JP4357369B2 - Method for screening substances that change hair shape - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for evaluating the shape of a fiber, by which the complicated various shapes of the fiber can objectively and quantitatively be digitalized and utilized as accurate standards. <P>SOLUTION: This method for evaluating the shape of the fiber comprises the first step for obtaining a three-dimensional point group image of the fiber H, the second step for making a three-dimensional fiber curve h on the basis of the three-dimensional point group image, and the third step for drawing (a) tangent vectors Vt contacting with the three-dimensional fiber curve h at calculated points P determined on the three-dimensional fiber curve h at an arbitrary equal distance, (b) curvature vectors Vc contacting with the three-dimensional fiber curve h at the calculated points P, (c) normal line vectors Vn of planes formed with the mutually adjacent tangent vectors, or the like, and then determining the shape F of the fiber H on the bases of angles &theta;t between the mutually adjacent tangent vectors Vt, angles &theta;c between the mutually adjacent curvature vectors Vc, angles &theta;n between the mutually adjacent normal line vectors Vn, or the like. <P>COPYRIGHT: (C)2006,JPO&amp;NCIPI

Description

The present invention relates to a method for screening a substance that changes hair shape .

  Hair shape or hair style is one of the factors that determine a person's first impression, and various research and development have been conducted from a cosmetic and psychological viewpoint. In addition, the shape of hair is an important subject of evaluation and research in the fields of forensic medicine and anthropology. In these research and development, when analyzing, defining, classifying and evaluating the actual shape of hair, it is necessary to quantify the hair shape objectively and quantitatively. Conventionally, methods for evaluating the shape of hair include a hair cross-section ratio measurement method, an end-to-end distance ratio measurement method, and a curl diameter measurement method, as shown below.

  In the hair cross-section ratio measuring method, the minimum diameter a and the maximum diameter b in the hair cross section are measured from the viewpoint that the hair cross section is closer to a perfect circle, and the hair shape is the roundness ratio = (a / B) × 100 (%) (see Patent Document 1 and Non-Patent Document 1). In the end-to-end distance ratio measurement method, the distance a from the tip to the end of the hair in a normal state where the hair is curled, and the distance b from the tip to the end of the hair in a state where the hair is linearly stretched are measured. The hair shape is evaluated as a / b (see Non-Patent Document 1). The curl diameter measurement method measures the curl diameter (curvature radius, curvature, etc.) at an arbitrary point on the hair and evaluates the shape of the hair (see Non-Patent Document 1).

  On the other hand, as a method for evaluating the shape of wool, there are a bulk measurement method, a crimp frequency measurement method, and the like, as described below, in addition to the curl diameter measurement method. The bulk measurement method is a method of measuring the volume of wool per unit weight and evaluating its shape, and the crimp frequency measurement method is a method of measuring the frequency of wool curl appearing on one side per certain length. This is a method for evaluating the shape (see Non-Patent Document 2).

JP 2002-111284 A D. Hrdy, Am. J. et al. Phys. Anthrop. , 39, p7, 1973 W. V. Bergen, WOOL HANDBOOK Vol. 1,3rd edition, John Wiley & Sons, 1970

  However, conventional methods for evaluating the shape of hair have the following problems. In the hair cross-section ratio measurement method, when the hair cross-section to be measured is not perpendicular to the hair axis, an accurate roundness rate cannot be obtained. In addition, even when the roundness is close to 100 (%), the hair shape cannot be accurately quantified because bent hair exists. The shape of the hair evaluated by the end-to-end distance ratio measurement method or the curl diameter measurement method reflects the shape in a limited situation such as when the hair has no inflection point or when the hair is bent to some extent. Although it showed an accurate value, it did not show an accurate value when the hair had a three-dimensionally complicated shape, and it was not a standard for broadly classifying and evaluating human hair.

  On the other hand, conventional methods for evaluating the shape of wool are effective for wool with a relatively uniform bend, but are a standard for broadly classifying wool with various bends. It wasn't. Further, since the conventional method for evaluating the shape of wool is a method of treating wool as a bundle or lump, it has not been a method for accurately evaluating the shape of each wool fiber.

An object of the present invention is to provide a method for screening a substance that measures the shape of the hair and changes the shape of the hair .

  The present inventors obtain a three-dimensional point cloud image of a fiber and represent it as a three-dimensional fiber curve. On the three-dimensional fiber curve, a tangent vector, a curvature vector, or two adjacent to each other at an equal interval. When drawing a normal vector of a plane formed by tangent vectors, the value obtained based on the angle between adjacent tangent vectors, adjacent curvature vectors, or adjacent normal vectors is the actual fiber It was found that this is a method that can objectively and quantitatively quantify the shape.

The present invention has been made on the basis of the above-mentioned findings. The shape of the hair before applying the substance that changes the shape of the hair, and the change of the shape of the hair after applying the substance to the hair. The object is achieved by providing a method for screening a substance that changes the shape of the hair, comprising measuring the shape of the hair by a method including the following steps, comprising comparing the shapes of the hair. is there.
A first step of placing the hair attached to the fixture and hanging down in a measurable area of the three-dimensional digitizer, and obtaining a three-dimensional point cloud image of the hair by the three-dimensional digitizer.
A second step of creating a three-dimensional hair curve based on the three-dimensional point cloud image;
(A) a tangent vector Vt tangent to the three-dimensional hair curve on the calculation point P, and (b) the cubic on the calculation point P. Curvature vector Vc tangent to the original hair curve, (c) a normal vector Vn of a plane formed by two tangent vectors adjacent to each other, an angle θt between the tangent vectors Vt adjacent to each other, or curvature vectors adjacent to each other A third step of obtaining the hair shape F based on an angle θc between Vc or an angle θn between adjacent normal vectors Vn.

  According to the present invention, the fiber shape F can be used as an accurate reference by digitizing the fiber shape based on the three-dimensional change angle θ. Further, by using the fiber shape F as an accurate reference, it is possible to screen for substances that change the fiber shape.

Hereinafter, the most preferred embodiment of the screening method of the present invention will be described in detail. As shown in FIGS. 2 to 4, in the present embodiment, the shape of the hair H, a first step of obtaining a three-dimensional point cloud images of the hair H, the three-dimensional hair curve h based on the three-dimensional point cloud images a second step of creating, with respect to calculation point P which defines a plurality of any equal intervals in the three-dimensional hair curve h, the tangent vector Vt contacting the three-dimensional hair curve h on (a) calculation points P, (b ) A curvature vector Vc tangent to the three-dimensional hair curve h on the calculation point P, or (c) a normal vector Vn of a plane formed by two tangent vectors adjacent to each other, and between the tangent vectors Vt adjacent to each other A third step of determining the shape F of the hair based on the angle θt, the angle θc between adjacent curvature vectors Vc, the angle θn between adjacent normal vectors Vn, or the like . Hair shape To measure. First, the hair shape measuring system for realizing the shape evaluation method of the hair, H, will be described with reference to FIG.

  As shown in FIG. 1, the hair shape measurement system 1 of the present embodiment includes a three-dimensional digitizer 2, a digitizer body device 3, an analysis device 4, a temperature / humidity meter 5, a hair fixture 6, a vibration isolation plate 7, and a windshield case 8. Etc. The three-dimensional digitizer 2 and the analysis device 4 are each electrically connected to the digitizer main body device 3. The digitizer body device 3 is configured to transmit the three-dimensional point cloud image acquired by the three-dimensional digitizer 2 to the analysis device 4. The analysis device 4 has a built-in memory in which a predetermined analysis program is recorded. The analysis device 4 is configured to execute predetermined steps in the shape evaluation method based on the three-dimensional point cloud image received from the digitizer body device 3 in accordance with an instruction from the analysis program (details will be described later). ).

  The thermohygrometer 5 is electrically connected to the analysis device 4 and transmits temperature and humidity information at the time of measurement. The hair fixture 6 supports the hair H to be measured in the measurable area of the three-dimensional digitizer 2. The vibration isolation plate 7 is for reducing vibration generated by the operation of the three-dimensional digitizer 2 and preventing the hair H supported by the hair fixing tool 6 from vibrating. The windshield case 8 covers the hair fixing tool 6, the three-dimensional digitizer 2, and the like, and prevents the hair H supported on the hair fixing tool 6 from vibrating due to the influence of the outside environment such as wind.

  Next, the hair shape evaluation method of this embodiment will be described. As shown in FIG. 1 or FIG. 2, in the first step, a predetermined number (for example, 10) of hairs H are measured, and one hair H selected from these is attached to the hair fixing tool 6, and the tertiary Place in the measurable area of the original digitizer 2. A three-dimensional point cloud image of the hair H is acquired by the three-dimensional digitizer 2. This three-dimensional point cloud image is transmitted to the analysis device 4 via the digitizer body device 3.

  In the second step, as shown in FIG. 3, the analysis device 4 creates a NURBS curve along the shape of the original hair H from the three-dimensional point cloud image of the hair H in the xyz space coordinates, The hair curve is h (three-dimensional fiber curve).

  In the third step, as shown in FIG. 4, the calculation point P0 of the starting point is taken at one end on the root side of the three-dimensional hair curve h, and m calculation points P1 are taken every arbitrary curve distance q (for example, 1 mm). ~ Pm is defined along the three-dimensional hair curve h. The number m of calculation points is a number determined by the length of the three-dimensional hair curve h and the curve distance q between the calculation points. Then, the next operation (a), (b) or (c) is performed.

(A) For each of the measurement points P0, P1, P2, P3, P4,..., Pm, tangent vectors Vt0, Vt1, Vt2, Vt3, Vt4,.
(B) For each measurement point P0, P1, P2, P3, P4,..., Pm, draw curvature vectors Vc0, Vc1, Vc2, Vc3, Vc4,.
(C) For the tangent vectors Vt0, Vt1, Vt2, Vt3, Vt4,..., Vtm, the normal vectors Vn0, Vn1, Vn2, Vn3, Vn4,. m-1) is drawn.

  In (a), for two tangent vectors Vt0 and Vt1 adjacent to each other, one plane passing through them is defined as xyz space coordinates, and an angle θt1 between the tangent vectors (Vt0 and Vt1) is obtained on this plane. . Thereafter, in the same manner as described above, the angle between the vectors θt2, θt3, θt4 between the tangent vectors (Vt1, Vt2), (Vt2, Vt3), (Vt3, Vt4),. ,..., Θtm are obtained sequentially. The angles θt1, θt2,..., Θtm between the vectors obtained here are absolute values of 0 ° to 180 °.

  In (b), for two curvature vectors Vc0 and Vc1 adjacent to each other, one plane passing through these is defined as xyz space coordinates, and an angle θc1 between the curvature vectors (Vc0 and Vc1) is obtained on this plane. . Thereafter, in the same manner as described above, the angle between the vectors θc2, θc3, θc4 between the curvature vectors (Vc1, Vc2), (Vc2, Vc3), (Vc3, Vc4),..., {Vc (m−1), Vcm}. ..., Θcm is obtained sequentially. The angles θc1, θc2,..., Θcm between the vectors obtained here are absolute values of 0 ° to 180 °.

  In (c), for two normal vectors Vn0 and Vn1 adjacent to each other, one plane passing through them is defined as xyz space coordinates, and an angle θn1 between the normal vectors (Vn0 and Vn1) is defined on this plane. Ask for. Thereafter, in the same manner as described above, between the normal vectors (Vn1, Vn2), (Vn2, Vn3), (Vn3, Vn4),..., {Vn (m-2), Vn (m-1)} The angles θn2, θn3, θn4,..., Θn (m−1) are obtained sequentially. The angles θn1, θn2,..., Θn (m−1) between the vectors obtained here are absolute values from 0 ° to 180 °.

In (a), the angles θt1, θt2,..., Θtm between vectors, the distance between points q, and the number m of calculation points are substituted into the following equation (1), and the hair shape F Calculated as the change angle per unit length. The hair shape F obtained here is an index representing the degree of bending of the hair H.
F = (θt1 + θt2 +... + Θtm) / (q × m) (1)

In (b), the angles θc1, θc2,..., Θcm between vectors, the distance between points q, and the number m of calculation points are substituted into the following equation (2), and the hair shape F Calculated as the change angle per unit length. The hair shape F obtained here is an index representing the degree of twist of the hair H.
F = (θc1 + θc2 + ... + θcm) / (q × m) (2)

Furthermore, in (c), the angles θn1, θn2,..., Θn (m−1) between the vectors, the distance between points q, and the number m of calculation points are substituted into the following equation (3) to obtain the hair shape F For the hair H as a change angle per unit length. The hair shape F obtained here is an index representing the degree of twist of the hair H.
F = {θn1 + θn2 +... + Θn (m−1)} / {q × (m−1)} (3)

  Thereafter, in any of the cases (a) to (c), the second hair H is set as a measurement target, and the three-dimensional hair is based on the first step of obtaining a three-dimensional point cloud image and the three-dimensional point cloud image as described above. A second step of creating the curve h and a third step of obtaining the hair shape F are performed. Such measurement of the hair shape F is repeated for the remaining hair H.

  The shape F of the hair H obtained in this way is the degree to which the shape of the hair H is quantified objectively and quantitatively by averaging the three-dimensional change angle θ per unit length of the hair H. Thus, for example, in the technical field of hair research, the actual condition of hair shape is analyzed, defined, and used as an accurate standard when performing classification and evaluation.

  For example, in the technical field of hair research, in the development of substances that change the shape of hair, by comparing the values of the shape F before application of the substance and the form F after application of the substance, Screen effective substances that change shape.

  For example, in the technical field of psychological research, when examining the effect of hair shape and styling on psychology, the effect of hair shape F should be used as a reference index to evaluate the effect. To.

  For example, in the technical field of forensic research, objectively and quantitatively digitized hair shape F is used as a reference index and applied to identification, classification, criminal investigation and the like of individuals.

  Also, for example, in the technical field of anthropological research, the anthropological characteristics are evaluated by the shape of the hair H, and in the field to classify, objective, regardless of rough classification such as Asian, white, black, etc. Using the quantitatively quantified hair shape F as a reference index, classification and evaluation are performed in a more detailed manner.

  As described above, according to the present embodiment, the shape of the hair H is objectively determined by averaging the three-dimensional change angle θ per unit length of the hair H with respect to the shape F of the hair H. Since it is quantitatively digitized, the shape F of the hair H can be used as an accurate reference in technical fields such as hair research, psychological research, forensic research, and anthropological research.

  In particular, in the case of this embodiment, since the shape F of the hair H is represented by the three-dimensional change angle θ based on the three-dimensional hair curve h that accurately reproduces the actual hair shape, such a shape F is used. As a result, the actual shape of the hair H can be expressed as an accurate measure in a three-dimensional space, compared to the case where an evaluation method such as a two-dimensional end-to-end distance ratio measurement method or a curl diameter measurement method is used. .

  The present invention is not limited to the above-described embodiment, and various changes can be made. For example, in the present invention, not only hair, but also protein fibers such as wool, natural polymer fibers such as cellulose, alginic acid and chitin, synthetic polymer fibers such as polyamide, polyester and polyolefin, inorganic fibers such as carbon and metal For example, various fibers can be measured. When wool is used as a measurement object, the shape F of wool is an accurate reference when subdividing wool in the field of classifying wool by its shape.

Further, if the shape F is obtained based on the angle θ between the vectors V adjacent to each other, the shape F is not limited to the above formulas (1) to (3). It may be obtained according to 5), (6), etc.
F = (1 / m−1) {(θt1−Θt) ² + (θt2−Θt) ² +... + (Θtm−Θt) ² } Equation (4)
F = (1 / m−1) {(θc1−Θc) ² + (θc2−Θc) ² +... + (Θcm−Θc) ² } (5)
F = (1 / m−2) [(θn1−Θn) ² + (θn2−Θn) ² +... + {Θn (m−1) −Θn} ² ] (6)
(However, Θt, Θc, and Θn represent the average value of the angles θ between the vectors V adjacent to each other.)

  Hereinafter, the present invention will be described in more detail with reference to examples. However, the scope of the present invention is not limited to such examples.

[Example 1]
[1] Measurement accuracy verification and its verification method 11 hairs having various shapes were used as standard hair for measurement accuracy verification, and the measurement accuracy was verified for the hair shape evaluation method of this embodiment. A gonio-rotating device was attached to the hair fixture 6 to support standard hair. In gonio, standard hair is -15 ° to 15 ° (7 points) at 5 ° intervals in the same direction as the 3D digitizer axis, and -15 ° to 15 ° at 5 ° intervals in the direction orthogonal to the 3D digitizer axis. The first step processing was performed while changing to (7 points) to obtain a three-dimensional point cloud image. Moreover, the process of the 1st step was performed, rotating a standard hair to 0 degrees-360 degrees (13 points) at intervals of 30 degrees using the rotation device, and the three-dimensional point cloud image was acquired. The analysis process of the 2nd step and the 3rd step was performed with respect to these three-dimensional point cloud images, and the measurement accuracy with respect to the hair support method was verified. Subsequently, each standard hair was repeatedly measured 10 times from the place where it was supported on the hair fixing device 6, and the accuracy of the repeated measurement was performed. Table 1 shows the measurement accuracy test results for the hair support method and the repeat measurement accuracy test results.

[2] Measurement accuracy test results As shown in Table 1, the variation coefficient (CV value) is less than 15% for the measurement accuracy test results for the hair support method and the repeat measurement accuracy test results. Thus, it was revealed that the shape of the standard hair can be accurately measured by using the hair shape evaluation method of the present embodiment.

[Example 2]
[1] Standard hair shape measurement and method The relationship between the hair shape F of the hair shape evaluation method of the present embodiment and the actual shape of the hair shape obtained by sensory evaluation was investigated, and the hair of the present embodiment The accuracy of the shape evaluation method was investigated. The shape F of 11 standard hairs having various shapes was determined according to the formula (1) in the hair shape evaluation method of this embodiment. On the other hand, with respect to these 11 standard hairs, 6 expert panelists scored the degree of apparent bending with a numerical value from 1 (low bending degree) to 11 (high bending degree), and calculated the average value. The relationship between the standard hair shape F and the average bending degree score is shown in FIG.

[2] Measurement Results of Standard Hair Shape As shown in FIG. 5, it is clear that the hair shape F of the hair shape evaluation method of the present embodiment and the average score of the degree of bending by appearance have a positive correlation. Became. Accordingly, if the hair shape F of the hair shape evaluation method of the present embodiment is used as a reference, the actual shape of the hair shape can be quantified more objectively, quantitatively, and accurately.

Example 3
[1] Simulation Evaluation The hair shape evaluation method A of the present embodiment was compared and evaluated by the conventional end-to-end distance ratio measurement method B and the conventional minimum curl diameter measurement method C by simulation analysis. As described above, the end-to-end distance ratio measurement method B includes the distance a from the tip of the hair to the end in a normal state where the hair is curled, and the distance from the tip to the end of the hair in a state where the hair is linearly extended This is a method of measuring the distance b and obtaining the hair shape as a / b. The minimum curl diameter measuring method is a method for obtaining the hair shape as the minimum curl diameter by comparing the hair with a curvature radius chart.

[2] Simulation evaluation method A pseudo hair curve in which a plurality of arcs having a constant radius of curvature r (0.1 cm, 0.2 cm,..., 1 cm, 2 cm,. In the hair shape evaluation method A of the present embodiment, the hair shape F was determined from the pseudo hair curve according to the equation (1). In the end-to-end distance ratio measurement method B, the end-to-end distance ratio was determined, and in the minimum curl diameter measurement method C, the minimum curl diameter was determined.

[3] Simulation evaluation results The following (1) to (3) were clarified as an analysis result of the simulation evaluation.
(1) The end-to-end distance ratio obtained by the end-to-end distance ratio measurement method B correlates with the hair shape F obtained by the shape evaluation method A for a pseudo hair curve having no inflection point (FIG. 6). For a pseudo hair curve with an inflection point, a result smaller than the hair shape F obtained by the shape evaluation method A is shown (FIG. 7).
(2) Human hair is roughly divided into “straight hair”, “almost straight hair (weak wave hair)”, “wave hair”, “curl hair (strong wave hair)”, and “curly hair” according to the degree of comb hair. However, “curly hair” and “curled hair (strong wave hair)” are often composed of hair having an inflection point. Therefore, it should be judged that the hair having an inflection point has a large degree of comb hair, and the end-to-end distance ratio obtained by the end-to-end distance ratio measuring method B cannot be accurately evaluated.
(3) The minimum curl diameter obtained by the minimum curl diameter measuring method C cannot be accurately evaluated with respect to the pseudo hair curve (FIG. 8).

  From the above-mentioned points, the hair shape evaluation method A of the present embodiment is quantified in accordance with the actual situation compared to the conventional end-to-end distance ratio measurement method B or the conventional minimum curl diameter measurement method C. It became clear that it was suitable for.

Example 4
[1] Screening for substances that change the shape of hair Glycolic acid, pyruvic acid, 2-hydroxyisobutyric acid, 3-chloropropionic acid, and 2-chloropropionic acid are used as carboxylic acid derivatives. Whether or not to change the shape of the hair was evaluated using the hair shape evaluation method of the present embodiment.

[2] Screening evaluation method After the collected hair was washed and air-dried, the hair shape F of the hair shape evaluation method of this embodiment was determined according to the formula (1). Then, the said substance etc. were applied to hair, and it processed for 24 hours at 3M density | concentration and 40 degreeC, respectively. Distilled water was used as a control. The treated hair was washed with water, air-dried, and the hair shape F was again determined according to the formula (1). From the measurement result of the hair shape F before and after the treatment, it was evaluated whether or not the above-described substances changed the hair shape. The measurement result of the hair shape F before and after the treatment is shown in FIG.

[3] Results of screening evaluation As shown in FIG. 9, it was revealed that the shape F of the hair changes variously by applying the above substances to the hair. As a result, a substance or the like is applied to the hair or scalp, and the hair shape before and after the treatment is evaluated based on the hair shape F of the hair shape evaluation method of the present embodiment, thereby changing the shape of the hair. It becomes possible to use for screening of a given substance.

The fiber screening method of the present invention can be applied to, for example, the technical field of hair research such as the actual state analysis survey of the hair shape, the classification / evaluation of the hair shape, the development of substances that change the hair shape, and the hair shape, for example. Technical field of psychological research such as investigation of relation between human and psychology, for example, identification and classification of individuals, technical field of forensic research such as criminal investigation, such as relationship between hair shape and human evolution, movement, distribution, etc. Technical field of anthropological research such as research, for example, classification and evaluation of wool shape, technical field of wool research such as development of substances that change the shape of wool, and fiber research such as production of synthetic polymer fibers It can be used widely in various technical fields.

It is a figure which shows schematic structure of the hair shape measuring system of this embodiment. It is a figure used for description of the 1st step of the shape evaluation method of the hair of this embodiment. It is a figure used for description of the 2nd step of the hair shape evaluation method of this embodiment. It is a figure used for description of the 3rd step of the hair shape evaluation method of this embodiment. It is a graph which shows the relationship between the shape F of the standard hair of Example 2, and an average bending degree score. It is a graph which shows the analysis result (there is no inflection point) of simulation evaluation of Example 3. It is a graph which shows the analysis result (with an inflection point) of the simulation evaluation of Example 3. 10 is a graph showing an analysis result (minimum curl diameter) of simulation evaluation of Example 3. It is a graph which shows the screening evaluation result of Example 4.

Explanation of symbols

F Hair (fiber) shape H Hair (fiber)
h Three-dimensional hair curve (three-dimensional fiber curve)
m number of calculation points P calculation point q curve distance between calculation points Vt tangent vector Vc curvature vector Vn plane normal vector formed by two adjacent tangent vectors θt angle between two adjacent tangent vectors θc Angle between two adjacent curvature vectors θn Angle between two adjacent normal vectors

Claims (4)

Comparing the shape of the hair before applying the substance that changes the shape of the hair and the shape of the hair after applying the substance to the hair and changing the shape of the hair,
A method for screening for a substance that changes hair shape, wherein the hair shape is measured by a method comprising the following steps.
The hair is suspended by attaching the fixture placed measurable range of the three-dimensional digitizer, the first step of obtaining a three-dimensional point cloud image of the hair by the three-dimensional digitizer.
A second step of creating a three-dimensional hair curve based on the three-dimensional point cloud image ;
The contrast calculation point P which defines a plurality of any equal intervals on a three-dimensional hair curves, (a) the tangent vector Vt in contact with the three-dimensional hair curve on a computing point P, the tertiary over (b) calculation points P Curvature vector Vc tangent to the original hair curve, (c) normal vector Vn of a plane formed by two adjacent tangent vectors, angle θt between adjacent tangent vectors Vt, or adjacent curvature vectors A third step of obtaining the hair shape F based on the angle θc between Vc or the angle θn between the normal vectors Vn adjacent to each other . The method according to claim 1, wherein in the third step, the hair shape F is calculated as a change angle per unit length according to the following formula (1) to represent the degree of bending of the hair .
F = (θt1 + θt2 +... + Θtm) / (q × m) (1)
(However, when the calculation point of the starting point on the three-dimensional hair curve is P0 and the number of calculation points other than P0 is m (1 ≦ k ≦ m), q is the calculation point Pk on the three-dimensional hair curve. −1 and Pk, and θtk is the absolute value of the angle between the tangent vectors Vtk−1 and Vtk for the calculation points Pk−1 and Pk.) The method according to claim 1, wherein in the third step, the hair shape F is calculated as a change angle per unit length according to the following equation (2) to represent the degree of twist of the hair .
F = (θc1 + θc2 + ... + θcm) / (q × m) (2)
(However, when the calculation point of the starting point on the three-dimensional hair curve is P0 and the number of calculation points other than P0 is m (1 ≦ k ≦ m), q is the calculation point Pk on the three-dimensional hair curve. −1 and Pk, θck is the absolute value of the angle between the curvature vectors Vck−1 and Vck for the calculation points Pk−1 and Pk.) The method according to claim 1, wherein in the third step, the hair shape F is calculated as a change angle per unit length according to the following expression (3), and represents the degree of twist of the hair .
F = {θn1 + θn2 +... + Θn (m−1)} / {q × (m−1)} (3)
(However, when the calculation point of the starting point on the three-dimensional hair curve is P0 and the number of calculation points other than P0 is m (1 ≦ k ≦ m), q is the calculation point Pk on the three-dimensional hair curve. −1 and Pk, and θnk is a plane formed by the normal vector Vnk−1 of the plane formed by the two tangent vectors Vtk−1 and Vtk, and the plane formed by the two tangent vectors Vtk and Vtk + 1. (The absolute value of the angle between the normal vectors Vnk of

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