3D Part Toolpaths Using Implicit Geometry to Shrink File Size
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Solution Overview
Problem
Existing 3D production files are voluminous due to the use of piecewise representation, which requires large amounts of data to define motion commands, especially for longer movements, leading to increased file sizes and processing requirements.
Innovation Solution
The use of implicit representation in 3D production files to define motion commands through closed-form functional parameters of geometric structures, such as Gyroid and Schwarz Diamond, reduces data storage and processing needs by representing motion with fewer parameters, allowing for more efficient storage and transmission of 3D production files.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If piecewise representation is used to define motion commands in 3D production files, then the motion paths can be precisely controlled, but the file size becomes voluminous and processing time increases
Solution Approach 1:
The patent transforms the representation parameters from piecewise segments (x1, y1, x2, y2, x3, y3, ...) to implicit function parameters (a, b, c, d, e, f for quadratic curves). This parameter transformation reduces the data quantity while preserving motion precision, as the implicit function can generate infinite points from limited parameters.
Solution Approach 2:
Instead of defining motion through discrete segments (traditional approach), the patent inverts the approach by defining motion through continuous implicit functions. The function f(x, y) = 0 implicitly defines the curve, reversing the conventional explicit parameterization method and achieving compact representation.
2Manufacturing precision
If piecewise representation is used to define motion commands, then detailed control is achieved, but the number of segments scales linearly with movement length increasing file size
Solution Approach 1:
The patent changes the parameter representation from O(n) piecewise segments to O(1) implicit function parameters. A single quadratic implicit function with 6 parameters can represent entire curves regardless of length, eliminating the linear scaling issue and reducing processing time for file interpretation.
3Manufacturing precision
If more piecewise segments are stored to maintain quality for longer movements, then production accuracy is maintained, but file size increases significantly
Solution Approach 1:
The patent inverts the traditional approach by using implicit functions where the curve is defined by the relationship f(x, y) = 0 rather than explicit point sequences. This allows maintaining production quality through the mathematical continuity of the implicit function while dramatically reducing data storage requirements from hundreds of megabytes to kilobytes.
Data Source
AI summary
A 3D production apparatus and method that receives a 3D production file, the 3D production file containing at least one positional command defined based on an implicit representation, the at least one positional command including at least one parameter of the implicit representation. At least one tool command is generated based on the parameters of the implicit representation. A position of a tool is controlled based on the generated at least one tool command, to produce at least a portion of a 3D part corresponding to the 3D production file.