TWI616271B - Expansion and layout methods for vector object - Google Patents

Abstract

The invention is a vector object expansion and typesetting method. The expansion method is: I. taking a plurality of vector coordinate points a _i along a contour of an object; II. assuming that the cutting distance to be retained between the object and another object is D, the object is to be expanded. The distance d is D/2; III. After the adjacent line segment with the vector coordinate point a _i is the intersection point, the vector coordinate of the intersection point b _i is recalculated to obtain the actual expansion distance of the vector coordinate point a _i . _i - a _i ; IV. Obtain the actual expansion distance of each vector coordinate point a _i to form an expansion contour. The typesetting method is: I. making an object a reference object, and another object being close to the object; II. approaching the object toward the reference object until the object close to the reference object, and then drawing the reference object and The minimum outer frame of one of the objects; III. bringing the adjacent object closer to the reference object from a 360 degree direction to obtain a plurality of minimum outer frames; IV. taking the smallest of the plurality of minimum outer frames as a typesetting frame.

Description

Vector object expansion and typesetting method

The invention relates to a method for expanding and formatting a vector object, in particular to an invention for expanding a crop item and cutting a piece in a vector space.

Before making the typesetting of the cut object, it is necessary to first calculate the expansion of the cut object, which can ensure sufficient cutting gap between adjacent cut objects, avoiding the positioning error of the punch due to the cutting. The problem of cutting a part of the object.

The expansion of traditionally cut objects is the processing of image pixels using the image of the cropped object, which is the calculation of Erosion/Dilation with limited precision.

After the object is expanded, typesetting is performed. Referring to the eleventh figure, a schematic diagram of manual layout of the cut object (A) is known in the industry. It is not only time-consuming and inaccurate to manually plan the layout of the cut objects, but also the edges and gaps that are vacant are still large, which often causes waste of the paving parts.

Accordingly, the present invention proposes a vector object expansion and typesetting method, which is a crop item expansion and object typesetting in a vector space.

The vector object expansion method of the present invention comprises the following steps: I. Obtaining a plurality of vector coordinate points along a contour of an object, and expressing the contour A as: A = {a ₁ , a ₂ , a ₃ ...a _n }, where each vector coordinate point a _i is a plane coordinate point [x _i , y _i ] ^T , and the vector coordinate points adjacent to one of the vector coordinate points a _i are a _i-1 and a _i+1 , the outline is represented as a plurality of line segments L={a ₂ -a ₁ , a ₃ -a ₂ , a ₄ -a ₃ ... a _i -a _i-1 ... a _n -a _n-1 , a ₁ - a _n }={L ₁ , L ₂ , L ₃ ... L _i ... L _n-1 , L _n }; II. given that the cutting pitch to be retained between the object and another object is D, the object The distance d to be expanded is D/2; III. The adjacent line segment L _i (a _i+1 -a _i ) and L _i-1 (a _i -a _i-1 ) with the vector coordinate point a _i as the intersection point After the distance d is shifted outward, the vector coordinate of the intersection point b _i is recalculated to obtain the actual expansion distance of the vector coordinate point a _i is b _i -a _i ; IV. Repeat step III to obtain the contour A The actual expansion distance of a vector coordinate point a _i is calculated to form an expansion contour.

Further, when the vector coordinate point a _i forms a convex angle with the line segments L ₁ and L _{2 of the} adjacent vector coordinate points a _i-1 , a _i+1 , if the vector coordinate point a _i to the vector coordinate point b _i When the length s is greater than 2 times d, then at least 3 points with s equal to d are used to describe the expanded outer frame; when the vector coordinate point a _i and the adjacent vector coordinate points a _i-1 and a _i+1 When the line segments L ₁ and L ₂ form a concave angle, if the expanded vector coordinate point b _i forms a convex angle, the vector coordinate point a _i is deleted; when the outline of the object is expanded, the expanded contour overlaps. Then, the contour of the outermost periphery of the expansion contour is taken as a new expansion contour.

Further, the length of the vector coordinate point a _i to the vector coordinate point b _i is s=|b _i -a _i |=dcscθ/2, if the length s of the vector coordinate point a _i to the vector coordinate point b _i is greater than 2 When double d, set s=d: And use at least 3 points to describe the expanded outer frame. Further, when the expanded outer frame is described by three points, the three points are set to b _i , b _i ^' , b _i ^〞 , wherein

Further, when the vector coordinate points a _{i -1} and a _i+1 adjacent to the vector coordinate point a _i form a concave angle, a critical point is set on the angle bisector of the angle , the vector coordinate point a _i to the critical point The distance is Where L is min{|L _i-1 |, |L _i |}, if the vector coordinate point a _i to the vector coordinate point b _{i has} a length s=|b _i -a _i | greater than Lsec θ/2, this Then, the vector coordinate point a _i is removed.

Further, when the contour of the object is expanded, the expansion contours overlap, first calculate the overlap of each line in the expansion contour, and insert the calculated intersection into the two lines of the point series. In the meantime, mark the point as the intersection point and establish a connection with the point series; then find a point that can determine the outermost edge of the expansion contour, start searching from that point, and jump to the link every time the intersection is encountered. Point, otherwise continue to the next point; according to the above rules, you can get the list of peripheral points.

Further, in step III, when calculating the intersection point b _i , first define a counterclockwise rotation matrix Solving the vector coordinate point a _i to the vector of the vector coordinate point b _i by a trigonometric function; the direction of the first segment vector V ₁ is perpendicular to L _i-1 and the length is fixed to d, then The direction of the second segment vector V ₂ is parallel to L _i-1 and the length is d/tan ,among them, , Then, the vector coordinate point b _i = a _i + V ₁ + V ₂ .

The method for formatting a vector object according to the present invention comprises the following steps: I. in a two object, one of the objects is a reference object, and the other object is close to the object; II. centering on the reference object, the object is moved toward the reference object Close to the object until the object touches the reference object, at this time, draw a minimum outer frame including the reference object and the adjacent object; III. scan a 360 degree range, so that the close object approaches the reference object to obtain a plurality of The minimum outer frame; IV. The smallest one of the plurality of minimum outer frames is a typesetting outer frame.

Further, the vector object typesetting method of the present invention is combined with the vector object expansion method. When the two objects are to be brought close, a contour expansion of each contour of each object is performed, including the following steps: I. along the contour of each object The line takes a plurality of vector coordinate points, and the contour A is represented as: A = {a ₁ , a ₂ , a ₃ ... a _n }, where each vector coordinate point a _i is a plane coordinate point [x _i , y _i ] ^T , and the vector coordinate points adjacent to one of the vector coordinate points a _i are a _i-1 and a _i+1 , and the contour is represented as a plurality of line segments L={a ₂ -a _i ,a ₃ - a ₂ , a ₄ - a ₃ ... a _i - a _i-1 ... a _n - a _{n - 1} , a ₁ - a _n } = {L ₁ , L ₂ , L ₃ ... L _i ... L _{n- 1} , L _n }; II. Assuming that the cutting pitch to be retained between the two objects is D, the distance d to be expanded by each object is D/2; III. The vector coordinate point a _i will be the intersection point After the adjacent line segments L _i (a _i+1 -a _i ) and L _i-1 (a _i -a _i-1 ) are shifted outward by the distance d, the vector coordinates of the intersection point b _{i are} recalculated to obtain the vector coordinate point a. the actual expansion of the distance _i b _i -a _i; IV repeat step III, thereby obtaining each vector a _i of the coordinate points. Inter-distance expansion, expansion of the composition of a contour, the contour of the expansion of the article as a new contour typesetting.

Further, the approaching object approaches the reference object at an angle of 360 degrees with respect to the reference object, and in each angular direction, the approaching object approaches the reference object at an angular orientation rotated by 360 degrees. Further, the reference object is brought close to the adjacent object in a diagonally opposite manner. The diagonally adjacent manner takes a plurality of vector coordinate points along the contour of each object, and the contour A is represented as: A = {a ₁ , a ₂ , a ₃ ... a _n }, wherein Each vector coordinate point a _i is a plane coordinate point [x _i , y _i ] ^T , and the vector coordinate points adjacent to one of the vector coordinate points a _i are a _i-1 and a _i+1 , then the contour The line is represented as a plurality of line segments L={a ₂ -a ₁ , a ₃ -a ₂ , a ₄ -a ₃ ... a _i -a _i-1 ... a _n -a _n-1 , a ₁ -a _n }= {L ₁ , L ₂ , L ₃ ... L _i ... L _n-1 , L _n }, such that each vector coordinate point a _i close to the object approaches each line segment of the reference object to obtain a vector of minimum distance The coordinate point a _i and the line segment, that is, the minimum close distance of the proximity object and the reference object in the orientation, the minimum outer frame can be depicted after the proximity object and the reference object are close to the minimum close distance.

Further, the shape of the minimum outer frame is a rectangle.

Further, the two types of typographic outer frames are stacked in a horizontal or vertical manner by using the two objects as a group.

Through the above technical features, the following effects can be produced: the cutting gap of the object can be accurately calculated in the cutting tool machine, and the problem of excessive cutting of the object when the cutting die is cut can be avoided, and the vector object expansion method has more effect than the expansion of the general image object. High precision and efficiency; At the same time, based on the object expansion results, we propose a practical compact object layout method, which can make a close layout of various polygon objects, so that the material can be effectively utilized in the cutting layout, and the waste of cutting materials can be reduced.

(1) ‧‧‧ benchmark objects

(2) ‧ ‧ close to objects

(3) ‧‧‧Layout frame

(A) ‧‧‧cut objects

[First figure] is a schematic diagram of the expansion of the vector object of the present invention.

[Second image] is a schematic diagram showing the convexity of the convex object when the vector object is expanded by the present invention.

[Third image] is a schematic diagram of a solution when the lobes are over convex for the second figure.

[Fourth figure] is a schematic view showing a concave angle becoming a convex angle when the vector object is expanded by the present invention.

[Fifth figure] is a schematic diagram showing the overlap of the expansion contour lines when the vector object is expanded in the present invention.

[Sixth Graph] is a schematic diagram of a solution when the overlap contour is generated for the fifth graph.

[Seventh figure] is a schematic diagram of the approach of edge-to-corner when performing vector typesetting for the present invention.

[Eighth image] is a schematic diagram of the proximity of the object to the reference object in various angular directions of 360 degrees with respect to the reference object when the vector object is typeset according to the present invention.

[Ninth diagram] is a schematic diagram of approaching a reference object in an angular direction of an object rotated by 360 degrees in each angular direction when the vector object is typeset according to the present invention.

[Tenth Image] is a schematic diagram in which the objects are arranged in a tightly arranged layout by using a typesetting outer frame when the vector object is typeset.

[11th] is a schematic diagram of a conventional typesetting.

In summary of the above technical features, the main effects of the vector object expansion and typesetting method of the present invention will be clearly shown in the following embodiments.

In this embodiment, when the typesetting of the object to be cut is performed, the expansion of the crop member is first performed, and the cutting tool is prevented from being cut to the object itself, wherein the expansion of the object is performed in the vector space.

Referring to the first figure, the vector object expansion method includes: I. Obtaining a plurality of vector coordinate points along a contour of an object, and expressing the contour A as: A={a ₁ , a ₂ , a ₃ ...a _n }, where each vector coordinate point a _i is a plane coordinate point [x _i , y _i ] ^T , and the vector coordinate points adjacent to one of the vector coordinate points a _i are a _i-1 and a _{i +1} , the outline is represented as a plurality of line segments L={a ₂ -a ₁ , a ₃ -a ₂ , a ₄ -a ₃ ... a _i -a _i-1 ... a _n -a _n-1 ,a ₁ - a _n }={L ₁ , L ₂ , L ₃ ... L _i ... L _n-1 , L _n }. II. Given that the cutting pitch to be retained between the object and another object is D, the distance d to be expanded by the object is D/2. III. Recalculate the intersection point after the adjacent line segments L _i (a _i+1 -a _i ) and L _i-1 (a _i -a _i-1 ) with the vector coordinate point a _i as the intersection point are shifted outward by the distance d The vector coordinate of b _i to obtain the actual expansion distance of the vector coordinate point a _i is b _i -a _i , wherein when calculating the intersection point b _i , a counterclockwise rotation matrix is first defined Solving the vector coordinate point a _i to the vector of the vector coordinate point b _i by a trigonometric function; the direction of the first segment vector V ₁ is perpendicular to L _i-1 and the length is fixed to d, then The direction of the second segment vector V ₂ is parallel to L _i-1 and the length is d/tan ,among them, , Then, the vector coordinate point b _i = a _i + V ₁ + V ₂ . IV. Repeat step III to obtain the actual expansion distance of each vector coordinate point a _i on the contour A, and calculate an expansion contour.

However, when vector object expansion is performed, three problems may occur for some graphics, including: 1. convex over convex, 2. concave angle changing convex angle, 3. expansion contour generating overlap.

Referring to the second and third figures, the solution to the problem 1: the length of the vector coordinate point a _i to the vector coordinate point b _i s=|b _i -a _i |=dcscθ/2, if the vector When the coordinate point a _i to the length s of the vector coordinate point b _i is greater than 2 times d, then s=d is set: And use at least 3 points to describe the expanded outer frame. For example, as shown in the third figure, when three points are used to describe the expanded outer frame, the three points are set to b _i , b _i ^' , b _i ^〞 , , ,

Referring to the fourth figure, the solution to the problem 2 is: when the vector coordinate point a _i forms a concave angle with the adjacent vector coordinate points a _i-1 and a _i+1 , a criticality is set on the angle bisector of the angle point , the vector coordinate point a _i to the critical point The distance is Where L is min{|L _i-1 |, |L _i |}, if the vector coordinate point a _i to the vector coordinate point b _{i has} a length s=|b _i -a _i | greater than Lsec θ/2, this The vector coordinate point a _i is removed from the list of all vector coordinate points.

Referring to the fifth and sixth figures, the solution to the problem 3 is: when the contour of the object is expanded, the expansion contour is overlapped, and the outermost contour of the expansion contour is taken as a new expansion. contour line. For example, in the sixth figure, the point series of the expanded contour line after the object is expanded is [1234567], and the overlap of each line in the expanded contour is calculated first, and the calculated intersection point is inserted into the point series. Between the two lines, mark the point as the intersection point and establish a connection with the point string to form a point series [12●▲3■★45★●6▲■7]; then find another one to determine At the outermost point of the expansion contour, for example, point 1 in the figure, the search starts from this point, and jumps to the joint point every time the intersection point is encountered, otherwise the next point is continued, for example, point 1 starts and then continues to point 2, point 2 Then meet the intersection point ● jump to the connection point 6, after the connection point 6 is followed by the intersection point ▲, then jump to the connection point 3, after the connection point 3 is the intersection point ■, then jump to the connection point 7, according to the above rules, the point of the outermost contour of the expansion contour line can be obtained Tandem [12 ● 6 ▲ 3 ■ 7].

When the object to be cut is expanded, the object typesetting is performed. Similarly, the object typesetting is performed in the vector space.

The vector object layout method includes the following steps:

I. Referring to the seventh figure, one of the two objects is the reference object (1), and the other object is close to the object (2).

II. centering on the reference object (1), approaching the object (2) toward the reference object (1) until the adjacent object (2) contacts the reference object (1), and at this time, drawing the reference The object (1) and the smallest outer frame of the object (2), wherein the reference object (1) and the adjacent object (2) are brought close to each other in a diagonally opposite manner. The diagonally adjacent manner takes a plurality of vector coordinate points along the contour of each object, and the contour A is represented as: A = {a ₁ , a ₂ , a ₃ ... a _n }, wherein Each vector coordinate point a _i is a plane coordinate point [x _i , y _i ] ^T , and the vector coordinate points adjacent to one of the vector coordinate points a _i are a _i-1 and a _i+1 , then the contour The line is represented as a plurality of line segments L={a ₂ -a ₁ , a ₃ -a ₂ , a ₄ -a ₃ ... a _i -a _i-1 ... a _n -a _n-1 , a ₁ -a _n }= {L ₁ , L ₂ , L ₃ ... L _i ... L _n-1 , L _n }, so that each vector coordinate point a _i close to the object approaches each line segment of the reference object to obtain a minimum distance D The vector coordinate point a _i and the line segment, that is, the minimum close distance of the approaching object (2) and the reference object (1) in the orientation, the approaching object (2) and the reference object (1) approaching the minimum close distance , the minimum outer frame can be depicted.

III. Referring to the eighth and ninth diagrams, the 360 degree range is scanned so that the approaching object (2) approaches the reference object (1) to obtain a plurality of minimum frames. Wherein, as shown in the eighth figure, the approaching object (2) approaches the reference object (1) at an angle of 360 degrees with respect to the reference object (1). Again as the first As shown in the figure nine, and in each angular direction, the approaching object (2) approaches the reference object (1) at an angular orientation rotated by itself by 360 degrees. Thereby, the minimum outer frame of the object (2) and the reference object (1) in any direction and position is obtained.

IV. Referring to the tenth figure, the smallest one of the plurality of minimum outer frames is a typesetting outer frame (3), and the two objects are grouped, and the plurality of groups are arranged in a frame (3) ) Stacked horizontally or vertically, so the minimum outer frame is rectangular in shape, making it easy to stack the most densely.

Through the method of the present invention, the expansion of the object can achieve the aforementioned higher precision and efficiency; and the layout of the object can achieve a more compact effect.

In view of the foregoing description of the embodiments, the operation and the use of the present invention and the effects of the present invention are fully understood, but the above described embodiments are merely preferred embodiments of the present invention, and the invention may not be limited thereto. Included within the scope of the present invention are the scope of the present invention.

Claims (14)

A vector object expansion method comprising the steps of: I. taking a plurality of vector coordinate points along a contour of an object, and expressing the contour A as: A = {a ₁ , a ₂ , a ₃ ... a _n }, wherein each vector coordinate point a _i is a plane coordinate point [x _i , y _i ] ^T , and the vector coordinate points adjacent to one of the vector coordinate points a _i are a _i-1 and a _i+1 , Then the outline is represented as a plurality of line segments L={a ₂ -a ₁ , a ₃ -a ₂ , a ₄ -a ₃ ... a _i -a _i-1 ...a _n -a _n-1 , a ₁ -a _n }={L ₁ , L ₂ , L ₃ ... L _i ... L _n-1 , L _n }; II. Given that the cutting pitch to be retained between the object and another object is D, the object is to be The distance d of the expansion is D/2; III. After the adjacent line segments L _i and L _i-1 with the vector coordinate point a _i as the intersection point are shifted outward by the distance d, the vector coordinates of the intersection point b _{i are} recalculated to obtain the The actual expansion distance of the vector coordinate point a _i is b _i -a _i ; IV. Repeat step III to obtain the actual expansion distance of each vector coordinate point a _i on the contour A, and calculate an expansion contour. The vector object expansion method according to claim 1, further, when the vector coordinate point a _i forms a lobe with the line segments L ₁ and L _{2 of the} adjacent vector coordinate points a _i-1 , a _i+1 If the length s of the vector coordinate point a _i to the vector coordinate point b _i is greater than 2 times d, then at least 3 points with s equal to d are used to describe the expanded outer frame; when the vector coordinate point a _i and When the line segments L ₁ and L _{2 of the} adjacent vector coordinate points a _i-1 and a _i+1 form a concave angle, if the expanded vector coordinate point b _i forms a convex angle, the vector coordinate point a _i is deleted; After the contour of the object is expanded, the expansion contour is overlapped, and the outermost contour of the expansion contour is taken as a new expansion contour; wherein the angle of the convex angle or the concave angle is θ. The vector object expansion method according to claim 1, wherein in step III, when calculating the intersection point b _i , first defining a counterclockwise rotation matrix Solving the vector coordinate point a _i to the vector of the vector coordinate point b _i by a trigonometric function; the direction of the first segment vector V ₁ is perpendicular to L _i-1 and the length is fixed to d, then The direction of the second segment vector V ₂ is parallel to L _i-1 and the length is d/tan ,among them, , Then, the vector coordinate point b _i = a _i + V ₁ + V ₂ . The vector object expansion method according to claim 2, wherein the vector coordinate point a _i to the vector coordinate point b _{i has} a length s=|b _i -a _i |=dcscθ/2, if the vector coordinate When the point a _i to the length s of the vector coordinate point b _i is greater than 2 times d, then s=d is set: And use at least 3 points to describe the expanded outer frame. The vector object expansion method according to claim 4, wherein, when the expanded outer frame is described by three points, the three points are set to b _i , b _i ^' , b _i ^〞 , wherein , b _i = a _i + , , It is a counterclockwise rotation matrix. Expansion methods such as the application of the article vector patentable scope of item 2, wherein, when the vector a _i coordinate point adjacent to the vector coordinate point a _i-1 and a _{i + 1} form a concave angle, the angle bisector of the angle setting a critical point , the vector coordinate point a _i to the critical point The distance is Where L is min{|L _i-1 |, |L _i |}, if the vector coordinate point a _i to the vector coordinate point b _{i has} a length s=|b _i -a _i | greater than Lsec θ/2, this Then, the vector coordinate point a _i is removed. The vector object expansion method of claim 2, wherein when the contour of the object is expanded, the expansion contour is overlapped, and an overlap of each of the expansion contours is first calculated, and Insert the calculated intersection point between the two lines of the point string, mark the point as the intersection point and connect the point to the point string; then find a point that can determine the outermost edge of the expansion contour Start searching from this point, jump to the connection point every time you encounter the intersection point, otherwise continue to the next point; according to the above rules, you can get the list of peripheral points. A vector object typesetting method comprises the following steps: I. In a two object, one of the objects is a reference object, and the other object is close to the object; II. centering on the reference object, bringing the object closer to the reference object, Until the close object contacts the reference object, at this time, draw a minimum outer frame including the reference object and the close object; III. scan a 360 degree range, so that the close object approaches the reference object to obtain a plurality of minimum outer Box; IV. The smallest of the plurality of minimum frames is a typesetting frame. The vector object typesetting method according to claim 8, wherein, when the two objects are brought close, a contour expansion of each contour of each object is performed, including the following steps: I. along each object The contour line takes a plurality of vector coordinate points, and the contour line A is represented as: A = {a ₁ , a ₂ , a ₃ ... a _n }, wherein each vector coordinate point a _i is a plane coordinate point [x _i , y _i ] ^T , and the vector coordinate points adjacent to one of the vector coordinate points a _i are a _i-1 and a _i+1 , and the contour line is represented as a plurality of line segments L={a ₂ -a ₁ , a ₃ -a ₂ , a ₄ -a ₃ ... a _i -a _i-1 ... a _n -a _n-1 , a ₁ -a _n }={L ₁ , L ₂ , L ₃ ... L _i ... L _{n -1} , L _n }; II. Assuming that the cutting pitch to be retained between the two objects is D, the distance d to be expanded by each object is D/2; III. The vector coordinate point a _{i will} be the intersection point After the adjacent line segments L _i (a _i+1 -a _i ) and L _i-1 (a _i -a _i-1 ) are shifted outward by the distance d, the vector coordinates of the intersection point b _{i are} recalculated to obtain the vector coordinate point. the actual expansion of the distance a _i b _i -a _i; IV repeat step III, thereby obtaining the actual expansion of each vector a _i of the coordinate points. From the composition of a contour line expansion, the expansion contour of the object as a new contour line layout. The vector object typesetting method according to claim 8, wherein the proximity object approaches the reference object in a direction rotated 360 degrees with respect to the reference object, and in each direction, the proximity object rotates 360 by itself. The orientation is close to the reference object. The vector object typesetting method according to claim 9, wherein the reference object and the adjacent object are approached in a diagonally opposite manner. The vector object typesetting method according to claim 11, wherein the edge diagonal approach is performed to obtain a plurality of vector coordinate points along an outline of each object, and the outline A is represented as: A = {a ₁ , a ₂ , a ₃ ... a _n }, where each vector coordinate point a _i is a plane coordinate point [x _i , y _i ] ^T and is adjacent to one of the vector coordinate points a _i The vector coordinate points are a _i-1 and a _i+1 , and the outline is represented as a plurality of line segments L={a ₂ -a ₁ , a ₃ -a ₂ , a ₄ -a ₃ ... a _i -a _{i- 1} ... a _n - a _{n - 1} , a ₁ - a _n } = {L ₁ , L ₂ , L ₃ ... L _i ... L _n-1 , L _n }, such that each vector coordinate point a of the object is close _i , approaching each line segment of the reference object to obtain a vector coordinate point a _i and a line segment of a minimum distance, that is, a minimum close distance between the object and the reference object in the orientation, the proximity object and the reference object at the minimum The minimum outer frame can be depicted when the proximity is close. The vector object typesetting method according to claim 8, wherein the minimum outer frame has a rectangular shape. The vector object typesetting method according to claim 8, wherein the plurality of group layout frames are stacked in a horizontal or vertical manner by using the two objects as a group.