CN103065362A - Grid-free surface drawing method with sharp feature - Google Patents
Grid-free surface drawing method with sharp feature Download PDFInfo
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- CN103065362A CN103065362A CN2012105717685A CN201210571768A CN103065362A CN 103065362 A CN103065362 A CN 103065362A CN 2012105717685 A CN2012105717685 A CN 2012105717685A CN 201210571768 A CN201210571768 A CN 201210571768A CN 103065362 A CN103065362 A CN 103065362A
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Abstract
The invention relates to a grid-free surface drawing method with a sharp feature. The grid-free surface drawing method with the sharp feature includes that firstly, surface of an object to be drawn can be molded by utilizing a point-edge-mixed model; secondly, the surface points of the model and corresponding cut edges are related and relevancy results are kept; thirdly, all cut edges of the model are projected on an observing plane to form projection cut edges; fourthly, the surface points of the model are projected on the observing plane to form ovals, wherein the oval are overlapped mutually; fifthly, each oval projected on the observing plane can be cut through a zigzag clipping algorithm after utilizing the projected cut edges in the third step; and sixthly, after each oval projected on the observing plane is cut, pixel points on the whole observing plane can be normalized to obtain the grid-free surface of the object to be drawn. Compared with the prior art, the grid-free surface drawing method with the sharp feature has the advantages of being stable, reliable, convenient to achieve, suitable for practical engineering application extremely, and the like.
Description
Technical field
The present invention relates to a kind of without the surface mesh method for drafting, especially relate to a kind of with sharp features without the surface mesh method for drafting.
Background technology
What 3 D scanning system was exported is sampled point unit, can express exactly the geometric configuration of object by the first set of the resulting point of this technology.Owing to do not have annexation between the each point unit, do not need to preserve topology information yet, therefore when processing complicated three-dimensional body, seem flexible especially and simple.Therefore, field of Computer Graphics in receive increasing concern without the grid Geometric Modeling with being plotted in based on what put.
Using some unit to carry out surface rendering as fundamental element is proposed by people such as Levoy the earliest.Afterwards, occurred various without the surface mesh method for drafting, for example, the method etc. of using method, the QSplat system of image space surface reconstruction and utilizing Moving Least Squares (MLS, Moving Least Square).The Splatting algorithm is the real time algorithm that a kind of ratio is faster also easily realized.In this mode, each surface point unit is approximate with a roundel, and this approximate roundel is called as Splat.Yet the Splatting algorithm is the sharp features in the treatment surface model well, such as limit or angle etc.These sharp features are very important in some applications, such as CSG (constructive solid geometry) modeling, Cutting etc.
The people such as Adams propose to resample with very little splat in corner areas.Yet this method needs very high sampling rate, and this also is a kind of approximation method, when corner areas is amplified, still can see distortion.The splat that it is special that the people such as Pauly have proposed a kind of usefulness draws the method at edge.This splat is comprised of two crossing disks, and these two disks have the public center of circle.The edge of cutting is exactly the intersection of two disks.A major defect of this method is to draw angle point.Zwicker etc. propose the concept of line of cut (clip line), point out that marginal information can obtain by the intersection that calculates plane, two crossing disk places.
Wicke etc. have proposed how to draw sharp features in the CSG model.The method is converted into interior exterior point test problem (inside/outside test, judging in the space a bit is in model inside or the model outside) with the cutting of splat.The method is present method the most accurately, but the method depends on the CSG model, has limited its application.Recently, in order to remove the dependence to the CSG model, Ivo etc. have used adaptive splat method of cutting out.But the method still can't be processed some complex situations.
Point limit mixture model is the another kind of strategy of drawing sharp features, by propositions such as Zhang.Except unit's set, this model has also comprised the set of a line of cut, is used for drawing the corner.But three restrictions are arranged, therefore before drafting, need model is carried out preprocessing process one time, when certain restriction is not satisfied, increase the sampling rate of some unit set, all be satisfied until institute is restricted.
Summary of the invention
Purpose of the present invention be exactly provide in order to overcome the defective that above-mentioned prior art exists a kind of reliable and stable, realize convenient, be very suitable for practical engineering application with sharp features without the surface mesh method for drafting.
Purpose of the present invention can be achieved through the following technical solutions:
A kind of with sharp features without the surface mesh method for drafting, the method may further comprise the steps:
The first step adopts some limit mixture model to treat the surface of drawing object and carries out modeling;
Second step carries out the surface point in the model and corresponding cutting edge related, and preserves association results;
The 3rd step projected to cutting edges all in the model on the viewing plane, formed the projection cutting edge;
The 4th step projected to surface points all in the model on the viewing plane, formed overlapped one by one ellipse;
The 5th step, utilize the cutting edge after the projection in the 3rd step, by the zigzag clipping algorithm ellipse that each is projected on the viewing plane is carried out cutting;
The 6th the step, after cutting is complete, the pixel on the whole viewing plane is carried out normalization, obtain object to be drawn without surface mesh.
Describedly be comprised of several smooth surfaces s without surface mesh, described sharp features only appears between two or more adjacent smooth surfaces, for each smooth surface s, has
s＝{P
n，L
t}
Wherein, P
nBe the set of n surface point, n＞0 comprises the attribute of this point, L in each surface point
tBe the set of t cut ring, t 〉=0, each cut ring comprises the sequence of an edge point, and in each cut ring, the line segment that connects any two edge point is called cutting edge.
The attribute of described point comprises the radius of the splat of a little position, normal vector, color value and this representative.
Described some limit mixture model PEM is defined as follows:
PEM＝{S
K，V
m}
Wherein, S
KExpression comprises the set of K smooth surface, V
mSet for m edge point.
Described edge point is the point on the limit in the sharp features.
Described surface point carries out related referring in each smooth surface with cutting edge, and the distance between reckoner millet cake and cutting edge realizes association, specifically describes to be:
Take the position of surface point as the centre of sphere, the radius of the splat that surface point is represented is the encirclement ball that radius is made each surface point, simultaneously cutting edge is got up with the encirclement bag, then make to surround the collision detection between ball, if a certain encirclement ball and a certain cutting edge intersect, then show relevant relation between them.
Described zig-zag type trimming algorithm refers to have the ray of discrete point and cutting edge to judge whether this discrete point need be cropped on the plane according to the observation, and gives up the cropped discrete point of need, is specially:
1) for a certain discrete point D on the viewing plane, from ray of this strokes and dots, make this ray through the center c of article one cutting edge;
2) calculate the intersection point of this ray and all projection cutting edges, and the nearest intersection point of recording distance point D, the cutting edge at this intersection point place is defined as crucial cutting edge e;
3) whether judging point D satisfies
If, then put D for needing cropped discrete points, cut-off point D, if not, retention point D then.
When the nearest intersection point of range points D was the common point of two projection cutting edges, other got a ray, made it pass through the wherein mid point of a cutting edge, and calculated the intersection point on itself and another limit, chose crucial cutting edge according to intersection point and the distance of some D.
Compared with prior art, the present invention has the following advantages:
(1) saves this complicated preprocessing process of increase sampled point, simplified whole modeling process;
(2) drawing process is that the part of doing in the Splatting of classics algorithm is improved, and whole drawing process is highly susceptible to realizing;
(3) the present invention is very good for processing various sharp edges effects.
Description of drawings
Fig. 1 is schematic flow sheet of the present invention;
The model of gear design sketch of Fig. 2 for adopting the inventive method to draw.
Embodiment
The present invention is described in detail below in conjunction with the drawings and specific embodiments.Present embodiment is implemented as prerequisite take technical solution of the present invention, provided detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.
Embodiment
As shown in Figure 1, a kind of with sharp features without the surface mesh method for drafting, the method may further comprise the steps:
The first step before drafting, adopts some limit mixture model to treat the surface of drawing object and carries out modeling;
In a limit mixture model, come the presentation surface point with P; And represent point on the limit in the sharp features with v, and be called edge point.Describedly be comprised of several smooth surfaces s without surface mesh, the regulation sharp features only appears between two or more adjacent smooth surfaces, for each smooth surface s, has
s＝{P
n，L
t}
Wherein, P
nBe the set of n surface point, n＞0 comprises the attribute of this point in each surface point, comprise the radius of the splat of a little position, normal vector, color value and this representative; L
tBe the set of t cut ring, t 〉=0.Each cut ring comprises the sequence of an edge point, these edge points is coupled together by this sequence, and connect it end to end, just can form the cut ring of a ring-type.Owing to stipulated that sharp features can only appear between two or more adjacent smooth surfaces before us, so these features can only be present in the model with annular form.Edge point in the cut ring is by counterclockwise tactic, and the opposite direction of the normal vector of namely putting surfacewise when sight line is seen over, and putting in order of edge point is counterclockwise.It is pointed out that in addition each smooth surface can not have cut ring, for example a smooth sphere; Cut ring more than one also can be arranged, and this situation occurs in the situation that the hole is arranged in the surface.In each cut ring, the line segment that connects any two edge point is called cutting line segment or cutting edge.
Described some limit mixture model PEM is defined as follows:
PEM＝{S
K，V
m}
Wherein, S
KExpression comprises the set of K smooth surface, S
K={ s
i| i=1 ..., K}, V
mSet for m edge point.
Second step carries out the surface point in the model and corresponding cutting edge related, and preserves association results.
Described surface point carries out related referring in each smooth surface with cutting edge, and the distance between reckoner millet cake and cutting edge realizes association, specifically describes to be:
Take the position of surface point as the centre of sphere, the radius of the splat that surface point is represented is the encirclement ball that radius is made each surface point, simultaneously cutting edge is got up with the encirclement bag, then make to surround the collision detection between ball, if a certain encirclement ball and a certain cutting edge intersect, then show relevant relation between them.
In the 3rd step, drawing process projected to all cutting edges in the model on the viewing plane from this step, formed the projection cutting edge.
The 4th step projected to surface points all in the model on the viewing plane, formed overlapped one by one ellipse.
The 5th step, utilize the cutting edge after the projection in the 3rd step, by the zigzag clipping algorithm ellipse that each is projected on the viewing plane is carried out cutting.
Described zig-zag type trimming algorithm is as follows:
Described zig-zag type trimming algorithm refers to have the ray of discrete point and cutting edge to judge whether this discrete point need be cropped on the plane according to the observation, and gives up the cropped discrete point of need, is specially:
1) for a certain discrete point D on the viewing plane, from ray of this strokes and dots, make this ray through the center c of article one cutting edge;
2) calculate the intersection point of this ray and all projection cutting edges, and the nearest intersection point of recording distance point D, the cutting edge at this intersection point place is defined as crucial cutting edge e;
3) whether judging point D satisfies
If, then put D for needing cropped discrete points, cut-off point D, if not, retention point D then.
It is pointed out that in addition which is crucial cutting edge then may to judge these two cutting edges when ray just in time passes through the common point of two cutting edges.Solution is to draw in addition a ray, makes it pass through the wherein mid point of a cutting edge, and calculates the intersection point on itself and another limit, sees which is exactly crucial cutting edge to which intersection point recently.
The false code of this trimming algorithm is as follows:
The 6th the step, after all surface vertices are projected on the viewing plane and have done correctly cutting, the pixel on the whole viewing plane is carried out normalization, obtain object to be drawn without surface mesh.
Adopt said method to create and draw a model of gear.This example is Pentuim IV2.67GHz at CPU, and video card is NVIDIA GT240, in save as 2.0GB, operating system is to realize in the computing machine of Window XPProfessional, the algorithm of whole modeling and rendering uses the c++ language compilation.Final drafting effect as shown in Figure 2.
Claims (8)
- One kind with sharp features without the surface mesh method for drafting, it is characterized in that the method may further comprise the steps:The first step adopts some limit mixture model to treat the surface of drawing object and carries out modeling;Second step carries out the surface point in the model and corresponding cutting edge related, and preserves association results;The 3rd step projected to cutting edges all in the model on the viewing plane, formed the projection cutting edge;The 4th step projected to surface points all in the model on the viewing plane, formed overlapped one by one ellipse;The 5th step, utilize the cutting edge after the projection in the 3rd step, by the zigzag clipping algorithm ellipse that each is projected on the viewing plane is carried out cutting;The 6th the step, after cutting is complete, the pixel on the whole viewing plane is carried out normalization, obtain object to be drawn without surface mesh.
- According to claim 1 a kind of with sharp features without the surface mesh method for drafting, it is characterized in that describedly be comprised of several smooth surfaces s without surface mesh, described sharp features only appears between two or more adjacent smooth surfaces, for each smooth surface s, haves＝{P n，L t}Wherein, P nBe the set of n surface point, n＞0 comprises the attribute of this point, L in each surface point tBe the set of t cut ring, t 〉=0, each cut ring comprises the sequence of an edge point, and in each cut ring, the line segment that connects any two edge point is called cutting edge.
- According to claim 2 a kind of with sharp features without the surface mesh method for drafting, it is characterized in that the attribute of described point comprises the radius of the splat of a little position, normal vector, color value and this representative.
- According to claim 2 a kind of with sharp features without the surface mesh method for drafting, it is characterized in that described some limit mixture model PEM is defined as follows:PEM＝{S K，V m}Wherein, S KExpression comprises the set of K smooth surface, V mSet for m edge point.
- According to claim 2 or 4 described a kind of with sharp features without the surface mesh method for drafting, it is characterized in that described edge point is the point on the limit in the sharp features.
- According to claim 3 a kind of with sharp features without the surface mesh method for drafting, it is characterized in that described surface point and cutting edge carry out relatedly referring in each smooth surface the distance between reckoner millet cake and cutting edge, realization is related, specifically describes to be:Take the position of surface point as the centre of sphere, the radius of the splat that surface point is represented is the encirclement ball that radius is made each surface point, simultaneously cutting edge is got up with the encirclement bag, then make to surround the collision detection between ball, if a certain encirclement ball and a certain cutting edge intersect, then show relevant relation between them.
- According to claim 1 a kind of with sharp features without the surface mesh method for drafting, it is characterized in that, described zig-zag type trimming algorithm refers to have the ray of discrete point and cutting edge to judge whether this discrete point need be cropped on the plane according to the observation, and give up the cropped discrete point of need, be specially:1) for a certain discrete point D on the viewing plane, from ray of this strokes and dots, make this ray through the center c of article one cutting edge;2) calculate the intersection point of this ray and all projection cutting edges, and the nearest intersection point of recording distance point D, the cutting edge at this intersection point place is defined as crucial cutting edge e;3) whether judging point D satisfiesIf, then put D for needing cropped discrete points, cut-off point D, if not, retention point D then.
- According to claim 7 a kind of with sharp features without the surface mesh method for drafting, it is characterized in that, when the nearest intersection point of range points D is the common point of two projection cutting edges, other gets a ray, make it pass through the wherein mid point of a cutting edge, and calculate the intersection point on itself and another limit, choose crucial cutting edge according to intersection point and the distance of some D.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111063015A (en) * | 2019-12-13 | 2020-04-24 | 重庆首厚智能科技研究院有限公司 | Method and system for efficiently drawing point locations |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101763649A (en) * | 2009-12-30 | 2010-06-30 | 北京航空航天大学 | Method for drawing enhanced model contour surface point |
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|---|---|---|---|---|
| CN101763649A (en) * | 2009-12-30 | 2010-06-30 | 北京航空航天大学 | Method for drawing enhanced model contour surface point |
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|---|
| HAITAO ZHANG等: "Point-and-edge model for edge-preserving splatting", 《THE VISUAL COMPUTER》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111063015A (en) * | 2019-12-13 | 2020-04-24 | 重庆首厚智能科技研究院有限公司 | Method and system for efficiently drawing point locations |
| CN111063015B (en) * | 2019-12-13 | 2023-07-21 | 重庆首厚智能科技研究院有限公司 | Method and system for efficiently drawing point positions |
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