CN117272420B - Clipping curved surface representation method based on normalized parameter domain and storage medium - Google Patents
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Abstract
The application provides a clipping curved surface representation method based on a normalized parameter domain, which comprises the following steps: dividing a Bezier curved surface of a geometric model of a product to be processed into a plurality of sub-curved surface pieces based on equal parameter lines of curved surface intersection points, and ensuring that the intersection lines of the curved surfaces have one point and only have one point passing through one vertex of a standard parameter domain of the sub-curved surface piece where the intersection lines are positioned; remapping an irregular parameter domain of a curved trapezoid formed by the intersection line of the curved surface and three edges of a standard parameter domain of a sub-curved sheet where the intersection line is located into the standard parameter domain; the clipping surface is normalized on the remapped standard parameter domain. According to the scheme, each curved surface piece of the geometric model is represented in a standardized form, so that the geometric model has a unified curved surface data structure, definition and maintenance are convenient, a large amount of storage space is saved, rapid and seamless connection of each curved surface piece is convenient, and the efficiency of model generation, manufacturing and the like is improved. Particularly convenient for the subsequent treatment of large-scale product design.
Description
Technical Field
The invention belongs to the field of computer aided design, and relates to a data processing method of a geometric model of a product.
Background
Geometric models are widely used in the fields of computer graphics, computer aided design, computer aided manufacturing, computer aided engineering, etc. to characterize the shape of a product or object. These geometric models describe the three-dimensional geometry precisely in a manner that can be understood by a computer. Most geometric models are designed by parameterization and stored in a specific data structure, so that the efficiency of product model design, generation, simulation, modification and optimization is greatly improved. The mainstream geometric model at present mostly adopts a curved surface model, and a series of regular curved surfaces and/or irregular curved surfaces are used for representing the three-dimensional geometric shape of a product or an object. The non-uniform rational B-spline (non-uniform rational B-splines, NURBS) method, which is the dominant technique for surface representation in Computer Aided Design (CAD) and Computer Aided Geometry Design (CAGD), has been a common ISO international standard, and plays an important, indispensable role in the design, analysis and manufacture of industrial products. Bezier surfaces (also known as Bezier surfaces) are a special expression of NURBS, all of which can be represented by segmented Bezier surface patches. The Bezier curved surface sheet is defined in a standard parameter interval [0,1] × [0,1], and is convenient to calculate, store and transform. The Decastejau (de Casteljau) algorithm provides a tool for Bezier patches to extract partial patches along rectangular sub-regions enclosed by arbitrary isoparametric lines, which can be transformed into standard parameter intervals by linear parametric transformation.
However, complex curved surface shapes are often involved in product design, and require that the curved surfaces be mutually manipulated to determine intersecting lines, and then cut and combined to define the curved surfaces. I.e. the problem of clipping surfaces needs to be addressed. The boundary of such a clipping surface is not generally along an isoparametric line, but may be an arbitrary curve, and is generally not converted into a standard parameter interval by simple linear transformation. Thus, it presents challenges to clipping curved surface representations.
There are two general methods of treatment. Firstly, adding a data structure of a boundary curve as a supplement to the definition of a clipping curved surface; and secondly, the method is represented by adopting a grid or other similar approximation method. The former changes the unified curved surface data structure of the system, brings inconvenience for definition and maintenance, and particularly brings trouble to the subsequent processing of large-scale design; the latter brings unavoidable errors and adversely affects the subsequent application of high-precision analysis and the like.
It should be noted that the foregoing is only for aiding in understanding the technical solution of the present application, and is not used as a basis for evaluating the prior art of the present application.
Disclosure of Invention
Therefore, to solve the above-mentioned drawbacks of the prior art, the present application provides a new cut surface representation based on normalized parameter fields to process product geometry model data.
According to a first aspect of an embodiment of the present application, there is provided a clipping curved surface representation method based on normalized parameter domain, including the steps of:
S0, dividing a Bezier curved surface of a geometric model of a product to be processed into a plurality of sub-curved surface pieces based on an isoparametric line of the curved surface intersection point, and ensuring that the intersection line of the curved surface has one point and only one point passes through one vertex of a standard parameter domain of the sub-curved surface piece where the intersection line is positioned;
s1, remapping an irregular parameter domain of a curved trapezoid formed by the intersection line of the curved surface and three edges of a standard parameter domain of a sub-curved surface sheet where the intersection line is located into a standard parameter domain;
s2: the clipping surface is normalized on the remapped standard parameter domain.
In some embodiments, the irregular parameter domains of the curved trapezoid in the step S1 may be divided into eight types, and one type of irregular parameter domain is selected, and the other seven types of irregular parameter domains may be respectively and symmetrically transformed to be equivalent to the optional one type of irregular parameter domain.
In some embodiments, step S1 may further include:
S1-1, selecting one type of irregular parameter domain, and respectively carrying out rotational symmetry transformation on the rest seven types of irregular parameter domains to make the rest seven types of irregular parameter domains equivalent to the optional one type of irregular parameter domain;
s1-2, mapping the optional irregular parameter domain of one type into a standard parameter domain.
In some embodiments, step S1 may further include: eight types of irregular parameter domains are mapped to standard parameter domains, respectively.
In some embodiments, the optional one type of irregular parameter domain is a curved trapezoidal region in parameter domain uOv described by the following conditions:
the method of mapping it to the standard parameter domain in the parameter domain sOt is:
Wherein, α∈ (0, 1), the sign of the form f (x) is a polynomial about x, the degree of the polynomial is designed according to the precision requirement of the application, and the standard parameter domain in the parameter domain sOt is a rectangular area described by the following conditions:
in some embodiments, the f (x) specification is f (x) =a pxp+ap-1xp-1+…+a0, p e N, ap≠0。
In some embodiments, step S2 may further include:
S2-1, expanding the expression of the clipping curved surface into polynomials about S and t on the remapped standard parameter domain s×t epsilon [0,1] x [0,1 ];
s2-2, enabling the value of the element A ij of the mapping matrix A to be the coefficient of S itj term in the polynomial in the step S2-1;
s2-3, solving a mapped control point matrix And the clipping surface is normalized on the remapped standard parameter domain.
In some embodiments, the mapped control point matrixThe calculation method of (1) can be as follows:
Wherein, Is the inverse matrix of matrix B m of m-th order basis function coefficients,/>Is the transposed matrix of the inverse of the m x p + n basis function coefficient matrix B m×p+n.
According to a second aspect of embodiments of the present application, there is also provided a method for processing product geometric model data, comprising:
receiving data related to the product geometric model, wherein the product geometric model is a curved surface model;
The received data is normalized in a method according to the first aspect of an embodiment of the application.
According to a third aspect of embodiments of the present application, there is also provided a computer readable medium having stored thereon a computer program, characterized in that the computer program, when executed by a processor, implements the method according to the first or second aspect of embodiments of the present application.
According to a fourth aspect of an embodiment of the present application, there is also provided an electronic device including: a processor and a memory, wherein the memory is for storing executable instructions; the processor is configured to perform the method of the first or second aspect of the embodiments of the present application via execution of the executable instructions.
Compared with the prior art, in the solution of the application, each curved surface piece of the geometric model is characterized in a standardized form, so that the geometric model has a unified curved surface data structure, the definition and maintenance are convenient, a large amount of storage space is saved, the rapid and seamless connection of each curved surface piece is convenient, and the production, manufacturing and other efficiencies of the geometric model of the product are improved. Particularly convenient for the subsequent treatment of large-scale product design.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application as claimed.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the application and together with the description, serve to explain the principles of the application. It is evident that the drawings in the following description are only some embodiments of the present application and that other drawings may be obtained from these drawings without inventive effort for a person of ordinary skill in the art. In the drawings:
FIG. 1 is a flow chart of a clipping surface representation method according to one embodiment of the application;
FIG. 2 is a schematic diagram of a segmentation of a clipping surface parameter domain according to one embodiment of the application;
FIGS. 3 (a) -3 (h) are eight parameter space type diagrams of clipping surface boundaries according to one embodiment of the application;
FIGS. 4 (a) - (b) are diagrams of normalized mapping of a clipping surface parameter space according to one embodiment of the application;
FIG. 5 is a schematic diagram of a clipping surface generated according to one embodiment of the application.
Detailed Description
For the purpose of making the technical solutions and advantages of the present application more apparent, the present application will be further described in detail by way of specific embodiments with reference to the accompanying drawings. It should be understood that the described embodiments are some, but not all, embodiments of the application. All other embodiments, which can be made by those skilled in the art without the inventive effort, are intended to be within the scope of the present application, based on the embodiments herein.
Furthermore, the described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a thorough understanding of embodiments of the application. One skilled in the relevant art will recognize, however, that the application may be practiced without one or more of the specific details, or with other methods, components, devices, steps, etc. In other instances, well-known methods, devices, implementations, or operations are not shown or described in detail to avoid obscuring aspects of the application.
The block diagrams depicted in the figures are merely functional entities and do not necessarily correspond to physically separate entities. That is, the functional entities may be implemented in software, or in one or more hardware modules or integrated circuits, or in different networks and/or processor devices and/or microcontroller devices.
The flow diagrams depicted in the figures are exemplary only, and do not necessarily include all of the elements and operations/steps, nor must they be performed in the order described. For example, some operations/steps may be decomposed, and some operations/steps may be combined or partially combined, so that the order of actual execution may be changed according to actual situations.
As mentioned above, complex curved surface shapes are often involved in product design, requiring inter-operation between curved surfaces to determine intersection lines, and then cutting and combining to define the intersection lines. I.e. the problem of clipping surfaces needs to be addressed. The boundary of such a clipping surface is not generally along an isoparametric line, but may be an arbitrary curve, and is generally not converted into a standard parameter interval by simple linear transformation.
After analyzing various conditions of cutting the boundary of the curved surface, the inventor finds that after the curved surface is segmented along an equal parameter line by utilizing a de Casteljau algorithm, the cut curved surface can be always segmented into a union of a plurality of sub-curved surface pieces, wherein the parameter space of each sub-curved surface piece containing the boundary can be summarized into a quasi-trapezoid domain of a curved trapezoid containing only one curve boundary. These "quasi-trapezoidal" domains, which contain only one curved edge, have a total of eight cases. Further analysis found that the above eight cases were equivalent under rotational symmetry. Based on the above findings, in the embodiment of the present application, a clipping curved surface representation method based on a normalized parameter domain is provided, which can re-normalize a non-regular parameter domain after division into a standard parameter domain, so that the clipping curved surface still has the same data structure and normalized representation as the original curved surface, no additional data structure of a boundary curve is required, and no approximate representation such as a grid is required, so that "closure" in mathematical sense is realized for the calculation of the curved surface.
FIG. 1 shows a flow diagram of a method for clipping a surface representation based on normalized parameter fields, in accordance with one embodiment of the present application. The method mainly comprises the following steps: s0, dividing a Bezier curved surface of a geometric model of a product to be processed into a plurality of sub-curved surface pieces based on an isoparametric line of the curved surface intersection point, and ensuring that the intersection line of the curved surface has one point and only one point passes through one vertex of a standard parameter domain of the sub-curved surface piece where the intersection line is positioned; s1, remapping an irregular parameter domain of a curved trapezoid formed by the intersection line of the curved surface and three edges of a standard parameter domain of a sub-curved surface sheet where the intersection line is located into a standard parameter domain; s2: the clipping surface is normalized on the remapped standard parameter domain.
More specifically, in step S0, for a geometric model of a product or object represented in the form of a Bezier curved surface, the Bezier curved surface is divided into a plurality of sub-curved surface slices based on an isoparametric line of intersection points of the curved surfaces, so that the intersection line of the curved surfaces is ensured to have and have only one point passing through one vertex of a standard parameter domain of the sub-curved surface slice where the intersection line is located.
In one embodiment, in a given parameter domain uOv, the Bezier surface may be grid-partitioned based on the isoparametric line u=u i∈[0,1],v＝vi e [0,1] (i=1, 2, …), ensuring that the intersection of the surfaces has and only has one point passing through one vertex of the standard parameter domain of the sub-surface patch where it is located. As shown in fig. 2, the intersection of the surfaces (line BDG) passes through the standard parameter domain of the two sub-surface patches. Only one vertex D of the parameter domain passes through in the standard parameter domain of each sub-curved surface sheet, and the curved trapezoid ABCD and the curved trapezoid DEFG which only contain one curve boundary are formed by surrounding three edges of the parameter domain.
The curved trapezoid having only one curved boundary generated according to the above-described dividing method is of eight types in total, as shown in fig. 3 (a) -3 (h), wherein the curved trapezoid ABCD and the curved trapezoid DEFG shown in fig. 2 correspond to the curved trapezoids in fig. 3 (a) and 3 (c), respectively. As can be seen from fig. 3 (a) -3 (h), these eight types of curved-edge trapezoids are equivalent after being rotationally symmetrically transformed, one type of irregular parameter domain is selected, and the remaining seven types of irregular parameter domains can be respectively rotationally symmetrically transformed and equivalent to the optional one type of irregular parameter domain, so that one of them can be optionally discussed.
In step S1, the irregular parameter domain of the curved trapezoid formed by the intersection line of the curved surface and the three edges of the standard parameter domain of the sub-curved sheet is remapped into the standard parameter domain. The specific mapping method is set forth below.
In one embodiment, the eight types of irregular parameter domains shown in fig. 3 (a) -3 (h) may be mapped to standard parameter domains, respectively.
In yet another embodiment, fig. 3 (b) -3 (h) can be transformed into fig. 3 (a), and then the irregular parameter domain shown in fig. 3 (a) can be normalized to the standard parameter domain.
In the present application, the method for normalizing the irregular parameter domain shown in fig. 3 (a) into the standard parameter domain is to build a parameter mapping model, specifically, as shown in fig. 4 (a) -4 (b), and the general form of the parameter equation of the curved-edge curve in fig. 4 (a) is set to be f (x). When the irregular parameter domain shown in fig. 4 (a) is mapped to the standard parameter domain shown in fig. 4 (b), the surface thereon has a standard Bezier surface form, and thus has a uniform data structure.
The model assumption conditions in the pre-mapping (fig. 4 (a)) parameter domain are:
Condition 1:
where α ε (0, 1). After mapping (FIG. 4 (b)), new parameters sxtε [0,1] × [0,1] model assumptions in parameter domain
The conditions are as follows:
Condition 2:
the conditions for implementing the mapping Γ are:
Condition 3:
The model expression implementing the mapping Γ is:
Wherein the sign of the form f (x) is a polynomial of degree p with respect to x, f (x) =a pxp+ap-1xp-1+…+a0, p e N, A p noteq 0. According to the precision requirements of different applications, f (x) can be designed into mapping of primary, secondary, tertiary or higher order, and coefficients of the polynomial can be obtained through spline curve interpolation according to intersection points obtained when curved surfaces are intersected.
When the irregular parameter domain is the standard parameter domain according to the above mapping model specification, the clipping curved surface established on the irregular parameter domain can be correspondingly specified as the standard Bezier curved surface form, so in step S2, the clipping curved surface is specified and expressed on the remapped standard parameter domain, which is specifically described as follows.
The general expression for Bezier surfaces is:
Wherein, The symbol of the shape B k,l (x) is the kth one time Bezier basis function, which is the control vertex of the curved surface and is expressed as/>Is a combination coefficient. Substituting the formula (4) corresponding to the mapping Γ into S (u, v) in the formula (5) to obtain a Bezier curved surface expression on the standard parameter domain, and note that the number of times of the Bezier base function on the standard parameter domain after renormalization is changed from m, n times of the original (u, v) to m, m x p+n times of the original (S, t) respectively:
Wherein, Is the mapped control vertex.
Let B q be the coefficient matrix of the Bezier basis function of q times, and be the square matrix of (q+1) x (q+1), then there are: [ B 0,q B1,q... Bq,q]＝[1 w w2 ... wq]Bq; note that the control point matrix r= (R ij)(m+1)×(n+1), the general expression of the matrix form of the Bezier surface is:
wherein the superscript "T" denotes the transpose of the matrix.
Control vertex matrix after being mapped againThe expression of the matrix form of the mapped Bezier surface is:
mapping matrix For the inverse matrix of matrix B q, the solution formula of the mapped control point is: /(I)Therefore, after the mapping matrix A is obtained, the mapped control point matrix can be obtained, and the clipping curved surface expression on the standard parameter domain is obtained.
The solving process of the mapping matrix A is as follows: expanding equation (6) into a polynomial for s and t, determining the values of the elements in matrix A from the coefficients of the polynomial, i.e., the values of element A ij are the coefficients of the s itj term in the polynomial.
The following illustrates the solution process for matrix a.
Memory matrix
If in uOv parameter domain, i 4: u=f (v), v e [0,1] is once about v, i.e. p=1, f (v) =a 1v+a0,a1 +.0. When m=n=3, a= (a i,j)4×7,B3,The method comprises the following steps of:
Substituting the above known parameters into formula (6) and expanding to obtain a curved surface expression represented by parameters s and t, as follows:
according to the coefficient of s itj, the expression of each element in the matrix A is obtained as follows:
It is further possible that, Wherein,
FIG. 5 is a schematic diagram of a clipping surface generated according to one embodiment of the application. In fig. 5, a curved surface sf 1 is a clipping curved surface to be left, and a curved surface sf 2 is a clipped curved surface. Curve cu 1 is a clipping boundary and the asterisk points are control vertices regenerated according to the method of the application.
According to the existing method, when the problems of generating the curved surface sf 1 in the system or processing the geometric product represented by the curved surface sf 1 are faced, the information of the clipping boundary curve cu1 needs to be stored and represented to assist in judging whether the clipping boundary is reached. In practical application, the clipping curved surface is often formed by intersecting hundreds of thousands of curved surfaces, and the existing method is adopted, so that the amount of boundary information required to be stored and represented is huge, and the process of judging whether the boundary is reached is complex. According to the method of the application, the clipping curved surface to be reserved is expressed into the standard form as the formula (5), no additional data need to be stored, no boundary information need to be expressed, the process of judging the boundary is omitted, and the efficiency of subsequent processing is improved.
The method of the embodiment of the application expresses the boundary of the cutting curved surface by a group of patches, each patch is expressed in a standardized way, has a uniform data structure, and solves the problem of irregular data structure caused by expressing the boundary of the cutting curved surface by additional data. In addition, the scheme maps the irregular parameter domain to the regular parameter domain, and the clipping curved surface defined on the irregular parameter domain keeps the original shape, so that the problem that the subsequent high-precision analysis and other applications are adversely affected due to large grid approximation errors is solved.
In yet another embodiment of the present application, a method for processing product geometric model data is also provided. The method mainly comprises the steps of obtaining data related to a geometric model of a product, and carrying out normalization processing on the obtained geometric model data by utilizing the clipping curved surface representation method based on a normalization parameter domain. Wherein the product geometry model data may be obtained via a communication connection such as a wired network or a wireless network, or may be obtained from a database or computer readable storage medium. The geometric model data of the product processed by the method of the embodiment not only can save a large amount of storage space, but also is beneficial to subsequent analysis, processing, manufacturing and other processes by the normalized clipping curved surface, and the uncertainty and errors in the data sharing process between different clients or systems are reduced.
The method of the embodiment is suitable for defining, representing and applying geometric models in the fields of computer graphics, computer aided design, computer aided manufacturing, computer aided engineering and the like. Because each patch of the geometric model of the product or object is normalized, such geometric model has a unified data structure, facilitating rapid generation of models of the product or object model. In addition, the surface of the geometric model of the product or the object is composed of standardized patches, so that the geometric model can be converted and interpreted in different systems more easily, data sharing among suppliers, clients or cooperation partners is facilitated, risks of misunderstanding and mistakes are reduced, subsequent analysis and processing and manufacturing processes can be facilitated, risks in the product research and development process are reduced, the research and development period is shortened, and the productivity is improved.
Therefore, the solution of the application can improve the quality and reliability of the geometric model of the product, is beneficial to the smooth proceeding and high-efficiency output of the product design, analysis and manufacturing process, and has wide application prospect in the aspect of computer aided design.
In an embodiment of the application, a computer program product is also provided, comprising program code means for performing the steps of the method as described in the preceding embodiments, when these program code means are run on any computing device or data processing apparatus.
In yet another embodiment of the present application, a computer readable storage medium is provided, on which a computer program or executable instruction is stored, which when executed by a processor or other computing unit implements the technical solution described in the foregoing embodiment, and the implementation principle is similar, and is not repeated herein. In embodiments of the present application, a computer-readable storage medium may be any tangible medium that can store data and that can be read by a computing device. Examples of a computer-readable storage medium include a hard disk drive, network Attached Storage (NAS), read-only memory, random-access memory, CD-ROMs, CD-R, CD-RWs, magnetic tapes, and other optical or non-optical data storage devices. The computer-readable storage medium may also include a computer-readable medium distributed over a network coupled computer system so that the computer program or instructions may be stored and executed in a distributed fashion.
In yet another embodiment of the present application, there is provided an electronic device, including a processor and a memory, where the memory is configured to store executable instructions executable by the processor, where the processor is configured to execute the executable instructions stored on the memory, where the executable instructions when executed implement the technical solution described in any of the foregoing embodiments, and implementation principles are similar and are not repeated herein.
Reference in the specification to "various embodiments," "some embodiments," "one embodiment," or "an embodiment" or the like, means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, appearances of the phrases "in various embodiments," "in some embodiments," "in one embodiment," or "in an embodiment" in various places throughout this specification are not necessarily referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. Thus, a particular feature, structure, or characteristic described in connection with or illustrated in one embodiment may be combined, in whole or in part, with features, structures, or characteristics of one or more other embodiments without limitation, provided that the combination is not non-logical or inoperable.
The terms "comprises," "comprising," and "having" and the like, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not limited to only those steps or elements but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus. Nor does "a" or "an" exclude a plurality. Additionally, the various elements of the drawings are for illustrative purposes only and are not drawn to scale.
While the invention has been described in terms of preferred embodiments, the invention is not limited to the embodiments described herein, but encompasses various changes and modifications that may be made without departing from the scope of the invention.
Claims (8)
1. A clipping curved surface representation method based on a normalized parameter domain is characterized by comprising the following steps:
S0, dividing the Bezier curved surface of the product geometric model to be processed into a plurality of sub-curved surface pieces based on an isoparametric line of the curved surface intersection point, ensuring that the intersection line of the curved surface is provided with one point passing through one vertex of a standard parameter domain of the sub-curved surface piece where the intersection line is located, wherein the product geometric model data is obtained through one of the following steps: a communication connection, a database, a computer readable storage medium;
S1, remapping an intersection line of the curved surface and an irregular parameter domain of a curved trapezoid formed by three edges of a standard parameter domain of a sub-curved surface sheet where the intersection line is located into a standard parameter domain, wherein eight types of irregular parameter domains of the curved trapezoid exist, one type of irregular parameter domain is selected, the other seven types of irregular parameter domains can be respectively and symmetrically transformed to be equivalent to the optional one type of irregular parameter domain, and the optional one type of irregular parameter domain is a curved trapezoid area described by the following conditions in the parameter domain uOv:
the method of mapping it to the standard parameter domain in the parameter domain sOt is:
Wherein, α∈ (0, 1), the sign of the form f (x) is a polynomial about x, the degree of the polynomial is designed according to the precision requirement of the application, and the standard parameter domain in the parameter domain sOt is a rectangular area described by the following conditions:
s2: the clipping surface is normalized on the remapped standard parameter domain.
2. The method of clipping surface representation according to claim 1, wherein step S1 further comprises:
S1-1, selecting one type of irregular parameter domain, and respectively carrying out rotational symmetry transformation on the rest seven types of irregular parameter domains to make the rest seven types of irregular parameter domains equivalent to the optional one type of irregular parameter domain;
s1-2, mapping the optional irregular parameter domain of one type into a standard parameter domain.
3. The method of clipping surface representation according to claim 1, wherein step S1 further comprises: eight types of irregular parameter domains are mapped to standard parameter domains, respectively.
4. The clipping surface representation method according to claim 1, wherein the f (x) concrete expression is
5. The clipping curved surface representation method according to claim 1, wherein step S2 further comprises:
S2-1, expanding the expression of the clipping curved surface into polynomials about S and t on the remapped standard parameter domain s×t epsilon [0,1] x [0,1 ];
s2-2, enabling the value of the element A ij of the mapping matrix A to be the coefficient of S itj term in the polynomial in the step S2-1;
s2-3, solving a mapped control point matrix And the clipping surface is normalized on the remapped standard parameter domain.
6. The method of claim 5, wherein the mapped control point matrixThe calculation method of (1) is as follows:
Wherein, Is the inverse matrix of matrix B m of m-th order basis function coefficients,/>Is the transposed matrix of the inverse of the m x p + n basis function coefficient matrix B m×p+n.
7. A method for processing product geometric model data, comprising:
receiving data related to the product geometric model, wherein the product geometric model is a curved surface model;
normalization of received data is performed in a method according to any of the claims 1-6.
8. A computer readable medium, on which a computer program is stored, which computer program, when being executed by a processor, implements the method according to any one of claims 1 to 7.
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