CN105719347A

CN105719347A - Recurrent curve surface construction method based on LW curve surface and device thereof

Info

Publication number: CN105719347A
Application number: CN201610038290.8A
Authority: CN
Inventors: 罗笑南; 林格; 卢慧阳; 林淑金
Original assignee: Sun Yat Sen University
Current assignee: Sun Yat Sen University
Priority date: 2016-01-20
Filing date: 2016-01-20
Publication date: 2016-06-29

Abstract

The invention discloses a recurrent curve surface construction method based on LW curve surface and a device thereof. The recurrent curve surface construction method is characterized in that points of a curve can be calculated by adopting the recurrent algorithm, and then the points of the curve can be acquired; the derivative calculation of the points of the L curve can be carried out, and the higher derivative of the L curve can be acquired; by setting n+m vertexes and correcting node information, W curves of m segments can be generated; and the recurrent curve can be acquired according to the weights of the vertexes and the node information. The recurrent nature of the form can be expressed by adopting the curves of different forms, and the node parameters suitable for the recurrent curves can be defined, and then the object of unifying the curve surfaces of different forms can be expressed in a unified way. The conversion with different curve surface forms can be carried out, and the curve surfaces of different definition forms can be expressed by the computer using the same data format.

Description

A method and device for constructing recursive curves and surfaces based on LW curves and surfaces

技术领域technical field

本发明涉及计算机辅助设计技术领域，尤其涉及一种基于LW曲线曲面的递归曲线曲面构建方法及其装置。The invention relates to the technical field of computer aided design, in particular to a method and device for constructing a recursive curve and surface based on LW curves and surfaces.

背景技术Background technique

计算机辅助几何设计(ComputerAidedGeometricDesign，CAGD)是密切联系生产实践且随着生产实践的需要而不断完善发展的新兴学科，其应用范围除了航空、造船、汽车这三大制造业外，还涉及建筑设计、生物工程、医疗诊断、航天材料、电子工程、机器人、服装鞋帽模型设计等技术领域。随着计算机图形学的发展，还广泛应用于计算机视觉、地形地貌、军事作战模拟、动画制作、多媒体技术等领域。因此随着计算机图形显示对于真实性、实时性和交互性要求的日益增强，随着几何设计对象向着多样性、特殊性和拓扑结构复杂性靠拢这种趋势的日益明显，对于外形设计的要求也就越来越高，于是曲面曲线造型技术的得到了长足的发展。Computer Aided Geometric Design (CAGD) is an emerging discipline that is closely related to production practice and is constantly improving and developing with the needs of production practice. Bioengineering, medical diagnosis, aerospace materials, electronic engineering, robotics, clothing, shoes and hat model design and other technical fields. With the development of computer graphics, it is also widely used in computer vision, topography, military combat simulation, animation production, multimedia technology and other fields. Therefore, with the increasing requirements for authenticity, real-time and interactivity of computer graphic display, and the increasingly obvious trend of geometric design objects approaching diversity, specificity and topology complexity, the requirements for shape design are also increasing. It is getting higher and higher, so the surface curve modeling technology has been greatly developed.

在外形设计中，曲线曲面不能用二次方程来描述，常常只给出大致形状或只知道它通过一些空间点列，需要特殊的方法构造，长期以来，参数曲线曲面表示一直是描述几何形状的主要工具。采用递归形式的曲线曲面，相比曲线曲面的最初定义的公式，更适合在计算机中进行计算，且计算更为稳定。现有的一系列的CAGD软件采用不同的造型方法，而它们之间的数据交换却变得很频繁，因此在L曲线曲面基础上，建立一致的曲线曲面表示形式是很有必要的。In shape design, curves and surfaces cannot be described by quadratic equations. Usually, only the approximate shape is given or only know that it passes through some spatial point columns, which requires special methods to construct. For a long time, parametric curves and surfaces have been used to describe geometric shapes. main tool. The recursive form of the curve and surface is more suitable for calculation in the computer than the original definition formula of the curve and surface, and the calculation is more stable. A series of existing CAGD softwares adopt different modeling methods, but the data exchange between them becomes very frequent. Therefore, it is necessary to establish a consistent representation of curves and surfaces on the basis of L curves and surfaces.

对于递归曲线的研究中，由包络定义得出的L曲线由于其优良的特性得到了广泛关注。L曲线具有几种不同的表示方式，基于的L曲线的定义形式如下：In the study of recurrence curves, the L curve defined by the envelope has been widely concerned because of its excellent characteristics. The L-curve has several different representations, and the definition of the L-curve based on it is as follows:

定义1：Definition 1:

${Q Q}_{i i}^{r r} ((t t)) = = \{\begin{matrix} {p p}_{i i},, r r = = 00;; i i = = 00,, 1.. 1.. n no \\ \frac{{β β}_{i i} - - t t}{{β β}_{i i} - - {α α}_{i i + + r r - - 11}} {Q Q}_{i i - - 11}^{r r - - 11} ((t t)) + + \frac{t t - - {α α}_{i i + + r r - - 11}}{{β β}_{i i} - - {α α}_{i i + + r r - - 11}} {Q Q}_{i i}^{r r - - 11} ((t t)),, r r = = 11,, 2... 2... n no,, i i = = r r,, r r + + 11,, ... ... n no \end{matrix};;$

所得到的为n次L曲线。其中got It is n times L curve. in

$00 \leq \leq \frac{{β β}_{i i} - - t t}{{β β}_{i i} - - {α α}_{i i + + r r - - 11}},, \frac{t t - - {α α}_{i i + + r r - - 11}}{{β β}_{i i} - - {α α}_{i i + + r r - - 11}} \leq \leq 11;;$

如果 if

则该L曲线称为W曲线Then the L curve is called the W curve

定义2：Definition 2:

给定n+1歌平面或空间上的顶点Given n+1 vertices on a plane or space

${ω ω}_{i i}^{r r} ((t t)) = = \{\begin{matrix} {ω ω}_{i i},, r r = = 00;; i i = = 00,, 1... 1... n no \\ \frac{{β β}_{i i} - - t t}{{β β}_{i i} - - {α α}_{i i + + r r - - 11}} {ω ω}_{i i - - 11}^{r r - - 11} ((t t)) + + \frac{t t - - {α α}_{i i + + r r - - 11}}{{β β}_{i i} - - {α α}_{i i + + r r - - 11}} {ω ω}_{i i}^{r r - - 11} ((t t)),, r r = = 11,, 2... 2... n no,, i i = = r r,, r r + + 11,, ... ... n no \end{matrix};;$

${Q Q}_{i i}^{r r} ((t t)) = = \{\begin{matrix} {p p}_{i i},, r r = = 00;; i i = = 00,, 1... 1... n no \\ \frac{{β β}_{i i} - - t t}{{β β}_{i i} - - {α α}_{i i + + r r - - 11}} \frac{{ω ω}_{i i - - 11}^{r r - - 11} ((t t))}{{ω ω}_{i i}^{r r} ((t t))} {Q Q}_{i i - - 11}^{r r - - 11} ((t t)) + + \frac{t t - - {α α}_{i i + + r r - - 11}}{{β β}_{i i} - - {α α}_{i i + + r r - - 11}} \frac{{ω ω}_{i i}^{r r - - 11} ((t t))}{{ω ω}_{i i}^{r r} ((t t))} {Q Q}_{i i}^{r r - - 11} ((t t)),, r r = = 11,, 2... 2... n no,, i i = = r r,, r r + + 11,, ... ... n no \end{matrix};;$

所获得的为n次有理L曲线。其中obtained is a rational L curve of degree n. in

$00 \leq \leq \frac{{β β}_{i i} - - t t}{{β β}_{i i} - - {α α}_{i i + + r r - - 11}},, \frac{t t - - {α α}_{i i + + r r - - 11}}{{β β}_{i i} - - {α α}_{i i + + r r - - 11}} \leq \leq 11$

如果 $0 \leq \frac{β_{i} - t}{β_{i} - α_{i + r - 1}} \leq 1, 0 \leq \frac{β_{i} - t}{β_{i} - α_{i + r - 1}} \leq 1;$ if $0 \leq \frac{β_{i} - t}{β_{i} - α_{i + r - 1}} \leq 1, 0 \leq \frac{β_{i} - t}{β_{i} - α_{i + r - 1}} \leq 1;$

则该有理L曲线称为有理W曲线。Then this rational L curve is called a rational W curve.

现有技术中无法统一表示不同形式的曲线曲面，同时无法对不同的曲线曲面形式进行转换。In the prior art, different forms of curves and surfaces cannot be uniformly represented, and at the same time, different forms of curves and surfaces cannot be converted.

发明内容Contents of the invention

本发明的目的在于克服现有技术的不足，本发明提供了一种基于LW曲线曲面的递归曲线曲面构建方法及其装置，提供不同造型技术在数据上的统一形式，实现不同造型方法的数据转换。The purpose of the present invention is to overcome the deficiencies of the prior art. The present invention provides a method and device for constructing recursive curves and surfaces based on LW curves and surfaces, providing a unified form of data for different modeling techniques, and realizing data conversion of different modeling methods .

为了解决上述问题，本发明提出了一种基于LW曲线曲面的递归曲线曲面构建方法，所述方法包括：In order to solve the above problems, the present invention proposes a method for constructing recursive curves and surfaces based on LW curves and surfaces, said method comprising:

采用递推算法对曲线上的点进行计算，获得曲线上的点；Use the recursive algorithm to calculate the points on the curve to obtain the points on the curve;

对L曲线上的点进行导数计算，获得L曲线的高阶导数；Calculate the derivative of the points on the L curve to obtain the higher order derivative of the L curve;

设定n+m个顶点以及相应的节点信息，产生m段W曲线；Set n+m vertices and corresponding node information to generate m segment W curves;

根据顶点的权值和节点信息获得递归曲线。Obtain the recurrence curve according to the weight of the vertices and the information of the nodes.

优选地，所述采用递推算法对曲线上的点进行计算，获得曲线上的点的步骤包括：Preferably, said recursive algorithm is used to calculate the points on the curve, and the step of obtaining the points on the curve includes:

初始化曲线的数据结构；Initialize the data structure of the curve;

对曲线进行K次迭代；Perform K iterations on the curve;

获得上三角矩阵，该矩阵的值为所求曲线上的点。Obtains an upper triangular matrix whose values are the points on the sought curve.

相应地，本发明还提供一种基于LW曲线曲面的递归曲线曲面构建装置，所述装置包括：Correspondingly, the present invention also provides a device for constructing recursive curves and surfaces based on LW curves and surfaces, the device comprising:

点获取模块，用于采用递推算法对曲线上的点进行计算，获得曲线上的点；The point acquisition module is used to calculate the points on the curve by using a recursive algorithm to obtain the points on the curve;

导数获取模块，用于对L曲线上的点进行导数计算，获得L曲线的高阶导数；The derivative acquisition module is used to calculate the derivative of the point on the L curve to obtain the higher order derivative of the L curve;

W曲线产生模块，用于设定n+m个顶点以及相应的节点信息，产生m段W曲线；The W curve generation module is used to set n+m vertices and corresponding node information to generate m segments of W curves;

递归曲线获取模块，用于根据顶点的权值和节点信息获得递归曲线。The recursion curve acquisition module is used to obtain the recursion curve according to the weight of the vertices and node information.

优选地，所述点获取模块包括：Preferably, the point acquisition module includes:

初始化单元，用于初始化曲线的数据结构；The initialization unit is used to initialize the data structure of the curve;

迭代单元，用于对曲线进行K次迭代；An iteration unit is used to perform K iterations on the curve;

矩阵获取模块，用于获得上三角矩阵，该矩阵的值为所求曲线上的点。The matrix obtaining module is used to obtain the upper triangular matrix, the value of which is the point on the curve to be obtained.

在本发明实施例中，利用不同形式的曲线表示形式的递归本质，通过定义递归曲线合适的节点参数，来达到统一表示不同形式的曲线曲面的目的，可以与不同的曲线曲面形式进行转换，方便计算机使用同一种数据格式表示出不同定义形式下的曲线曲面。In the embodiment of the present invention, the recursive nature of different forms of curve representations is used to achieve the purpose of uniformly representing different forms of curves and surfaces by defining appropriate node parameters for recursive curves, which can be converted with different forms of curves and surfaces, which is convenient The computer uses the same data format to represent curves and surfaces under different definition forms.

附图说明Description of drawings

为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其它的附图。In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. Those skilled in the art can also obtain other drawings based on these drawings without creative work.

图1是本发明实施例的基于LW曲线曲面的递归曲线曲面构建方法的流程示意图；1 is a schematic flow diagram of a method for constructing a recursive curve and surface based on an LW curve and surface in an embodiment of the present invention;

图2是本发明实施例的LW曲线递归计算示意图；Fig. 2 is the LW curve recursive calculation schematic diagram of the embodiment of the present invention;

图3是本发明实施例中采用递推算法对曲线上的点进行计算的过程示意图；Fig. 3 is a schematic diagram of the process of calculating the points on the curve using a recursive algorithm in an embodiment of the present invention;

图4是本发明实施例的LW曲面单次计算示意图；Fig. 4 is a schematic diagram of a single calculation of an LW curved surface according to an embodiment of the present invention;

图5是本发明实施例的基于LW曲线曲面的递归曲线曲面构建装置的结构组成示意图。FIG. 5 is a schematic diagram of the structural composition of a recursive curve and surface construction device based on an LW curve and surface according to an embodiment of the present invention.

具体实施方式detailed description

下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有作出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

图1是本发明实施例的基于LW曲线曲面的递归曲线曲面构建方法的流程示意图，如图1所示，该方法包括：Fig. 1 is the schematic flow chart of the recursive curve surface construction method based on LW curve surface of the embodiment of the present invention, as shown in Fig. 1, this method comprises:

S1，采用递推算法对曲线上的点进行计算，获得曲线上的点；S1, using a recursive algorithm to calculate the points on the curve to obtain the points on the curve;

S2，对L曲线上的点进行导数计算，获得L曲线的高阶导数；S2, performing derivative calculation on points on the L curve to obtain a higher-order derivative of the L curve;

S3，设定n+m个顶点以及相应的节点信息，产生m段W曲线；S3, setting n+m vertices and corresponding node information, generating m segments of W curves;

S4，根据顶点的权值和节点信息获得递归曲线。S4. Obtain a recurrence curve according to the weights of vertices and node information.

其中，S1进一步包括：Among them, S1 further includes:

初始化曲线的数据结构；Initialize the data structure of the curve;

对曲线进行K次迭代；Perform K iterations on the curve;

具体实施中，如图2、图3所示，包括：(1)初始化数据结构：定义状态次数p＝0；m指向α[1]，n指向β[1]，二维数组vex[n][p]的第一列保存控制点，其后每一列保存迭代一次后计算得到的结果，取定s0<＝t<＝s1，迭代开始；In the specific implementation, as shown in Fig. 2 and Fig. 3, it includes: (1) initializing data structure: defining state times p=0; m points to α[1], n points to β[1], two-dimensional array vex[n] The first column of [p] saves the control points, and each subsequent column saves the result calculated after one iteration, set s0<=t<=s1, and the iteration starts;

(2)第K次迭代：(2) Kth iteration:

a)初始i＝0，m＝i+k,n＝i计算:a) Initial i=0, m=i+k, n=i calculation:

$v v e e x x = = \frac{β β [[n no]] - - t t}{β β [[n no]] - - α α [[m m]]} v v e e x x [[i i]] [[k k - - 11]] + + \frac{t t - - α α [[m m]]}{β β [[n no]] - - α α [[m m]]} v v e e x x [[i i + + 11]] [[k k - - 11]]$

将结果保存到vec[i][k]；save the result to vec[i][k];

b)i++，m++，n++；b) i++, m++, n++;

c)直到i＝n；重复a，退出本次迭代；c) until i=n; repeat a, exit this iteration;

(3)直到k＝p，重复步骤2；退出算法；(3) until k=p, repeat step 2; Exit the algorithm;

最后得到的结果vex矩阵是一个上三角矩阵，其中，vex[n][p]上的值即为所求曲线上的点。The final result vex matrix is an upper triangular matrix, where the value on vex[n][p] is the point on the desired curve.

在S2中，L曲线上点的导数计算公式如下：In S2, the formula for calculating the derivative of a point on the L curve is as follows:

${Q Q}^{,,} ((t t)) = = {na na}_{00}^{n no} (({L L}_{00}^{n no - - 11} ((t t)) - - {L L}_{11}^{n no - - 11} ((t t))));;$

其中 $a_{0}^{n} = \frac{1}{β [n] - α [2 n]};$ in $a_{0}^{no} = \frac{1}{β [no] - α [2 no]};$

而分别保存在vex[0][p-1]，vex[1][p-1]中。and Stored in vex[0][p-1], vex[1][p-1] respectively.

因此根据公式即可计算出曲线上点的一阶导数，递归地应用该式可以求得曲线的高阶导数。Therefore, the first-order derivative of the point on the curve can be calculated according to the formula, and the higher-order derivative of the curve can be obtained by recursively applying the formula.

在S3中，m段W曲线的拼接连续性需要满足一定的条件：In S3, the splicing continuity of m segment W curve needs to meet certain conditions:

考虑其中的两段曲线：Consider two of these curves:

$\{\begin{matrix} {w w}_{00}^{n no} ((t t)),, t t &Element; &Element; [[{s the s}_{00},, {s the s}_{11}]] \\ {w w}_{11}^{n no} ((t t)),, t t &Element; &Element; [[{s the s}_{11},, {s the s}_{22}]] \end{matrix}$

在拼接处达到C^n-1连续的条件为：The condition to achieve C ^n-1 continuity at the splice is:

$- - \frac{{b b}_{00}^{n no}}{{a a}_{00}^{n no}} = = \frac{11 - - {b b}_{11}^{n no}}{{a a}_{11}^{n no}},, {a a}_{i i}^{j j} < < 00$

或or

$- - \frac{11 - - {b b}_{00}^{n no}}{{a a}_{00}^{n no}} = = - - \frac{{b b}_{11}^{n no}}{{a a}_{11}^{n no}},, {a a}_{i i}^{j j} > > 00$

且and

是严格单调同增同减数列。 is a strictly monotonically increasing and decreasing sequence.

依据上述条件，数据格式下计算a，b：According to the above conditions, calculate a, b in the data format:

${a a}_{i i}^{j j} = = \frac{- - 11}{β β [[i i]] - - α α [[i i + + j j]]}$

${b b}_{i i}^{j j} = = \frac{β β [[i i]]}{β β [[i i]] - - α α [[i i + + j j]]}$

即可得出是否满足相应连续性的拼接条件。It can be obtained whether the splicing condition of the corresponding continuity is satisfied.

在S4中，节点信息则决定曲线类型，虽然递归曲线可以表示很多曲线，其中包含常用的一些曲线。In S4, the node information determines the curve type, although the recursive curve can represent many curves, including some commonly used curves.

参数t∈[s₀,s₁]时，When parameter t∈[s ₀ ,s ₁ ],

设置节点值α为定值-s₁，节点值β为定值s₀，则曲线为bezier形式等价的L曲线：Set the node value α to a fixed value -s ₁ , and the node value β to a fixed value s ₀ , then the curve is an equivalent L curve in Bezier form:

设置节点值α为属于[s₀,s₁]的递增数列且α[1]＝s₀，Set the node value α as an increasing sequence belonging to [s ₀ ,s ₁ ] and α[1]=s ₀ ,

α[n+p-1]＝s1，节点值β为α[1],α[2]…α[n]，则曲线为Lagrange插值形式等价的递归曲线，注意虽然拉格朗日插值曲线不是L曲线，但依然具有相似的递归形式，故本发明实施例中数据结构依然适用。α[n+p-1]=s1, the node value β is α[1], α[2]...α[n], then the curve is a recursive curve equivalent to the Lagrange interpolation form, note that although the Lagrange interpolation curve It is not an L curve, but still has a similar recursive form, so the data structure in the embodiment of the present invention is still applicable.

设置节点值α为任意递增节点，节点值Set node value α to any incremental node, node value

β[i]＝-α[i+p-1],i＝1,2,...,n，则曲线为与nurbs曲线某一段等价的L曲线。β[i]=-α[i+p-1], i=1,2,...,n, then the curve is an L curve equivalent to a section of the nurbs curve.

递归曲线对于细分方法的表示具有天然的优势，因为曲线细分方法本质上就是递归插值。每一个插值段上选取不同的分割就可以得出不同的细分方法，主要在于调配函数的选取，而节点值直接相关与调配函数。以DeRham算法(即割角算法)为例进行说明：Recursive curves have a natural advantage for the representation of subdivision methods, because curve subdivision methods are essentially recursive interpolation. Different subdivision methods can be obtained by selecting different divisions on each interpolation segment, mainly in the selection of the allocation function, and the node value is directly related to the allocation function. Take the DeRham algorithm (that is, the cutting corner algorithm) as an example to illustrate:

初始条件：n+1个顶点，节点信息；Initial conditions: n+1 vertices, node information;

进行一次迭代：Do an iteration:

a)利用节点信息计算割角参数a) Use node information to calculate cutting angle parameters

b)以一个固定的参数值t1进行计算，得到n个新顶点；b) Calculate with a fixed parameter value t1 to obtain n new vertices;

c)再以一个固定的参数值t2进行计算，也得到n个新顶点；c) Calculate with a fixed parameter value t2, and also get n new vertices;

d)将这2n歌顶点组合起来得到2n+1个新顶点，这就是下一次割角的控制点；d) Combine these 2n song vertices to get 2n+1 new vertices, which is the control point for the next corner cut;

一次迭代结束。One iteration ends.

本发明实施例所定义的数据结构中的权因子若制定为非定值，那么说明所表示的曲线是有理递归曲线，从有理L曲线的定义中可以看出，权因子与控制点每一步递归都是应用了相同的计算转换，因此，可以使用齐次坐标将控制点坐标从三维映射到4维，在4维的齐次坐标中，有理L曲线变为非有理L曲线，因而可以应用非有理形式下的大部分计算方法，得到结果后再投影回3维空间即可。If the weight factor in the data structure defined in the embodiment of the present invention is formulated as an indefinite value, then the curve represented is a rational recursive curve. As can be seen from the definition of the rational L curve, the weight factor and the control point are recursive in each step The same calculation transformation is applied, therefore, the control point coordinates can be mapped from 3D to 4D using homogeneous coordinates. In 4D homogeneous coordinates, rational L curves become non-rational L curves, so non-rational L curves can be applied For most calculation methods in rational form, it is enough to project back to 3-dimensional space after obtaining the result.

采用与二次bezier形式等价的有理L曲线形式，可以精确表示圆锥曲线，其中三个控制点权因子的选择分别为w₀，w₁，w₂。Using the rational L-curve form equivalent to the quadratic bezier form, the conic section can be accurately represented, and the weight factors of the three control points are selected as w ₀ , w ₁ , and w ₂ .

设定w₀＝w₂，设定不同关系的w₁以表示不同类型的圆锥曲线：Set w ₀ =w ₂ , set w ₁ of different relations to represent different types of conic sections:

(W₁/w₀)²＝1，则表示的是抛物线；(W ₁ /w ₀ ) ² =1, it means a parabola;

(W₁/w₀)²>1，则表示的是双曲线；(W ₁ /w ₀ ) ² >1, it means a hyperbola;

(W₁/w₀)²<1，则表示的是椭圆。(W ₁ /w ₀ ) ² <1 means an ellipse.

从曲面的定义上看，L曲面是张量积形式的曲面，采用曲线上点的递归计算算法可以求出曲面上的点，2次应用算法1即可求出曲面上的点。至于先计算u方向还是先计算v方向，有边界曲线的次数决定。From the definition of a surface, an L surface is a surface in the form of a tensor product. The points on the surface can be obtained by using the recursive calculation algorithm of points on the curve, and the points on the surface can be obtained by applying Algorithm 1 twice. Whether to calculate the u direction or the v direction first depends on the number of boundary curves.

如图4所示，初始化数据结构，定义状态次数p＝0，q＝0；i指向α[1]，j指向β[1]，a指向φ[1]，b指向二维数组vex[n][m]的保存初始(n+1)(m+1)个控制点，取定s₀<＝u<＝s₁，z₀<＝v<＝z₁；As shown in Figure 4, initialize the data structure, define the number of states p=0, q=0; i points to α[1], j points to β[1], a points to φ[1], b points to Preserve the initial (n+1)(m+1) control points of the two-dimensional array vex[n][m], set s ₀ <= u<=s ₁ , z ₀ <= v<= z ₁ ;

若p<q；if p<q;

使用q，a，b，v，vex[n][k]作为初始条件应用q次算法1；Apply Algorithm 1 q times using q, a, b, v, vex[n][k] as initial conditions;

使用p，i，j，u，第二步的结果，作为初始条件应用q次算法1；Using p, i, j, u, the result of the second step, as initial conditions, apply Algorithm 1 q times;

最后得到的记过就是曲面上的点。The resulting demerits are points on the surface.

相应地，本发明实施例还提供一种基于LW曲线曲面的递归曲线曲面构建装置，如图5所示，该装置包括：Correspondingly, the embodiment of the present invention also provides a device for constructing recursive curves and surfaces based on LW curves and surfaces, as shown in FIG. 5 , the device includes:

点获取模块1，用于采用递推算法对曲线上的点进行计算，获得曲线上的点；The point acquisition module 1 is used to calculate the points on the curve by using a recursive algorithm to obtain the points on the curve;

导数获取模块2，用于对L曲线上的点进行导数计算，获得L曲线的高阶导数；The derivative acquisition module 2 is used to calculate the derivative of the point on the L curve to obtain the higher order derivative of the L curve;

W曲线产生模块3，用于设定n+m个顶点以及相应的节点信息，产生m段W曲线；W curve generation module 3, used to set n+m vertices and corresponding node information, and generate m segments of W curve;

递归曲线获取模块4，用于根据顶点的权值和节点信息获得递归曲线。The recurrence curve obtaining module 4 is used to obtain the recurrence curve according to the weights of vertices and node information.

进一步地，点获取模块1包括：Further, point acquisition module 1 includes:

本发明的装置实施例中各功能模块的功能可参见本发明方法实施例中的流程处理，这里不再赘述。For the functions of each functional module in the device embodiment of the present invention, refer to the process processing in the method embodiment of the present invention, which will not be repeated here.

本领域普通技术人员可以理解上述实施例的各种方法中的全部或部分步骤是可以通过程序来指令相关的硬件来完成，该程序可以存储于一计算机可读存储介质中，存储介质可以包括：只读存储器(ROM，ReadOnlyMemory)、随机存取存储器(RAM，RandomAccessMemory)、磁盘或光盘等。Those of ordinary skill in the art can understand that all or part of the steps in the various methods of the above-mentioned embodiments can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium, and the storage medium can include: Read-only memory (ROM, ReadOnlyMemory), random access memory (RAM, RandomAccessMemory), magnetic disk or optical disk, etc.

另外，以上对本发明实施例所提供的基于LW曲线曲面的递归曲线曲面构建方法及其装置进行了详细介绍，本文中应用了具体个例对本发明的原理及实施方式进行了阐述，以上实施例的说明只是用于帮助理解本发明的方法及其核心思想；同时，对于本领域的一般技术人员，依据本发明的思想，在具体实施方式及应用范围上均会有改变之处，综上所述，本说明书内容不应理解为对本发明的限制。In addition, the method and device for constructing recursive curves and surfaces based on LW curves and surfaces provided by the embodiments of the present invention have been introduced in detail above. In this paper, specific examples are used to illustrate the principles and implementation methods of the present invention. The above embodiments The description is only used to help understand the method of the present invention and its core idea; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation and scope of application. In summary , the contents of this specification should not be construed as limiting the present invention.

Claims

1. a method for constructing recursive curves and surfaces based on LW curves and surfaces, is characterized in that, said method comprises:

Use the recursive algorithm to calculate the points on the curve to obtain the points on the curve;

Calculate the derivative of the points on the L curve to obtain the higher order derivative of the L curve;

Set n+m vertices and corresponding node information to generate m segment W curves;

Obtain the recurrence curve according to the weight of the vertices and the information of the nodes.

2. the recursive curve surface construction method based on LW curve surface as claimed in claim 1, is characterized in that, described adopting recursive algorithm to calculate the point on the curve, the step of obtaining the point on the curve comprises:

Initialize the data structure of the curve;

Perform K iterations on the curve;

Obtains an upper triangular matrix whose values are the points on the sought curve.

3. a kind of recursive curve surface construction device based on LW curve surface, it is characterized in that, described device comprises:

The point acquisition module is used to calculate the points on the curve by using a recursive algorithm to obtain the points on the curve;

The derivative acquisition module is used to calculate the derivative of the point on the L curve to obtain the higher order derivative of the L curve;

The W curve generation module is used to set n+m vertices and corresponding node information to generate m segments of W curves;

The recursion curve acquisition module is used to obtain the recursion curve according to the weight of the vertices and node information.

4. the recursive curve surface construction device based on LW curve surface as claimed in claim 3, is characterized in that, described point acquisition module comprises:

The initialization unit is used to initialize the data structure of the curve;

An iteration unit is used to perform K iterations on the curve;

The matrix obtaining module is used to obtain the upper triangular matrix, the value of which is the point on the curve to be obtained.