CN101604452A - The closed curve that utilizes open curve and close on makes up the method for new closed curve - Google Patents

Abstract

The invention discloses the method that a kind of closed curve that utilizes open curve and close on makes up new closed curve, when the open curve that closed curve closes in the prior art is converted into closed curve, do not have intersection point or only have under the situation of an intersection point at open curve and closed curve and can't utilize the geometric attribute of open curve self, thereby cause the closed curve of generation unsmooth.Method of the present invention is at first by first section and three Bezier (Bezier) curve of latter end generation based on open curve, determine the intersection point of first section of the location, four reference mark of three Beziers and three Beziers of latter end and closed curve, utilize at last first section of open curve and latter end three Beziers and with two new closed curves of two intersection points generations of closed curve.Method of the present invention can make full use of open curve existing geometric attribute information, and by utilizing first section and three Bezier nature extension modes of latter end of open curve, the new closed curve of generation is level and smooth naturally.

Description

The closed curve that utilizes open curve and close on makes up the method for new closed curve

Technical field

The invention belongs to the computer information processing field, relate to a kind of computer graphical editing technique, particularly a kind of closed curve that utilizes open curve and close on makes up the method for new closed curve.

Background technology

Handle in the application scenario at a lot of computer graphicals, need ask its regional overall profile or its integrally closed region area is carried out the integration summation the zone that comprises open curve, the typical case uses as needs in packages printing to asking the cut out areas of figure integral body, as the scanning unbroken curve is being asked application scenarios such as its area integral.

In the prior art, when the open curve that closed curve closes on is converted into closed curve, do not have intersection point or only have under the situation of an intersection point at open curve and closed curve, often do not utilize open curve existing geometric attribute, generally do not make an amendment processing, as when open curve and closed curve do not have any intersection point, directly use straight line to link to each other, when open curve and closed curve intersect, given up the part curve on the open curve, thereby cause newly-generated closed curve unsmooth, visual effect can't reach gratifying effect.Have under the situation of a plurality of (＞=2) intersection point at open curve and closed curve, existing scheme is to adopt following method mostly: along the direction of open curve, find first and last intersection point respectively, so just found two (a pair of) intersection points.Might as well remember that first intersection point is A, last intersection point is B, extracts A on the open curve then, and the segment of curve between 2 of the B is replaced different segment of curve on closed curve with its then, just obtains new closed curve.

Specifically in technical field of packaging and printing, how (trapping also makes mending-leakage white in the packing trapping, be called scalable again, mainly be to cause two leakages between the adjacent different colours white in order to remedy because of the printing register trouble) in the process that generates of zone, make full use of the existing attribute of the open curve that closes on closed curve, naturally level and smooth extension is the present technical issues that need to address to generate the closed curve of visual effect nature.Therefore also need to provide a kind of new method to come the closed curve of packing area of trap is made amendment.

Summary of the invention

At problems of the prior art, purpose of the present invention provides a kind of closed curve that utilizes open curve and close on to make up the method for new closed curve, this method can make full use of the geometric attribute information of the open curve that closes on closed curve closed curve is made amendment, and the closed curve that obtains after feasible final the modification reaches gratifying visual effect.

Another object of the present invention is that this method can reach good visual effect after packing area of trap closed curve is made amendment.

For achieving the above object, the technical solution used in the present invention is: a kind of closed curve that utilizes open curve and close on makes up the method for new closed curve, may further comprise the steps:

(1) first section and three Beziers of latter end of location open curve;

(2) the location open curve is with the closed curve first and last intersection point that closes on and revise open curve: based on the location, reference mark of first section of open curve and three Beziers of latter end and the first and last intersection point of closed curve, and by revising first section and three Beziers of latter end to realize the modification of whole open curve;

(3) make up two new closed curves: utilize first section of open curve and the first and last intersection point of three Beziers of latter end and closed curve to constitute two new closed curves.

Further, in the step (1), if open curve is made up of three Beziers of multistage, then three of the open curve two ends Beziers be respectively first section of open curve with three Beziers of latter end.

Further, in the step (1), if open curve only is made up of one section three Bezier, then this open curve is carried out two fens subdivisions, two three Beziers of formation are respectively first section and three Beziers of latter end of open curve.

Further, the described method that one section three Bezier is carried out two fens subdivisions comprises:

With three Beziers with three real coefficient polynomial functions of monobasic $f_3\left(x\right)=\underset{i=0}{\overset{3}{\mathrm{\Σ}}}{a}_i{x}^i$ Expression, parameter x ∈ [0,1] wherein, a _i(i=0,1,2,3) are real number, a ₃≠ 0;

The point of getting the x=0.5 place carries out two fens subdivisions, obtains three Beziers of head-end sections.

Three times further again, as to form behind the subdivision in two minutes Beziers can carry out two fens subdivisions once more.

Further, if first section or three Beziers of latter end and closed curve do not have intersection point, then construct an intersection point and revise this first section or three Beziers of latter end in the step (2), concrete grammar comprises:

Calculate the reference mark P of first section or three Bezier one ends of latter end ₀Minimum distance point P to closed curve ₀" and minimum distance d;

By a P ₀Naturally extend first section or three Beziers of latter end, if intersect at a P with closed curve ₀' and $\left|\stackrel{\&cap;}{P_0{P}_0^{\&prime;}}\right|<N\&times;d,$ Then with this intersection point P ₀' be labeled as the intersection point of this first section or three Beziers of latter end and closed curve, if intersect at a P with closed curve ₀' and $\left|\stackrel{\&cap;}{P_0{P}_0^{\&prime;}}\right|\&GreaterEqual;N\&times;d$ Or do not have intersection point with closed curve, then minimum distance is put P ₀" as the intersection point of this first section or three Beziers of latter end and closed curve, wherein the span of N (0,3], preferred value is 2;

Revise first section or three Beziers of latter end: if the intersection point of first section or three Beziers of latter end and closed curve is intersection point P ₀', then with reference mark P ₀Adjust to P ₀', utilize adjusted four reference mark to revise this first section or three Beziers of latter end; If the intersection point of first section or three Beziers of latter end and closed curve is minimum distance point P ₀", then with reference mark P ₀Adjust to P ₀", utilize adjusted four reference mark to revise this first section or three Beziers of latter end.

Further, in the step (2) if there are one or more intersection points in first section or three Beziers of latter end and closed curve, then locate this first section or three Beziers of latter end and closed curve intersection point and revise first section or three Beziers of latter end, concrete grammar comprises:

By reference mark P ₀Determine and the first intersection point A of closed curve along first section or three Beziers of latter end, calculate $\mathrm{\&alpha;}=\left|\stackrel{\&cap;}{P_{0}A}\right|/\left|\stackrel{\&cap;}{P_0{P}_3}\right|,$ Wherein, reference mark P ₀Be positioned at the head end or the end of open curve, P ₃Be positioned at the other end of first section or three Beziers of latter end; If α＜M, the span of M [0,1] wherein, preferred value is 0.7, then clips P ₀The A part; If α 〉=M then calculates first section or three Bezier reference mark of latter end P ₀Minimum distance point P to closed curve ₀", then with reference mark P ₀Adjust to P ₀", utilize adjusted four reference mark to revise this first section or three Beziers of latter end, minimum distance is put P ₀" be adjusted into this first section or three Beziers of latter end and closed curve intersection point.

Further, the zone that described closed curve surrounded is the packing area of trap, described open curve be the user around the packing area of trap drawn one with closed curve crossing or disjoint non-closed curve.

Effect of the present invention is: adopt method of the present invention, first section and three Bezier (Bezier) curve of latter end generation based on open curve, determine first section of the location, four reference mark of three Beziers and the intersection point of three Beziers of latter end and closed curve, at last by open curve, closed curve, three Beziers of first section of open curve and latter end and generate two new closed curves with two intersection points of closed curve can't be handled the curve modification that open curve and closed curve do not have the intersection point situation thereby solved effectively in the prior art.Simultaneously, the situation of intersection point is arranged, can also make full use of the geometric attribute information of open curve, carry out the modification of closed curve, make to reach gratifying visual effect through amended closed curve for open curve and closed curve.Specifically be applied in the treatment technology of packing area of trap, method of the present invention can be made amendment to the closed curve of area of trap effectively.

Description of drawings

Fig. 1 is a method flow diagram of the present invention;

Fig. 2 is the embodiment of the invention 1 Central Plains open curve and closed curve synoptic diagram;

Fig. 3 is three Bezier reference mark sign pictures forming open curve in the embodiment of the invention 1;

Fig. 4 is the design sketch after the curve modification in the embodiment of the invention 1;

Fig. 5 is the embodiment of the invention 2 Central Plains open curves and closed curve synoptic diagram;

Fig. 6 is a reference mark sign picture of only being made of open curve in the embodiment of the invention 2 one section three Bezier;

Fig. 7 is two sections three Bezier reference mark sign pictures forming open curve in the embodiment of the invention 2 in two minutes behind the subdivision;

Fig. 8 is the design sketch after the curve modification in the embodiment of the invention 2;

Fig. 9 is the embodiment of the invention 3 Central Plains open curves and closed curve synoptic diagram;

Figure 10 is three Bezier reference mark sign pictures forming open curve in the embodiment of the invention 3;

Figure 11 is the design sketch after the curve modification in the embodiment of the invention 3.

Embodiment

The present invention is described in further detail below in conjunction with Figure of description and specific embodiment.

As shown in Figure 1, a kind of closed curve that utilizes open curve and close on makes up the method for new closed curve, may further comprise the steps:

(1) first section and three Bezier S11 of latter end of location open curve;

(2) the location open curve is with the closed curve first and last intersection point that closes on and revise open curve S12: based on the location, reference mark of first section of open curve and three Beziers of latter end and two intersection points of first and last of closed curve, and by revising first section and three Beziers of latter end to realize the modification of whole open curve;

(3) make up two new closed curve S13: utilize first section of open curve and two intersection points of first and last of three Beziers of latter end and closed curve to constitute two new closed curves.

Embodiment 1:

In the present embodiment, not having the graphics edition object of making amendment under the intersection point situation with open curve and closed curve is example, and wherein open curve is made up of three Beziers of multistage.As shown in Figure 1, a kind of closed curve that utilizes open curve and close on makes up the method for new closed curve, may further comprise the steps:

(1) first section and three Beziers of latter end of location open curve 21;

As shown in Figure 2, in the present embodiment, open curve 21 and closed curve 22 no intersection points.As shown in Figure 3, open curve is made up of four sections three Beziers, i.e. curve 30-33, curve 33-34, curve 34-35 curve 35-38; Wherein first section curve 30-33 and latter end curve 35-38 are respectively first section and three Beziers of latter end of open curve.

(2) location open curve 21 is with the closed curve 22 first and last intersection points that close on and revise open curve 21: based on the location, reference mark of first section of open curve 21 and three Beziers of latter end and two intersection points of first and last of closed curve, and by revising first section and three Beziers of latter end to realize the modification of whole open curve;

As shown in Figure 3, first section three Bezier 30-33 of open curve 21 and three Bezier 35-38 of latter end all do not have intersection point with closed curve in the step in the present embodiment (2), then construct an intersection point respectively and revise the first section concrete grammar with three Beziers of latter end to comprise:

For first section three Bezier 30-33, calculate the reference mark P of these three Bezier one ends ₀30 minimum distance point P to closed curve ₀" 39 and minimum distance d, its mid point P ₀30 is three Bezier reference mark, and this point is positioned at the end points place of open curve 21;

In the present embodiment, extend three Beziers, intersect at a P with closed curve to closed curve ₀' 40 and $\left|\stackrel{\&cap;}{P_0{P}_0^{\&prime;}}\right|<N\&times;d,$ Then with this intersection point P ₀The intersection point of Duan Sanci Bezier and closed curve headed by ' 40 marks, wherein N is a controlled variable, wherein the span of N (0,3], N=2 in the present embodiment.

If extend three Beziers to closed curve, intersect at a P with closed curve ₀' and $\left|\stackrel{\&cap;}{P_0{P}_0^{\&prime;}}\right|\&GreaterEqual;N\&times;d,$ Then minimum distance is put P ₀" as the intersection point of open curve and closed curve;

Revise first section three Bezier 30-33: the intersection point of first section three Bezier 30-33 and closed curve is P ₀' 40, then with reference mark P ₀30 adjust to P ₀' 40, utilize adjusted four reference mark P ₀40, some P ₁31, some P ₂32 and the some P ₃33 revise this Duan Sanci Bezier.

Intersection point as if first section three Bezier 30-33 and closed curve is minimum distance point P ₀", then with reference mark P ₀Adjust to P ₀", utilize adjusted four reference mark to revise this Duan Sanci Bezier.

Equally according to above-mentioned steps, for three Bezier 35-38 of latter end, the reference mark P of these three Bezier one ends ₀38 minimum distance point P to closed curve ₀" 41 and minimum distance d.

In the present embodiment, extend three Bezier 35-38 of latter end, intersect at a P with closed curve 22 to closed curve 22 ₀' 42 and $\left|\stackrel{\&cap;}{P_0{P}_0^{\&prime;}}\right|<N\&times;d,$ Then with this intersection point P ₀' 42 are labeled as the intersection point of three Beziers of latter end and closed curve, and wherein N is a controlled variable, N=2 in the present embodiment.

Revise three Bezier 35-38 of latter end: the intersection point of three Bezier 35-38 of latter end and closed curve is intersection point P ₀' 42, then with reference mark P ₀38 adjust to P ₀' 42, utilize adjusted four reference mark P ₀42, some P ₁37, some P ₂36 and the some P ₃35 revise this Duan Sanci Bezier.

(3) make up two new closed curves: as shown in Figure 4, utilize first section three Bezier of open curve and two intersection points 40 of first and last and two new closed curves of 42 formations of latter end cubic curve and closed curve.

In the time of in the treatment technology that method of the present invention specifically is applied to the packing area of trap, normally draw an open curve by user oneself earlier, it is placed on closed curve (promptly need revise area of trap) or be in intersection location on every side, adopt method of the present invention that open curve and closed curve are made amendment then, obtain two new closed curves at last.In the present embodiment, the user can keep any closed curve wherein according to different demands, also can keep two closed curves simultaneously.

Embodiment 2:

In the present embodiment, not having the graphics edition object of making amendment under the intersection point situation with open curve and closed curve is example, and wherein open curve only is one section three Bezier.As shown in Figure 1, a kind of closed curve that utilizes open curve and close on makes up the method for new closed curve, may further comprise the steps:

(1) first section and three Beziers of latter end of location open curve;

As Fig. 5, Fig. 6 and shown in Figure 7, in the present embodiment, open curve 51 and closed curve 52 no intersection points.Open curve 51 only is made up of one section three Bezier, and its four reference mark are respectively 60,61,62 and 63.Therefore need this curve is carried out two fens subdivisions, two three Beziers of formation are respectively first section three Bezier 70-73 and three Bezier 73-76 of latter end of open curve.In the present embodiment, the described method that one section three Bezier is carried out two fens subdivisions comprises:

With three Beziers with three real coefficient polynomial functions of monobasic $f_3\left(x\right)=\underset{i=0}{\overset{3}{\mathrm{\&Sigma;}}}{a}_i{x}^i$ Expression, parameter x ∈ [0,1] wherein, a _i(i=0,1,2,3) are real number;

The point of getting the x=0.5 place carries out two fens subdivisions, obtains three Beziers of head-end sections.

(2) the location open curve is with the closed curve first and last intersection point that closes on and revise open curve: based on the location, reference mark of first section of open curve and three Beziers of latter end and two intersection points of first and last of closed curve, and by revising first section and three Beziers of latter end to realize the modification of whole open curve;

In the present embodiment, there are not intersection point in first section three Bezier 70-73 and closed curve, and the concrete grammar of then constructing an intersection point and revising this open curve 51 comprises:

Calculate the reference mark P of first section three Bezier 70-73 one ends ₀70 minimum distance point P to closed curve ₀" and minimum distance d, wherein P ₀Headed by Duan Sanci Bezier reference mark, this point is positioned at the end points place of open curve;

In the present embodiment, extend first section three Beziers, do not have intersection point, then minimum distance is put P with closed curve to closed curve ₀" 77 intersection points as these three Bezier 70-73 and closed curve;

Revise first section three Bezier 70-73: the intersection point of first section three Bezier 70-73 and closed curve 52 is minimum distance point P ₀" 77, then with reference mark P ₀70 adjust to P ₀" 77, utilize adjusted four reference mark P ₀77, P ₁71, P ₂72 and P ₃73 revise this Duan Sanci Bezier.

According to above-mentioned steps, three Bezier 73-76 make amendment to latter end equally, obtain the intersection point 78 of three Beziers of this latter end and closed curve, utilize four adjusted reference mark P simultaneously ₀78, P ₁75, P ₂74 and P ₃73 obtain three Beziers of amended latter end.

(3) make up two new closed curves: as shown in Figure 8, utilize first section of open curve and two intersection points 77 of first and last and 78 of three Beziers of latter end and closed curve to constitute two new closed curves.

In the above-mentioned steps (2), three Beziers that formed behind the subdivision in two minutes can carry out two fens subdivisions once more, finally determine first section and three Beziers of latter end.

Embodiment 3:

In the present embodiment, having the graphics edition object of making amendment under one or more intersection point situations with open curve and closed curve is example.As shown in Figure 1, a kind of closed curve that utilizes open curve and close on makes up the method for new closed curve, may further comprise the steps:

(1) first section and three Beziers of latter end of location open curve;

As shown in Figures 9 and 10, there are a plurality of intersection points in open curve 91 with closed curve 92 in the present embodiment.Open curve 91 is by four sections three Beziers, i.e. curve 100-101, curve 101--102, curve 102-103 curve 103-106; Wherein first section curve 100-101 and latter end curve 103-106 are respectively first section and three Beziers of latter end of open curve.

(2) the location open curve is with the closed curve first and last intersection point that closes on and revise open curve: based on the location, reference mark of first section of open curve and three Beziers of latter end and two intersection points of first and last of closed curve, and by revising first section and three Beziers of latter end to realize the modification of whole open curve;

In the present embodiment, for first section three Bezier 100-101 and closed curve 92 intersection point is arranged, the concrete grammar of then constructing a suitable intersection point and revising this open curve comprises:

In the present embodiment, as shown in figure 10, by a P ₀100 determine and the first intersection point A107 of closed curve 92 along first section three Bezier 100-101, calculate $\mathrm{\&alpha;}=\left|\stackrel{\&cap;}{P_{0}A}\right|/\left|\stackrel{\&cap;}{P_0{P}_3}\right|$ Whether greater than M, the span of M [0,1], wherein, the reference mark P of three Beziers ₀100 are positioned at the head end of open curve 91, reference mark P ₃101 are positioned at the other end of three Bezier 100-101; M=0.7 in the present embodiment, back as calculated a 〉=0.7 is so calculate first section three Bezier reference mark P ₀100 minimum distance point P to closed curve 92 ₀" 108, then with reference mark P ₀Adjust to a little 108 by point 100, other three reference mark invariant positions utilize adjusted four reference mark to revise this Duan Sanci Bezier, and minimum distance is put P ₀" 108 are adjusted into first section three Bezier 100-101 of open curve and the first intersection point of closed curve.

Have an intersection point for three Beziers of latter end and closed curve, the concrete grammar of locating these three Beziers and closed curve intersection point and revising three Beziers comprises:

In the present embodiment, by a P ₀106 determine and the first intersection points B 109 of closed curve 92 along three Bezier 103-106 of latter end, calculate $\mathrm{\&alpha;}=\left|\stackrel{\&cap;}{P_{0}B}\right|/\left|\stackrel{\&cap;}{P_0{P}_3}\right|,$ The span of M [0,1], wherein, the reference mark P of three Beziers ₀106 are positioned at the end of open curve 91, reference mark P ₃104 are positioned at the other end of three Bezier 100-101, M=0.7 in the present embodiment.Because a＜M is a＜0.7, then clips P ₀B part 106-109, some B109 is three Bezier 103-106 of open curve latter end and closed curve intersection point.

In the present embodiment, if there are a plurality of intersection points in first section or three Beziers of latter end and closed curve, then by a P ₀Determine and the first intersection point A of closed curve along three Beziers, ignore other intersection point, carry out follow-up processing, method is the same.

(3) make up two new closed curves: as shown in figure 11, utilize first section of open curve and two intersection points 108 of first and last and 109 of three Beziers of latter end and closed curve to constitute two new closed curves.

By the foregoing description and design sketch as can be seen, the invention discloses the method that the closed curve that utilizes open curve and close on makes up new closed curve, by open curve being divided into three Beziers of multistage and locating first section and three Beziers of latter end, based on first section of the location, four reference mark of three Beziers and the intersection point of three Beziers of latter end and closed curve, utilize two intersection points of first and last of open curve and closed curve to constitute two new closed curves at last.Method of the present invention is utilized the geometric attribute information of open curve self, by revising the first and last section curve of open curve, to reach the purpose that closed curve is revised.

Those skilled in the art can carry out various changes and modification to the present invention and not break away from the spirit and scope of the present invention.Like this, if of the present invention these are revised and modification belongs within the scope of claim of the present invention and equivalent technologies thereof, then the present invention also is intended to comprise these changes and modification interior.

Claims (10)

1, a kind of closed curve that utilizes open curve and close on makes up the method for new closed curve, may further comprise the steps:

(1) first section and three Beziers of latter end of location open curve;

(2) the location open curve is with the closed curve first and last intersection point that closes on and revise open curve: based on the location, reference mark of first section of open curve and three Beziers of latter end and the first and last intersection point of closed curve, and by revising first section and three Beziers of latter end to realize the modification of whole open curve;

(3) make up two new closed curves: utilize first section of open curve and the first and last intersection point of three Beziers of latter end and closed curve to constitute two new closed curves.

2, a kind of closed curve that utilizes open curve and close on as claimed in claim 1 makes up the method for new closed curve, it is characterized in that: in the step (1) if open curve forms by three Beziers of multistage, then three of the open curve two ends Beziers be respectively first section of open curve with three Beziers of latter end.

3, a kind of closed curve that utilizes open curve and close on as claimed in claim 1 makes up the method for new closed curve, it is characterized in that: only form as if open curve in the step (1) by one section three Bezier, then this open curve is carried out two fens subdivisions, two three Beziers of formation are respectively first section and three Beziers of latter end of open curve.

4, a kind of closed curve that utilizes open curve and close on as claimed in claim 3 makes up the method for new closed curve, and it is characterized in that: the described method that one section three Bezier is carried out two fens subdivisions may further comprise the steps:

Three Beziers are represented with three real coefficient polynomial functions of monobasic f (x), wherein parameter x ∈ [0,1];

The point of getting the x=0.5 place carries out two fens subdivisions, obtains three Beziers of head-end sections.

5, a kind of closed curve of utilizing open curve and closing on as claimed in claim 3 makes up the method for new closed curve, it is characterized in that: three Beziers that formed behind the subdivision in two minutes are carried out two fens subdivisions once more.

6, make up the method for new closed curve as the described a kind of closed curve that utilizes open curve and close on of one of claim 1 to 5, it is characterized in that: in the step (2) if first section or three Beziers of latter end and closed curve do not have intersection point, then construct an intersection point and revise this first section or three Beziers of latter end, concrete grammar comprises:

Calculate the reference mark P of first section or three Bezier one ends of latter end ₀Minimum distance point P to closed curve ₀" and minimum distance d, wherein reference mark P ₀Be positioned at the head end or the end of open curve;

By reference mark P ₀Naturally extend first section or three Beziers of latter end, if intersect at a P with closed curve ₀' and $\left|\stackrel{\&cap;}{P_0{P}_0^{\&prime;}}\right|<N\&times;d,$ The span of N be (0,3], then with this intersection point P ₀' be labeled as the intersection point of this first section or three Beziers of latter end and closed curve, if intersect at a P with closed curve ₀' and $\left|\stackrel{\&cap;}{P_0{P}_0^{\&prime;}}\right|\&GreaterEqual;N\&times;d$ Or do not have intersection point with closed curve, then minimum distance is put P ₀" as the intersection point of this first section or three Beziers of latter end and closed curve;

Revise first section or three Beziers of latter end: if the intersection point of first section or three Beziers of latter end and closed curve is intersection point P ₀', then with reference mark P ₀Adjust to P ₀', utilize adjusted four reference mark to revise this first section or three Beziers of latter end; If the intersection point of first section or three Beziers of latter end and closed curve is minimum distance point P ₀", then with reference mark P ₀Adjust to P ₀", utilize adjusted four reference mark to revise this first section or three Beziers of latter end.

7, a kind of closed curve that utilizes open curve and close on as claimed in claim 6 makes up the method for new closed curve, and it is characterized in that: the value of described N is 2.

8, make up the method for new closed curve as the described a kind of closed curve that utilizes open curve and close on of one of claim 1 to 5, it is characterized in that: in the step (2) if there are one or more intersection points in first section or three Beziers of latter end and closed curve, then locate this first section or three Beziers of latter end and closed curve intersection point and revise first section or three Beziers of latter end, concrete grammar comprises:

By reference mark P ₀Determine and the first intersection point A of closed curve along first section or three Beziers of latter end, calculate $\mathrm{\&alpha;}=\left|\stackrel{\&cap;}{P_{0}A}\right|/\left|\stackrel{\&cap;}{P_0{P}_3}\right|,$ Wherein, reference mark P ₀Be positioned at the head end or the end of open curve, P ₃Be positioned at the other end of first section or three Beziers of latter end; If α＜M, the span of M is [0,1], then clips P ₀The A part; If α 〉=M then calculates first section or three Bezier reference mark of latter end P ₀Minimum distance point P to closed curve ₀", then with reference mark P ₀Adjust to P ₀", utilize adjusted four reference mark to revise this first section or three Beziers of latter end, minimum distance is put P ₀" be adjusted into this first section or three Beziers of latter end and closed curve intersection point.

9, a kind of closed curve that utilizes open curve and close on as claimed in claim 8 makes up the method for new closed curve, and it is characterized in that: the value of described M is 0.7.

10, make up the method for new closed curve as the described a kind of closed curve that utilizes open curve and close on of one of claim 1 to 5, it is characterized in that: the zone that described closed curve surrounded is the packing area of trap, described open curve be the user around the packing area of trap drawn one with closed curve crossing or disjoint non-closed curve.

Images