel：
Hypothesis θ to be drawns≤θeCircular arc as shown in figure 3, circular arc r radius be 100 pixels, the start angle θ of circular arcsFor
48 °, termination point θeFor 253 °, then initiate interval a=2, terminate interval b=6.Then current interval c that pixel to be judged is located
When interval 3～interval 5, en=1, do not need judgement can directly draw corresponding pixel points.
In initial interval a=2, starting point coordinate isWherein [] represents four houses five
Enter to round, pixel rectangular coordinate to be judged is (x, y), if then (x, y) is in initial interval a, and x≤xs, y >=ys, then paint
Make this pixel, otherwise, do not draw.
In terminating interval b=6, terminating point coordinates isWherein [] represents four houses
Five enter to round, and pixel rectangular coordinate to be judged is (x, y), if then (x, y) is in terminating interval b, and x≤xe, y >=ye, then
Draw this pixel, otherwise, do not draw.
Fig. 4 is the hard-wired Showing Effectiveness On Screen figure of the corresponding circular arc of Fig. 3.
In embodiment one, the inventive method and angle diagnostic method amount of calculation is compared as follows shown in table：
Embodiment two,
In the present embodiment, Ideal graph to be drawn is θs＞ θeCircular arc, then described circular arc is through x positive axis.
Fig. 5 is θs＞ θeCircular arc judge schematic diagram whether in the range of drawing for the pixel, in the range of drawing, then paint
System, otherwise abandons：
In formula, en indicates whether to draw this pixel, and 1 represents drafting, and 0 expression is not drawn；C represents currently pixel to be judged
Interval, then 1≤c≤8 that point is located；En ' represents in initial interval a and terminates needing in interval b to further determine whether to draw.?
In initial interval a, the judgement in the range of arc drafting is as follows for pixel：
In terminating interval b, the judgement in the range of arc drafting is as follows for pixel：
Hypothesis θ to be drawns＞ θeCircular arc as shown in fig. 6, circular arc r radius be 120 pixels, the start angle θ of circular arcsFor
280 °, termination point θeFor 65 °, then initiate interval a=7, terminate interval b=2.Then current interval c that pixel to be judged is located
When interval 8 and interval 1, en=1, do not need judgement can directly draw corresponding pixel points.
In initial interval a=7, starting point coordinate isWherein [] represents four houses
Five enter to round, and pixel rectangular coordinate to be judged is (x, y), if then (x, y) is in initial interval a, and x >=xs, y >=ys, then
Draw this pixel, otherwise, do not draw.
In terminating interval b=2, terminating point coordinates isWherein [] represents four houses five
Enter to round, pixel rectangular coordinate to be judged is (x, y), if then (x, y) is in terminating interval b, and x >=xe, y≤ye, then paint
Make this pixel, otherwise, do not draw.
Fig. 7 is the hard-wired Showing Effectiveness On Screen figure of the corresponding circular arc of Fig. 6.
In embodiment two, the inventive method and angle diagnostic method amount of calculation is compared as follows shown in table：
Claims (3)
1. a kind of fast drawing method of circular arcs with arbitrary angles is it is characterised in that fast and effeciently judge whether pixel is being justified
Arc is drawn in angular range, in the range of drawing, then draws, otherwise abandons：Indicator screen is divided into area according to symmetry
Between 1～interval 8, interval 1 corresponding angle [0 °, 45 °]；Interval 2 corresponding angles (45 °, 90 °]；Interval 3 corresponding angles (90 °,
135°]；Interval 4 corresponding angles (135 °, 180 °]；Interval 5 corresponding angles (180 °, 225 °]；Interval 6 corresponding angles (225 °,
270°]；Interval 7 corresponding angles (270 °, 315 °]；Interval 8 corresponding angles (315 °, 360 °]；All circular arcs are all using counterclockwise
The technique of painting, then exchanges initial angle and end angle for clockwise arc, is continuing with the technique of painting counterclockwise；Circular arc initial angle θs(0°≤θs
≤ 360 °) and end angle θe(0°≤θe≤ 360 °) place interval is referred to as initial interval a and terminates interval b, and whether pixel
Judgement in the range of arc drafting is as follows：
If θs≤θe, then
If θs＞ θe, then
In formula, en indicates whether to draw this pixel, and 1 represents drafting, and 0 expression is not drawn；C represents currently pixel institute to be judged
In interval, then 1≤c≤8；En ' represents in initial interval a and terminates needing in interval b to further determine whether to draw, circular arc rises
Beginning angle θsWith end angle θeCorresponding rectangular coordinate is (xs, ys) and (xe, ye), pixel rectangular coordinate currently to be judged is
(x, y), then in initial interval a pixel the judgement in the range of arc drafting is as follows：
In terminating interval b, the judgement in the range of arc drafting is as follows for pixel：
.
If 2. the fast drawing method of circular arcs with arbitrary angles as claimed in claim 1 is it is characterised in that θs≤θe, then described any
Angle circular arc is without x positive axis；The described circular arc without x positive axis is drawn, specifically includes following steps：
Step 1, to intercept one section of wherein a line in a circle in circular arc parallel with the pixel column/pixel column of displayCircle
Arc, obtains remaining corresponding pixel point coordinates in 7 intervals using symmetry；
Step 2, judge pixel whether in arc drafting angular range, in the range of drawing, then draw, otherwise abandon：
In formula, en indicates whether to draw this pixel, and 1 represents drafting, and 0 expression is not drawn；C represents currently pixel institute to be judged
In interval, then 1≤c≤8；En ' represents in initial interval a and terminates needing in interval b to further determine whether to draw；
Step 3, pixel in initial interval a or terminate needing to further determine whether in the range of arc drafting in interval b：?
In initial interval a, the judgement in the range of arc drafting is as follows for pixel：
In terminating interval b, the judgement in the range of arc drafting is as follows for pixel：
.
If 3. the fast drawing method of circular arcs with arbitrary angles as claimed in claim 1 is it is characterised in that θs＞ θe, then described any
Angle circular arc is through x positive axis；The described circular arc through x positive axis is drawn, specifically includes following steps：
Step 1, to intercept one section of wherein a line in a circle in circular arc parallel with the pixel column/pixel column of displayCircle
Arc, obtains remaining corresponding pixel point coordinates in 7 intervals using symmetry；
Step 2, judge pixel whether in arc drafting angular range, in the range of drawing, then show, otherwise abandon：
In formula, en indicates whether to draw this pixel, and 1 represents drafting, and 0 expression is not drawn；C represents currently pixel institute to be judged
In interval, then 1≤c≤8；En ' represents in initial interval a and terminates needing in interval b to further determine whether to draw；
Step 3, pixel in initial interval a or terminate needing to further determine whether in the range of arc drafting in interval b：?
In initial interval a, the judgement in the range of arc drafting is as follows for pixel：
In terminating interval b, the judgement in the range of arc drafting is as follows for pixel：
.
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| CN201410457445.2A CN104217450B (en) | 2014-09-05 | 2014-09-05 | Quick drawing method of any-angle circular arc |
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| CN104217450B true CN104217450B (en) | 2017-02-22 |
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Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN106340048A (en) * | 2016-09-12 | 2017-01-18 | 福建中金在线信息科技有限公司 | Pie chart rendering method and apparatus thereof |
| CN106910230B (en) * | 2016-12-21 | 2020-07-03 | 中国航空工业集团公司雷华电子技术研究所 | Radar background video drawing method |
| CN113034644A (en) * | 2019-12-25 | 2021-06-25 | 华润微电子（重庆）有限公司 | Method and system for drawing circular arc in integrated circuit layout design, storage medium and terminal |
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| US6441822B1 (en) * | 1999-04-02 | 2002-08-27 | Bruce H. Johnson | Drawing with circular arcs |
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| CN101625765A (en) * | 2009-08-18 | 2010-01-13 | 上海可鲁系统软件有限公司 | Method for drawing rotating elliptical arc |
| CN102982198A (en) * | 2012-11-01 | 2013-03-20 | 江苏科技大学 | Computer drawing method for centrifugal label calibration tail |
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|---|---|---|---|---|
| US6441822B1 (en) * | 1999-04-02 | 2002-08-27 | Bruce H. Johnson | Drawing with circular arcs |
| CN1633659A (en) * | 2002-02-15 | 2005-06-29 | 电脑联合想象公司 | System and method for specifying elliptical parameters |
| CN101625765A (en) * | 2009-08-18 | 2010-01-13 | 上海可鲁系统软件有限公司 | Method for drawing rotating elliptical arc |
| CN102982198A (en) * | 2012-11-01 | 2013-03-20 | 江苏科技大学 | Computer drawing method for centrifugal label calibration tail |
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