CN111353941A - Space coordinate conversion method - Google Patents
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Abstract
The invention discloses a space coordinate conversion method, which utilizes Euler angle absolute world coordinates of two points which continuously move in a three-dimensional space to obtain the space position variation of the latter moving point relative to the former moving point, namely the vector variation of the Euler angle, and projects the space coordinate variation of the Euler angle onto a plane, so that the space position variation is converted into the horizontal and vertical vector displacement variation in the plane, and the space motion control is converted into the position motion control on the plane.
Description
Technical Field
The invention relates to the technical field of coordinate conversion from three-dimensional space motion to two-dimensional plane motion control, in particular to a space coordinate conversion method.
Background
In the existing virtual reality development and application, quaternion space attitude binding of a virtual reality 3D game engine is adopted to control the attitude of a virtual object model in a virtual reality scene, interaction among virtual models is completed through the collision attribute of the models, in some control system applications combining virtual reality and reality, the motion control of a real system can be realized only by converting space attitude information and real coordinates, the applied patent CN201610970481.8 describes the conversion of a two-dimensional plane coordinate system into a three-dimensional panoramic spherical coordinate system, and the applied patent CN201710979751.6 describes a three-dimensional coordinate conversion method for any rotation angle, but does not relate to a parameter information conversion method from the three-dimensional spherical motion coordinate system to the two-dimensional plane motion coordinate system.
Disclosure of Invention
The invention aims to solve the defects and provides a consistent space coordinate conversion method to realize the parameter information conversion from a three-dimensional spherical motion coordinate system to a two-dimensional plane motion coordinate system;
in order to realize the design purpose of the invention, the following technical scheme is adopted to realize the following steps:
1. the invention provides a space coordinate conversion method, which comprises the following steps,
obtaining the space attitude variation of the latter moving point relative to the former moving point, namely the vector variation of an Euler angle by utilizing the quaternion world coordinates of two points in a three-dimensional space spherical surface, and projecting the space coordinate variation of the Euler angle onto a plane to convert the space position variation of the moving point into the horizontal and vertical vector displacement variation in the plane;
the invention relates to a space coordinate conversion method, in particular to a method for converting world coordinates of a moving point on a three-dimensional space spherical surface into two-dimensional plane moving coordinates, which comprises a coordinate information conversion process and a coordinate calibration method.
2. The coordinate information conversion process of the space coordinate conversion method of the invention comprises the following steps,
step one, establishing a conversion matrix according to a Cartesian coordinate system and two world coordinate representation methods of quaternion (w, x, y, z) and Euler angle (phi, theta, psi) in a three-dimensional space
The conversion matrix formula (2) for obtaining the conversion of quaternion to Euler angle by the formula (1) is as follows
Wherein phi is a roll angle, theta is a yaw angle, and psi is a pitch angle;
step two, setting any two points P on the three-dimensional space sphere1And P2From P1Move to P2In which P is1Defined as the reference point of motion, P2Is defined as a motion point, P1、P2With world coordinates expressed in quaternions (w, x, y, z), P can be calculated by equation (2)1、P2Euler angular coordinates: p1（Φ1,θ1,Ψ1）， P2（Φ2,θ2,Ψ2) Then from P1Move to P2The spatial attitude change of (a) is as follows:
step three, according to the characteristics of Euler angles, wherein-180。<Φ<180。、-180。<θ<180。、-180。<Ψ<180。According to the three formulas in the step one, the calculated space attitude variation △ phi, △ theta, △ psi is calculated when P is1、P2Move to the critical point-180。Or 180。In time, detecting spatial attitude changes △ Φ, △ θ, △ Ψ will occur in an infinite approximation of 360。The method for removing the sudden change singularity comprises the following steps of setting space attitude change thresholds phi ', theta ', psi ' according to the motion speed characteristics, and aiming at P1、P2When the motion reaches the critical point, the following compensation correction is needed to be carried out on the formula (3):
selecting two suitable euler angles from the three euler angles with the space attitude change to perform two-dimensional plane projection motion processing according to the requirement of the two-dimensional plane motion coordinate, for example, selecting a pitch angle psi and a yaw angle theta to perform two-dimensional plane projection motion, and moving a point P1And P2Projected point on two-dimensional plane is P'1And P'2And if the yaw angle theta is converted into a transverse motion coordinate x after being projected by a two-dimensional plane, and the pitch angle psi is converted into a longitudinal motion coordinate y after being projected by the two-dimensional plane, the coordinate variation of two adjacent motion points projected onto the two-dimensional plane by the space attitude variation is calculated by the following formula:
wherein KxCompensating coefficient, K, for lateral motionyFor longitudinal motion compensation coefficient, Kx、KyIs determined according to the motion characteristics required on the two-dimensional plane;
according to actual needs, the two-dimensional plane projection motion coordinate change calculation can be carried out on the roll angle phi and the yaw angle theta, the two-dimensional plane projection motion coordinate change calculation can also be carried out on the roll angle phi and the pitch angle psi, and the calculation method is similar to the formula (7);
step five, adding P2As the reference point of the next moving point, the coordinate information conversion process of the next moving point is carried out。
3. The coordinate calibration method of the space coordinate conversion method of the invention comprises the following steps,
first, the current moving point P is checkedxWhether or not it is a starting point, e.g. PxIf the motion point is the starting point of the motion, the motion point P is processed according to the coordinate information conversion process stepxConverting the space attitude change coordinate information relative to the motion point PxSimultaneously as P in the coordinate information conversion process1And P2Converting the three-dimensional space motion coordinate information into two-dimensional plane motion coordinate information, and converting the coordinate information into a motion point PxAs a reference point for the next point of movement, e.g. PxIf not, then according to the coordinate information conversion process step, making information conversion from three-dimensional space motion coordinate to two-dimensional plane motion coordinate, and after completing coordinate information conversion making motion point PxAs a reference point for the next motion point.
The invention can complete the information conversion from the three-dimensional space motion coordinate to the two-dimensional plane motion coordinate, and can be conveniently applied to virtual reality interaction application and the conversion from the space attitude motion to the plane motion control.
Drawings
FIG. 1 is a schematic system flow diagram according to the present invention;
fig. 2 is a schematic diagram of projecting a three-dimensional space motion point to a two-dimensional plane according to the technical scheme of the invention.
Detailed Description
In order to make the technical purpose, the adopted technical scheme and the implementation effect of the invention clearer, the invention is further described in detail with reference to the attached drawings:
1. the invention provides a space coordinate conversion method, which comprises the following steps,
obtaining the space attitude variation of the latter moving point relative to the former moving point, namely the vector variation of an Euler angle by utilizing the quaternion world coordinates of two points in a three-dimensional space spherical surface, and projecting the space coordinate variation of the Euler angle onto a plane to convert the space position variation of the moving point into the horizontal and vertical vector displacement variation in the plane;
the invention relates to a space coordinate conversion method, in particular to a method for converting world coordinates of a moving point on a three-dimensional space spherical surface into two-dimensional plane moving coordinates, which comprises a coordinate information conversion process and a coordinate calibration method.
2. The coordinate information conversion process of the space coordinate conversion method of the invention comprises the following steps,
as shown in fig. 2, a three-dimensional space motion point P1And P2Projected to two-dimensional plane of P'1And P'2，
Step one, establishing a conversion matrix according to a Cartesian coordinate system according to two world coordinate representation methods of quaternions (w, x, y, z) and Euler angles (phi, theta, psi) in a three-dimensional space:
the conversion matrix formula (2) for obtaining the conversion of quaternion to Euler angle by the formula (1) is as follows
Wherein phi is a roll angle, theta is a yaw angle, and psi is a pitch angle;
step two, setting any two points P on the three-dimensional space sphere1And P2From P1Move to P2In which P is1Defined as the reference point of motion, P2Is defined as a motion point, P1、P2With world coordinates expressed in quaternions (w, x, y, z), P can be calculated by equation (2)1、P2Euler angular coordinates: p1（Φ1,θ1,Ψ1）， P2（Φ2,θ2,Ψ2) Then from P1Move to P2The spatial attitude change of (a) is as follows:
step three, according to the characteristics of Euler angles, wherein-180。<Φ<180。、-180。<θ<180。、-180。<Ψ<180。According to the three formulas in the step one, the calculated space attitude variation △ phi, △ theta, △ psi is calculated when P is1、P2Move to the critical point-180。Or 180。In time, detecting spatial attitude changes △ Φ, △ θ, △ Ψ will occur in an infinite approximation of 360。The method for removing the sudden change singularity comprises the following steps of setting space attitude change thresholds phi ', theta ', psi ' according to the motion speed characteristics, and aiming at P1、P2When the motion reaches the critical point, the following compensation correction is needed to be carried out on the formula (3):
selecting two suitable euler angles from the three euler angles with the space attitude change to perform two-dimensional plane projection motion processing according to the requirement of the two-dimensional plane motion coordinate, for example, selecting a pitch angle psi and a yaw angle theta to perform two-dimensional plane projection motion, and moving a point P1And P2Projected point on two-dimensional plane is P'1And P'2And if the yaw angle theta is converted into a transverse motion coordinate x after being projected by a two-dimensional plane, and the pitch angle psi is converted into a longitudinal motion coordinate y after being projected by the two-dimensional plane, the coordinate variation of two adjacent motion points projected onto the two-dimensional plane by the space attitude variation is calculated by the following formula:
wherein KxCompensating coefficient, K, for lateral motionyFor longitudinal motion compensation coefficient, Kx、KyIs determined according to the motion characteristics required on the two-dimensional plane;
according to actual needs, the two-dimensional plane projection motion coordinate change calculation can be carried out on the roll angle phi and the yaw angle theta, the two-dimensional plane projection motion coordinate change calculation can also be carried out on the roll angle phi and the pitch angle psi, and the calculation method is similar to the formula (7);
step five, adding P2And as the reference point of the next moving point, the coordinate information conversion process of the next moving point is carried out.
3. The coordinate calibration method of the space coordinate conversion method of the invention comprises the following steps,
first, the current moving point P is checkedxWhether or not it is a starting point, e.g. PxIf the motion point is the starting point of the motion, the motion point P is processed according to the coordinate information conversion process stepxConverting the space attitude change coordinate information relative to the motion point PxSimultaneously as P in the coordinate information conversion process1And P2Converting the three-dimensional space motion coordinate information into two-dimensional plane motion coordinate information, and converting the coordinate information into a motion point PxAs a reference point for the next point of movement, e.g. PxIf not, then according to the coordinate information conversion process step, making information conversion from three-dimensional space motion coordinate to two-dimensional plane motion coordinate, and after completing coordinate information conversion making motion point PxAs a reference point for the next motion point.
Claims (3)
1. A space coordinate transformation method is characterized in that,
obtaining the space attitude variation of the latter moving point relative to the former moving point, namely the vector variation of an Euler angle by utilizing the quaternion world coordinates of two points in a three-dimensional space spherical surface, and projecting the space coordinate variation of the Euler angle onto a plane to convert the space position variation of the moving point into the horizontal and vertical vector displacement variation in the plane;
the invention provides a space coordinate conversion method, which is a method for converting world coordinates of a moving point on a three-dimensional space spherical surface into two-dimensional plane motion coordinates and comprises a coordinate information conversion process and a coordinate calibration method.
2. The coordinate information conversion process according to claim 1,
step one, establishing a conversion matrix according to a Cartesian coordinate system and two world coordinate representation methods of quaternion (w, x, y, z) and Euler angle (phi, theta, psi) in a three-dimensional space
The conversion matrix formula (2) for obtaining the conversion of quaternion to Euler angle by the formula (1) is as follows
Wherein phi is a roll angle, theta is a yaw angle, and psi is a pitch angle;
step two, setting any two points P on the three-dimensional space sphere1And P2From P1Move to P2In which P is1Defined as the reference point of motion, P2Is defined as a motion point, P1、P2With world coordinates expressed in quaternions (w, x, y, z), P can be calculated by equation (2)1、P2Euler angular coordinates: p1（Φ1,θ1,Ψ1）， P2（Φ2,θ2,Ψ2) Then from P1Move to P2The spatial attitude change of (a) is as follows:
step three, according to the characteristics of Euler angles, wherein the angle is-180 degrees<Φ<180 degrees, -180 degrees<θ<180 degrees, -180 degrees<Ψ<180 degrees, and the space attitude variation amounts △ phi, △ theta, △ psi calculated according to the three formulas in the step one are calculated when P is equal to1、P2When the motion reaches a critical point of-180 degrees or 180 degrees, detecting the change quantity △ phi, △ theta and △ psi of the spatial attitude, an infinite sudden change singularity approaching 360 degrees appears, and the sudden change singularity removing method comprises the following steps of setting spatial attitude change thresholds phi ', theta ' and psi ' according to the motion speed characteristic, and aiming at P1、P2When the motion reaches the critical point, the following compensation correction is needed to be carried out on the formula (3):
selecting two suitable euler angles from the three euler angles with the space attitude change to perform two-dimensional plane projection motion processing according to the requirement of the two-dimensional plane motion coordinate, for example, selecting a pitch angle psi and a yaw angle theta to perform two-dimensional plane projection motion, and moving a point P1And P2Projected point on two-dimensional plane is P'1And P'2Wherein the yaw angle θ is transformed into a horizontal motion coordinate x after being projected by the two-dimensional plane, and the pitch angle Ψ is transformed into a longitudinal motion coordinate y after being projected by the two-dimensional plane, and then the motion coordinate change projected onto the two-dimensional plane by the spatial attitude change is calculated by the following formula:
wherein KxIs a cross barCoefficient of motion compensation, KyFor longitudinal motion compensation coefficient, Kx、KyIs determined according to the motion characteristics required on the two-dimensional plane;
according to actual needs, the two-dimensional plane projection motion coordinate change calculation can be carried out on the roll angle phi and the yaw angle theta, the two-dimensional plane projection motion coordinate change calculation can also be carried out on the roll angle phi and the pitch angle psi, and the calculation method is similar to the formula (7);
step five, adding P2And as the reference point of the next moving point, the coordinate information conversion process of the next moving point is carried out.
3. The coordinate calibration method according to claim 1,
first, the current moving point P is checkedxWhether or not it is a starting point, e.g. PxIf it is a motion start point, the coordinate information conversion process step of claim 2 is performed for the motion point PxConverting the space attitude change coordinate information relative to the motion point PxSimultaneously as P in the coordinate information conversion process1And P2Converting the three-dimensional space motion coordinate information into two-dimensional plane motion coordinate information, and converting the coordinate information into a motion point PxAs a reference point for the next point of movement, e.g. PxIf the motion point is not the starting point of the motion, the information conversion from the three-dimensional space motion coordinate to the two-dimensional plane motion coordinate is performed according to the coordinate information conversion process of claim 2, and the motion point P is converted after the coordinate information conversion is completedxAs a reference point for the next motion point.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115639910A (en) * | 2022-10-28 | 2023-01-24 | 武汉恒新动力科技有限公司 | All-dimensional somatosensory interaction method facing operation space of operation object and operation device |
| WO2023097447A1 (en) * | 2021-11-30 | 2023-06-08 | 深圳市韶音科技有限公司 | Movement data calibration method and system |
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| CN107330862A (en) * | 2017-06-30 | 2017-11-07 | 广州幻境科技有限公司 | Conversion method between two autonomous system coordinate systems based on quaternary number |
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| CN105160673A (en) * | 2015-08-28 | 2015-12-16 | 山东中金融仕文化科技股份有限公司 | Object positioning method |
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| CN107330862A (en) * | 2017-06-30 | 2017-11-07 | 广州幻境科技有限公司 | Conversion method between two autonomous system coordinate systems based on quaternary number |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| WO2023097447A1 (en) * | 2021-11-30 | 2023-06-08 | 深圳市韶音科技有限公司 | Movement data calibration method and system |
| CN115639910A (en) * | 2022-10-28 | 2023-01-24 | 武汉恒新动力科技有限公司 | All-dimensional somatosensory interaction method facing operation space of operation object and operation device |
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