CN103473811A - Convenient generation method of three-dimensional solid model based on two-dimensional freehand line drawing - Google Patents
Convenient generation method of three-dimensional solid model based on two-dimensional freehand line drawing Download PDFInfo
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Abstract
The invention provides a convenient generation method of a three-dimensional solid model based on a two-dimensional freehand line drawing. The convenient generation method comprises the following three steps: 1) artificially hand-drawing the parallel projection line drawing of a solid model needing to be reconstructed on a design board by a designer according to a predefined freehand line input rule, and then assigning some vertexes to form all plane information of a plane by the designer by using the two-dimensional freehand line drawing, and specifying an initial vertex as a cubic angle; 2) starting from the initial cubic angle, gradually recovering the three-dimensional coordinate information of all the vertexes according to the cubic angle theory based on the hypothesis that the two-dimensional line drawing is the parallel projection of the three-dimensional model; and 3) identifying all plants and curved surfaces on a three-dimensional solid according to the input information of the designer, performing gridding triangularization on a polygonal surface, a banding curved surface, a hollow internal cylindrical surface or a hollow polygonal surface on the model, respectively, and outputting the three-dimensional solid model. The invention provides the accurate generation method of a three-dimensional complex solid which is simple, convenient and quick to operate and rich in modeling.
Description
Technical field
Patent design of the present invention is drawn for the two-dimentional hand-drawing line of deviser's input, and a kind of method of the solid model of generating three-dimensional quickly and easily is provided.
Background technology
In field of computer aided design, the research of the two-dimentional hand-drawing line picture generating three-dimensional solid model correlation technique of inputting according to the deviser has obtained general attention.Before building a three-dimensional entity model, the deviser tends to the line drawing figure of two-dimensional projection that requirement artificial hand on the two-dimensional design plate on and function upper according to design is drawn solid model, and computing machine can reconstruct the target three-dimensional entity model directly and accurately according to the two-dimensional line picture.The research of such technology can make the mentality of designing convenient generation various solid models of deviser according to oneself, thereby breaks away from the complicated processes of the very professional 3 d modeling software of operation as softwares such as AutoCAD, and this respect research will be highly significant.
Existing three-dimensional entity model reconstruction technique can be divided into optimization method and method two classes based on the reconstruction of accurate two-dimensional line picture of based on non-accurate two-dimensional line, drawing and rebuilding.Two-dimensional line for user's input is drawn, method based on optimizing is mainly to solve the target three-dimensional model by building an objective function and objective function being carried out to optimization, this objective function can comprise the regularity requirement of some weightings, and these regularities require often, by exploring, geometrical constraint in two-dimentional Freehandhand-drawing figure builds.3D solid method for reconstructing based on optimizing is often more consuming time, and the searching of geometrical constraint and definition be a more professional and complicated problem, the result of reconstruction easily is subject to the impact that used geometrical constraint regularity and weighting factor thereof choose and causes inaccurate.
The method of rebuilding based on accurate two-dimensional line picture is using the projection on XOY plane as the target 3D solid of two-dimensional line picture.In other words, the summit x coordinate on two-dimensional line can being drawn and y coordinate reality are corresponding to x coordinate and the y coordinate on summit on 3D solid.If the subject matter that 3D solid is rebuild is exactly the z coordinate that recovers each summit.Existingly based on accurate two-dimensional line, draw and carry out the reconstruction of the method for 3D solid reconstruction mainly for the simple polyhedron object, the three-dimensional entity model type of reconstruction is single, is difficult to meet various actual demands.The present invention is mainly for the reconstruction of complex three-dimensional solid model, the two-dimensional line that deviser's input contains Freehandhand-drawing straight line and Freehandhand-drawing curve is drawn, method is the complicated solid model of generating three-dimensional quickly and easily, and these models can comprise polygon facet, banded curved surface, hollow inner cylinder or hollow polygon facet etc.
Summary of the invention
In order to overcome the deficiency that existing three-dimensional entity model complicated operation, the reconstructed results in generating is not accurate enough, rebuild the aspects such as the 3D solid profile simple types generated is single, the two-dimentional hand-drawing line of designing according to the deviser is drawn, and the invention provides a kind of accurate generation method of simple, convenient quick, 3 D complex entity that moulding is abundant.
The technical solution adopted for the present invention to solve the technical problems is:
The convenient generation method of three-dimensional entity model of drawing based on two-dimentional hand-drawing line comprises the following steps:
Step 1, the deviser is according to predefined Freehandhand-drawing lines input rule, and the requirement artificial hand on layout board according to design on upper and function is drawn the two-dimentional parallel projection line drawing figure of the solid model that needs reconstruction; Then utilize two-dimentional hand-drawing line to draw and specify all surface informations which summit to be formed a face by, and specify the initial vertax as cube corner;
Step 2, from initial cube corner, based on two-dimensional line, drawing is this hypothesis of parallel projection of three-dimensional model, according to the cube corner theory, progressively recovers the three-dimensional coordinate information on all summits;
Based on two-dimensional line, drawing is the hypothesis of three-dimensional entity model parallel projection, and the summit x coordinate on two-dimensional line can being drawn and y coordinate reality are corresponding to x coordinate and the y coordinate on summit on 3D solid, and what need recovery is only the z coordinate on each summit.Suppose that initial cube corner summit z coordinate is 0, utilize the cube corner theory can calculate the z coordinate on each summit as follows: the O that sets up an office is cube corner, suppose that a, b and c are respectively three space vector OA perpendicular to each other, OB of take that an O is starting point and the angle between OC, the z coordinate of summit A, B and C can obtain with following formula (1) so:
Cosa wherein, cosb, cosc ≠ 0; | OA|, | OB|, | OC| is respectively vectorial OA, OB, the length of OC; z
o, z
a, z
b, z
cbe respectively the z coordinate of an O and some A, B and C;
For the plane in three dimensions, can uniquely determine a plane at known 3, its equation can be expressed as: Ax+By+Cz+D=0; If the x coordinate of any and y coordinate on known this plane, can be as follows in the hope of third dimension z coordinate: z=-(D+Ax+By)/C, C ≠ 0.Utilize the method can recover the summit z coordinate of known x coordinate and y coordinate on all known planes;
The curved surface situation formed for Freehandhand-drawing curve lines, method utilizes the second order B-spline curves to be similar to the Freehandhand-drawing curve, difference intensive sampling series of discrete sampling summit on the second order B-spline curves, and carry out discrete trigonometric ratio to curved surface, thereby can utilize said method to recover the third dimension z coordinate on discrete summit;
Step 3, input message according to the deviser, identify all planes and curved surface on 3D solid, respectively the polygon facet on model, banded curved surface, hollow inner cylinder or hollow polygon facet are carried out to mesh triangles by connecting successively the neighbouring sample summit, and the output three-dimensional entity model.
Further, the described Freehandhand-drawing lines of step 1 input rule is:
Rule one: straight line represents the limit on plane;
Rule two: curve represents the curved boundaries of curved surface;
Rule three: the straight dashed line representative is positioned at the polygonal limit of hollow of a face inside, and the dashed curve representative is positioned at the hole of a face inside;
Rule four: generate connecting line, which face connecting line can be positioned at by the apprizing system hole, or informs that two hole formation cylinders;
In step 3 according to deviser's input message, identify all planes and curved surface on 3D solid, as the polygon facet on model, banded curved surface, hollow inner cylinder or hollow polygon facet carry out mesh triangles by connecting successively the neighbouring sample summit, concrete identification and method for reconstructing are:
(a) identification of banded curved surface and reconstruction: a given face, if this face meets: a1) formed by four summits, two straight flanges and two bent limits; A2) four summits are not shared by two bent limits; This face is actually a banded face so, will complete the reconstruction of this face after its trigonometric ratio;
(b) may comprise identification and the reconstruction of the space plane polygon facet of lagoon island: b1) check and if having bent limit between two adjacent vertexs, so the approximate vertex sequence on this song limit is inserted into to two positions between summit by the vertex sequence that forms this plane; B2) search for all connecting lines and find all holes that are attached thereto, the lagoon island using these holes as this plane polygon; Can obtain a space plane polygon that may comprise lagoon island through these two steps, will complete the reconstruction of this face after its trigonometric ratio;
(c) identification and the reconstruction of hollow inner cylinder and hollow polygon facet: for any connecting line, if it is connecting two holes, interior curved surface of column of the actual formation of these two holes, will complete the reconstruction of this face after its trigonometric ratio so.
Technical conceive of the present invention is: in theories of vision, so-called cube corner refers to three structures that ray perpendicular to each other forms of being launched by a summit in three dimensions.Utilize the cube corner theory, and the coordinate on known cube corner summit, can recover the apex coordinate adjacent with cube corner, and then progressively recover all apex coordinates.Some input rules of drawing according to predefined two-dimentional hand-drawing line, method can identify the elements such as the plane that forms object module and curved surface fast, and the apex coordinate generating three-dimensional solid model recovered according to it.This patent provides a kind of convenient generation method of three-dimensional entity model of drawing based on two-dimentional hand-drawing line.
Beneficial effect of the present invention is mainly manifested in: simple, convenient quick, moulding abundant.
The accompanying drawing explanation
Fig. 1 is that the user inputs two-dimentional hand-drawing line picture example;
Fig. 2 is the 3D solid reconstructed results that the two-dimensional line of 1 input is with reference to the accompanying drawings drawn;
Fig. 3 is the cube corner exemplary plot;
Fig. 4 is patch Triangulation Algorithm exemplary plot;
Fig. 5 a is that the two-dimentional hand-drawing line that the user inputs is drawn;
Fig. 5 b, Fig. 5 c are the three-dimensional entity model design sketchs of Fig. 5 a.
Fig. 6 a is that the two-dimentional hand-drawing line that the user inputs is drawn;
Fig. 6 b, Fig. 6 c are the three-dimensional entity model design sketchs of Fig. 6 a.
Embodiment
Various 3D solid effects below in conjunction with accompanying drawing to technical method of the present invention and generation are further described and describe in detail.
With reference to accompanying drawing 1---accompanying drawing 6, the convenient generation method of 3D solid of drawing based on two-dimentional hand-drawing line, described method comprises following three steps:
1) deviser is according to predefined Freehandhand-drawing lines input rule, and the requirement artificial hand on layout board according to design on upper and function is drawn the parallel projection line drawing figure of the solid model that needs reconstruction.The Freehandhand-drawing lines input rule of definition is as follows:
Rule one: straight line represents the limit on plane.Article one, limit can be shared by two faces, as the straight line AB in accompanying drawing 1 and straight line AD etc.
Rule two: curve represents the curved boundaries of curved surface.As the bent limit C~D in accompanying drawing 1.
Rule three: the straight dashed line representative is positioned at the polygonal limit of hollow of a face inside, and the dashed curve representative is positioned at the hole of a face inside.As the polygon F in accompanying drawing 1, it is positioned at face ABC~DA inside, and the zone that it surrounds so will form the hollow polygon in face ABC~DA, as the F in the reconstruction effect in accompanying drawing 2.As the E~E in accompanying drawing 1, the hole of a hollow will be formed.
Rule four: generate connecting line.Which face connecting line can be positioned at by the apprizing system hole, or informs that two hole formation cylinders.As connecting line EA, EB in accompanying drawing 1 and EC mean that hole E is positioned at face ABC~DA inside, connecting line FA, FC and FD mean that polygon hole F is positioned at face ABC~DA inside; And connecting line EE ' means that hole E and hole E ' form an inner cylinder (as the E in accompanying drawing 2), connect FF ' and mean that inner polygon hole F and inner polygon hole F ' form polygon cylinder (as the F in accompanying drawing 2).
According to above input rule, the deviser can draw the two-dimentional parallel projection line drawing figure of solid model according to designing requirement and functional requirement at two-dimentional painting canvas left-hand seat, then which some the deviser need to specify form a face, these information will be as the initial information of identification special surface that object module comprises, and to specify which summit be initial cube corner.
2), from initial cube corner, according to the cube corner theory, progressively recover the three-dimensional coordinate information on all summits.Based on two-dimensional line, drawing is the hypothesis of three-dimensional entity model parallel projection, and the summit x coordinate on two-dimensional line can being drawn and y coordinate reality are corresponding to x coordinate and the y coordinate on summit on 3D solid, thereby the needs recovery is only the z coordinate on each summit.Suppose that initial cube corner summit z coordinate is 0, utilize the cube corner theory can calculate the z coordinate on each summit as follows:
As accompanying drawing 3 is cubical parallel projection figure, its mid point O is cube corner, and cube corner normally forms by sharing three of starting point limit perpendicular to each other in space.According to the cube corner theory, can set up the two-dimentional vertical parallel projection of cube corner and the relation of its three-dimensional structure.In accompanying drawing 3, the x coordinate on each summit and y coordinate can conveniently obtain from line drawing figure, and what need recovery is its third dimension z coordinate.Suppose that a, b and c are the angles between vectorial OA, OB and OC in figure, the z coordinate of summit A, B and C can obtain with following formula (1) so:
Cosa wherein, cosb, cosc ≠ 0; | OA|, | OB|, | OC| is respectively vectorial OA, OB, the length of OC; z
o, z
a, z
b, z
cbe respectively the z coordinate of an O and some A, B and C.
For the plane in three dimensions, can uniquely determine a plane at known 3, its equation can be expressed as: Ax+By+Cz+D=0.If the x coordinate of any and y coordinate on known this plane, can be as follows in the hope of third dimension z coordinate: z=-(D+Ax+By)/C, C ≠ 0.Utilize the method can recover the summit z coordinate of known x coordinate and y coordinate on all known planes.The accompanying drawing 1 of below take is illustrated as example, suppose that it is 0 as the z coordinate of cube corner postulated point A that the user has selected summit A, according to formula (1), can calculate and recover the coordinate of summit A ', B and D, and then can determine the equation of plane ABCD, plane ABB ' A ' and plane ADD ' A ', utilize the equation of plane ABCD can calculate and recover the coordinate of summit C, in like manner summit B ' and summit D ' also can be resumed, and the recovery on these summits can, so that plane A ' B ' C ' D ' equation is determined, finally can recover summit C '.So far the coordinate on all summits can be determined.
It is to be noted, the curved surface situation formed for Freehandhand-drawing curve lines, method utilizes the second order B-spline curves to be similar to the Freehandhand-drawing curve, difference intensive sampling series of discrete sampling summit on B-spline curves, and carry out discrete trigonometric ratio to curved surface, thereby utilize said method to recover the third dimension z coordinate on discrete summit.Patch Triangulation Algorithm wherein adopts the method that connects successively as shown in Figure 4 the neighbouring sample summit to form gore.3) according to deviser's input message, identify all planes and curved surface on 3D solid, respectively the polygon facet on model, banded curved surface, hollow inner cylinder or hollow polygon facet are carried out to mesh triangles by connecting successively the neighbouring sample summit, and the output three-dimensional entity model.
After utilizing the cube corner theory to recover the coordinate on all summits of 3D solid, method also needs each face according to the further reconstruction of three-dimensional solid model of deviser's input message, and its identification and method for reconstructing are as follows:
(a) identification of banded curved surface and reconstruction: a given face, if this face meets: a1) formed by four summits, two straight flanges and two bent limits; A2) four summits are not shared by two bent limits.This face is actually a banded face so, and by its trigonometric ratio.As accompanying drawing 1, below initial situation, to be treated as be a plane to DCC ' D ', but it meets above-mentioned two conditions, by four summits, formed, article two, straight flange CC ' and DD ', article two, bent limit C~D is being connected on these four summits and is not sharing summit with C '~D ', and face DCC ' D ' is considered to a banded face D~CC '~D ' D so, and it is rebuild effect and sees accompanying drawing 2.
(b) may comprise identification and the reconstruction of the space plane polygon facet of lagoon island: b1) check and if having bent limit between two adjacent vertexs, so the approximate vertex sequence on this song limit is inserted into to two positions between summit by the vertex sequence that forms this plane; B2) search for all connecting lines and find all holes that are attached thereto, the lagoon island using these holes as this plane polygon.Can obtain a space plane polygon that may comprise lagoon island through this two step, will complete the reconstruction of this face after its trigonometric ratio.As accompanying drawing 1, plane ABB ' A ', do not have bent limit between summit, do not have lagoon island yet, and it is regarded common space plane polygon so.There is bent limit in plane ABCD between summit C and D, so the approximate vertex sequence on this song limit is inserted between C and D, becomes plane ABC~D; Further, by connecting line EA, EB and the known hole E of EC, be positioned at this internal plane, by connecting line FA, FC and the known polygon F of FD, be positioned at this internal plane, hole E and F will be as the lagoon islands of plane ABC~D so.
(c) identification and the reconstruction of hollow inner cylinder and hollow polygon facet: for any connecting line, if it is connecting two holes, interior curved surface of column of the actual formation of these two holes so, method is carried out trigonometric ratio by it.In accompanying drawing 1, connecting line EE ' is connecting hole E and E ', interior curved surface of column of they actual formations so, and it rebuilds effect as shown in the hollow inner cylinder E in accompanying drawing 2.If connecting line is connecting two inner polygons, polygon inner cylinder of they actual formation so.In accompanying drawing 1, connecting line FF ' is connecting polygon F and polygon F ', and these two polygons lay respectively at plane ABC~D and A ' B ' C '~D ' inside, these two polygons are actual has so formed a hollow polygon facet, and it rebuilds effect as shown in the F in accompanying drawing 2.
Utilize the result of above-mentioned identification and reconstruction, the method is reconstruction of three-dimensional entity object module in accordance with the following steps: 1) travel through each face, by method (a), judge and rebuild this face; If do not meet (a) use method (b) to be processed.2) retrieve each connecting line, by method (c), judged whether to exist hollow inner cylinder and hollow polygon facet, if exist, by its trigonometric ratio, finally complete reconstruction and the generation of target three-dimensional entity model.
Accompanying drawing 5 is the complex parts effects of according to two-dimensional line, drawing and rebuilding, accompanying drawing 5 (a) is that the two-dimentional hand-drawing line that the user inputs is drawn, and accompanying drawing 5 (b) and accompanying drawing 5 (c) are respectively to observe the three-dimensional entity model result of utilizing two-dimensional line to draw and rebuild under different observation visual angles; Accompanying drawing 6 is the complicated entity effects of according to two-dimensional line, drawing and rebuilding, accompanying drawing 6 (a) is that the two-dimentional hand-drawing line that the user inputs is drawn, and accompanying drawing 6 (b) and accompanying drawing 6 (c) are respectively to observe the three-dimensional entity model result of utilizing two-dimensional line to draw and rebuild under different observation visual angles.
Claims (2)
1. the convenient generation method of three-dimensional entity model of drawing based on two-dimentional hand-drawing line comprises the following steps:
Step 1, the deviser is according to predefined Freehandhand-drawing lines input rule, and the requirement artificial hand on layout board according to design on upper and function is drawn the two-dimentional parallel projection line drawing figure of the solid model that needs reconstruction; Then utilize two-dimentional hand-drawing line to draw and specify all surface informations which summit to be formed a face by, and specify the initial vertax as cube corner;
Step 2, from initial cube corner, based on two-dimensional line, drawing is this hypothesis of parallel projection of three-dimensional model, according to the cube corner theory, progressively recovers the three-dimensional coordinate information on all summits;
Based on two-dimensional line, drawing is the hypothesis of three-dimensional entity model parallel projection, and the summit x coordinate on two-dimensional line can being drawn and y coordinate reality are corresponding to x coordinate and the y coordinate on summit on 3D solid, and what need recovery is only the z coordinate on each summit.Suppose that initial cube corner summit z coordinate is 0, utilize the cube corner theory can calculate the z coordinate on each summit as follows: the O that sets up an office is cube corner, suppose that a, b and c are respectively three space vector OA perpendicular to each other, OB of take that an O is starting point and the angle between OC, the z coordinate of summit A, B and C can obtain with following formula (1) so:
Cosa wherein, cosb, cosc ≠ 0; | OA|, | OB|, | OC| is respectively vectorial OA, OB, the length of OC; z
o, z
a, z
b, z
cbe respectively the z coordinate of an O and some A, B and C;
For the plane in three dimensions, can uniquely determine a plane at known 3, its equation can be expressed as: Ax+By+Cz+D=0; If the x coordinate of any and y coordinate on known this plane, can be as follows in the hope of third dimension z coordinate: z=-(D+Ax+By)/C, C ≠ 0.Utilize the method can recover the summit z coordinate of known x coordinate and y coordinate on all known planes;
The curved surface situation formed for Freehandhand-drawing curve lines, method utilizes the second order B-spline curves to be similar to the Freehandhand-drawing curve, difference intensive sampling series of discrete sampling summit on the second order B-spline curves, and carry out discrete trigonometric ratio to curved surface, thereby can utilize said method to recover the third dimension z coordinate on discrete summit;
Step 3, input message according to the deviser, identify all planes and curved surface on 3D solid, respectively the polygon facet on model, banded curved surface, hollow inner cylinder or hollow polygon facet are carried out to mesh triangles by connecting successively the neighbouring sample summit, and the output three-dimensional entity model.
2. the convenient generation method of three-dimensional entity model of drawing based on two-dimentional hand-drawing line as claimed in claim 1 is characterized in that:
The described Freehandhand-drawing lines of step 1 input rule is:
Rule one: straight line represents the limit on plane;
Rule two: curve represents the curved boundaries of curved surface;
Rule three: the straight dashed line representative is positioned at the polygonal limit of hollow of a face inside, and the dashed curve representative is positioned at the hole of a face inside;
Rule four: generate connecting line, which face connecting line can be positioned at by the apprizing system hole, or informs that two hole formation cylinders;
In step 3 according to deviser's input message, identify all planes and curved surface on 3D solid, as the polygon facet on model, banded curved surface, hollow inner cylinder or hollow polygon facet carry out mesh triangles by connecting successively the neighbouring sample summit, concrete identification and method for reconstructing are;
(a) identification of banded curved surface and reconstruction: a given face, if this face meets: a1) formed by four summits, two straight flanges and two bent limits; A2) four summits are not shared by two bent limits; This face is actually a banded face so, will complete the reconstruction of this face after its trigonometric ratio;
(b) may comprise identification and the reconstruction of the space plane polygon facet of lagoon island: b1) check and if having bent limit between two adjacent vertexs, so the approximate vertex sequence on this song limit is inserted into to two positions between summit by the vertex sequence that forms this plane; B2) search for all connecting lines and find all holes that are attached thereto, the lagoon island using these holes as this plane polygon; Can obtain a space plane polygon that may comprise lagoon island through these two steps, will complete the reconstruction of this face after its trigonometric ratio;
(c) identification and the reconstruction of hollow inner cylinder and hollow polygon facet: for any connecting line, if it is connecting two holes, interior curved surface of column of the actual formation of these two holes, will complete the reconstruction of this face after its trigonometric ratio so.
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CN104143209A (en) * | 2014-06-20 | 2014-11-12 | 浙江工业大学 | Method for engraving three-dimensional model based on line pattern |
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CN104143211A (en) * | 2014-06-20 | 2014-11-12 | 浙江工业大学 | Method for generating three-dimensional free body based on one image |
CN110714259A (en) * | 2019-11-04 | 2020-01-21 | 南京航空航天大学 | Method for simulating layering yarn path of woven ceramic matrix composite preform |
CN110714259B (en) * | 2019-11-04 | 2020-06-30 | 南京航空航天大学 | Method for simulating layering yarn path of woven ceramic matrix composite preform |
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