Polygonal Line Curvature Modeling via Vertex Turn Radius
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Solution Overview
Problem
Current 3D modeling techniques for curved lines, such as roads, lack a definition of turn radius at each vertex, making it difficult to capture road curvature and determine speed limits, especially in mine hauling simulations where additional information is required, increasing model complexity and cost.
Innovation Solution
A new definition of turn radius is introduced for each vertex of a polygonal line, calculated using a single additional parameter, 'lane width', allowing for the measurement of curvature without extensive additional information, enabling the modeling of real-world curves in a simpler, more efficient manner.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If additional points and parameters are used to model curved lines, then the curve smoothness and model robustness are improved, but the model complexity and development cost increase
Solution Approach 1:
The invention changes the parameter representation from using multiple points to using a single turn radius parameter at each vertex. This parameter transformation allows the model to capture curve characteristics with fewer parameters, reducing model complexity while maintaining the ability to represent curved lines accurately.
Solution Approach 2:
The invention extracts the essential curvature information into a single turn radius parameter at each vertex, separating the curvature characterization from the need for multiple intermediate points. This extraction allows the model to maintain curve smoothness without requiring extensive additional points.
2Measurement precision
If additional information is required to calculate turn radius at each vertex, then the curvature measurement accuracy is improved, but the information overhead and model complexity increase
Solution Approach 1:
The invention transforms the curvature measurement approach by using only two parameters (coordinates of the vertex and the turn radius) instead of requiring multiple additional points or complex parameter sets. This parameter transformation achieves accurate curvature measurement with minimal information overhead.
Solution Approach 2:
The turn radius parameter serves multiple functions simultaneously: it defines the curvature at the vertex, determines the speed limit, and characterizes the road geometry. This self-service approach eliminates the need for separate parameters for each function, reducing information overhead while maintaining measurement precision.
3Device complexity
If polygonal line segments are used to represent roads, then the model simplicity and computational efficiency are improved, but the ability to capture real-world curve characteristics is worsened
Solution Approach 1:
The invention adds the turn radius parameter to the polygonal line model, transforming it from a purely geometric representation to one that incorporates physical curve characteristics. This parameter change allows simple polygonal segments to represent real-world curves by associating turn radius with each vertex.
Solution Approach 2:
The invention introduces curvature characteristics to straight polygonal segments by defining turn radius at vertices. This allows the model to represent curved road characteristics using straight line segments with associated curvature parameters, maintaining model simplicity while capturing real-world curve features.
Data Source
AI summary
An embodiment may include, for a real world moving object moving along a real world path, modeling trajectory of the moving object along a polygon. The polygon may have a plurality of line segments and vertices and may represent the real world path for the moving object. A turn radius may be calculated at each vertex of the polygon. For a given vertex, the calculated turn radius may be associated with line segments of the polygon that originate from the given vertex. Using the calculated turn radii, a single-dimensional model may be formed of the real world path, where a respective calculated turn radius of the given vertex may serve as a measure of curvature of that portion of the real world path represented by the given vertex. The calculated turn radius of the respective given vertex may be defined by lane width of the real world path.