Sectional Curve Fitting With Tangent Arcs for CNC Splines
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Solution Overview
Problem
In CNC machining, manually fitting first-order continuous curves composed of multiple splines is inefficient, error-prone, and lacks accuracy due to the complexity of mathematical expressions required.
Innovation Solution
A curve fitting method and apparatus based on a drawing tool that determines a fitting area and performs sub-fitting operations using tangent arcs to generate fitting arcs, improving efficiency and accuracy by automatically fitting the original curve in sections within the defined area.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If manual curve fitting is used for first-order continuous curves composed of multiple splines, then flexibility in handling complex curves is maintained, but fitting efficiency is low and accuracy is poor
Solution Approach 1:
The system performs automatic curve fitting without requiring manual intervention. The computer executes the drawing tool to automatically perform sub-fitting operations, generate fitting arcs, and splice them into a complete fitting curve, eliminating the need for manual curve fitting while maintaining high accuracy through the automated algorithmic process
Solution Approach 2:
The curve fitting process is divided into multiple sub-fitting operations that work on different segments of the original curve. Each sub-fitting operation generates a fitting arc for a specific portion of the curve, and these segments are then spliced together to form the complete fitting curve, improving both efficiency and accuracy
2Adaptability or versatility
If multiple splines are used to compose the first-order continuous curve, then the curve can represent complex engineering shapes, but the mathematical expression becomes difficult to fit
Solution Approach 1:
The patent extracts the curve fitting problem from the complex mathematical domain into a geometric construction domain. Instead of dealing with difficult mathematical expressions of multiple splines, the system uses geometric operations (tangent arcs, splicing) to directly construct the fitting curve, simplifying the problem while maintaining the ability to handle complex shapes
Solution Approach 2:
The patent introduces fitting arcs as an intermediary element between the original complex spline curve and the final processed curve. These fitting arcs serve as geometric mediators that approximate the original curve segments, making the complex curve representation manageable for further processing without requiring direct mathematical manipulation of the splines
3Productivity
If automatic curve fitting is implemented, then fitting efficiency is improved, but the number of fitting arcs increases which may reduce precision
Solution Approach 1:
The system performs sub-fitting operations on portions of the curve rather than attempting to fit the entire curve at once. Each sub-fitting operation works on a specific segment within a fitting area, generating an appropriate number of fitting arcs for that segment. This partial action approach maintains precision by focusing computational effort on local curve characteristics while improving overall efficiency
Data Source
AI summary
A curve fitting method, apparatus and device based on a drawing tool for improving the accuracy of curve fitting. The method includes: determining a fitting area containing the original curve, in the fitting area, performing at least one sub-fitting operation on the original curve until the end condition of the curve fitting is satisfied, and generating a fitting curve corresponding to the original curve based on the fitting curve corresponding to each sub-fitting operation. This method can fit the original curve segments in the fitting area, which improves the accuracy of the obtained fitting curve.