D-dimensional Virtual Trackball for Multidimensional Space Rotation
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Solution Overview
Problem
Current user interfaces are inadequate for rotating multidimensional spaces beyond three dimensions, as they fail to provide intuitive navigation and projection methods, especially when axes overlap, limiting the ability to effectively visualize and interact with higher-dimensional data.
Innovation Solution
A method and device for rotating a multidimensional space using a 2D visualization space, where a D-dimensional virtual trackball is projected, allowing users to specify points to determine a rotation matrix through singular value decomposition, enabling rotation along a static hyperplane, and displaying regions in the 2D space to facilitate intuitive interaction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If a 3D virtual trackball is used for rotating 3D data, then rotation control is improved, but the solution cannot be extended to higher dimensional spaces
Solution Approach 1:
The patent extends the 3D virtual trackball concept to D-dimensional space by adding outer shells for each additional dimension beyond 3D. The inner sphere handles 3D rotations, while D-3 outer shells enable rotation control in higher dimensions, allowing a single unified interface to control rotations in any dimensional space.
2Ease of operation
If additional interfaces are added to handle overlapping axes in high dimensional space, then navigation capability is improved, but device complexity increases
Solution Approach 1:
The patent creates a universal D-dimensional virtual trackball interface that handles all rotation operations across any dimensional space with a single unified interface. The interface consists of an inner sphere and D-3 outer shells that work together to provide comprehensive rotation control without requiring multiple separate interfaces or modes.
3Ease of manufacture
If multidimensional data is projected to 2D or 3D visualization space, then visualization becomes possible, but navigation through the original high dimensional space becomes difficult
Solution Approach 1:
The patent introduces a D-dimensional virtual trackball as an intermediary control interface between the user and the high-dimensional data space. This virtual object serves as a mediator that translates 2D/3D input device movements into meaningful rotations in D-dimensional space, bridging the gap between limited input device capabilities and high-dimensional navigation requirements.
Data Source
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AI summary
Embodiments relates to a method for rotating a multidimensional space and a device for rotating a multidimensional space. The method may comprise: - obtaining (S1) 2D coordinates of a first point (p1) and a second point (p2) of a 2D visualization space input by a user, - determining (S2) a first D-dimensional vector (p1) and a second D-dimensional vector (p2) by projecting said first point (p1) and said second point (p2) into a D-dimensional space, wherein D is equal to or greater than 4, - determining (S3) a rotation matrix (R) in function of said first D-dimensional vector (p1) and said second D-dimensional vector (p2). The D-dimensional space has a first dimension, a second dimension and D-2 other dimensions, and the 2D visualization space has D-2 predefined regions associated with respective dimensions among said D-2 other dimensions. The method may comprise projecting (S2b) said 2D coordinates on said first dimension, said second dimension and, among the D-2 other dimensions, mostly on a third dimension associated with the region wherein at least one of the first point (p1) and the second point (p2) is located.