Apparatus and method of designing polynomial curves

Abstract

The present invention relates to polynomial curve design technology, and more specifically, to an apparatus and method for designing polynomial curves using radial polygons and interpolation polygons. According to an embodiment of the present invention, the radial polygon and the curve itself can be controlled simultaneously, and local control is enabled to finely adjust the curve in specific sections by allowing the curve to accurately pass through designated points, thereby improving the precision and flexibility of curve design. Furthermore, by supporting precise data interpolation adjustment even for high-order polynomial curves, complex curves can be designed more efficiently, and the shape and length of the curve can be precisely controlled simultaneously.

Description

Technology Field

[0001] The present invention relates to a polynomial curve design technique, and more specifically, to an apparatus and method for designing a polynomial curve using radial polygons and interpolation polygons. Background Technology

[0003] In fields such as computer graphics, font design, and computer-aided design / manufacturing (CAD / CAM), various types of curves are used to represent geometric shapes or the movement trajectories of objects. Among these curves, the most fundamental are polynomial curves, and the most widely used method of representing polynomial curves in the design process is the Bézier curve ( It is a Curve). Bézier curves have a simple mathematical structure, and Bézier controlled polygons ( It has the advantage of enabling intuitive design using control polygons. On the other hand, if the shape of the curve to be designed becomes complex, more control points are required, and consequently, the degree of the curve increases. In high-order polynomial curves, Bézier control polygons can become excessively large compared to the curve, which has the disadvantage of making curve design increasingly difficult. To address this problem, the Gauss-Legendre (GL) curve was proposed as a polynomial curve representation method utilizing hodograph control polygons. This method has the advantage of enabling the design of high-order polynomial curves by precisely designing the shape of the curve based on nodes and weights. While the Gauss-Legendre curve maintains the endpoint interpolation characteristic, it has a limitation in that it is difficult to finely adjust the curve in specific sections because the direct influence of the hodograph polygon is limited only to the curve's hodograph, thereby restricting control over intermediate curve points.

[0004] Therefore, improved polynomial curve design technology is required that enables local control and fine-tuning while maintaining the advantages of the Gauss-Legendre curve.

[0005] The background technology of the present invention is disclosed in Korean Registered Patent No. 10-262060. The problem to be solved

[0007] The present invention provides a polynomial curve design apparatus and method that defines the basic shape of a curve using hodograph polygons and enables detailed adjustment of the curve using interpolation polygons.

[0008] The technical problems that the present invention aims to solve are not limited to those mentioned above, and other unmentioned technical problems will be clearly understood by those skilled in the art to which the present invention belongs from the description below. means of solving the problem

[0010] According to one aspect of the present invention, a polynomial curve design device is provided.

[0011] A polynomial curve design device according to one embodiment of the present invention may include a node determination unit for determining a node, a weight determination unit for determining a weight, a polynomial calculation unit for calculating a polynomial basis using the node and the weight, a radiograph polygon generation unit for setting a curve tangent vector at the node using an input point and generating a radiograph polygon, an interpolation polygon generation unit for setting a point that the curve must pass through using an input point and generating an interpolation polygon, and a polynomial curve generation unit for generating a curve using the radiograph polygon, the interpolation polygon, and the polynomial basis.

[0012] According to another aspect of the present invention, a method for designing a polynomial curve and a computer program for executing the same are provided.

[0013] A method for designing a polynomial curve according to one embodiment of the present invention and a computer program for executing the same may include the steps of determining a node, determining a weight, calculating a polynomial basis using the node and the weight, setting a tangent vector of the curve at the node using an input point and generating a radial polygon, setting a point that the curve must pass through using an input point and generating an interpolation polygon, and generating a curve using the radial polygon, the interpolation polygon, and the polynomial basis. Effects of the invention

[0015] According to an embodiment of the present invention, the hodograph and the curve itself can be controlled simultaneously, and local control is enabled so that the curve can accurately pass through a designated interpolation point, thereby allowing for fine adjustment of the curve in a specific section, which improves the precision and flexibility of the curve design.

[0016] In addition, it supports precise data interpolation adjustments even for high-order polynomial curves, enabling more efficient design of complex curves and precise simultaneous control of the curve's shape and length.

[0017] The effects of the present invention are not limited to the effects described above, and should be understood to include all effects that can be inferred from the composition of the invention described in the description or claims of the present invention. Brief explanation of the drawing

[0019] FIG. 1 is a drawing for explaining a polynomial curve design device according to one embodiment of the present invention. FIG. 2 is an exemplary diagram showing the form of a polynomial basis function of a Gauss-Legendre-Lagrange curve (GLL) defined according to an embodiment of the present invention. FIG. 3 is an example diagram showing the difference between a Gauss-Legendre curve generated based on a hodograph polygon according to an embodiment of the present invention and a Gauss-Legendre-Lagrange curve generated based on a hodograph polygon and an interpolation polygon. FIG. 4 is an exemplary drawing showing a change in the shape of a curve that occurs when the control points of a Gauss-Legendre-Lagrange curve are modified according to an embodiment of the present invention. FIG. 5 is a rational Bézier curve using the Gauss-Legendre-Lagrange curve according to one embodiment of the present invention. Example drawing showing a method for approximating a curve. FIG. 6 is an exemplary drawing showing various Gauss-Legendre-Lagrange curves obtained by fine-tuning a Gauss-Legendre curve, which is a high-order polynomial curve, using a polynomial curve design device according to one embodiment of the present invention. FIG. 7 is a drawing for explaining a polynomial curve design method according to an embodiment of the present invention. Specific details for implementing the invention

[0020] The present invention is susceptible to various modifications and may have various embodiments; therefore, specific embodiments are illustrated in the drawings and described in detail. However, this is not intended to limit the present invention to specific embodiments, and it should be understood that the invention includes all modifications, equivalents, and substitutions that fall within the spirit and scope of the invention. In describing the present invention, detailed descriptions of related prior art are omitted if it is determined that such detailed descriptions would unnecessarily obscure the essence of the invention. Furthermore, singular expressions used in this specification and claims should generally be interpreted to mean "one or more" unless otherwise stated.

[0021] Throughout the specification, when it is stated that a part is "connected (connected, in contact, combined)" with another part, this includes not only cases where they are "directly connected," but also cases where they are "indirectly connected" with other members interposed between them. Furthermore, when it is stated that a part "includes" a certain component, this means that, unless specifically stated otherwise, it does not exclude other components but rather allows for the inclusion of additional components.

[0022] The terms used herein are merely for describing specific embodiments and are not intended to limit the invention. Singular expressions include plural expressions unless the context clearly indicates otherwise. In this specification, terms such as “comprising” or “having” are intended to indicate the presence of the features, numbers, steps, actions, components, parts, or combinations thereof described in the specification, and should be understood as not precluding the existence or addition of one or more other features, numbers, steps, actions, components, parts, or combinations thereof.

[0023] The present invention will be described below with reference to the attached drawings. However, the present invention may be implemented in various different forms and is not limited to the embodiments described herein. Furthermore, in order to clearly explain the present invention in the drawings, parts unrelated to the explanation have been omitted, and similar parts throughout the specification have been given similar reference numerals.

[0025] FIG. 1 is a drawing for explaining a polynomial curve design device according to one embodiment of the present invention.

[0026] Referring to FIG. 1, the polynomial curve design device (10) includes a node determination unit (100), a weight determination unit (110), a polynomial calculation unit (130), a radial polygon generation unit (150), an interpolation polygon generation unit (170), and a polynomial curve generation unit (190).

[0027] The node determination unit (100) determines a node. At this time, the node determination unit (100) can determine the node according to a numerical quadrature such as the Gauss-Legendre quadrature or the Gauss-Lobatto quadrature. The node determination unit (100) determines different given within the domain range of the curve. individual (single, A node of (natural number) can be used. For example, the node determination unit (100) uses a polynomial curve design device (10) in a section function in The definite integral of Used when calculating numerically nodes You can select the node determination unit (100). In addition, the node determination unit (100) can select the integration interval. Assuming The definite integral of You can select a node for the Gauss-Legendre numerical quadrature or the Gauss-Lovato numerical quadrature used when calculating.

[0028] The weight determination unit (110) at each node A weight is determined that reflects the contribution of. At this time, the weight determining unit (110) can determine the weight according to the Gauss-Legendre numerical quadrature, the Gauss-Lovato numerical quadrature, etc. The weight determining unit (110) determines different given within the domain range of the curve. individual (single, is a natural number) corresponding to the node individual (single, It can determine the weight of (natural number). The node determined in this way and weights If you use the section Function defined in The definite integral of It can calculate. For example, the weight determination unit (110) can calculate the integration interval. Assuming The definite integral of The weights used when calculating the Gauss-Legendre numerical quadrature or the Gauss-Lovato numerical quadrature of the following mathematical formula 1 can be obtained. At this time, if the weights obtained from the weight determination unit (110) are used, the function Approximate value even in situations where it is difficult to calculate the integral value You can obtain.

[0029] [Mathematical Formula 1]

[0030]

[0031] In this equation is the number of nodes, and the node silver Gauss-Legendre polynomial of degree It is the roots of arranged in order from smallest to largest. The weight corresponding to each node is determined by mathematical formula 2.

[0032] [Mathematical Formula 2]

[0033]

[0034] Here, Is of the Gauss-Legendre polynomial of degree It is the derivative value at, and silver of the Gauss-Legendre polynomial of degree It means the function value at.

[0035] The polynomial calculation unit (130) calculates a polynomial basis using the node determined by the node determination unit (110) and the weight determined by the weight determination unit (130). For example, the polynomial calculation unit (130) second polynomial basis when referred to as a Gauss-Legendre polynomial basis or a Gauss-Lovato polynomial basis can calculate, second When referred to as a Gauss-Legendre-Lagrange polynomial basis, the polynomial basis It can calculate.

[0036] In the polynomial calculation unit (130) The process of calculating the Gauss-Legendre-Lagrange polynomial basis of the difference The process may include calculating a polynomial that satisfies a specific condition in which only one of the values ​​is 1 and the rest are all 0. First, the polynomial calculation unit (130) calculates the polynomial The degree given by mathematical formula 3 If we call it a polynomial, then and the rest ( and A polynomial where all values ​​of are 0 It may include.

[0037] [Mathematical Formula 3]

[0038]

[0039] The polynomial calculation unit (130) person Regarding the degree polynomial When is equal to mathematical equation 4, the polynomial The degree given as If we say that it is a polynomial, and the rest , and , (step, Igo A polynomial where all values ​​of ) are 0 It may include.

[0040] [Mathematical Formula 4]

[0041]

[0042] The polynomial calculation unit (130) person and polynomial polynomial for cast The degree given as If we say that it is a polynomial, and the rest , and , (step, Igo A polynomial where all values ​​of ) are 0 It may include.

[0043] Additionally, the polynomial calculation unit (130) may include generating a polynomial basis for generating a curve having two given polygons A and B as a hodograph polygon and an interpolation polygon, respectively. For example of (single, is a natural number) having a side Polygons in space and having dog dots Polygons in space For , having this as a Gaussian-Legendre polygon and an interpolation polygon, respectively Polynomial curves of degree or less to ensure that is determined as in mathematical formula 5 Gauss-Legendre-Lagrange polynomial basis of difference It may include generating.

[0044] [Mathematical Formula 5]

[0045]

[0046] At this time Gauss-Legendre-Lagrange polynomial basis of difference It can be created as follows.

[0047] First, in the case of a problem in one-dimensional space, ordered pairs of real numbers class ordered pairs of real numbers Regarding (however, is a natural number) , and (step, Is The degree that satisfies all conditions (all natural numbers) Polynomials less than or equal to is a polynomial defined in the polynomial calculation unit (130) Using a linear combination of It can be summarized as mathematical equation 6.

[0048] [Mathematical Formula 6]

[0049]

[0050] polynomial cast Equation 6 can be rearranged into Equation 7 to be expressed in the form of a barycentric combination.

[0051] [Mathematical Formula 7]

[0052]

[0053] In this equation person About Igo am.

[0054] To simplify mathematical equation 7, first Functions that constitute the Gaussian-Legendre-Lagrange polynomial basis of the difference ( ) can be defined as mathematical formula 8.

[0055] [Mathematical Formula 8]

[0056] , , ( )

[0057] Gauss-Legendre-Lagrange polynomial basis of difference If you use it, the polynomial of mathematical expression 7 It can be expressed as mathematical formula 9.

[0058] [Mathematical Formula 9]

[0059]

[0060] At this time, a mistake class Regarding the degree Polynomials less than or equal to The necessary and sufficient condition for ga to be given by mathematical equation 9 is , and (step, Is It satisfies all natural numbers (and), and in this case am.

[0061] thus of (single, is a natural number) having a side Polygons in space and having dog dots Polygons in space For , having this as a Gaussian-Legendre polygon and an interpolation polygon, respectively Polynomial curves of degree or less Is Gauss-Legendre-Lagrange polynomial basis It is determined as in mathematical formula 5 using .

[0062] Also, the Gaussian-Legendre-Lagrange polynomial basis in the polynomial calculation unit (130) The degree is Vector space of polynomials less than or equal to It forms the basis of and is a unit partition property It satisfies the unit partitioning property. The unit partitioning property plays a very important role in the process of generating polynomial curves from control polygons, because if the polynomial bases do not have the unit partitioning property, the polynomial curve generated using them will not maintain its shape and will be deformed as the control polygon is translated.

[0063] The hodograph polygon generation unit (150) uses points input by the user to specify the tangent vector of the curve at the node and determines the hodograph polygon that serves as a sketch in the curve design. Specifically, the hodograph polygon of the curve is a polygon determined by the node and weights and is constructed from the tangent vector information of the curve at the node. For example, interval Defined in Curves in space For , the node and weight respectively class The curve when The hodograph polygon is the point determined by mathematical formula 10 Variation obtained by connecting in order individual polygons am.

[0064] [Mathematical Formula 10]

[0065]

[0066] For example, the hodograph polygon generating unit (150) of (single, polygons with sides that are natural numbers It can generate. Here, the curve generated based on this A given polygon About , , that is, it means that mathematical equation 10 must be satisfied. At this time, Since it satisfies, the curve generated through the hodograph polygon The tangent vector at the point and the position of the curve at both endpoints can be adjusted. At this time, the hodograph polygon generated by the hodograph polygon generator (150) may be a Gauss-Legendre polygon, which is a hodograph polygon using nodes and weights of the Gauss-Legendre numerical quadrature, or a Gauss-Lovato polygon, which is a hodograph polygon using nodes and weights of the Gauss-Lovato numerical quadrature. The hodograph polygon generator (150) can freely adjust the shape of the polygon by utilizing a polynomial curve design device to allow the user to change the position of each point of the hodograph polygon. Ultimately, this allows the hodograph of the curve at the node and the position of the curve at both endpoints to be adjusted.

[0067] The interpolation polygon generation unit (170) uses points input by the user to set points that the curve must pass through and determines the interpolation polygon. Specifically, the interpolation polygon of the curve is a polygon determined by the nodes and is constructed from the position of the curve at the nodes. Specifically, the interval Defined in Curves in space Regarding , the node When this of (single, silver natural number) node The interpolation polygon for is a point individual polygons is. For example, the interpolation polygon generation unit (170) is generated by the node determination unit (100). Based on the interpolation conditions in of (single, is a natural number) point A polygon composed of It can generate. Here, the point is (however, The curve generated go A point that must be passed, that is This means that it must satisfy [the condition]. The interpolation polygon generation unit (170) can use a polynomial curve design device to set or change the position of the interpolation point that the user must pass through, thereby finely adjusting the curve and designing a curve of the desired shape. In addition, the interpolation polygon generation unit (170) can use a polynomial curve design device to move the interpolation point while the curve is drawn, thereby precisely designing the shape of the entire curve by reflecting the position of the new interpolation point while maintaining the slope at the interpolation point.

[0068] The polynomial curve generation unit (190) generates a polynomial curve using the generated hodograph polygon, the interpolation polygon, and the polynomial basis. For example, the polynomial curve generation unit (190) second When calling it a Gauss-Legendre polynomial basis of degree spatial An arbitrary polygon with sides For this polygon, the one that has this polygon as a Gauss-Legendre polygon Polynomial curves of degree less than or equal to are determined as in Equation 11. (However, is a natural number)

[0069] [Mathematical Formula 11]

[0070]

[0071] At this time, spatial polynomial curves of degree or less The necessary and sufficient condition for to be equal to mathematical equation 11 is and, in this case am.

[0072] As another example of a polynomial curve generation unit (190) generating a polynomial curve using a generated hodograph polygon, an interpolation polygon, and a polynomial basis, second Assuming it is a Gaussian-Legendre-Lagrange polynomial basis of the difference, a curve is generated according to Equation 5. To explain in more detail: Having dog feces Polygons in space class having dog dots Polygons in space For , this polygon has a Gaussian-Legendre polygon and an interpolation polygon, respectively. The spatial order Gauss-Legendre-Lagrange (GLL) curve Generate according to mathematical formula 5. At this time The spatial order Polynomial curves less than or equal to The necessary and sufficient condition for satisfying mathematical equation 5 is , It is satisfying, and when satisfying this am.

[0074] FIG. 2 is an example diagram showing the form of a function constituting a Gaussian-Legendre-Lagrange polynomial basis defined according to one embodiment of the present invention.

[0075] Referring to FIG. 2, (a), (b), and (c) of FIG. 2 are polynomial basis functions at The value of ( The degree of the polynomial basis function changes depending on ), and changes differently according to that degree These are drawings for representing graphs. The polynomial curve design device (10) is according to the user's needs. It can be seen that higher-dimensional polynomials and curves can be generated by increasing . First, When, a polynomial of degree 2 , , The graph of can be represented as (a). When, a polynomial of degree 4 , , , , The graph of can be represented as (b). When, a polynomial of degree 6 , , , , , , The graph of can be represented as (c).

[0077] FIG. 3 is an example diagram showing the difference between a Gauss-Legendre curve generated based on a hodograph control polygon according to one embodiment of the present invention and a Gauss-Legendre-Lagrange curve generated based on a hodograph polygon and an interpolation polygon.

[0078] Referring to FIG. 3, FIG. 3(a) shows a Gauss-Legendre curve generated based on a hordograph control polygon, FIG. 3(b) shows a Gauss-Legendre-Lagrange curve generated using a hordograph polygon and an interpolation polygon, and FIG. 3(c) is a diagram showing curve (a) and curve (b) together for comparison. Specifically, points , , , For , the curve in (a) is space A polygon with 3 sides A cubic Gauss-Legendre curve that has a Gauss-Legendre polygon is. The curve in (b) is a polygon Although it has a Gaussian-Legendre polygon, the point , , Regarding polygons A Gauss-Legendre-Lagrange curve of degree 6 that has as its interpolation polygon .... Comparing the two curves (a) and (b) in (c), since the two curves share a hodograph polygon with the same three sides, the tangent vector at each node and You can see that it matches. However, the points at each node and is different, and this interpolation polygon reflecting the condition point of It is the result of passing exactly.

[0080] FIG. 4 is an example diagram showing a change in the shape of a curve that occurs when the control points of a Gauss-Legendre-Lagrange curve are modified according to one embodiment of the present invention.

[0081] Referring to Fig. 4, the Gauss-Legendre polygon and interpolation polygon The Gauss-Legendre-Lagrange curve of degree 6 or less generated by is a point or point You can check how the shape of the curve changes when modifying it. Fig. 4(a) is the interpolation point of the interpolation polygon. It shows the change in the curve when only the polygon is modified. In Fig. 4(a), the polygon Gauss-Legendre curves of degree 3 or less that have as a Gauss-Legendre polygon (400) appears. At this time, the interpolation point cast ( and polygon A Gauss-Legendre-Lagrange curve of degree 6 or less that has as a Gauss-Legendre polygon is exactly a curve It is identical to. (a) is the interpolation point on this Gauss-Legendre-Lagrange curve (400). A Gauss-Legendre-Lagrange curve (410) generated by continuously moving only to the right is shown. The interpolation point of the Gauss-Legendre-Lagrange curve in (a) When shifting to the right, the parameter t In the region close to it, the curve shifts to the right, but In regions far from it, the curve points hardly change.

[0082] Figure 4(b) shows the control points of a Gaussian-Legendre polygon. It shows the change in the curve when only the X point-dashed line (430) is the same curve as the Gauss-Legendre-Lagrange curve (400) in (a), and in (b) the control point on the X point-dashed line (430) curve The Gauss-Legendre-Lagrange curve (450) when moving only to points c and d, and the control point on the curve of point X-dashed line (430). The Gauss-Legendre curve (470) appears when only is moved to points c and d. A point of the Gauss-Legendre polygon in (b) If you keep moving it to the bottom left, for the Gauss-Legendre-Lagrange curve (450), the parameter t In the range, the curve is deformed to the lower left, but in other ranges, the curve hardly changes. In contrast, the Gauss-Legendre curve (470) changes very severely overall regardless of the range of the parameter t. That is, the polynomial curve design device (10) is designed to modify the control points of the Gauss-Legendre-Lagrange curve so as not to affect the entire curve, but to affect a locally limited range, thereby allowing only specific parts to be modified while maintaining the overall shape of the curve.

[0084] FIG. 5 is a rational Bézier curve using the Gauss-Legendre-Lagrange curve according to one embodiment of the present invention. This is an example diagram showing a method for approximating a curve.

[0085] Referring to FIG. 5, FIG. 5(a) is a Bézier curve and glass Bézier curve This is a diagram representing. The two curves are identical Bézier controlled polygons. It is defined by the rational Bézier curve The weight It is a curve generated by... (b) Gauss-Legendre curve is a Bézier curve A curve generated from a Gaussian-Legendre controlled polygon, a curve is a curve It is exactly the same curve as (b). The Gauss-Legendre-Lagrange curve is a curve Having the Gauss-Legendre control polygon as a Gauss-Legendre polygon, A rational Bézier curve is a 6th-order curve that has as an interpolation polygon. is an approximate curve. As can be seen in Fig. 5, the shape of a rational Bézier curve can be approximated using higher-order polynomial curves through the Gauss-Legendre-Lagrange curve. (c) is a rational Bézier curve and the Gauss-Legendre-Lagrange curve This is a drawing that compares shapes by overlaying them, which confirms the high approximation accuracy of the Gauss-Legendre-Lagrange curve. In other words, it can be seen that fine-tuning is easy using the Gauss-Legendre-Lagrange curve.

[0087] FIG. 6 is an exemplary diagram illustrating the process of fine-tuning a high-order polynomial curve into a Gaussian-Legendre-Lagrange curve using a polynomial curve design device according to one embodiment of the present invention.

[0088] Referring to FIG. 6, (a) is the Gaussian-Legendre polygon of the curve being designed (b) is a diagram showing a Gauss-Legendre polygon, which has 16 sides. (b) is a diagram showing a Gauss-Legendre curve of degree 16 generated by a Gauss-Legendre polygon. (c) is a diagram showing the Gauss-Legendre polygon and the Gauss-Legendre curve generated therefrom together, showing how the curve follows the shape of the Gauss-Legendre polygon. (d) to (i) are example diagrams showing Gauss-Legendre-Lagrange curves designed using a Gauss-Legendre polygon and an interpolation polygon, showing various forms of curves generated by adjusting the interpolation points while maintaining the Gauss-Legendre polygon. In (d) to (i), the Gauss-Legendre curve of (b) is shown as a dotted line, and each Gauss-Legendre-Lagrange curve modified from it is shown as a solid line to facilitate comparison. The curves indicated by solid lines in (d) through (i) are Gauss-Legendre-Lagrange curves obtained by fine-tuning the Gauss-Legendre curve indicated by dotted line in (b). These curves are generated by fine-tuning them using interpolation points to possess unique detailed features while maintaining a shape similar to the Gauss-Legendre curve. In other words, this example demonstrates that it is easy to fine-tune curves using Gauss-Legendre-Lagrange curves.

[0090] FIG. 7 is a drawing for explaining a polynomial curve design method according to one embodiment of the present invention.

[0091] Referring to FIG. 7, in step S710, the polynomial curve design device (10) determines nodes and weights. The polynomial curve design device (10) determines different given within the domain range of the curve. of (but, Nodes (natural numbers) can be used, and weights corresponding to each node can be determined. Additionally, the polynomial curve design device (10) can determine nodes and weights based on the Gaussian-Legendre numerical quadrature method. Integration interval Assuming The definite integral of Calculate the function using the Gauss-Legendre numerical quadrature. Approximate value even in situations where it is difficult to calculate the integral value You can obtain.

[0092] In step S730, the polynomial curve design device (10) can calculate a polynomial basis using the nodes and weights determined in step S710. The polynomial curve design device (10) second When referred to as a Gauss-Legendre polynomial basis of degree can produce, second When referred to as a Gauss-Legendre-Lagrange polynomial basis of degree It can produce.

[0093] In step S750, the polynomial curve design device (10) generates a radial polygon using points input by the user and generates an interpolation polygon using points that the curve must pass through. The polynomial curve design device (10) allows the user to freely adjust the shape of the polygon by changing the position of each control point of the radial polygon, and allows the user to fine-tune the curve and design a curve of the desired shape by setting or changing the position of the interpolation point that the user must pass through. Additionally, when the interpolation point is moved while the curve is drawn, the polynomial curve design device (10) can precisely design the shape of the entire curve by reflecting the position of the new interpolation point while maintaining the slope at the interpolation point.

[0094] In step S770, the polynomial curve design device (10) generates a polynomial curve using each control point of the generated hodograph polygon, the interpolation points of the interpolation polygon, and a polynomial basis. The polynomial curve design device (10) hodograph polygon with sides Adjust the overall shape of the curve with, interpolation polygon with points A Gauss-Legendre-Lagrange (GLL) curve is generated to pass through the interpolation point. At this time, the polynomial curve design device (10) uses a hodograph polygon to adjust the velocity vector of the curve and interpolates the curve while maintaining the slope.

[0096] The polynomial curve design method described above can be implemented as computer-readable code on a computer-readable medium. The computer-readable recording medium may be, for example, a removable recording medium (CD, DVD, Blu-ray disc, USB storage device, removable hard disk) or a fixed recording medium (ROM, RAM, computer-equipped hard disk). The computer program recorded on the computer-readable recording medium can be transmitted to another computing device via a network such as the Internet and installed on the other computing device, thereby allowing it to be used on the other computing device.

[0097] Although it has been described above that all components constituting an embodiment of the present invention are combined or operate as a single unit, the present invention is not necessarily limited to such an embodiment. That is, within the scope of the purpose of the present invention, all components may be selectively combined in one or more ways to operate.

[0098] Although operations are depicted in a specific order in the drawings, it should not be understood that the operations must be executed in the specific order depicted or in a sequential order, or that all depicted operations must be executed to obtain the desired result. In certain situations, multitasking and parallel processing may be advantageous. Furthermore, the separation of various configurations in the embodiments described above should not be understood as a necessary separation, and it should be understood that the described program components and systems can generally be integrated together into a single software product or packaged into multiple software products.

[0099] The present invention has been described above with reference to its embodiments. Those skilled in the art will understand that the present invention may be embodied in modified forms without departing from the essential characteristics of the invention. Therefore, the disclosed embodiments should be considered in an illustrative rather than a restrictive sense. The scope of the invention is defined by the claims, not by the foregoing description, and all variations within the scope of the claims should be interpreted as being included in the invention. Explanation of the symbols

[0101] 10: Polynomial Curve Design Device 100: Node decision unit 110: Weight determination unit 130: Polynomial Calculation Unit 150: Hodograph Polygon Generator 170: Interpolation Polygon Generator 190: Polynomial curve generator 400: Polygon Gauss-Legendre curves of degree 3 or less that have as a Gauss-Legendre polygon 410: Curve interpolation point The Gauss-Legendre-Lagrange curve generated by continuously shifting only to the right 430: X dot-dashed line 450: X point - control point on the dashed curve Gauss-Legendre-Lagrange curve when only [man] is moved to points c and d 470: X point - Control point on the dashed curve Gauss-Legendre curve when only [man] is moved to points c and d

Claims

Claim 1 A polynomial curve design device comprising: a node determination unit for determining a node; a weight determination unit for determining a weight; a polynomial calculation unit for calculating a polynomial basis using the node and the weight; a radiograph polygon generation unit for generating a radiograph polygon using an input point; an interpolation polygon generation unit for setting a point that a curve must pass through using an input point and generating an interpolation polygon; and a polynomial curve generation unit for generating a curve using the radiograph polygon, the interpolation polygon, and the polynomial basis. Claim 2 In claim 1, the node determination unit and the weight determination unit have an integration interval Assuming The definite integral of A polynomial curve design device using nodes and weights when calculating with the Gauss-Legendre numerical quadrature. Claim 3 In claim 1, the node determination unit and the weight determination unit have an integration interval Assuming The definite integral of A polynomial curve design device using nodes and weights when calculating with the Gauss-Lobatto quadrature. Claim 4 In claim 1, the hodograph polygon generating part of (single, a hodograph polygon with edges that are natural numbers A polynomial curve design device that defines the approximate path a curve must take by defining the slope of the curve at a node. Claim 5 In claim 1, the interpolation polygon generating part of (single, An interpolation polygon composed of points (natural number) A polynomial curve design device that finely adjusts a curve of a desired shape by setting or changing the position of a new interpolation point while maintaining the slope at the interpolation point. Claim 6 In paragraph 1, the polynomial curve generating part has a degree A polynomial curve design device for generating a Gauss-Legendre-Lagrange (GLL) curve of less than or equal to the following. Claim 7 A polynomial curve design method comprising: a step of determining a node; a step of determining a weight; a step of calculating a polynomial basis using the node and the weight; a step of generating a radiograph polygon using an input point; a step of setting a point that the curve must pass through using the input point and generating an interpolation polygon; and a step of generating a curve using the radiograph polygon, the interpolation polygon, and the polynomial basis. Claim 8 In claim 7, the step of determining the node and the step of determining the weight are integration intervals Assuming The definite integral of A polynomial curve design method using nodes and weights when calculating with the Gauss-Legendre quadrature. Claim 9 In claim 7, the step of determining the node and the step of determining the weight are integration intervals Assuming The definite integral of A polynomial curve design method using nodes and weights when calculating with the Gauss-Lobatto quadrature. Claim 10 In paragraph 7, the step of generating a hodograph polygon using input points of (single, a hodograph polygon with edges that are natural numbers A polynomial curve design method that defines the approximate path a curve must take by defining the slope of the curve at a node. Claim 11 In claim 7, the step of setting points that the curve must pass through using the input points and generating interpolation polygons of (single, An interpolation polygon composed of points (natural number) A polynomial curve design method for finely adjusting a curve of a desired shape by setting or changing the position of a new interpolation point while maintaining the slope of the interpolation point. Claim 12 In claim 7, the step of generating a curve using the above hodograph polygon, interpolation polygon, and polynomial basis is of degree A polynomial curve design method for generating a Gauss-Legendre-Lagrange (GLL) curve. Claim 13 A computer program recorded on a computer-readable recording medium that executes any one of the polynomial curve design methods of paragraphs 7 through 12.

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