WO2022030104A1 - Dispositif de génération de surface incurvée, et programme de génération de surface incurvée - Google Patents

Dispositif de génération de surface incurvée, et programme de génération de surface incurvée Download PDF

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Publication number
WO2022030104A1
WO2022030104A1 PCT/JP2021/022168 JP2021022168W WO2022030104A1 WO 2022030104 A1 WO2022030104 A1 WO 2022030104A1 JP 2021022168 W JP2021022168 W JP 2021022168W WO 2022030104 A1 WO2022030104 A1 WO 2022030104A1
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reference curve
curve
curved surface
sweep
curvature
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PCT/JP2021/022168
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English (en)
Japanese (ja)
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庄一 土江
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日本ユニシス株式会社
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/12—Geometric CAD characterised by design entry means specially adapted for CAD, e.g. graphical user interfaces [GUI] specially adapted for CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/30—Polynomial surface description

Definitions

  • the present invention relates to a curved surface generation device and a curved surface generation program, and is particularly suitable for use in a curved surface generation device for generating a smooth curved surface with a change in curvature required in the field of design design.
  • the shape data of the product is generated by CAD (Computer Aided Design).
  • CAD Computer Aided Design
  • a method of reconstructing a curved surface model of the object from the measurement data of the object to be a model by CAD is widely used.
  • CAD data is created from the measurement data of a clay model formed by a clay modeler using a clay spatula (curve ruler).
  • the generated curved surface can sufficiently approximate the measured data within the specified tolerance, and (ii) the generated curved surface has a smooth change in curvature.
  • the generated curved surface has a smooth change in curvature.
  • a curved surface model by CAD for a clay model is reconstructed by using a curve with a shape determined like a curve ruler as a reference curve and sweeping the reference curve along a certain flow (direction). Is being done. If both the reference curve and the flow of the reference curve are correctly expressed, it is possible to generate a high-quality curved surface.
  • the present inventor has proposed a method capable of efficiently generating a high-quality curved surface without repeating many trials and errors by the user (see, for example, Patent Documents 1 and 2).
  • a reference curve fitted to a part of the measurement data of the model is set, and the reference curve is swept so as to satisfy a predetermined condition, and the reference is swept.
  • a curved surface is generated by interpolation from the boundary of the curved surface defined by the locus of the curve.
  • the curvature representing the flow of the curved surface is represented by the condition that the above-mentioned predetermined condition is "the locus formed by one point on the cross-sectional curve becomes the curvature line of the curved surface to be generated". It makes it possible to efficiently generate a high-quality curved surface that uses the line as a guide line for the sweep method.
  • Patent Document 2 the above-mentioned predetermined condition is set to "the adjacent curved surfaces intersect each other and the magnitude of the torsion of the intersecting lines is minimized", so that the intersecting lines of the adjacent curved surfaces are high. It makes it possible to efficiently generate quality curved surfaces.
  • the shape of the reference curve is fixed at the time of sweeping, and the shape of the curve is constant.
  • the shape of the sweep surface in the u direction is equal to the shape of the reference curve.
  • a method called a gradual change sweep is known.
  • the shape of the reference curve is allowed to change during the sweep.
  • the surface created by sweeping while gradually deforming the reference curve is hereinafter referred to as a gradual change sweep surface, and the shape of the gradual change sweep surface in the u direction is variable.
  • the clay modeler at the site makes full use of a special tool called a scraper to perform clay modeling equivalent to the gradually changing sweep surface.
  • a special tool called a scraper to perform clay modeling equivalent to the gradually changing sweep surface.
  • the sweep method described in Patent Documents 1 and 2 when the reference curve is swept, it is not deformed so as to fit the measurement data of the clay model well.
  • the gradual change sweep method since a dedicated command is also implemented in a commercially available CAD system, it is possible to create a gradual change sweep surface using the command. However, it is difficult to create a gradual change sweep surface with a smooth change in curvature, which requires a lot of trial and error.
  • the present invention has been made to solve such a problem, and it is possible to efficiently generate a gradual change sweep surface having a smooth change in curvature without repeating a lot of trial and error by the user. With the goal.
  • a reference curve fitted to a part of the measurement data of the model is set, and the shape of the reference curve gradually changes at the time of sweeping so as to satisfy a predetermined condition.
  • the reference curve is gradually changed and swept in an manner permitting the process, and a target curved surface (gradual change sweep surface) is generated based on the locus of the sweeped slowly changing curve.
  • the predetermined condition is that the difference curved surface between the gradually changing sweep surface generated by the gradually changing sweep of the reference curve and the reference curved surface generated when the reference curve is swept in a manner in which the shape does not change is at least.
  • the condition is that the curvature is monotonic with respect to the direction of the gradual curve.
  • the gradually changing sweep surface to be generated is the sum of the reference curved surface (the curved surface generated by sweeping the reference curve in such a manner that its shape does not change) and the difference curved surface.
  • the condition of curvature monotonicity is imposed on the difference curved surface, and the condition of the curvature monotonicity of the gradual change sweep surface itself is not a condition, so that the gradual change sweep can be easily handled. This makes it possible to efficiently generate a gradual change sweep surface with a smooth change in curvature without repeating a lot of trial and error by the user.
  • FIG. 1 is a block diagram showing a functional configuration example of the curved surface generator according to the present embodiment.
  • the curved surface generation device includes a measurement data input unit 1, a reference curve setting unit 2, a reference curve gradual change sweep unit 3, and a curved surface generation unit 4 as its functional configuration. ing.
  • Each of the above functional blocks 1 to 4 can be configured by any of hardware, DSP (Digital Signal Processor), and software.
  • DSP Digital Signal Processor
  • each of the above functional blocks 1 to 4 is actually configured to include a computer CPU, RAM, ROM, etc., and is a program stored in a recording medium such as RAM, ROM, a hard disk, or a semiconductor memory. Is realized by the operation of.
  • FIG. 2 is a diagram for explaining an example of a curved surface generated by the curved surface generator of the present embodiment.
  • the curve C 0 (u) obtained by gradually changing the reference curve C (u) in a manner that allows the shape to gradually change.
  • This gradually changing sweep surface S ⁇ (u, v) is the target curved surface to be generated.
  • the target curved surface S ⁇ (u, v) is represented by, for example, a B-spline curved surface or a Bezier curved surface.
  • C 0 (u) shows the initial reference curve at the start of the sweep
  • C 1 (u)'to C 4 (u)' shows the gradual change curves at the time of the sweep and at the end of the sweep.
  • the symbol of the dash (') in C 1 (u)'to C 4 (u)' indicates that the shape of the initial reference curve C 0 (u) has changed.
  • C 1 (u)'to C 4 (u)' shall be generic.
  • the slow change curves C 1 (u)'to C 4 (u)' at the time of sweep and the end of sweep are generically referred to.
  • ⁇ 0 (u) and ⁇ 1 (u)'to ⁇ 4 (u)' are curvature functions of the gradual curve C ⁇ (u)
  • FIG. 2 (a) shows the gradual curve C ⁇ (u).
  • the magnitude of the curvature at each of the above points is shown in the form of a curvature comb.
  • curvature ⁇ ⁇ (u) the gradual curve C 0 (u), C 1 (u) in the u direction on the gradual sweep surface S ⁇ (u, v). It is assumed that the curvatures ⁇ 0 (u) and ⁇ 1 (u)'to ⁇ 4 (u)'of' ⁇ C 4 (u)' are generically used.
  • curvature ⁇ ⁇ (u)' When writing "curvature ⁇ ⁇ (u)'", the curvature ⁇ 1 (u)'to ⁇ 4 of the gradual change curves C 1 (u)'to C 4 (u)' at the time of sweeping and at the end of sweeping. (u)'is a generic term. As shown in FIG. 2A, the curvature ⁇ ⁇ (u) of the gradual change curve C ⁇ (u) is gradually deformed during the gradual change sweep.
  • the gradually changing sweep surface S ⁇ ( u , v) is the reference curved surface SU (u, v) shown in FIG. 2 (b). ) And the difference curved surface S ⁇ (u, v) described later.
  • the reference curved surface SU ( u , v) is a curved surface obtained by sweeping the reference curve C 0 (u) in such a manner that its shape does not change.
  • S ⁇ (u, v) SU ( u , v) + S ⁇ (u, v) ⁇ ⁇ ⁇ (1)
  • C 0 (u) shows the initial reference curve at the start of the sweep (same as the reference curve C 0 (u) in FIG. 2 (a)), and C 1 (u) to C 4 ( u) shows the reference curve at the time of sweep and at the end of sweep.
  • C 1 (u) to C 4 (u) without the dash (') symbol indicate that the shape of the reference curve C 0 (u) does not change.
  • ⁇ 0 (u) to ⁇ 4 (u) are curvature functions of the reference curves C 0 (u) to C 4 (u) in the u direction on the reference curved surface SU (u, v), and the reference curve C 0 .
  • the measurement data input unit 1 inputs the measurement data of the model.
  • the measurement data input unit 1 inputs measurement data (point cloud data or mesh data) of a shape such as a clay model.
  • the reference curve setting unit 2 sets a reference curve fitted to a part of the measurement data input by the measurement data input unit 1.
  • the reference curve is created by imitating a curve ruler used by a design designer (clay modeler) when creating a clay model of an automobile.
  • the reference curve C 0 (u) shown in FIG. 2 is an example of the reference curve set by the reference curve setting unit 2.
  • the reference curve gradual change sweep unit 3 slowly changes the reference curve C 0 (u) initially set by the reference curve setting unit 2 at the time of sweeping so as to satisfy a predetermined condition.
  • a gradual change sweep process is performed in such a manner as to allow the shape of the variable curve C 1 (u)'to C 4 (u)' to gradually change.
  • FIG. 2 for convenience of explanation, only four gradual change curves C 1 (u)'to C 4 (u)' at the time of sweeping and at the end of sweeping are sampled and shown, but in reality, the gradual change curve C is shown.
  • the movement of ⁇ (u)' is continuous.
  • the predetermined conditions to be satisfied when the reference curve gradual change sweep unit 3 slowly changes the reference curve C 0 (u) are generated by the gradual change sweep of the reference curve C 0 (u) in FIG. 2 (a).
  • the reference curved surface SU (u, v) of FIG. 2 (b) generated when the gradually changing sweep surface S ⁇ ( u , v) and the reference curve C 0 (u) are swept in a manner in which the shape does not change.
  • the difference curved surface S ⁇ (u, v) has a curvature monotonicity at least in the u direction, which is the direction of the gradual curve C ⁇ (u) (hereinafter, this is referred to as the first condition). do).
  • the reference curve C j U (u) at a certain position in the v direction for sweeping the reference curve C 0 (u) with respect to the reference curved surface SU (u, v) and the gradually changing sweep surface S ⁇ (u, v).
  • the curvature difference function ⁇ j (u) as shown in the following equation (2) is defined.
  • ⁇ j (u) F (C j ⁇ (u)') -F (C j U (u)) ⁇ ⁇ ⁇ (2)
  • F ( ⁇ ) is a function of the curvature of the curve, and in the simplest case, it is the curvature itself.
  • the first condition that the difference curved surface S ⁇ (u, v) has curvature monotonicity with respect to the u direction is the following equation (3) using the curvature difference function ⁇ j (u) defined in equation (2).
  • the first condition represented by this equation (3) is the curvature ⁇ j of the gradual change curve C j ⁇ (u)'generated by the gradual change sweep of the reference curve C 0 (u) by the reference curve gradual change sweep unit 3.
  • FIG. 3 and 4 are schematic views for explaining the first condition.
  • the curve C 4 ⁇ (u)' is shown with the curvature combs of curvature ⁇ 4 U (u) and ⁇ 4 ⁇ (u)', respectively.
  • FIG. 4 (b) shows the curvature ⁇ 4 ⁇ (u)'of the gradual curve C 4 ⁇ (u)'and the curvature ⁇ 4 U (u) of the reference curve C 4 U (u) shown in FIG. 4 (a).
  • the difference between the curvatures ⁇ 4 ⁇ (u)'and ⁇ 4 U (u) (hereinafter, may be referred to as the curvature difference value) is obtained at all sampling points in the u direction. It increases monotonically in the u direction and satisfies the first condition of the above equation (3) at all sampling points in the u direction.
  • a reference curve C 0 (u) having an inflection point in which the sign of the curvature ⁇ 0 (u) changes may be set in the middle.
  • FIGS. 5 and 6 show an example of a reference curve C 0 (u) with an inflection and a gradual curve C j ⁇ (u)'and curvatures ⁇ j ⁇ (u)', ⁇ j U (u). It is a figure.
  • the curvatures ⁇ j ⁇ (u)'and ⁇ j U (u) in FIGS. 5 (b) and 6 (b) are schematically shown in FIGS. 5 (a) and 6 (a). It is not an illustration that accurately reflects the curvature ⁇ j ⁇ (u)'and ⁇ j U (u) shown in.
  • the direction of increase / decrease of the absolute value of the curvature ⁇ j ⁇ (u)'of the gradual curve C j ⁇ (u)' obtained by the gradual change sweep of the reference curve C 0 (u) is an inflection point.
  • An example of different cases on both sides of is shown. That is, as the sweep of the reference curve C 0 (u) progresses, the absolute value of the curvature ⁇ j ⁇ (u)'is increased on one side (the positive curvature side in the example of FIG. 5) across the inflection point, while the absolute value is increased.
  • the curvature ⁇ 0 (u) of the reference curve C 0 (u) and the curvature ⁇ j ⁇ (u)'of the gradual curve C j ⁇ (u)' is expressed by the absolute value curvature
  • the graph of the curvature difference value ⁇ j ⁇ (u) is expressed by the monotonous change. That is, a gradual change sweep surface in which the difference curved surface S ⁇ (u, v) has a curvature monotonicity with respect to the u direction and satisfies the first condition can be obtained.
  • one interesting property is obtained.
  • the graph of the curvature difference value ⁇ j ⁇ (u) is represented by a monotonous change, that is, the position P of the inflection point of the reference curve C 0 (u) and the gradual change curve C j ⁇ (u)'. It means that the position P of the inflection point coincides. This is because otherwise the graph of the curvature difference value ⁇ j ⁇ (u) will not change monotonically.
  • the inflection point is the increasing / decreasing direction of the absolute value of the curvature ⁇ j ⁇ (u)'of the gradual curve C j ⁇ (u)' obtained by the gradual sweep of the reference curve C 0 (u).
  • An example of the case where they are the same on both sides of is shown. That is, as the sweep of the reference curve C 0 (u) progresses, the absolute value of the curvature ⁇ j ⁇ (u)'is increased on one side (the positive curvature side in the example of FIG. 6) across the inflection point, while the absolute value is increased.
  • the absolute value of the curvature ⁇ j ⁇ (u)' is also increasing on the other side (the negative curvature side in the example of FIG. 6) across the inflection point.
  • the curvature ⁇ j U (u) of the reference curve C 0 (u) and the curvature ⁇ j ⁇ (u) of the gradual curve C j ⁇ (u)' is expressed as a signed curvature
  • the graph of the curvature difference value ⁇ j ⁇ (u) is expressed as a monotonous change. That is, a gradual change sweep surface in which the difference curved surface S ⁇ (u, v) has a curvature monotonicity with respect to the u direction and satisfies the first condition can be obtained.
  • the position of the inflection point on the reference curve C 0 (u) and the gradual inflection curve C j are different from the case where the increasing / decreasing directions of the absolute value of the curvature ⁇ j ⁇ (u)'are different on both sides of the inflection point.
  • the position of the inflection point of ⁇ (u)'does not always match.
  • the predetermined conditions to be satisfied when the reference curve gradual change sweep unit 3 slowly changes the reference curve C 0 (u) are generated by the gradual change sweep of the reference curve C 0 (u) in FIG. 2 (a). It further includes a second condition of minimizing the error between the gradually changing sweep surface S ⁇ (u, v) and the curved surface represented by the measurement data input by the measurement data input unit 1.
  • the sampling point ⁇ Q x ⁇ is preferably extracted from the entire measurement data without bias, and is appropriately extracted so as to cover the entire curved surface.
  • the reference curve gradual change sweep unit 3 takes into consideration the first condition and the second condition described above, and the reference curve C 0 (u) so as to minimize the objective function J defined by the following equation (5), for example. To sweep slowly.
  • the first term on the right side of the equation (5) is a function for evaluating the second condition shown in the equation (4)
  • the second term on the right side is a function for evaluating the first condition
  • ⁇ 1 and ⁇ 2 are weight parameters.
  • FIG. 7 is a diagram for explaining a penalty function together with an example of this monotonic change function.
  • the monotonic change functions f 2 and f 4 are shown.
  • the vertical axis is the curvature difference value.
  • the positions of the sampling points of the gradual change curves C 2 ⁇ (u)'and C 4 ⁇ (u)' and the curvature difference values are linear.
  • a linear function with a relationship is used.
  • a monotonic change function f2 by a linear function is calculated by using a linear fitting such as a least squares method.
  • the reference curve gradual change sweep unit 3 has the monotonic change function f 2 calculated in this way and the curvature difference value ⁇ 2 ⁇ (u) at each sampling point on the gradual change curve C 2 ⁇ (u)'.
  • the error of is calculated, and the sum of the calculated errors is added as the value of the penalty function ⁇ .
  • the curved surface generation unit 4 generates a target curved surface based on a locus in which the reference curve C 0 (u) moves while gradually changing its shape by the reference curve gradual change sweep unit 3. For example, the curved surface generation unit 4 generates a target curved surface S ⁇ (u, v) by a skinning method from M slowly changing curves C ⁇ (u) swept by the reference curve gradually changing sweep unit 3.
  • the skinning method is a known technique that takes a plurality of cross-sectional curves as inputs and generates a curved surface that passes through them.
  • the reference curve C 0 (u) fitted to a part of the measurement data of the model is set, and the first condition and the second condition are satisfied at the time of sweeping.
  • the reference curve C 0 (u) is slowly swept in an manner that allows the shape of the gradual change curve C ⁇ (u) to gradually change, and the gradual change sweeped M gradual change curves C ⁇ (u). ) Is used to generate a gradually changing sweep surface S ⁇ (u, v).
  • the first condition is the shape of the slowly changing sweep surface S ⁇ (u, v) generated by the gradually changing sweep of the reference curve C 0 (u) and the initially set reference curve C 0 (u).
  • the difference curved surface S ⁇ ( u , v) from the reference curved surface SU (u, v) generated when sweeping in a manner that does not change is relative to the direction (u direction) of the gradual curve C ⁇ (u).
  • the condition is that the curvature is monotonic.
  • the gradually changing sweep surface S ⁇ (u, v) to be generated has the reference curved surface SU ( u , v) and the difference curved surface S ⁇ as shown in the equation (1). It is expressed as the sum of (u, v), of which only the condition of curvature monotonicity is imposed on the difference curved surface S ⁇ (u, v), and the gradually changing sweep surface S ⁇ (u, v) itself. Since the curvature monotonicity of is not a condition, the gradual change sweep becomes easy to handle. This is also the case when the reference curve C 0 (u) has a non-monotonic change in curvature.
  • condition that the difference curved surface S ⁇ (u, v) has curvature monotonicity with respect to the u direction is used as the first condition, but both the u direction and the v direction have been described. It may be a condition that the curvature is monotonic.
  • the condition regarding the curvature monotonicity in the v direction can be applied in the same manner as the condition regarding the curvature monotonicity in the u direction. For example, even when the reference curve C 0 (u) set by the reference curve setting unit 2 does not have curvature monotonicity, the difference curved surface S ⁇ (u, v) is a gradual curve as the first condition. It is also possible to use the condition that both the direction of C ⁇ (u) (u direction) and the sweep direction (v direction) of the reference curve C 0 (u) have curvature monotonicity.
  • the reference curve C 0 (u) may be set according to the shape of the target curved surface S ⁇ (u, v) to be generated.
  • the target curved surface S ⁇ (u, v) is the curvature value of the gradual curve C ⁇ (u) with respect to the u direction and the curvature value of the reference curve C 0 (u) with respect to the reference curved surface S U (u, v). It suffices if the difference (and the difference between the curvature value of the gradual change curve C ⁇ (u) with respect to the v direction and the curvature value of the reference curve C 0 (u)) becomes a monotonous change.

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Abstract

La présente invention comprend : une unité de définition de courbe de référence (2) qui définit une courbe de référence adaptée à des données de mesure d'un modèle ; une unité de balayage conique de courbe de référence (3) qui crée un balayage conique de la courbe de référence de façon à satisfaire une condition prescrite ; et une unité de génération de surface incurvée (4) qui génère une surface incurvée cible sur la base de la courbe conique balayée. La manipulation du balayage conique devient facile par l'application de la condition selon laquelle une surface incurvée différentielle, entre une surface de balayage conique générée par un balayage conique de la courbe de référence et une surface incurvée de référence générée lorsque la courbe de référence est balayée sans changer de forme, présente une monotonie de courbure par rapport à au moins la direction de la courbe de référence, de sorte qu'une condition de monotonie de courbure n'est imposée que sur la courbe différentielle et une condition de monotonie de courbure pour la surface de balayage conique elle-même n'est pas prise en compte.
PCT/JP2021/022168 2020-08-07 2021-06-10 Dispositif de génération de surface incurvée, et programme de génération de surface incurvée WO2022030104A1 (fr)

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Cited By (1)

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CN116306088A (zh) * 2023-01-13 2023-06-23 华中科技大学 基于共形参数化的多尺度扫掠曲面结构设计方法及设备

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WO2009148157A1 (fr) * 2008-06-05 2009-12-10 国立大学法人静岡大学 Dispositif de traitement d'informations graphiques pour former des courbes esthétiques, procédé de traitement d'informations graphiques et programme de traitement d'informations graphiques
WO2018131304A1 (fr) * 2017-01-11 2018-07-19 日本ユニシス株式会社 Dispositif et programme de génération de surface incurvée
WO2019202813A1 (fr) * 2018-04-20 2019-10-24 日本ユニシス株式会社 Dispositif de génération de surface incurvée, et programme de génération de surface incurvée

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KR100753537B1 (ko) 2006-06-09 2007-08-30 주식회사 아이너스기술 메시 데이터를 피처로 이용한 역설계 방법
JP2008165644A (ja) 2006-12-28 2008-07-17 Canon Software Inc ３次元形状生成装置および３次元形状生成方法およびプログラムおよび記録媒体

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WO2009148157A1 (fr) * 2008-06-05 2009-12-10 国立大学法人静岡大学 Dispositif de traitement d'informations graphiques pour former des courbes esthétiques, procédé de traitement d'informations graphiques et programme de traitement d'informations graphiques
WO2018131304A1 (fr) * 2017-01-11 2018-07-19 日本ユニシス株式会社 Dispositif et programme de génération de surface incurvée
WO2019202813A1 (fr) * 2018-04-20 2019-10-24 日本ユニシス株式会社 Dispositif de génération de surface incurvée, et programme de génération de surface incurvée

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116306088A (zh) * 2023-01-13 2023-06-23 华中科技大学 基于共形参数化的多尺度扫掠曲面结构设计方法及设备
CN116306088B (zh) * 2023-01-13 2024-02-06 华中科技大学 基于共形参数化的多尺度扫掠曲面结构设计方法及设备

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