B-Spline Drawing Data Intersection Checks Using Integer Geometry
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Solution Overview
Problem
Existing methods for examining drawing data represented by B-spline curves face challenges in accurately determining intersection points due to the use of float calculations and high-order equations, leading to potential errors and inefficiencies.
Innovation Solution
A drawing data examination method that acquires coordinates of control points, sets examination regions using straight lines connecting adjacent control points, and determines the relative position of target control points within these regions using integer-based outer product calculations to assess intersections without requiring float calculations or solving high-order equations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If float calculations and high-order equations are used to calculate intersection points of B-spline curves, then the examination can be performed, but unexpected examination errors occur and large amounts of time are required
Solution Approach 1:
The patent replaces the conventional float-based calculation system with an integer-based coordinate system. By transforming the B-spline curve examination into integer coordinate geometry problems, the method eliminates floating-point precision errors while maintaining examination accuracy. The control points and intersection points are all represented using integer coordinates, avoiding the fundamental source of examination errors.
Solution Approach 2:
The patent changes the parameter representation from float coordinates to integer coordinates. By scaling the coordinate system appropriately, the method transforms continuous float parameters into discrete integer parameters, which can be processed exactly without precision loss. This parameter transformation resolves the reliability issue while preserving measurement precision.
2Measurement precision
If float calculations and high-order equations are used to calculate intersection points, then the examination can be performed, but a large amount of time is required
Solution Approach 1:
The patent substitutes complex float-based high-order equation solving with simple integer coordinate comparisons and linear operations. By reformulating the intersection examination as integer geometry problems rather than float algebra problems, the computational complexity is dramatically reduced, enabling high-speed processing while maintaining exact accuracy.
Solution Approach 2:
The patent segments the B-spline curve examination into discrete integer coordinate points along the curve. Instead of continuously solving for intersection points using high-order equations, the method examines discrete integer points that lie on or near the curve, transforming a continuous complex problem into a discrete simple problem that can be processed rapidly.
3Device complexity
If integer coordinates are used for control points, then the data is simpler, but float calculations are still needed for intersection points leading to errors
Solution Approach 1:
The patent extends the integer coordinate parameter system from control points to all geometric elements including intersection points. By maintaining consistent integer parameter representation throughout the entire geometric model, the method eliminates the need to switch to float parameters, thereby preventing precision errors while preserving data structure simplicity.
Solution Approach 2:
The patent creates a universal integer coordinate system that handles all geometric entities uniformly - control points, curve points, and intersection points all use integer coordinates. This universal representation eliminates the need for different data types and prevents the reliability issues that arise from mixing integer and float representations.
Data Source
AI summary
A drawing data examination method acquires coordinates representing the positions of a plurality of control points forming the B-spline curve; sets, as an examination target region of the drawing data, a region surrounded by a line segment connecting at least three or more control points adjacent to each other in the drawing data with a straight line after acquiring the coordinates; performs calculation processing of specifying a relative position of an examination target control point with respect to the examination target region by using the coordinates of the examination target control point and control points of the examination target region with respect to the examination target region; and determines whether the figure of the drawing data has an intersection by determining whether the examination target control point exists inside the examination target region based on the relative position.