WO2009149591A1

WO2009149591A1 - Method for constructing new closed curves by using an open curve and an adjacent closed curve

Info

Publication number: WO2009149591A1
Application number: PCT/CN2008/002077
Authority: WO
Inventors: 常先堂; 李平立; 姜建军
Original assignee: 方正国际软件(北京)有限公司; 北京大学
Priority date: 2008-06-13
Filing date: 2008-12-25
Publication date: 2009-12-17
Also published as: CN101604452B; CN101604452A

Abstract

A method for constructing new closed curves by using an open curve and an adjacent closed curve. In prior art, when the open curve being adjacent to the close curve is transferred to a closed curve, the geometric property of the open curve itself can not be utilized in the case of there being no crossing points or one and only one crossing point between the open curve and the closed curve, so it causes the generated closed curve not smooth. In the method, firstly, four control points of the Bezier cubic curves are determined to locate the cross points between the head/tail segment Bezier cubic curve and the closed curve, wherein the Bezier cubic curves are generated by using the head segment and tail segment of the open curve. Finally, two new closed curves are constructed by using the head segment Bezier cubic curve, tail segment Bezier cubic curve, and two crossing points between the Bezier cubic curves and the closed curve. The current geometric property information of the open curve is enough utilized and the newly constructed curves are naturally smooth by using the nature extension of the Bezier cubic curves generated by head segment and tail segment of the open curve.

Description

Method for constructing a new closed curve using an open curve and an adjacent closed curve

Technical field

The invention belongs to the field of computer information processing, and relates to a computer graphics editing technology, in particular to a method for constructing a new closed curve by using an open curve and an adjacent closed curve. Background technique

In many computer graphics processing applications, it is necessary to find the overall contour of the area of the area containing the open curve or to integrate and sum the area of the entire enclosed area. Typical applications, such as packaging, need to cut the entire area of the graphic. For example, in the application of the area integral of the scan discontinuity curve.

In the prior art, when the open curve adjacent to the closed curve is converted into a closed curve, in the case where there is no intersection or only one intersection between the open curve and the closed curve, the existing geometric properties of the open curve are often not utilized, and generally no modification is performed. For example, when there is no intersection between the open curve and the closed curve, the straight line is directly connected. When the open curve intersects the closed curve, part of the curve on the open curve is discarded, so that the newly generated closed curve is not smooth, and the visual effect cannot be achieved. Satisfactory effect. In the case where there are multiple ( >= 2 ) intersections between the open curve and the closed curve, the existing solutions mostly adopt the following methods: Find the first and last intersections along the direction of the open curve, thus finding out Two (one pair) intersections. It is worthwhile to remember that the first intersection is A and the last intersection is B. Then extract the curve segment between the two points on the open curve, and then replace the different curve segments on the closed curve with it to get a new closed curve.

Specifically in the field of packaging and printing technology, how to trap in the package (trapping is also called trapping, also known as scaling, mainly to compensate for the gap between two adjacent different colors due to inaccurate printing overprinting) In the process of region generation, it is the technical problem that needs to be solved to make full use of the existing properties of the open curve adjacent to the closed curve, and the natural smooth extension to generate a closed curve with natural visual effects. Therefore, there is also a need to provide a new method to modify the closed curve of the package trapping area. Summary of the invention

In view of the problems in the prior art, the object of the present invention is to provide a method for constructing a new closed curve using an open curve and an adjacent closed curve, which can make full use of the closed curve. The geometric property information of the open curve modifies the closed curve so that the closed curve obtained after the final modification achieves a satisfactory visual effect.

Another object of the present invention is that the method can achieve a good visual effect by modifying the closed curve of the package trapping area. To achieve the above object, the technical solution adopted by the present invention is: A method for constructing a new closed curve using an open curve and a closed curve, including the following steps:

(1) Positioning the first and last cubic Bezier curves of the open curve;

(2) Positioning the open curve and the intersection of the adjacent closed curve and modifying the open curve: Based on the opening and ending points of the first and last cubic Bezier curves of the open curve, the first and last intersections of the closed curve, and by modifying the first paragraph And the last three cubic Bezier curves to achieve the modification of the entire open curve;

(3) Construct two new closed curves: The first and last three-part Bezier curves of the scaling curve and the first and last intersections of the closed curve form two new closed curves. The effect of the invention is: using the method according to the invention, based on the cubic Bezier curve generated by the first and last segments of the open curve, determining the first and the last of the four control points of the cubic Bezier curve The intersection of the segmental cubic Bezier curve and the closed curve, and finally two new closed curves are generated by the open curve, the closed curve, the cubic Bezier curve of the first and last segments of the open curve, and the two intersections with the closed curve. Therefore, the curve modification in the prior art that the open curve and the closed curve have no intersection point cannot be effectively solved. At the same time, for the case where the open curve and the closed curve have intersection points, the geometric property information of the open curve can be fully utilized to modify the closed curve, so that the modified closed curve achieves a satisfactory visual effect. The specific application is in the processing technique of packaging the trapping area, and the method of the present invention can effectively modify the closed curve of the trapping area. DRAWINGS

Figure 1 is a flow chart of the method of the present invention;

2 is a schematic diagram of an original open curve and a closed curve in Embodiment 1 of the present invention;

3 is a three-bezier curve control point indication map constituting an open curve in Embodiment 1 of the present invention; FIG. 4 is an effect diagram of a modified curve in Embodiment 1 of the present invention;

Figure 5 is a schematic view showing the original open curve and the closed curve in the second embodiment of the present invention;

6 is a control point of an open curve composed of only one cubic Bezier curve in Embodiment 2 of the present invention; Marking map

7 is a two-section cubic Bezier control point map showing an open curve after splitting in the second embodiment of the present invention;

8 is an effect diagram of a modified curve in Embodiment 2 of the present invention;

9 is a schematic diagram of an original open curve and a closed curve in Embodiment 3 of the present invention;

Figure 10 is a diagram showing a cubic Bezier curve control point of the open curve in the third embodiment of the present invention; and Figure 11 is a modified view of the curve in the third embodiment of the present invention. detailed description

The invention is further described in detail below with reference to the drawings and specific embodiments.

As shown in Figure 1, a method of constructing a new closed curve using an open curve and an adjacent closed curve includes the following steps:

( 1 ) Positioning the first and last third cubic Bezier curves of the open curve S11 ;

(2) locating the open curve and the intersection of the adjacent closed curve and modifying the open curve S12: the control points of the first and last cubic Bezier curves based on the open curve and the first and last intersections of the closed curve, and pass Modify the first and last three cubic Bezier curves to achieve the modification of the entire open curve;

(3) Construct two new closed curves S13: Use the first and last cubic Bezier curves of the open curve and the first and last intersections of the closed curve to form two new closed curves. Example 1:

In this embodiment, an example of modifying a graphic editing object is performed in the case where there is no intersection between the open curve and the closed curve, wherein the open curve is composed of a plurality of cubic Bezier curves. As shown in Figure 1, a method of constructing a new closed curve using an open curve and an adjacent closed curve includes the following steps:

(1) Positioning the first and last cubic Bezier curves of the open curve 21;

As shown in Fig. 2, in the present embodiment, the open curve 21 has no intersection with the closed curve 22. As shown in Figure 3, the open curve consists of a four-segment cubic Bezier curve, namely curve 30-33, curve 33-34, curve 34-35 curve 35-38; where the first segment curve 30_33 and the last segment curve 35-38 They are the first and last cubic Bezier curves of the open curve.

(2) Positioning the open curve 21 and the adjacent closed curve 22 at the end of the intersection and modifying the open curve 21: Based on the first and last cubic Bezier curves of the open curve 21, the control points are positioned and the first and last intersections of the closed curve And by modifying the first and last three-time Bezier curves to complete the entire open curve Change

As shown in FIG. 3, in the step (2) of the present embodiment, the first-stage cubic Bezier curve 30-33 and the last-stage cubic Bezier curve 35-38 of the open curve 21 have no intersection point with the closed curve, respectively, A specific method for intersecting and modifying the first and last cubic Bezier curves includes:

For the first cubic Bezier curve 30-33, the control point P at one end of the cubic Bezier curve is calculated. 30 to the closest distance point P of the closed curve. "39 and the nearest distance d, where p. 30 is the cubic Bezier curve control point, which is located at the end of the open curve 21;

In this embodiment, the cubic Bezier curve is extended to a closed curve, intersecting the closed curve at a point Ρ. ' 40 and ^. ^'|<^ then the intersection /. '40 is marked as the intersection of the first cubic Bezier curve and the closed curve, where N is an adjustable amount, where N has a range of values (0, 3), N = 2 in this embodiment.

n If you extend the Bezier curve three times to the closed curve, intersect the closed curve at point >. 'And PoP ₀ \≥Nx d , then the nearest distance is />. "as the intersection of the open curve and the closed curve;

Modify the first three-time Bezier curve 30-33: The intersection of the first three-time Bezier curve 30-33 with the closed curve is 40, then the control point P will be. 30 is adjusted to P. ' 40, using the adjusted four control points P. 40. Click Ρ 1, point P ₂ 32 and point P ₃ 33 to modify the three-time Bessel curve.

If the first three-time Bezier curve 30-33 and the closed curve intersection point is the closest distance to the corpse. ", adjust control point A to P.", modify the cubic Bezier curve with the adjusted four control points.

Also according to the above steps, for the last cubic Bezier curve 35-38, the control point P at one end of the cubic Bezier curve. 38 to the closest distance point P of the closed curve. "41 and the closest distance d.

In this embodiment, the Bezier curve 35-38 to the closed curve 22 intersects the closed curve 22 at the point Ρ. ' 42 , then the intersection point P. '42 is labeled as the last cubic Bezier curve

The intersection with the closed curve, where N is an adjustable amount, N = 2 in this embodiment.

Modify the last cubic Bezier curve 35-38: The intersection of the last cubic Bezier curve 35-38 and the closed curve is the intersection point P. ' 42, then the control point. 38 Adjust to P. ' 42, using the adjusted four control points P. 42, point? ^7, point P ₂ 36 and point P ₃ 35 modify the cubic Bezier curve of the segment.

(3) Construct two new closed curves: As shown in Fig. 4, the first three cubic Bezier curves and the last three cubic curves of the open curve and the first and last intersections 40 and 42 of the closed curve constitute two new ones. Close the curve. When the method of the present invention is specifically applied to the processing technique of packaging the trapping area, it is usually first drawn by the user to open an open curve and placed in a closed curve (ie, the trapping area to be modified). Surrounding or at the intersection, the open and closed curves are modified using the method of the present invention, and finally two new closed curves are obtained. In this embodiment, the user may retain any one of the closed curves according to different requirements, or may retain two closed curves at the same time. Example 2:

In this embodiment, an example of modifying a graphic editing object is performed in the case where there is no intersection between the open curve and the closed curve, wherein the open curve is only a cubic Bezier curve. As shown in Figure 1, a method of constructing a new closed curve using an open curve and an adjacent closed curve includes the following steps:

(1) Positioning the first and last cubic Bezier curves of the open curve;

As shown in FIG. 5, FIG. 6, and FIG. 7, in the present embodiment, the open curve 51 has no intersection with the closed curve 52. The open curve 51 consists of only one cubic Bezier curve with four control points of 60, 61, 62 and 63, respectively. Therefore, the curve needs to be split into two parts. The two cubic Bezier curves are the first cubic Bezier curve 70-73 and the last cubic Bezier curve 73-76 of the open curve. In this embodiment, the method for performing bisection for a cubic Bezier curve includes _3:

The cubic Bezier curve is represented by a one-dimensional cubic real coefficient polynomial function / ₃ = | ^, where

!-0

The parameters jc e [0,l] , α, ( ί = 0,1,2,3) are real numbers;

Take the point where 5 is divided into two points, and get the first and last three cubic Bezier curves.

(2) Positioning the open curve and the intersection of the adjacent closed curve and modifying the open curve: The control point of the first and last cubic Bezier curves based on the open curve and the first and last intersections of the closed curve, and modified The first and last three-time Bezier curves to achieve the modification of the entire open curve;

In this embodiment, the first cubic Bezier curve 70-73 does not have an intersection with the closed curve, and the specific method for constructing an intersection and modifying the open curve 51 includes:

Calculate the first-stage cubic Bezier curve 70-73-end control point Ρ. 70 to the closest distance of the closed curve Ρ. "and the nearest distance d, where the corpse is the first three-time Bezier curve control point, which is located at the end of the open curve;

In this embodiment, the first three-time Bezier curve is extended to the closed curve, and there is no intersection with the closed curve, and the closest distance point 77 is taken as the intersection of the cubic Bezier curve 70-73 and the closed curve;

Modify the first cubic Bezier curve 70-73: The intersection of the first cubic Bezier curve 70-73 and the closed curve 52 is the closest distance point 77, then the control point P will be. 70 is adjusted to 77, using the adjusted four control points P. 77, P, 7K Ρ ₂ 72 and Ρ ₃ 73 modify the cubic Bezier curve.

Also according to the above steps, the last three cubic Bezier curves 73-76 are modified to obtain the last segment. The intersection of the cubic Bezier curve with the closed curve 78 utilizes four adjusted control points P at the same time. 78, P.75, P ₂ 74 and P ₃ 73 obtain the modified last-stage cubic Bezier curve.

(3) Construct two new closed curves: As shown in Fig. 8, the first and last cubic Bezier curves of the open curve and the first and last intersections 77 and 78 of the closed curve constitute two new closed curves. .

In the above step (2), the cubic Bezier curve formed after the splitting can be divided into two parts, and the first and last cubic Bezier curves are finally determined. Example 3:

In this embodiment, the modification of the graphic editing object is taken as an example in the case where one or more intersection points exist in the open curve and the closed curve. As shown in Figure 1, a method of constructing a new closed curve using an open curve and an adjacent closed curve includes the following steps:

(1) Positioning the first and last cubic Bezier curves of the open curve;

As shown in Figs. 9 and 10, in the present embodiment, the open curve 91 and the closed curve 92 have a plurality of intersections. The open curve 91 is composed of a four-segment cubic Bezier curve, that is, a curve 100-101, a curve 101-102, and a curve 102-103 curve 103-106; wherein the first segment curve 100-101 and the last segment curve 103-106 are open curves, respectively. The first and last three cubic Bezier curves.

In this embodiment, for the first-stage cubic Bezier curve 100-101 and the closed curve 92, the specific method for constructing a suitable intersection point and modifying the open curve includes:

In this embodiment, as shown in FIG. 10, it is represented by a point P. 100 determines the first intersection A107 with the closed curve 92 along the first cubic Bezier curve 100-101, calculating = |,. ^ ^ / ρ ₃ is greater than Μ, Μ value range [0, 1], where the control point of the cubic Bezier curve Ρ. 100 is located at the head end of the open curve 91, and the control point Ρ ₃ 101 is located at the other end of the cubic Bezier curve 100-101; in the present embodiment, Μ = 0.7, after calculation, "≥0.7, so the first stage is calculated three times Bessel The curve controls the corpse. 100 to the closest distance point 108 of the closed curve 92, then the control point Ρ. Adjusted from point 100 to point 108, the other three control points are unchanged. The modified three control points are used to modify the three-time Bezier curve, and the nearest distance point 108 is adjusted to the first-stage cubic Bezier curve of the open curve. 100-101 and the closed curve first intersection.

There is an intersection point between the last cubic Bezier curve and the closed curve. The specific methods for locating the cubic Bezier curve and the closed curve and modifying the cubic Bezier curve include: In this embodiment, it is from point P. 106 determines the first intersection B109 with the closed curve 92 along the last cubic Bezier curve 103-106, and calculates the value range of "= | corpse M [0, 1], where the control point of the cubic Bezier curve P. 106 is located at the end of the open curve 91, and the control point corpse ₃ 104 is located at the other end of the cubic Bezier curve 100-101. In this embodiment, M = 0.7. Since α < Μ is α < 0.7, truncation / ^ In sections 106-109, the point is the intersection of the cubic Bezier curve 103-106 and the closed curve at the end of the open curve.

In this embodiment, if there are multiple intersection points between the first or last three-time Bezier curve and the closed curve, the first intersection point of the closed curve is determined by the point along the cubic Bezier curve, and the other intersection points are ignored, followed by The treatment, the method is the same as above.

(3) Construct two new closed curves: As shown in Fig. 11, the first and last cubic Bezier curves of the open curve and the first and last intersections 108 and 109 of the closed curve constitute two new closed songs.

As can be seen from the above embodiment and the effect diagram, the present invention discloses a method for constructing a new closed curve by using an open curve and an adjacent closed curve, by dividing the open curve into a multi-segment cubic Bezier curve and positioning the first and last segments. The cubic Bezier curve, based on the four control points of the cubic Bezier curve, locates the intersection of the first and last cubic Bezier curves and the closed curve, and finally uses the first and last intersections of the open curve and the closed curve to form two New closed curve. The method of the present invention utilizes the geometric property information of the open curve itself to modify the curve of the first and last segments of the open curve to achieve the purpose of modifying the closed curve. A person skilled in the art can make various modifications and variations to the invention without departing from the spirit and scope of the invention. Thus, it is intended that the present invention cover the modifications and the modifications of the invention

Claims

Rights request

1. A method of constructing a new closed curve using an open curve and an adjacent closed curve, comprising the following steps:

(1) Positioning the first and last cubic Bezier curves of the open curve;

(3) Construct two new closed curves: The first and last three-part Bezier curves of the open curve and the first and last intersections of the closed curve form two new closed curves.

2. A method for constructing a new closed curve using an open curve and an adjacent closed curve according to claim 1, wherein: in step (1), if the open curve is composed of a plurality of cubic Bezier curves, the method is open. The cubic Bezier curves at the ends of the curve are the first and last cubic Bezier curves of the open curve.

3. A method for constructing a new closed curve using an open curve and an adjacent closed curve according to claim 1, wherein: in step (1), if the open curve consists only of a cubic Bezier curve, The open curve is divided into two parts, and the two cubic Bezier curves are respectively formed as the first and last cubic Bezier curves of the open curve.

4. A method of constructing a new closed curve using an open curve and an adjacent closed curve as claimed in claim 3, wherein: said method of bisection for a cubic Bezier curve comprises the following steps :

The cubic Bezier curve is represented by a one-dimensional cubic real coefficient polynomial function /(X), where the parameter X e [0,1];

5. A method of constructing a new closed curve using an open curve and an adjacent closed curve according to claim 3, wherein: the cubic Bezier curve formed after the splitting is again divided into two.

6. A method for constructing a new closed curve using an open curve and an adjacent closed curve according to any one of claims 1 to 5, characterized in that: in step (2), if the first segment or the last segment is three times Bessel If there is no intersection between the curve and the closed curve, construct an intersection point and modify the first or last cubic Bezier curve. The specific methods include: Calculate the control point P at one end of the first or last three-time Bezier curve. The closest distance to the closed curve point ' and the closest distance d, where control point />. Located at the beginning or end of the open curve;

. Naturally extending the first or last cubic Bezier curve, if intersecting the closed curve at the point, N

If the value range is (0, 3), then the intersection point P.' is marked as the intersection of the first or last segment and the closed curve, if it intersects the closed curve at the point and |ρ.λ'|≥ ^ or If there is no intersection with the closed curve, the closest distance point is used as the intersection of the cubic Bezier curve and the closed curve of the first or last segment;

Modify the first or last three-time Bezier curve: If the intersection of the first or last three-time Bezier curve and the closed curve is the intersection point ρ. ', then the control point Ρ. Adjust to Ρ. ', modify the first or last cubic Bezier curve with the adjusted four control points; if the intersection of the first or last cubic Bezier curve and the closed curve is the closest distance point ρ. ", adjust the control point Λ- to ', and modify the first or last cubic Bezier curve with the adjusted four control points.

7. A method of constructing a new closed curve using an open curve and an adjacent closed curve according to claim 6, wherein: said N has a value of two.

8. A method for constructing a new closed curve using an open curve and an adjacent closed curve according to any one of claims 1 to 5, characterized in that: in step (2), if the first segment or the last segment is three times Bessel If there is one or more intersection points between the curve and the closed curve, the intersection of the cubic or Bezier curve and the closed curve of the first or last segment is located and the first or last cubic Bezier curve is modified, and the specific methods include:

By the control point Ρ. Determine the first intersection of the closed curve along the first or last cubic Bezier curve, and calculate " = |/^ ^/ 尸₃ |, where the control point is at the beginning or end of the open curve, ₃ Located at the other end of the first or last third Bezier curve; if <Μ, Μ is in the range [0, 1], the /^ part is truncated; if α≥Μ, the first or last stage is calculated The cubic Bezier curve controls the point Ρ. The closest distance to the closed curve is Ρ.", then the control point Ρ. Adjust to Ρ. ', modify the first or last three-time Bezier curve with the adjusted four control points, and click the nearest distance. "Adjust to the intersection of the first Bezier curve and the closed curve of the first or last segment.

The Μ value of the Μ is 0.7. The method of the Μ is taken as a value of 0.7.

10. A method of constructing a new closed curve using an open curve and an adjacent closed curve according to any one of claims 1 to 5, characterized in that: the area enclosed by the closed curve is a package trapping area The open curve is a non-closed curve drawn by the user around the package trapping area that intersects or does not intersect the closed curve.