Parametric Space-Time Curves for Smooth Input Motion
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Solution Overview
Problem
Existing methods for representing user input motion fail to provide a smooth path in both space and time, requiring dense keyframes and inefficient storage and communication resources, and lack the ability to adjust smoothness and accuracy.
Innovation Solution
A method and apparatus that generate a sequence of curves representing both the path and speed of user input motion, using curve-fitting algorithms to create compact and smooth representations of motion data, allowing independent control of smoothness and accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a series of keyframes is used to define movement along a curve, then the position and timing of motion can be specified, but the velocity is not smooth and a relatively dense amount of key times is required
Solution Approach 1:
The patent applies curvature by representing motion not as discrete keyframes but as continuous parametric curves ( Bézier or B-splines) in spacetime. This curvature transformation allows smooth interpolation between control points, eliminating the need for dense keyframes while achieving smooth velocity profiles. The mathematical curves inherently provide continuous derivatives, ensuring smooth motion representation.
Solution Approach 2:
The patent changes the parameterization approach by using parametric equations where position and time are both functions of a parameter t. This parameter transformation allows the motion to be defined by control points and weights rather than dense keyframe sequences, reducing complexity while maintaining accuracy through the mathematical properties of parametric curves.
2Reliability
If traditional keyframe methods are used to represent motion, then motion data can be stored, but storage and communication resources are used inefficiently
Solution Approach 1:
The patent extracts only the essential motion characteristics by fitting parametric curves to motion data, representing complex motion sequences with minimal control points. This extraction process removes redundant information while preserving the essential motion trajectory and timing, achieving compact representation that uses significantly less storage space.
Solution Approach 2:
By representing motion as continuous parametric curves rather than discrete data points, the patent achieves compact storage while maintaining smooth motion representation. The mathematical curves encode infinite precision motion paths using only a few control parameters, dramatically reducing storage requirements.
3Measurement precision
If dense keyframes are used to represent motion accurately, then motion details are preserved, but communication resources are consumed excessively
Solution Approach 1:
The patent extracts the essential motion characteristics by fitting parametric curves to the motion data, transmitting only the curve parameters (control points, weights, degrees) rather than dense keyframe sequences. This extraction maintains motion accuracy while dramatically reducing the data volume that needs to be communicated.
Solution Approach 2:
The patent transforms motion representation from time-series keyframe data to parametric curve parameters, changing the data structure to be much more compact. This parameter transformation enables accurate motion reconstruction at the receiving end with minimal communication overhead.
Data Source
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AI summary
Methods and apparatuses that accept user input of motion and produce a representation of the motion smoothly and compactly. The present invention provides a method that comprises accepting a plurality of positional data with corresponding times of the motion, determining one or more continuous positional functions that together represent an approximation of path of the positional data, and determining, for each positional function, one or more time functions that together represent an approximation of the times for the positional data corresponding to the positional functions. The present invention provides an apparatus that comprises an input device and a computer system configured to accept the motion signals generated by the input device, determine one or more continuous positional functions that together represent an approximation of the path of the positional data, and determine, for each positional function, one or more time functions that together represent an approximation of the times for the positional data corresponding to the positional functions.