Method and apparatus for measuring the angle between two bone blocks forming a joint

Abstract

The application provides a method and device for measuring the angle between two bone blocks forming a joint, which can be used for real-time measurement of the flexion, valgus and varus angles of a knee joint in computer-aided knee joint replacement. The conversion relationship between the coordinate system of a 3D virtual bone model and the coordinate system of the markers collected from the actual bone surface is established by using an optical tracking system, and the angles are calculated by using the marker points extracted from the model, which are selected from the hip joint center H, the femoral knee joint center FK, the lateral epicondyle LE, the medial epicondyle ME, the tibial knee joint center TK, the tibial tuberosity TB and the ankle joint center AK. The method comprises the following steps: calculating the femoral mechanical axis direction vector and the tibial mechanical axis direction vector; calculating the flexion angle when the knee joint moves around the transverse axis on the sagittal plane. The valgus and varus angles can be determined by projecting the femoral axis and the tibial axis on the coronal plane Pc or the transverse plane. The application also provides a surgical robot system, a storage medium and a measuring device.

Description

TECHNICAL FIELD

[0001] The present application relates to a method for calculating the angle between two bone blocks forming a joint, in particular for real-time measurement of the flexion, valgus and varus angles of the knee joint in computer-assisted knee replacement surgery. BACKGROUND

[0002] Total knee arthroplasty (TKA) is a surgical procedure for replacing the surface of the knee joint. One of the foundations of a successful TKA is to achieve mechanical alignment of the implants. Mechanical alignment (MA) in TKA aims to position the femoral and tibial components perpendicular to the mechanical axis of each bone. This results in a 0° hip-knee-ankle angle (∠HKA) of the extremity. The mechanical axis of the lower extremity (leg) is a line extending from the center of the femoral head to the center of the ankle, usually passing through the center of the knee joint. The femoral part of this line from the center of the femoral head to the center of the knee joint is defined as the femoral mechanical axis, while the tibial part from the center of the tibia to the center of the ankle joint is referred to as the tibial mechanical axis. Under normal circumstances, the angle between the femoral mechanical axis and the tibial mechanical axis is 0°.

[0003] During the operation, it is necessary to constantly check the flexion, varus and valgus angles of the moving leg to verify the effectiveness of the implants. Therefore, accurately determining the angles in real time is of great significance for the doctor to correctly install the artificial joint prosthesis and better monitor and evaluate the patient's condition.

[0004] In the past, there have been in vivo measurement techniques using 2D or 3D registration as a method for measuring the posture of the knee joint, but the process is complex and the calculation efficiency is relatively low. Even with the measurement method using an optical tracking system, it is only used to measure the posture and spatial position of the knee joint, and does not involve further accurate acquisition of parameters such as the flexion, valgus and varus angles of the knee joint. SUMMARY

[0005] In view of the above problems, the present application provides a method for calculating the angle between two bone blocks forming a joint, which can be used for real-time measurement of the flexion, valgus and varus angles of the knee joint in computer-assisted knee replacement surgery.

[0006] According to one aspect of the present application, a method for calculating the angle between two bone blocks forming a joint is provided for a computer-assisted surgical navigation system, wherein a conversion relationship between the coordinate system of a 3D virtual bone model and the coordinate system of a marker collected from the actual bone surface is established using an optical tracking system, wherein the angle is calculated using a marker point extracted from the 3D virtual bone model, wherein the marker point includes: the hip joint center H, the femoral knee joint center FK, the tibial knee joint center TK, and the ankle joint center AK, and further comprising the following steps:

[0007] The femoral mechanical axis direction vector is calculated as follows: , (formula 3), and

[0008] tibial mechanical axis direction vector: , (formula 4);

[0009] Thereby, as an angle, the flexion angle of the knee joint when flexing in the sagittal plane (around the transversal axis in the sagittal plane) is determined:

[0010] , (formula 5).

[0011] Preferably, the marker points further comprise the tibial tuberosity TB, further comprising the step of taking a line Ld from the 3D virtual bone model, which line Ld passes through the tibial tuberosity TB and is perpendicular to the tibial mechanical axis, and determining the direction vector of the line Ld and the direction vector of the femoral mechanical axis between the direction vector of the line Ld df to represent the inclination of the tibial mechanical axis relative to the femoral mechanical axis.

[0012] Preferably, if the angle a af is 90°, it is determined that the tibia is inclined neither anteriorly nor posteriorly; if the angle a df is greater than 90°, it is determined that the flexion angle a f is positive and the tibial mechanical axis is inclined posteriorly; if the angle a df is less than 90°, it is determined that the flexion angle a f is negative and the tibial mechanical axis is inclined anteriorly.

[0013] Preferably, the marker points further comprise the lateral epicondyle LE and the medial epicondyle ME, and when the flexion angle is in the range of 0° < a f < 60° or 120° < a f < 160°, a coronal plane P c defined by the hip joint center H, the lateral epicondyle LE and the medial epicondyle ME is used as a projection plane, based on which the varus angle and the valgus angle are determined based on the projection of the vectors , onto the coronal plane P c , which projection is calculated based on the following formula: Let v be the projection of the vector v onto a projection plane with a normal vector n , then

[0014] , (formula 6).

[0015] Preferably, further comprising the step of: if the lateral epicondyle LE and the medial epicondyle ME do not form a vector perpendicular to the vector v , then a vector with the vector v Plane P is a normal line that contains one of the two points, the lateral epicondyle (LE) and the medial epicondyle (ME). V In the plane P V Project another point upwards, and use the projected point and one of the aforementioned points paired with it to form a perpendicular line. A vector of vectors, passing through the paired point and vector. Obtain the projection surface P c ', using vectors , On projection plane P c 'Achieved by projection and This is used to determine the outward and inward angles.

[0016] Preferably, when the buckling angle is in the range of 60°≤αf≤120°, the angle perpendicular to the coronal plane P will be... c cross section P V 'As a projection plane through the lateral epicondyle (LE) and medial epicondyle (ME), the coronal plane is used.' P c normal vector sum vector In cross section P V 'projection on To determine the outward and inward angles.

[0017] According to another aspect of the present invention, a surgical robot system is provided, comprising a computer-aided surgical navigation system having an optical tracking system and a computer, wherein the computer executes the steps of any of the above-described calculation methods for calculating the angle between two bone fragments forming a joint.

[0018] According to another aspect of the present invention, a storage medium is provided, which is a computer-readable storage medium storing a computer program, characterized in that the computer program is executed to implement the steps of any of the above-described calculation methods.

[0019] According to another aspect of the present invention, a device for measuring the angle formed by two bone segments forming a joint is provided for a computer-aided surgical navigation system. The device utilizes an optical tracking system to establish a transformation relationship between the coordinate system of a 3D virtual skeleton model and the coordinate system of landmarks acquired from the actual bone surface. The device includes the following modules: a first module (landmark extraction module) for extracting landmarks from the 3D virtual skeleton model, wherein the landmarks are selected from: hip joint center H, femoral-knee joint center FK, lateral epicondyle LE, medial epicondyle ME, tibial-knee joint center TK, tibial tuberosity TB, and ankle joint center AK; and a second module (vector calculation module) for calculating the femoral mechanical axis direction vector. , (Equation 3), and the tibial mechanical axis direction vector: (Equation 4); The third module (flexion angle calculation module) is used to calculate the flexion angle of the knee joint during flexion in the sagittal plane:

[0020] (Equation 5).

[0021] Preferably, the measuring device further includes: a fourth module (outward and inward buckling angle calculation module), used when the buckling angle is 0° < α f <60° or 120° <α f When the angle is less than 160°, the coronal plane P defined by the hip joint center H, lateral epicondyle LE, and medial epicondyle ME will be used. c Used as the projection surface, based on vector , In coronal plane P c The projection onto the coronal plane determines the eversion and inversion angles. When the buckling angle is within the range of 60° ≤ αf ≤ 120°, it will be perpendicular to the coronal plane P. c cross section P V 'As a projection plane through the lateral epicondyle (LE) and medial epicondyle (ME), the coronal plane is used.' P c normal vector sum vector In plane P V 'projection on To determine the outward and inward folding angles; and the fifth module (projection calculation module), used to calculate the projection based on the following formula: Let vector... It is a vector In a normal vector The projection on the projection plane, then

[0022] (Equation 6).

[0023] According to the method of the present invention, it can be used for real-time measurement of knee flexion, valgus and varus angles in computer-assisted knee replacement surgery. Attached Figure Description

[0024] Figure 1 The locations of various landmarks in the CT skeleton model are schematically shown.

[0025] Figure 2 The directional vectors are shown schematically.

[0026] Figure 3 The diagram schematically shows a buckling angle of 0°. a f Left side view when <60°.

[0027] Figure 4Schematic representation of the flexion angle 0° a f Projection view at 60°.

[0028] Figure 5 Schematic representation of the flexion angle 120° a f Left view at 160°.

[0029] Figure 6 Schematic representation of the flexion angle 120° a f Projection view at 160°.

[0030] Figure 7 Schematic representation of the flexion angle a f Left view at 90°.

[0031] Figure 8 Schematic representation of the flexion angle 60° a f Projection view at 120°.

[0032] Figure 9 Schematic representation of the flexion movement and flexion angle of the knee joint. DETAILED DESCRIPTION

[0033] Exemplary embodiments of the present application are described in detail below with reference to the attached drawing figures. The exemplary embodiments described below and shown in the drawings are intended to teach the principles of the present application, with the understanding that the present application can be adapted or modified as necessary or desired by those skilled in the art for a wide variety of environments and applications. Accordingly, the protection afforded the present application by the appended claims should not be limited to the exemplary embodiments described below and shown in the drawings.

[0034] In the present embodiment, the present inventors propose a method for calculating the flexion, valgus and varus angles of the knee joint in real time in computer-aided surgery, however the present application is not limited to the post-implantation of implants, but can also be applied to the calculation of the distance between two bone blocks in various joints in pre-implantation or even normal conditions.

[0035] <Optical tracking system>

[0036] In TKA surgery, a real-time optical tracking system is used to find the conversion relationship between the preoperative plan coordinate system and the operating room coordinate system in the computer navigation software, so that the position and direction of each CT marker and surgical instrument can be intuitively known.

[0037] In this way, using the optical tracking system, the flexion, valgus and varus angles of the knee joint during movement of the lower limbs and the like can be calculated in real time as follows.

[0038] <CT marker>

[0039] For this purpose, the following marker points can be extracted from the CT bone model: the hip joint center H; the femoral knee joint center FK; the lateral epicondyle LE; the medial epicondyle ME; the tibial knee joint center TK; the tibial tuberosity TB; the ankle joint center AK, as Figure 1 shown in

[0040] Among them, the line HFK formed by the hip joint center H and the femoral knee joint center FK defines the mechanical axis of the femur, and the line TKAK formed by the tibial knee joint center TK and the ankle joint center AK defines the mechanical axis of the tibia. These lines will be used as references or benchmarks for the angles to be obtained.

[0041] For simplicity of description, the labeling of each point is sometimes omitted in the following drawings.

[0042] <Angle between lines>

[0043] Regarding the angle formed between two straight lines, it is defined as the minimum angle formed between their respective direction vectors.

[0044] More specifically, in the case of having two different points A and B belonging to the straight line L1, the direction vector of this straight line L1 is defined as:

[0045] , (Equation 1).

[0046] Thus, the included angle formed between two straight lines L1 and L2 having direction vectors 、 respectively is defined as:

[0047] , (Equation 2).

[0048] <Flexion angle>

[0049] As Figure 9 shown, the flexion (flexion and extension) movement of the knee joint occurs around the transverse axis on the sagittal plane (refer to, for example, Figure 9 the transverse axis of the knee joint in

[0050] Here, if the movement of the knee joint causes the tibial axis to be angled forward relative to the mechanical axis of the lower limb (formed by the hip joint center and the ankle joint center), then this flexion angle is considered negative, as Figure 9 the dashed line in

[0051] On the contrary, Figure 9 The buckling angles shown, for example, 0° to 155°, are positive (posterior (proximal) angulations).

[0052] The -10° and 155° shown here are not intended to limit the extreme values ​​of the buckling angle.

[0053] Based on the above definition of the angle between lines, the buckling angle corresponding to the angle between lines HFK and TKAK can be obtained, such as... Figure 2 , 3 As shown in 5 and 7:

[0054] Femoral mechanical axis direction vector: , (Equation 3), ;

[0055] Tibial mechanical axis direction vector: (Equation 4);

[0056] Buckling angle αf:

[0057] (Equation 5).

[0058] <Orientation of the tilt direction>

[0059] To determine the sign of the angle, it is necessary to know whether the angular direction of the tibial mechanical axis relative to the lower limb mechanical axis is forward or backward.

[0060] like Figure 2 , 3 As shown in Figures 5 and 7, from the 3D virtual skeleton model, take a line Ld that passes through the tibial tuberosity TB and is perpendicular to the mechanical axis of the tibia in the sagittal plane, and calculate its direction vector. Direction vector relative to the femoral mechanical axis The included angle α between them df (Not shown), which indicates whether the flexion of the knee joint causes tilting in the forward or backward direction. This angle value will indicate the degree of tilt of the tibial mechanical axis relative to the femoral mechanical axis in the forward and backward directions (corresponding to the front and back sides of the human anatomy), that is, this angle value will indicate the angle of the tibial mechanical axis relative to the femoral mechanical axis in the front and back sides of the human body.

[0061] If vector as well as If the angle formed between them is a right angle, then the tilt in the forward or backward direction is zero. For example, refer to... Figure 9 The 0° angle shown Figure 2 The lower limbs are shown in an extended position.

[0062] If the angle is greater than 90°, the flexion angle is positive, and the tibial axis is tilted posteriorly. For example, refer to... Figure 9The range of angles from 0° to 155° is shown in the figure.

[0063] If the angle is less than 90°, it is negative, and the tibia is tilted forward along the axis. For example, refer to... Figure 9 The range of angles from 0° to -10° is shown in the figure.

[0064] <Outward and inward angles>

[0065] The eversion and varus angles can be determined by the femoral and tibial mechanical axes projected onto the coronal plane Pc. Always check that this axis aligns with the aforementioned coronal plane Pc. c vertical.

[0066] like Figure 4 , 6 As shown in Figure 8, when the tibia and femur are tilted laterally to the lower limb mechanical axis, the varus angle is defined; when the tibia and femur are tilted medially to the lower limb mechanical axis, the valgus angle is defined.

[0067] With any vector The vector In a normal vector Projection on the plane It is given by the following formula:

[0068] (Equation 6).

[0069] Here, it is necessary to determine the inversion and eversion angles, when the flexion angle is 0° < α. f <60° or 120° <α f Within a range of <180°, the coronal plane P is defined by three anatomical points H, LE, and ME. c Used as the projection surface (corresponding to the above having a normal vector) (the plane).

[0070] It is important to note that points LE and ME must form a vector. Perpendicular vectors (see) Figure 4 , 6 If they are not perpendicular, then it can be solved by finding vectors. Plane P is a normal line and contains one of its points LE or ME. V (See) Figure 8 ), and in the plane P V Project another point LE or ME onto the top, so that the newly projected point (the "other point LE or ME" mentioned above) and its paired point LE or ME (one of the points LE or ME mentioned above) will form a line perpendicular to the top. A vector of vectors. Through vectors The plane is obtained by combining pairs of points LE or ME (or their projections). Pc (Not shown).

[0071] Therefore, vector , In plane P c 'Projected from above and , used to determine outward and inward angles.

[0072] On the other hand, when the buckling angle is within the range of 60°≤αf≤120°, the angle perpendicular to the coronal plane P c cross section P V 'As the projection plane passing through points LE and ME (or the projection points of both), P V There exists a vector on the plane. Perpendicular vectors coronal plane P c The normal vector.

[0073] Therefore, the coronal plane can be used. P c normal vector sum vector In plane P V 'projection on To determine the outward and inward angles.

[0074] The reason for using different planes P V P V This is because when the flexion angle is 90 degrees, the tibial axis is perpendicular to the coronal plane P. c There is no projection vector.

[0075] By projecting the mechanical axis of the lower limb together with the tibial and femoral axes onto P c On a plane, the tilt of the latter two relative to the mechanical axis can be determined, thus determining whether the angle is inward or outward.

[0076] <Technical Effects>

[0077] This mechanism is used to calculate the angles exposed during knee replacement surgery, and computer navigation systems and optical tracking technology can be used to calculate the flexion, varus, and valgus angles at each position of the lower limb in real time.

[0078] To achieve this, it is sufficient to convert the anatomical points given in the CT coordinates to camera coordinates for real-time optical tracking of the lower limbs. Once these points are converted, the procedure explained in this article is used.

[0079] For patients who have received artificial knee implants, real-time measurements can help improve surgical quality and facilitate more natural flexion and stable flexion movements.

[0080] To convert the anatomical points given in the CT coordinates into camera coordinates for real-time optical tracking of the lower limbs, known methods can be used. Specifically, registration can be used to achieve the conversion between the preoperative and intraoperative coordinate systems, thereby enabling visualization of the position and orientation of surgical instruments relative to the intraoperative 3D model.

[0081] For example, a suitable trackable marker can be fixed to the human body, and a high-precision optical motion tracking device or surgical navigation system can be used to measure the spatial coordinates and displacement of the marker according to a set sampling rate to capture the three-dimensional spatial movement of the femur and tibia.

[0082] In addition, the current methods for registering markers or points of interest used in surgical navigation systems may include: bone implant screw markers, anatomical markers, and markers pasted on the skin surface.

[0083] The above conversion can be achieved using existing technologies, which will not be elaborated upon here.

[0084] <Computer Devices>

[0085] According to another aspect of this application, a computer apparatus is provided, comprising a processor and a memory storing a computer program that, when executed by the processor, causes the processor to perform the steps of the method described above. This also includes situations involving remote computers. For example, the remote computer can be connected to a user computer via any type of network—including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computer.

[0086] <Storage Media>

[0087] According to another aspect of this application, a non-volatile computer-readable storage medium is provided, on which computer-readable instructions are stored, which, when executed by a processor, cause the processor to perform the steps of the above-described method. For example, it can be any tangible medium containing or storing a program that can be used by a computer device or a surgical robot system.

[0088] According to this embodiment, the steps of the method described above can be implemented as a computer software program. Each step can represent a module, program segment, or part of code. For example, it can include a computer program carried on a computer-readable medium, which contains program code for performing the method. The program code can be executed entirely on a user's computer, partially on a user's computer, as a standalone software package, partially on a remote computer, or entirely on a remote computer or server.

[0089] When the computer program is executed by a processor such as a central processing unit, it performs the functions defined in the above method.

[0090] <Measuring Device>

[0091] A calculation device for an intraoperative navigation system is also provided, comprising: a probe for acquiring intraoperative bone surface point set data of a patient; a computer connected to the probe for image input and point set output, capable of performing corresponding data calculations and processing; and a display device connected to the computer for displaying a registered three-dimensional image. The display device includes, but is not limited to, a monitor.

[0092] Alternatively, a 3D scanner can be used to acquire intraoperative bone surface point set data for the patient, instead of the probe.

[0093] The anatomical structures discussed above are not limited to the femur or tibia mentioned above, but can also be the whole or part of the anatomical structures of other two bones that make up a joint.

[0094] Thus, the computer-aided surgical navigation system according to the present invention can be applied to various surgical procedures to track the surgical situation, thereby improving the accuracy and precision of the surgery.

[0095] In this invention, the terms "step," "formula n," etc., are used to distinguish different objects, not to describe a specific order. The terms "anterior," "posterior," "anterior," and "proximal / distal" refer to their orientation relative to the patient's position or as shown in the accompanying drawings (e.g., ...). Figure 9 The orientation shown in the diagram.

[0096] Although the invention has been described with reference to various specific embodiments, it should be understood that modifications can be made within the spirit and scope of the described inventive concept. Therefore, it is intended that the invention be limited to the described embodiments but will have the full scope defined by the language of the appended claims.

Claims

1. A method for calculating the angle between two bone segments forming a joint, used in a computer-aided surgical navigation system, wherein, An optical tracking system is used to establish a transformation relationship between the coordinate system of a 3D virtual skeleton model and the coordinate system of landmarks acquired from the actual skeleton surface. Its features are, The angle is determined using the landmark points extracted from the 3D virtual skeleton model. The landmarks include: hip joint center H, femoral-knee joint center FK, tibia-knee joint center TK, ankle joint center AK, tibial tuberosity TB, lateral epicondyle LE, and medial epicondyle ME. It also includes the following steps: Determine the direction vector of the femoral mechanical axis: , (Equation 3), and Tibial mechanical axis direction vector: (Equation 4); Therefore, the flexion angle α of the knee joint during flexion in the sagittal plane is calculated. f : (Equation 5) Take a line Ld from the 3D virtual skeleton model that passes through the tibial tuberosity TB and is perpendicular to the mechanical axis of the tibia in the sagittal plane. Find the direction vector of the line Ld. Direction vector relative to the femoral mechanical axis The included angle α between them df , to indicate the tilt direction of the tibial mechanical axis relative to the femoral mechanical axis, Coronal P c Defined by the hip joint center H, lateral epicondyle LE, and medial epicondyle ME, when 0° < α f <60° or 120° <α f When <160°, the coronal plane P c Used as a projection surface Based on vectors , In coronal plane P c The projection on the surface determines the outward and inward angles. The projection is calculated based on the following formula: Let vector It is a vector In a normal vector The projection on the projection plane, then (Equation 6) If the outer epicondyle LE and the inner epicondyle ME do not form with the vector If the vector is perpendicular, then find the vector that has the specified value. Plane P, which is a normal and contains one of the points of the lateral epicondyle LE and the medial epicondyle ME. V In the plane P V Project one of the two points onto the top, and use the projected point and one of the aforementioned points paired with it to form a point perpendicular to the top. The vector of vectors, passing through the paired points and the vector. Obtain the projection plane P c ', Using vectors , On the projection plane P c 'Achieved by projection and To determine the outward and inward angles, When 60°≤α f When the angle is ≤120°, the angle will be perpendicular to the coronal plane P. c cross section P V 'As a projection plane through the outer epicondyle LE and the inner epicondyle ME, Using coronal P c normal vector and the vector In the cross section P V The projection on the 'a' determines the outward and inward angles. If the included angle α df If the angle is 90°, then the tilt of the tibial mechanical axis in the forward or backward direction is determined to be zero. If the included angle α df If the angle is greater than 90°, then the buckling angle α is determined. f It is positive, and the mechanical axis of the tibia is tilted in the posterior direction; If the included angle α df If the angle is less than 90°, then the buckling angle α is determined to be... f The value is negative, and the mechanical axis of the tibia is tilted forward. Real-time calculation of flexion angle α at each position of the lower limb f Inward and outward angles.

2. A surgical robot system, comprising a computer-aided surgical navigation system having an optical tracking system and a computer, wherein the computer executes the steps of the calculation method of claim 1 for calculating the angle between two bone blocks forming a joint.

3. A storage medium, which is a computer-readable storage medium, storing a computer program, characterized in that, The computer program is executed to implement the steps of the measurement method as described in claim 1.

4. A device for calculating the angle between two bone segments forming a joint, used in a computer-aided surgical navigation system, wherein, An optical tracking system is used to establish a transformation relationship between the coordinate system of a 3D virtual skeleton model and the coordinate system of landmarks acquired from the actual skeleton surface. Its characteristic is that it includes the following modules for implementing the calculation method described in claim 1: The first module is used to extract landmark points from the 3D virtual skeleton model. The landmark points are selected from: hip joint center H, femoral knee joint center FK, lateral epicondyle LE, medial epicondyle ME, tibial knee joint center TK, tibial tuberosity TB, and ankle joint center AK. The second module is used to determine the direction vector of the femoral mechanical axis: , (Equation 3), and the tibial mechanical axis direction vector: (Equation 4); The third module is used to calculate the flexion angle α of the knee joint during flexion in the sagittal plane. f : (Equation 5) The fourth module is used when 0° < α f <60° or 120° <α f When <160°, the coronal plane P c Used as the projection surface, based on vector , In coronal plane P c The projection onto the vector determines the lateral and medial folding angles, if the lateral epicondyle LE and the medial epicondyle ME do not form a vector. If the vector is perpendicular, then find the vector that has the specified value. Plane P, which is a normal and contains one of the points of the lateral epicondyle LE and the medial epicondyle ME. V In the plane P V Project one of the two points onto the top, and use the projected point and one of the aforementioned points paired with it to form a point perpendicular to the top. The vector of vectors, passing through the paired points and the vector. Obtain the projection plane P c ', using vectors , On the projection plane P c 'Achieved by projection and To determine the outward and inward angles, when 60° ≤ α f When the angle is ≤120°, the angle will be perpendicular to the coronal plane P. c cross section P V 'As a projection plane through the lateral epicondyle LE and the medial epicondyle ME, the coronal plane P' c normal vector and the vector In the cross section P V The projection on the 'a' determines the outward and inward folding angles; and The fifth module is used to calculate the projection based on the following formula: Let vector It is a vector In a normal vector The projection on the projection plane, then (Equation 6).

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