Virtual Object Rotation Matrix Control for Natural Two-Hand XR Manipulation

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Solution Overview

Problem

Existing methods for manipulating virtual objects in Extended Reality (XR) environments face issues with gimbal lock and unnatural rotations due to the use of Euler angles, particularly when handling objects with both hands, leading to lag and unbalanced rotations.

Innovation Solution

Utilizing a rotation matrix to determine the pose of virtual objects based on the positions and orientations of two manipulation devices, such as handles, to ensure smooth and natural rotation in XR environments.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Ease of operation

If Euler angles are used to manipulate virtual objects, then the manipulation method is simple, but gimbal lock occurs and rotation becomes unnatural

Engineering Contradiction:

Improvemanipulation simplicityVSAvoidrotation stability

Core Design Contradiction:

Ease of operationVSReliability

Solution Approach 1:

The patent changes the mathematical representation parameters from Euler angles to rotation matrices. This parameter change eliminates the gimbal lock problem inherent in Euler angle systems while providing a more robust framework for handling 3D rotations in virtual reality environments.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent replaces the Euler angle mathematical system with a rotation matrix system. This substitution resolves the fundamental limitations of Euler angles (gimbal lock and non-uniform rotation) by using linear algebra-based rotation matrices that provide continuous and smooth rotation control.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Ease of manufacture

If Euler angles are used for virtual object manipulation, then implementation is straightforward, but rotation becomes unbalanced and lags occur

Engineering Contradiction:

Improveimplementation easeVSAvoidrotation smoothness

Core Design Contradiction:

Ease of manufactureVSProductivity

Solution Approach 1:

The patent transforms the rotation representation from Euler angles to rotation matrices, enabling more accurate and smooth rotation calculations. This parameter change allows for better handling of dual-hand manipulation scenarios where synchronized and balanced rotation is critical.

Inventive Principle:

Principle #35Parameter changes

3Adaptability or versatility

If dual-hand manipulation is implemented with Euler angles, then both hands can control the object, but gimbal lock causes unnatural rotation behavior

Engineering Contradiction:

Improvedual-hand control capabilityVSAvoidrotation naturalness

Core Design Contradiction:

Adaptability or versatilityVSEase of operation

Solution Approach 1:

The patent changes from Euler angle representation to rotation matrix representation, which fundamentally resolves the gimbal lock issue. This enables natural and intuitive dual-hand manipulation where each hand can independently control aspects of the virtual object without encountering rotation singularities.

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS12586332B2Method, apparatus, device and storage medium for manipulating virtual object

Publication Date: 2026.03.24 BEIJING ZITIAO NETWORK TECH CO LTD

AI summary

According to the disclosed embodiments, a method, apparatus, device, and storage medium for manipulating a virtual object are provided. The method includes determining a first position of a first manipulation device associated with the virtual environment and a second position of a second manipulation device associated with the virtual environment; determining first orientation information based on the first position and the second position; determining a rotation matrix associated with the virtual object rendered in the virtual environment based on the first orientation information and the second orientation information of the first manipulation device; and determining the pose of the virtual object in the virtual environment based on the rotation matrix. Therefore, the user can manipulate the virtual object in the virtual environment to perform expected and natural rotation.