CN109887052A - A kind of planar polygons offset method - Google Patents
A kind of planar polygons offset method Download PDFInfo
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- CN109887052A CN109887052A CN201910085158.6A CN201910085158A CN109887052A CN 109887052 A CN109887052 A CN 109887052A CN 201910085158 A CN201910085158 A CN 201910085158A CN 109887052 A CN109887052 A CN 109887052A
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
Abstract
The present invention provides a kind of planar polygons offset methods, belong to computer geometric figure technical field.Technical solution of the present invention is the following steps are included: Step 1: judge whether incoming parameter is legal or reasonable；Step 2: polygon is splitted into multiple rings, each ring is separately handled；Step 3: the side after offset is connected two-by-two；Step 4: each end to end ring obtained in step 3 is carried out the selfing processing that disappears, legal ring is obtained；Step 5: establishing the corresponding relationship of offset front and back planar polygons.The present invention can handle the case where curve in planar polygons is made of various types curve, and the corresponding offset distance of each edge can be customized, and planar polygons can have the complicated case of multiple rings.The offset of planar polygons can be used in generation, shell thickening, post-cast strip moulding of the construction, decorative thread on the earthwork basis in architectural image etc..
Description
Technical field
The invention belongs to computer geometric figure technical fields, and in particular to a kind of planar polygons offset method, especially
It is the offset method that the offset distance of the planar polygons of multiple rings and each edge can not wait, complex building can be applied to
Generation, the generation of decorative thread on earthwork basis in threedimensional model etc..
Background technique
Planar polygons offset problem is one of the basic problem in computer graphics.Planar polygons offset is sought to
With certain algorithm by each of polygon while according to specified length along while normal direction deviate, be then then assembled into
New planar polygons.
The basis of planar polygons offset is the offset on every two-dimentional side, and R Kimmel and A M Bruckstein is using partially
The available curve of deviation for eliminating selfing of Methods of Differential Equations.
Planar polygons migration algorithm exists in many CAD softwares.For example, to provide two kinds of planar polygons inclined by CGAL
Algorithm is moved, one is Minkowski and method is based on, and obtained polygon is round and smooth in Jiao Chu；Another is base
In straight skeleton technique, the case where polygon is by rectilinear(-al) is only handled.
Deok-SooKim is given based on Voronoi diagram by circular arc and the polygon offset equidistance of rectilinear(-al)
Migration algorithm.
Due to there is special business demand in buildings model, each edge of planar polygons can be various curve types,
The offset distance of each edge of planar polygons can be unequal, and planar polygons may exist multiple rings.And it is current existing
Algorithm can not all meet these conditions simultaneously, and the present invention is handled for these scenes, ask planar polygons offset
Topic is no longer confined to a certain scene, so as to apply in the business moulding in much building, such as earthwork basis
It generates, shell thickeies moulding, post-cast strip moulding etc..
Summary of the invention
Present invention aim to address the three-dimensional modelings of complexity some in architectural business scene, such as earthwork basis, shell to add
Thick moulding, post-cast strip moulding etc..
For achieving the above object, the present invention provides a kind of planar polygons offset method, and its step are as follows:
Step 1: judge whether incoming parameter is reasonable
Whether the incoming planar polygons of judgement are legal, and whether incoming offset distance is reasonable.
Step 2: polygon is splitted into multiple rings, each ring is separately handled.For a ring, by every in ring
While being deviated according to shift value
According to each edge in a ring, given offset distance deviates each edge.
Step 3: the adjacent side after offset is connected two-by-two
Side after offset extend and asks friendship or addition circular arc, straight line connection, becomes end to end ring.
Step 4: cyclization handles all rings with same method.
Ring end to end obtained in step 3 is subjected to the selfing processing that disappears, obtains legal ring.And it traverses each
A ring, is handled in the same way.
Step 5: the corresponding relationship of offset front and back planar polygons is established
The each edge of the polygon of offset front and back is established into one-to-one corresponding relationship.It is more after offset can therefrom be found
Each edge in shape be by original polygon which ring and which while get, or addition new side.
Preferably, the planar polygons have multiple rings, and the offset distance of each edge is not all equal.
Preferably, the legal criterion is: planar polygons must not be selfed, in range of tolerable variance in step 1
It is end to end；The reasonable criterion of offset distance is: the item number on side of size and planar polygons of offset distance array is equal.
Preferably, the type on side can be straight line, circular arc, elliptic arc, NURBS, two-dimensional helical line, SIN in step 2
Trigonometric curve.
Preferably, step 3 specifically:
Adjacent curve is extended, line line is carried out and asks friendships, according to asking knot fruit selection different modes to connect；
If line line asks friendship to have intersection point, adjacent curve is attached using intersection point；
If line line asks friendship without intersection point, addition circular arc or straight line, specific rules are selected according to the curve type of adjacent curve
It is as follows:
If 1) adjacent curve is circular arc, according to the terminal of the last period in adjacent curve, latter section of starting point, two sections of circles
The average value of arc radius constructs new arc section and connects adjacent curve；
If 2) adjacent curve is not all circular arc, constructed according to the terminal of the last period in adjacent curve, latter section of starting point
Straightway connects adjacent curve.
Preferably, disappearing, to be selfed treatment process as follows:
Step 1, the intersection point for finding the intersection point of all curve intersections two-by-two and the selfing of single-ended curve in ring；
Step 2, the curve that intersection is interrupted according to intersection point；
Step 3 carries out searching ring according to intersection point, obtains all rings；
Step 4 deletes unreasonable ring, retains reasonable ring, the ring after finally being deviated.
It is selfed in treatment process preferably, disappearing, according to the suitable rule counterclockwise between polygon ring and ring, judges whether
Retain.
Preferably, the suitable rule counterclockwise between polygon ring and ring specifically:
Set outer ring must be counterclockwise or clockwise ring, if adjacent inner ring if with outer ring be all counterclockwise or
Person is invalid loops clockwise.
Preferably, from step 5 establish corresponding relationship in can find offset after polygon in each edge be by
What which ring and which side in original polygon were got, or the new side of addition.
The method of judgement selfing is: if the selfing of curve, on curve there are some neighborhood of a point not with straightway
Constitute homeomorphism；Single-segment curve selfing that ring selfing is divided into ring, two sections of curve intersections in ring.
The invention has the following advantages:
The present invention can handle the case where curve in planar polygons is made of various types curve, and each edge is corresponding partially
Moving distance can be customized, and planar polygons can have the complicated case of multiple rings.The offset of planar polygons can be used in
Generation, shell thickening, post-cast strip moulding of the construction, decorative thread on the earthwork basis in architectural image etc..
Detailed description of the invention
Fig. 1 is original two dimensional polygon schematic diagram
Fig. 2 is that each edge deviates distance to a declared goal schematic diagram in original polygon
Fig. 3 is that friendship connection schematic diagram is sought in the side extension after offset two-by-two
Fig. 4 is disappear each section of curve head and the tail endpoint and intersection point schematic diagram in selfing process；
Fig. 5 is the polygon of offset front and back, is the ring of inner ring before offset, is the ring schematic diagram of outer ring after offset
Fig. 6 is the more complicated earthwork basic schematic obtained using two-dimensional migration algorithm
Symbol description is as follows in figure:
A1 ... A9 is the end to end intersection point of ring, and 0 ... 10 is the serial number on side, and P is intersection point.
Specific embodiment
The present invention is further described in detail below with reference to the accompanying drawings and embodiments.It should be appreciated that described herein
Specific embodiment is only used to explain the present invention, is not intended to limit the present invention.
As shown in figure 1, figure 2, figure 3, figure 4 and figure 5, a kind of polygon of multiple rings and the offset distance of each edge can be with
A kind of equal migration algorithm, the specific implementation step of this method be not as follows:
Step 1: judge whether incoming parameter is reasonable
Incoming parameter includes planar polygons, offset distance array；
Whether the incoming planar polygons of judgement are legal, and whether incoming offset distance is reasonable.
Wherein legal planar polygons must not be selfed, end to end in range of tolerable variance.
The size of offset distance array must be equal with the item number on the side of planar polygons.
Step 2: polygon is splitted into multiple rings, each ring is separately handled.For a ring, by each edge according to
Shift value is deviated
According to each edge in a ring, given offset distance deviates each edge.
The type on side can be straight line, circular arc, elliptic arc, NURBS, two-dimensional helical line, SIN trigonometric curve.After offset
Curve may generate selfing, and at this moment program will do it the selfing processing that disappears, and obtain the curved section of non-selfing.
The polygon for a ring being made of with one 10 sides, offset distance be respectively -1, -2, -3, -4, -5, -6, -
7, -8, -9, -10 } for offset.Wherein, offset distance, which is negative, indicates that offset direction is the normal orientation of curve, positive to indicate inclined
Move the negative normal orientation that direction is curve.Original two dimensional polygon is as shown in Figure 1, each edge is carried out according to corresponding offset distance
Situation after offset is as shown in Figure 2.
Step 3: the side after offset is connected two-by-two
It is isolated curve by this group of curve that step 3 obtains, next needs for be attached on two adjacent sides,
Connection type has three ways, such as that friendship and addition circular arc, straight line are asked in extension.
First choice carries out line line and asks friendship to extend adjacent curve.
1. if adjacent curve is attached using intersection point line line asks friendship to have intersection point；
2. if selecting addition circular arc or straight line, specific rules according to the curve type of adjacent curve line line asks friendship without intersection point
It is as follows:
If 1) adjacent curve is circular arc, according to the terminal of the last period in adjacent curve, latter section of starting point, two sections of circles
The average value of arc radius constructs new arc section and connects adjacent curve.
2) other situations, according to the terminal of the last period in adjacent curve, latter section starting point construction straightway will be adjacent
In curve connection.
Adjacent line segment in Fig. 2 is subjected to head and the tail connection, obtained result is as shown in figure 3, in addition to the 5th article and the 6th article
Connection type be addition straight line because its extension asks friendship without intersection point, the connection type of other adjacent segments is to extend to ask friendship side
Formula.
Step 4: cyclization handles all rings with same method.
Planar polygons obtained in step 3 disappear selfing processing, in Fig. 3, the 3rd, 4,5 article of line segment has selfing
Phenomenon can be found from intersection point here, and the ring of selfing is eliminated.It is outer in planar polygons such as Fig. 5 after eliminating selfing
Shown in the ring of circle.
Disappear and be selfed treatment process:
1. finding the intersection point of the intersection point of all curve intersections two-by-two and the selfing of single-ended curve in ring.In Fig. 4, the 3rd article and
5th article of curve intersection, intersection point P
2. interrupting the curve of intersection according to intersection point.Such as Fig. 4, the 3rd article of curve is interrupted by two sections of A4P and PA5 according to intersection point P,
5th article of curve is also interrupted as two sections of A6P and PA7.
3. carrying out searching ring according to intersection point, all rings are obtained.For example, by using depth-first traversal mature in the prior art
Algorithm carries out searching ring, and details are not described herein.Such as Fig. 4, two rings, PA5A6P and A1A2A3A4PA7A8A9A1 are obtained.
4. deleting unreasonable ring, retain reasonable ring, the ring after finally being deviated.According between polygon ring and ring
Along counterclockwise rule, judge whether to retain, those skilled in the art implement when can be set as needed.For example, outer ring must
It must be ring counterclockwise, back to back inner ring cannot be counterclockwise, if as invalid loops counterclockwise.
If the ring of Fig. 4, outside are A1A2A3A4PA7A8A9A1 counterclockwise, the ring of the inside is also PA5A6P counterclockwise, is deleted
The ring PA5A6P of the inside obtains final ring A1A2A3A4PA7A8A9A1.
Step 5: the corresponding relationship of offset front and back planar polygons is established
The each edge of the polygon of offset front and back is established into one-to-one corresponding relationship.It is more after offset can therefrom be found
Each edge in shape be by original polygon which ring and which while get, or addition new side.
In Fig. 5, at the 0th article of the 0th article of the polygon after the offset polygon before corresponding original offset, polygon after offset
At the 1st article of the 1st article of polygon before corresponding original offset, before the 2nd article of side of the polygon after offset corresponds to original offset
Polygon the 2nd article of side, at the 3rd article of the 3rd article of the polygon after the offset polygon before corresponding original offset, offset
When corresponding to the 5th article of the polygon before original offset, the 5th article of side of the polygon after offset is the 4th article of polygon afterwards
Newly added side, the 6th article of the polygon after offset are more after offset when corresponding to the 6th article of the polygon before original offset
7th article of side of the polygon before corresponding to original offset in the 7th article of shape, the 8th article of side of the polygon after offset correspond to original
8th article of side of the polygon before offset, the 9th article of side of the polygon after offset correspond to the 9th article of the polygon before original offset
Side.
By above step, polygon after being deviated, and obtained each side of the polygon of offset front and back
Corresponding relationship.
It is capable of handling the moulding of some complexity with planar polygons migration algorithm, such as Fig. 6, the earthwork base in buildings model
Plinth.Planar polygons migration algorithm is applied to during constructing earthwork basis, the upper bottom surface of the earthwork can be regarded as
Deviate the polygon of front and back.
It is described the prefered embodiments of the present invention in detail above in conjunction with attached drawing, still, the present invention is not limited to above-mentioned realities
The detail in mode is applied, within the scope of the technical concept of the present invention, a variety of letters can be carried out to technical solution of the present invention
Monotropic type, these simple variants all belong to the scope of protection of the present invention.It is further to note that in above-mentioned specific embodiment
Described in each particular technique feature or step, process in the case of no contradiction can be by any suitable means
It is combined, in order to avoid unnecessary repetition, the invention will not be further described in various possible combinations.
Claims (10)
1. a kind of planar polygons offset method, for being deviated according to the offset distance of each edge to planar polygons,
It is characterized in that:
It the described method comprises the following steps:
Step 1: judging whether incoming parameter is legal or reasonable；
Incoming parameter includes planar polygons and the offset distance array for indicating each edge offset distance；
Whether the incoming planar polygons of judgement are legal, and whether incoming offset distance is reasonable；
Step 2: polygon is splitted into multiple rings, each ring is separately handled；
For a ring, each edge is deviated according to the shift value for indicating offset distance；
If the curve after offset generates selfing, the selfing processing that disappears is carried out, the curved section of non-selfing is obtained；
Step 3: the side after offset is connected two-by-two；
Two adjacent sides are attached, connection type includes extending to ask friendship, addition circular arc, addition three kinds of modes of straight line；
Step 4: each end to end ring obtained in step 3 is carried out the selfing processing that disappears, legal ring is obtained；
Step 5: establishing the corresponding relationship of offset front and back planar polygons；
The each edge of the polygon of offset front and back is established into one-to-one corresponding relationship.
2. according to the method described in claim 1, it is characterized by:
The planar polygons have multiple rings, and the offset distance of each edge is not all equal.
3. according to the method described in claim 1, it is characterized by:
In step 1, the legal criterion is: planar polygons must not be selfed, end to end in range of tolerable variance；
The reasonable criterion of offset distance is: the item number on side of size and planar polygons of offset distance array is equal.
4. according to the method described in claim 1, it is characterized by:
In step 2, the type on side can be straight line, circular arc, elliptic arc, NURBS, two-dimensional helical line, SIN trigonometric curve.
5. according to the method described in claim 1, it is characterized by:
Step 3 specifically:
Adjacent curve is extended, line line is carried out and asks friendships, according to asking knot fruit selection different modes to connect；
If line line asks friendship to have intersection point, adjacent curve is attached using intersection point；
If line line asks friendship without intersection point, select addition circular arc or straight line, specific rules as follows according to the curve type of adjacent curve:
If 1) adjacent curve is circular arc, according to the terminal of the last period in adjacent curve, latter section of starting point, two sections of circular arcs half
The average value of diameter constructs new arc section and connects adjacent curve；
If 2) adjacent curve is not all circular arc, straight line is constructed according to the terminal of the last period in adjacent curve, latter section of starting point
Section connects adjacent curve.
6. according to the method described in claim 1, it is characterized by:
Disappearing in step 4, it is as follows to be selfed treatment process:
Step 1, the intersection point for finding the intersection point of all curve intersections two-by-two and the selfing of single-ended curve in ring；
Step 2, the curve that intersection is interrupted according to intersection point；
Step 3 carries out searching ring according to intersection point, obtains all rings；
Step 4 deletes unreasonable ring, retains reasonable ring, the ring after finally being deviated.
7. according to the method described in claim 6, it is characterized by:
Disappear and be selfed in treatment process, according to the suitable rule counterclockwise between polygon ring and ring, judges whether to retain.
8. according to the method described in claim 7, it is characterized by:
Disappear and is selfed in treatment process, the suitable rule counterclockwise between polygon ring and ring specifically:
If setting outer ring must be the counterclockwise perhaps clockwise adjacent inner ring of ring if being all counterclockwise or suitable with outer ring
Hour hands are invalid loops.
9. according to the method described in claim 1, it is characterized by:
The each edge in polygon after it can find offset in the corresponding relationship that step 5 is established is by original polygon
Which ring and which side get, or the new side of addition.
10. according to the method described in claim 1, it is characterized by:
The method of judgement selfing is: if a curve selfing, there are some neighborhoods of a point not to constitute with straightway on curve
Homeomorphism；Single-segment curve selfing that ring selfing is divided into ring, two sections of curve intersections in ring.
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| CN111173234A (en) * | 2020-01-20 | 2020-05-19 | 广东三维家信息科技有限公司 | Automatic skirting line generation method and device |
| CN112560144A (en) * | 2020-12-15 | 2021-03-26 | 杭州群核信息技术有限公司 | Ceiling lamp strip generation method and system |
| WO2021142978A1 (en) * | 2020-01-19 | 2021-07-22 | 杭州群核信息技术有限公司 | Comprehensive contour curve offset method |
| CN113192158A (en) * | 2021-03-09 | 2021-07-30 | 刘梦祈 | 3D model lofting method based on computer geometric migration algorithm |
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