Error Image Generation Using Convex Hull Interpolation
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Solution Overview
Problem
Existing methods for generating error images from measurement points on free-form surfaces often produce unnatural images when the number of measurement points is low, failing to provide an intuitive understanding of the error distribution.
Innovation Solution
A method that calculates error data between measurement points and design data, triangulates the points, generates a convex hull, and interpolates error data to create a second point group, allowing for re-triangulation to produce a natural error image, even with few measurement points, using linear interpolation and grid points within the convex hull.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If a small number of measurement points are used, then measurement time is reduced, but the generated error image becomes unnatural and fails to reflect the actual profile
Solution Approach 1:
The patent performs preliminary triangulation and convex hull calculation on the sparse measurement points before interpolation. By pre-processing the point cloud to establish a convex hull structure, the system creates a framework that guides subsequent error value interpolation, ensuring that even with few measurement points, the resulting error image naturally reflects the actual surface profile rather than appearing distorted or unnatural
Solution Approach 2:
The patent introduces an intermediary interpolation process that uses the convex hull structure as a mediator between the sparse measurement points and the final error image. Error values are interpolated across the convex hull surface, creating intermediate error data points that fill gaps in the sparse measurement data. This intermediary step transforms discrete point measurements into a continuous, natural-looking error surface that accurately represents the actual profile
2Manufacturing precision
If error data is interpolated to fill gaps between measurement points, then the error image becomes more natural, but calculation time increases
Solution Approach 1:
The patent segments the interpolation process into distinct phases: first triangulating the measurement points to form a convex hull, then interpolating error values only within the boundaries of the convex hull structure. This segmentation allows the system to focus computational resources efficiently - performing detailed interpolation only where needed within the convex hull rather than across the entire measurement space, thereby reducing overall calculation time while maintaining error image naturalness
Solution Approach 2:
The patent performs preliminary triangulation and convex hull calculation before the main interpolation process. By pre-establishing the convex hull structure, the system creates a computational framework that accelerates subsequent error value interpolation. The pre-processed geometric structure serves as a template that guides efficient error distribution calculation, reducing the computational burden during the actual interpolation phase
Data Source
AI summary
A point group on a surface parametric space of free-form surface data corresponding to a measurement points is calculated as a first point group. Error data between each of measurement points and design points is calculated. The first point group is triangulated to generate first triangular facets and calculate a convex hull of the first point group. A second point group distributed in the calculated convex hull on the surface parametric space is set. Error data of the second point group is obtained from error data corresponding to the first point group. A point group including the first point group and the second point group is re-triangulated to generate a second triangular facets.