KR20110072462A - Modeling method and system for sketching 3d curved surface model, and program recording medium - Google Patents

Abstract

PURPOSE: A modeling method and system for a 3D curved model sketch, and a recording medium are provided to smoothly connect a generated curved surface. CONSTITUTION: Using an input device, a closed loop is created(S110). A vector generator obtains the normal vector of each vertex on the closed loop(S120). In case the normal vector on the each vertex accords, an interpolation unit interpolates with sample point values and normal vectors on one or more curved lines(S130,S150). A tessellation unit tessellates a generated curved surface(S160).

Description

MODELING METHOD AND SYSTEM FOR SKETCHING 3D CURVED SURFACE MODEL, AND PROGRAM RECORDING MEDIUM

The present invention relates to a modeling method and system for a three-dimensional model sketch, and a recording medium, and more particularly to a modeling method and system for a three-dimensional model sketch using a closed loop, and a recording medium for recording the method will be.

It is important for the 3D models used in the virtual world, mirror world, etc. to help users express the concepts they think, rather than mathematically accurate modeling.

Conventional surface modeling mainly uses non-uniform Rational B-Spline (NURBS) or subdivision surface (NURBS), one of the parametric modeling techniques.

However, a concept modeling tool that requires an easy user interface has the disadvantage of having an interface that is too complex for the user to manipulate / present. In particular, parametric modeling techniques extract curves first and then from curves. There is a difficulty, and in the case of a nongs surface, the quality of the generated surface varies considerably according to the degree of freedom of the surface (that is, the number of control points). Therefore, the user must adjust these variables to determine the quality of the surface There is difficulty.

The goal of concept modeling is to make three-dimensional modeling tools as easy as using word processors, with a focus on expression rather than accuracy. Therefore, easy surface representation and modeling techniques are becoming more and more important.

An object of the present invention is to provide a user with an easy interface and to smoothly connect the generated surface by sketching a three-dimensional model through an algorithm using at least one closed loop.

According to an aspect of the present invention, there is provided a modeling method for sketching a 3D surface model, the method comprising: generating at least one closed loop including a plurality of vertices on a three-dimensional surface and a plurality of curves passing through the vertices using an input device; At each of the vertices, generating a normal vector by interpolating a tangent vector of two curves passing through each of the vertices; Checking whether each of the normal vectors corresponds to a preset correction criterion, and if not, correcting the normal vectors; Generating a curved surface of the at least one closed loop using a radial basis function interpolation using the sampled points on the at least one closed loop and each of the normal vectors; And tessellating the generated curved surface.

The correction criteria may include a criterion for determining whether the inner product of the first normal vector and the second normal vector among the normal vectors is smaller than zero, and the correcting includes the normal vectors of each of the vertices. Rotation is performed along the curve passing through each of the vertices to determine whether it corresponds to the correction criteria, and the rotation correction of the direction of the second normal vector reversely according to a preset angle.

The generating of the at least one closed loop may include: a first selecting step of selecting a reference vertex and a reference curve passing through the reference vertex among the vertices; A second selection step of selecting a first curve closest to the counterclockwise rotation direction of the reference curve based on the reference vertex; A third selection step of selecting a second curve closest to a clockwise rotation direction of the reference curve with respect to a vertex other than the reference vertex of the reference curve; And setting the first curve or the second curve back to the reference curve, and repeating the second selection step and the third selection step until the selected curves form a closed loop.

The generating of the closed loop may include measuring the angle of the counterclockwise rotation or the clockwise rotation at the vertex of the at least one closed loop, and the number of angles of 180 degrees or more is 180 degrees or less. Removing more than the number of closed loops.

이고, (

는 상기 적어도 하나의 폐루프상의 샘플링된 포인트들의 3차원 좌표,

는 1차 아핀(affine) 함수,

는 실수 계수) 상기 곡면을 생성하는 단계는 각각의 상기 법선 벡터를 이용하여 상기 폐루프 외부의 적어도 하나의 포인트를 생 성하는 단계; 및 상기 래디얼 베이시스 함수, 상기 적어도 하나의 폐루프상의 샘플링된 포인트 및 상기 폐루프 외부의 적어도 하나의 포인트를 이용하여 상기

및 상기

의 계수를 구하고, 상기

이 되는 3차원 공간상의 포인트를 이용하여 곡면을 생성하는 단계를 포함할 수 있다.In addition, the radial basis function is

ego, (

Is a three-dimensional coordinate of the sampled points on the at least one closed loop,

Is the first affine function,

Generating a curved surface may include generating at least one point outside the closed loop using each of the normal vectors; And using the radial basis function, sampled points on the at least one closed loop, and at least one point outside the closed loop.

And said

Find the coefficient of, and

It may include the step of generating a curved surface using the point on the three-dimensional space.

In addition, a modeling method for sketching a 3D surface model is a step after generating a curved surface by performing a radial basis function interpolation, and includes at least one partition curve for partitioning the at least one closed loop. The method may further include generating a deformation surface by radially basis function interpolating the plurality of closed loops generated in the same manner as the at least one closed loop.

In addition, the curve may further include a similar curve consisting of a plurality of straight lines and vertices that are visually curved to the user.

In addition, the tessellation may include performing tessellation from three reference points on the curved surface.

In addition, the tessellation may include performing tessellation from one reference point on the curve and the curved surface.

In addition, a modeling system for sketching a three-dimensional surface model for solving the technical problem is an input device for generating a closed loop consisting of a plurality of vertices and a plurality of curves passing through the vertices in three dimensions; At each of the vertices, a vector generator for generating a normal vector on a three-dimensional cross-section of a tangent vector of two curves passing through each of the vertices; A correction unit for checking whether each of the normal vectors corresponds to a preset correction criterion, and correcting the normal vectors if not applicable; An interpolation unit configured to generate a curved surface of the at least one closed loop by performing a radial basis function interpolation using the sampled points on the at least one closed loop and each of the normal vectors; And a tessellation unit for tessellating the generated curved surface.

According to the present invention, by sketching a 3D model through an algorithm using at least one closed loop, it is possible to provide an easy interface to the user and to smoothly connect the generated curved surfaces.

Specific structural to functional descriptions of the embodiments of the present invention disclosed in the specification or the application are only illustrated for the purpose of describing the embodiments according to the present invention, and the embodiments according to the present invention may be embodied in various forms. It should not be construed as limited to the embodiments described in this specification or the application.

Since the embodiments according to the present invention can be variously modified and have various forms, specific embodiments will be illustrated in the drawings and described in detail in the present specification or application. However, this is not intended to limit the embodiments in accordance with the concept of the present invention to a particular disclosed form, it should be understood to include all changes, equivalents, and substitutes included in the spirit and scope of the present invention.

Terms such as first and / or second may be used to describe various components, but the components should not be limited by the terms. The terms are used only for the purpose of distinguishing one component from another, for example, without departing from the scope of rights in accordance with the inventive concept, and the first component may be called a second component and similarly The second component may also be referred to as the first component.

When a component is referred to as being "connected" or "connected" to another component, it may be directly connected to or connected to that other component, but it may be understood that other components may be present in between. Should be. On the other hand, when a component is said to be "directly connected" or "directly connected" to another component, it should be understood that there is no other component in between. Other expressions describing the relationship between components, such as "between" and "immediately between," or "neighboring to," and "directly neighboring to" should be interpreted as well.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. Singular expressions include plural expressions unless the context clearly indicates otherwise. As used herein, the terms "comprise" or "have" are intended to indicate that there is a feature, number, step, action, component, part, or combination thereof that is described, and that one or more other features It should be understood that it does not exclude in advance the possibility of the presence or addition of numbers, steps, operations, components, parts or combinations thereof.

Unless defined otherwise, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art. Terms such as those defined in the commonly used dictionaries should be construed as having meanings consistent with the meanings in the context of the related art, and are not construed in ideal or excessively formal meanings unless expressly defined herein. Do not.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. Like reference numerals in the drawings denote like elements.

1 is a diagram illustrating a modeling system 10 for sketching a 3D surface model according to an exemplary embodiment of the present invention. The modeling system 10 includes an input device 100, a vector generator 200, a corrector 300, an interpolation unit 400, and a tessellation unit 500.

The user may generate a closed loop including vertices and curves in three dimensions by using the input device 100. In this case, the input device 100 may include a mouse, a cursor, and a stylus.

The vector generator 200 may generate a tangential vector and a normal vector on each of the vertices, and the correction unit 300 may determine a reference (eg, any one) of the normal vector on each of the vertices. If the normal vector at the vertex is rotated along the closed loop and reaches another vertex, the normal vector can be corrected if it does not correspond to the normal vector at the other vertex).

The interpolation unit 400 may generate a curved surface by extracting a part of the closed loop and performing a radial basis function interpolation using the corrected normal vector and the sample point value of the closed loop.

The tessellation unit 500 may tessellate the curved surface generated by the interpolation unit 400.

2 is a flowchart illustrating a modeling method for sketching a 3D surface model according to an exemplary embodiment of the present invention. The modeling method for sketching the 3D curved model may be performed by the modeling system 10 of FIG. 1.

Referring to FIG. 2, a closed loop including at least one vertex and at least one curve in three dimensions is generated by the input device 100 (S110). In this case, the at least one curve may further include a similar curve composed of a plurality of straight lines and vertices, which are visually curved to the user.

Next, a normal vector at each vertex on the closed loop is obtained (S120).

Next, when the normal vector at one vertex rotates along the closed loop and reaches another vertex, it is determined whether or not it coincides with the normal vector at the other vertex (S130), and if it does not coincide with each other, it is corrected to match each other. (S140).

Next, an interpolation is performed using the sample point value and the normal vector on the at least one curve to generate a curved surface (S150). The interpolation may include radial basis function interpolation.

Next, the generated curved surface is tessellated (S160).

3 to 8 are diagrams illustrating an example for describing in detail a modeling method for sketching a 3D curved model of FIG. 2.

Referring to FIG. 3, a closed loop having a curve passing through at least one vertex P1 to P4 and the at least one vertex P1 to P4 is generated by the input device 100. In this case, the closed loop further includes a closed loop composed of at least one vertex and a straight line passing through the at least one vertex (however, the closed loop visually curved). In FIG. 3, the closed loops are illustrated as four vertices P1 to P4 and curves passing through them for convenience, but the scope of the present invention is not limited thereto and may include more vertices and curves.

Referring to FIG. 4, in order to generate a normal vector at the at least one vertex P1 to P4, three-dimensional tangent vectors T1 and T2 of two curves L1 and L2 passing through each vertex (eg, P1). ).

The normal vectors N1 to N4 at the at least one vertex P1 to P4 may be generated by cross-producting the generated tangent vectors T1 and T2.

Referring to FIG. 5, when the generated normal vectors N1 to N4 rotate a predetermined vector (eg, a normal vector at one vertex along a closed loop and reach another vertex), If it does not correspond to the normal vector) and if it does not correspond to the correction can be corrected.

For example, when the normal vector N1 at one vertex P1 is rotated three-dimensionally according to the curve A passing through the vertex P1 and reaches the other vertex P2, the vertex P1 is normal. It is determined whether the vector N1 and the normal vector N2 of the other vertex P2 coincide with each other.

In this case, since the normal vector N1 and the normal vector N2 coincide, the correction is not performed. In this case, the criterion for determining that the normal vector N1 and the normal vector N2 coincide is not only when the two vectors match perfectly, but also a preset reference (for example, the normal vector N1 and the normal vector N2). ) Can be considered a match, depending on whether the dot product of the) is less than zero).

Further, when the normal vector N1 at any one vertex P1 is rotated three-dimensionally according to the curve B passing through the vertex P1 and reaches another vertex P4, the normal of the vertex P1 is reached. It is determined whether the vector N1 and the normal vector N4 of the other vertex P4 coincide with each other.

In this case, since the normal vector N1 and the normal vector N4 do not match, a corrected normal vector N4 'is generated by correcting the normal vector N4. In this case, the correction of the normal vector N4 includes a case in which the direction of the normal vector N4 is rotated in a reverse direction according to a preset angle to generate a correction normal vector N4 ', but the scope of the present invention is It is not limited.

It may be assumed that all of the above processes are performed on the at least one vertex P1 to P4, and when the execution is completed, all the normal vectors N1 to N4 coincide.

Referring to FIG. 6, some of the at least one closed loop may be extracted (eg, two closed loops of the three closed loops).

Specifically, any curve L1 passing through any one vertex P1 is selected as a reference curve, and the other curve closest to the counterclockwise rotation direction of the curve L1 around the vertex P1 ( L2).

Further, another curve L3 closest to the clockwise direction of the curve L1 is selected about the other vertex P2 of the curve L1. If the closed loop is not formed, other curves L2 or L3 except for the curve L1 are again selected as the reference curve, and the above process is repeated until the closed loop 61 is formed.

By repeating the above process, at least one closed loop (61, 62 of FIG. 6 and 63 of FIG. 7) may be formed.

Once at least one closed loop (61, 62 in FIG. 6 and 63 in FIG. 7) is formed, a portion of the at least one closed loop is extracted according to the closed loop extraction criteria. In this case, the closed loop extraction reference measures an angle in the counterclockwise rotation direction and the clockwise rotation direction of the at least one closed loop formed, and the number of closed loops is greater than the number of angles of 180 degrees or more. A reference to extract (or a reference to remove more closed loops than the number of angles of 180 degrees or more) is included.

7 is a diagram illustrating a closed loop 63 removed according to the closed loop extraction criteria. The closed loop 63 selects one curve L3 passing through the vertex P3 as a reference curve, and the other curve closest to the counterclockwise rotation direction of the curve L3 around the vertex P3 ( L4).

Also, another curve L1 closest to the clockwise direction of the curve L3 is selected about the other vertex P2 of the curve L3. If the closed loop is not formed, other curves L1 or L4 except the curve L3 may be selected as the reference curve again, and the above process may be repeated to form the closed loop 63.

In this case, the closed loop 63 represents an angle of 180 degrees or more at three vertices P1, P3, and P4, and an angle of 180 degrees or less at one vertex P2. Since the number (three) of angles 180 degrees or more is larger than the number (1) of angles 180 degrees or less, the closed loop 63 is removed.

8 shows sampled points 81 on the closed loops 61 and 62. The points 81 are sampled on the closed loops 61 and 62, and a radial basis function interpolation is performed using the sampled points 81 and the normal vectors N1 to N4 to generate a curved surface.

는 이하 수학식 1과 같다.Radial Basis Function

Equation 1 is as follows.

는 상기 적어도 하나의 폐루프(61 및 62)상의 샘플링된 포인트(81)의 3차원 좌표에 해당하고,

는 1차 아핀(affine) 함수에 해당하며,

는 실수 계수에 해당한다.here,

Corresponds to the three-dimensional coordinates of the sampled point 81 on the at least one closed loop 61 and 62,

Corresponds to the first-order affine function,

Corresponds to the real coefficient.

및 상기

의 계수를 구하고, 상기

이 되는 3차원 공간상의 포인트들을 이용하여 곡면을 생성할 수 있다.Each of the normal vectors N1 to N4 can be used to obtain at least one point outside the closed loops 61 and 62, and sampled on the radial basis function, at least one closed loop 61 and 62. The point 81 and at least one point (not shown) outside the closed loop

And said

Find the coefficient of, and

The curved surface may be generated using the points in the 3D space.

FIG. 9 illustrates an embodiment in which a modeling method for sketching a 3D surface model of FIG. 2 is implemented using the modeling system 10 for sketching a 3D surface model of FIG. 1.

Referring to FIG. 9, a curve 91 is drawn using the input device 100, and if a closed loop is not configured, a curve is added to configure at least one closed loop (92).

When the at least one closed loop is configured, the closed loop for generating the curved surface may be selected (93), and the radial basis interpolation may be performed to generate the curved surface (94).

In addition, after adding at least one curve for partitioning the closed loop according to the shape of the desired surface (95), the radial basis interpolation may be performed again to generate a deformation surface (96).

FIG. 10 is a diagram illustrating a result of tessellation of the curved surface generated in FIG. 8. The generated curved surface may be subjected to tessellation using a predetermined tessellation method.

11 to 14 are diagrams for describing an example of the predetermined tessellation method. 11 to 14, the plurality of straight lines of the curves constituting the closed loops 61 and 62 (eg, similar curves which are visually curved to the user by being composed of a plurality of straight lines and vertices). Register the first list of (S10).

Next, any one straight line SL1 of the first list is selected, and the surface normal vector N5 of the generated curved surface is obtained from the midpoint M of the straight line (S20).

)에서 상기 직선(SL1)에 수직인 방향으로 일정거리 떨어진 포인트(Q1)를 구하고(S30), 상기 포인트(Q1)에서 상기 곡면상으로 가장 가까운 포인트(Q2)를 구한다(S40).Next, an imaginary plane composed of the midpoint M and the surface normal vector N5 (

In step S30, a point Q1 spaced apart in a direction perpendicular to the straight line SL1 is obtained (S30), and the point Q2 nearest to the curved surface is obtained from the point Q1 (S40).

Among the other straight lines included in the first list and not through the processes S20 to S40, the internal circumference SP_1 is circumscribed by a triangle TRI_1 including the straight line SL1 and the point Q2. If the dot product of the normal vector at the vertices of the straight lines SL2 and SL3 (except for the vertices overlapping the vertices of the straight line SL1) and the surface normal vector at the midpoint M is greater than zero (i.e. The second list by sorting the vertices P5 and P6 in ascending order according to the distances D1 and D2 between the vertices of the straight lines SL2 and SL3 and the midpoint M. Register (S50).

It is determined whether the second list is empty (S60), and if the second list is empty (not shown), tessellation is performed using a triangle TRI_1 composed of the straight line SL1 and the point Q2. Add to the result (S65). Next, except for the straight line SL1 from the first list, other straight lines SL4 and SL5 constituting the triangle TRI_1 excluding the straight line SL1 are added to the first list (S70). ).

If the second list is not empty (in the case of FIG. 13), the external opening SP_2 circumscribes a triangle TRI_2 composed of the straight line SL1 and the vertex P5 at the shortest distance on the second list. In operation S81, a vertex of the straight lines of the first list is not included in the circumferential opening SP_2.

When the test passes, the triangle TRI_2 is a forward condition (e.g., the cross product of the surface normal vector and the straight line SL1 at the midpoint M, and a vector toward the vertex P5 at the midpoint; Condition of determining whether the inner product is greater than or less than 0) (S82), and if so, adds it to the tessellation result using the triangle TRI_2 (S83). Next, except for the straight line SL1 from the first list, other straight lines constituting the triangle TRI_2 except for the straight line SL1 are added to the first list (S70).

If the test does not pass or does not correspond to the progress condition, the processes S81 to S83 are performed again at the vertex P6 located next to the vertex P5 (S84).

The tessellation method illustrated in FIGS. 11 to 14 has described one tessellation process and may be repeatedly performed to tessellate the entire curved surface.

By performing tessellation from a straight line on the closed loop as described above, the boundary between the closed loop and the closed loop is also naturally tesselated.

The present invention can also be embodied as computer-readable codes on a computer-readable recording medium. The computer-readable recording medium includes all kinds of recording devices in which data that can be read by a computer system is stored.

Examples of computer-readable recording media include ROM, RAM, CD-ROM, magnetic tape, floppy disks, optical data storage devices, and the like.

The computer readable recording medium can also be distributed over network coupled computer systems so that the computer readable code is stored and executed in a distributed fashion. And functional programs, codes and code segments for implementing the present invention can be easily inferred by programmers in the art to which the present invention belongs.

Although the present invention has been described with reference to one embodiment shown in the drawings, this is merely exemplary, and those skilled in the art will understand that various modifications and equivalent other embodiments are possible therefrom. Therefore, the true technical protection scope of the present invention will be defined by the technical spirit of the appended claims.

1 is a view showing a modeling system for sketching a three-dimensional surface model according to an embodiment of the present invention.

2 is a flowchart illustrating a modeling method for sketching a 3D surface model according to an exemplary embodiment of the present invention.

3 to 8 are diagrams illustrating an example for describing in detail a modeling method for sketching a 3D curved model of FIG. 2.

FIG. 9 illustrates an embodiment in which a modeling method for sketching a 3D surface model of FIG. 2 is implemented using a modeling system for sketching a 3D surface model of FIG. 1.

FIG. 10 is a diagram illustrating a result of tessellation of the curved surface generated in FIG. 8.

11 to 14 are diagrams for describing an example of a method for tessellation of FIG. 9.

Claims (14)

Generating at least one closed loop of a plurality of vertices on a three-dimensional plane and a plurality of curves passing through the vertices using an input device; At each of the vertices, generating a normal vector by interpolating a tangent vector of two curves passing through each of the vertices; Checking whether each of the normal vectors corresponds to a preset correction criterion, and if not, correcting the normal vectors; Generating a curved surface of the at least one closed loop using a radial basis function interpolation using the sampled points on the at least one closed loop and each of the normal vectors; And Tessellating the generated surface, the modeling method for sketching a three-dimensional surface model. The method of claim 1, The correction criterion includes a criterion for determining whether the inner product of the first normal vector and the second normal vector among the normal vectors is less than zero, The correcting may include rotating the normal vector of each of the vertices along a curve passing through each of the vertices to determine whether the normal vector corresponds to the correction criterion, and thereby rotating the second normal vector in a reverse angle according to a preset angle. A modeling method for sketching a 3D surface model comprising the step of. The method of claim 1, Generating the at least one closed loop A first selection step of selecting a reference vertex and a reference curve passing through the reference vertex among the vertices; A second selection step of selecting a first curve closest to the counterclockwise rotation direction of the reference curve based on the reference vertex; A third selection step of selecting a second curve closest to a clockwise rotation direction of the reference curve with respect to a vertex other than the reference vertex of the reference curve; And 3D surface model sketch including an iterative step of setting the first curve or the second curve back to the reference curve and repeating the second selection step and the third selection step until the selected curves form a closed loop. Modeling method for The method of claim 3, wherein generating the closed loop Measuring an angle of the counterclockwise rotation or the clockwise rotation direction at the vertex of the at least one closed loop, and removing more closed loops than the number of angles of 180 degrees or more is less than 180 degrees Modeling method for sketching 3D surface models, including. The method of claim 1, The radial basis function is

ego, (

Is a three-dimensional coordinate of the sampled points on the at least one closed loop,

Is the first affine function,

Is a real factor) The step of generating the surface Generating at least one point outside the closed loop using each normal vector; And Using the radial basis function, sampled points on the at least one closed loop, and at least one point outside the closed loop;

And said

Find the coefficient of, and

A modeling method for sketching a three-dimensional surface model comprising the step of generating a surface by using a point on the three-dimensional space. The method of claim 1, further comprising generating a curved surface by performing a radial basis function interpolation. Radial Basis Function Interpolation of a plurality of closed loops generated by adding at least one partition curve for partitioning the at least one closed loop in the same manner as the at least one closed loop to generate a deformation surface Modeling method for sketching a three-dimensional surface model further comprising the steps. The method of claim 1, The curve is a modeling method for sketching a three-dimensional surface model further comprises a plurality of straight lines and vertices similar curve that is visually curved to the user. The method of claim 1, The tessellation may include performing tessellation from three reference points on the surface. The method of claim 1, The tessellation may include performing tessellation from the curve and one reference point on the surface. A recording medium having recorded thereon a computer program for executing the method according to any one of claims 1 to 9. An input device for generating a closed loop consisting of a plurality of vertices in three dimensions and a plurality of curves passing through the vertices; At each of the vertices, a vector generator for generating a normal vector on a three-dimensional cross-section of a tangent vector of two curves passing through each of the vertices; A correction unit for checking whether each of the normal vectors corresponds to a preset correction criterion, and correcting the normal vectors if not applicable; An interpolation unit configured to generate a curved surface of the at least one closed loop by performing a radial basis function interpolation using the sampled points on the at least one closed loop and each of the normal vectors; And Modeling system for a three-dimensional surface model sketch including a tessellation unit for tessellation (tessellation) the generated surface. The method of claim 11, The curve is a modeling system for a three-dimensional surface model sketch further comprises a plurality of straight lines and vertices, similar curve that is visually curved to the user. The method of claim 11, The tessellation unit is a modeling system for a three-dimensional surface model sketch for performing a tessellation from the reference three points on the surface. The method of claim 12, The tessellation unit is a modeling system for a three-dimensional surface model sketch for performing tessellation from the reference point of the curve and the surface.

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