Spline Stiffness Parameter Evaluation for Smooth Curve Sampling
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Solution Overview
Problem
Existing methods for representing user input curves on displays suffer from excessive rendering overhead and visible staircase-like artifacts when display resolution changes, due to inadequate spline curve sampling.
Innovation Solution
A computer-implemented method and apparatus that detects input curves, samples them into discrete vertices, computes and normalizes tangent vectors, and sets spline stiffness parameters to convert the input curve into spline patches, ensuring smooth curve representation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If curve sampling is performed on a discrete grid to generate spline curves, then the curve can be represented at the sampling resolution, but when display resolution changes the sampling frequency becomes inappropriate resulting in excessive rendering overhead and visible staircase-like artifacts
Solution Approach 1:
The patent applies dynamics by making the spline curves adaptive to different display resolutions. Instead of using fixed sampling frequency, the system dynamically adjusts the spline parameters and control points based on the target resolution, allowing the same sampled curve to be smoothly rendered at any resolution without excessive rendering overhead or staircase artifacts.
Solution Approach 2:
The patent changes parameters by optimizing the spline stiffness parameter and control point placement. By evaluating and adjusting these parameters based on the input curve characteristics and target resolution, the system achieves smooth curve representation without requiring high sampling frequency, thus improving rendering performance while maintaining accuracy.
2Ease of manufacture
If spline curves are created using control points and stiffness parameter, then the curve can be represented at sampling resolution, but the curves are represented poorly resulting in jagged edges and stair-casing effects
Solution Approach 1:
The patent applies local quality by evaluating and setting different spline stiffness parameters for different segments of the curve based on local characteristics. Instead of using a uniform stiffness parameter, the system analyzes each curve segment and assigns appropriate stiffness values, resulting in smooth transitions and eliminating jagged edges while maintaining ease of curve generation.
Solution Approach 2:
The patent uses feedback by evaluating the normalized dot product of edges and tangents at each vertex to determine optimal spline parameters. This feedback mechanism allows the system to automatically adjust control point placement and stiffness parameters based on the actual curve geometry, ensuring smooth representation without manual intervention.
3Quantity of substance
If fixed sampling frequency is used to represent curves, then the curve can be displayed at the sampling resolution, but when zooming in the sampling frequency becomes inappropriate resulting in visible staircase-like artifacts
Solution Approach 1:
The patent applies universality by creating a curve representation system that works across multiple resolutions. By using optimized spline parameters and control points that are independent of specific sampling frequency, the same sampled curve can be smoothly displayed at any resolution level, from zoomed-out to zoomed-in views, eliminating staircase artifacts.
Data Source
AI summary
A computer implemented method and apparatus for reproducing an input curve on a mobile device comprising detecting the input curve, sampling the input curve into a discrete set of vertices, performing a normalized dot product of an edge leading into each one of the discrete set of vertices and a tangent to an edge leading from each one of the discrete set of vertices, setting one or more spline stiffness parameter based on the normalized dot product corresponding to each vertex; and converting the sampled input curve into one or more spline patch with the set spline stiffness parameter corresponding to each vertex.