Computer, method, and computer-readable medium for rendering extended reality based on a determined coordinate conversion equation

1 . A computer comprising:

a processor; and

a memory storing at least one program that, when executed by the processor, causes the processor to:

calculate first coordinates in a first coordinate system of a three-dimensional object rendered in an extended reality space defined by the first coordinate system, wherein the first coordinate system is of a first device tracked by a first tracking system, and the three-dimensional object is a virtual device corresponding to a second device and is displayed on a display;

calculate second coordinates in a second coordinate system of the second device tracked by a second tracking system related to the second coordinate system, wherein the second coordinate system is different from the first coordinate system; and

calculate a coordinate conversion equation that converts coordinates of the second coordinate system into coordinates of the first coordinate system based on the first coordinates and the second coordinates, in response to operation of an operation part provided in the second device while a user grips the second device and aligns the second device with the virtual device in the extended reality space.

2 . The computer according to claim 1 ,

wherein the display is a head-mounted display.

3 . The computer according to claim 1 , wherein the at least one program, when executed by the processor, causes the processor to:

calculate, in response to the operation of the operation part provided in the second device, a plurality of coordinates in the second coordinate system of at least three of a plurality of trackers provided on the second device;

calculate a plurality of coordinates in the first coordinate system of each position on the three-dimensional object corresponding to each position of the at least three of the plurality of trackers; and

calculate the coordinate conversion equation by deriving a parallel movement vector and a rotation matrix based on the plurality of coordinates in the first coordinate system and the plurality of coordinates in the second coordinate system.

4 . The computer according to claim 1 , wherein the at least one program, when executed by the processor, causes the processor to:

control the display such that first information indicating a tilt of the three-dimensional object in the first coordinate system and second information indicating a tilt of the second device in the second coordinate system indicated by a measurement result of an inertial measurement unit included in the second device in the extended reality space together with the three-dimensional object.

5 . The computer according to claim 1 , wherein the at least one program, when executed by the processor, causes the processor to:

acquire a first matrix indicating a posture of the second device in the second coordinate system from an inertial measurement unit included in the second device;

acquire a second matrix indicating a posture of the three-dimensional object in the first coordinate system;

derive a rotation matrix based on the first matrix and the second matrix;

specify a plurality of coordinates in the second coordinate system of one of a plurality of points provided on the second device;

specify a plurality of coordinates in the first coordinate system of a point on the three-dimensional object corresponding to the one of the plurality of points provided on the second device; and

calculate the coordinate conversion equation by deriving a parallel movement vector based on the coordinates in the first coordinate system, the coordinates in the second coordinate system, and the rotation matrix.

6 . A method comprising:

calculating first coordinates in a first coordinate system of a three-dimensional object rendered in an extended reality space defined by the first coordinate system, wherein the first coordinate system is of a first device tracked by a first tracking system, and the three-dimensional object is a virtual device corresponding to a second device and is displayed on a display;

calculating second coordinates in a second coordinate system of the second device tracked by a second tracking system related to the second coordinate system, wherein the second coordinate system is different from the first coordinate system; and

calculating a coordinate conversion equation for converting coordinates of the second coordinate system into coordinates of the first coordinate system based on the first coordinates and the second coordinates, in response to operation of an operation part provided in the second device while a user grips the second device and aligns the second device with the virtual device in the extended reality space.

7 . The method according to claim 6 ,

wherein the display is a head-mounted display.

8 . The method according to claim 6 , further comprising:

calculating, in response to the operation of the operation part provided in the second device, a plurality of coordinates in the second coordinate system of at least three of a plurality of trackers provided on the second device;

calculating a plurality of coordinates in the first coordinate system for each position on the three-dimensional object corresponding to each position of the at least three of the plurality of trackers; and

calculating the coordinate conversion equation by deriving a parallel movement vector and a rotation matrix based on the plurality of coordinates in the first coordinate system and the plurality of coordinates in the second coordinate system.

9 . The method according to claim 6 , further comprising:

controlling the display to display first information indicating a tilt of the three-dimensional object in the first coordinate system and second information indicating a tilt of the second device in the second coordinate system indicated by a measurement result of an inertial measurement unit included in the second device in the extended reality space together with the three-dimensional object.

10 . The method according to claim 6 , further comprising:

acquiring a first matrix indicating a posture of the second device in the second coordinate system from an inertial measurement unit included in the second device;

acquiring a second matrix indicating a posture of the three-dimensional object in the first coordinate system;

deriving a rotation matrix based on the first matrix and the second matrix;

specifying a plurality of coordinates in the second coordinate system of one of a plurality of points provided on the second device;

specifying a plurality of coordinates in the first coordinate system of a point on the three-dimensional object corresponding to the one of the plurality of points provided on the second device; and

calculating the coordinate conversion equation by deriving a parallel movement vector based on the coordinates in the first coordinate system, the coordinates in the second coordinate system, and the rotation matrix.

11 . A non-transitory computer-readable medium storing at least one program which, when executed by a processor, causes the processor to:

calculate first coordinates in a first coordinate system of a three-dimensional object rendered in an extended reality space defined by the first coordinate system, wherein the first coordinate system is of a first device tracked by a first tracking system, and the three-dimensional object is a virtual device corresponding to a second device and is displayed on a display;

calculate second coordinates in a second coordinate system of the second device tracked by a second tracking system related to the second coordinate system, wherein the second coordinate system is different from the first coordinate system; and

calculate a coordinate conversion equation for converting coordinates of the second coordinate system into coordinates of the first coordinate system based on the first coordinates and the second coordinates, in response to operation of an operation part provided in the second device while a user grips the second device and aligns the second device with the virtual device in the extended reality space.

12 . The computer-readable medium according to claim 11 ,

wherein the display is a head-mounted display.

13 . The computer-readable medium according to claim 11 , wherein the at least one program, when executed by the processor, cause the processor to:

calculate, in response to the operation of the operation part provided in the second device, a plurality of coordinates in the second coordinate system of at least three of a plurality of trackers provided on the second device;

calculate a plurality of coordinates in the first coordinate system of each position on the three-dimensional object corresponding to each position of the at least three of the plurality of trackers; and

calculate the coordinate conversion equation by deriving a parallel movement vector and a rotation matrix based on the plurality of coordinates in the first coordinate system and the plurality of coordinates in the second coordinate system.

14 . The computer-readable medium according to claim 11 , wherein the at least one program, when executed by the processor, cause the processor to:

control the display to display first information indicating a tilt of the three-dimensional object in the first coordinate system and second information indicating a tilt of the second device in the second coordinate system indicated by a measurement result of an inertial measurement unit included in the second device in the extended reality space together with the three-dimensional object.

15 . The computer-readable medium according to claim 11 , wherein the at least one program, when executed by the processor, cause the processor to:

acquire a first matrix indicating a posture of the second device in the second coordinate system from an inertial measurement unit included in the second device;

acquire a second matrix indicating a posture of the three-dimensional object in the first coordinate system;

derive a rotation matrix based on the first matrix and the second matrix;

specify a plurality of coordinates in the second coordinate system for one of a plurality of points provided on the second device;

specify a plurality of coordinates in the first coordinate system for a point on the three-dimensional object corresponding to the one of the plurality of points provided on the second device; and

calculate the coordinate conversion equation by deriving a parallel movement vector based on the coordinates in the first coordinate system, the coordinates in the second coordinate system, and the rotation matrix.