Trigonometric Measurement Computation via Angle Segmentation
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Solution Overview
Problem
Existing methods for computing high precision trigonometric measurements, such as the CORDIC method, face a trade-off between precision and processing speed, requiring multiple loops and significant computational resources.
Innovation Solution
An apparatus and method that separates the input angle into integral and fractional parts, uses an approximation for interpolation based on second-order differences of sine function values, and truncates the formula to achieve high precision with fewer computations, utilizing a processor and memory to execute machine-executable code.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the CORDIC method is used to compute trigonometric measurements, then measurement precision is improved, but processing time and computing resource requirements increase significantly
Solution Approach 1:
The patent segments the angle into two components: an integer angle portion and a fractional angle portion. The integer portion is handled through rotation matrices while the fractional portion uses interpolation, allowing the computation to be divided into manageable parts that can be processed efficiently without sacrificing precision.
Solution Approach 2:
The patent introduces rotation matrices as an intermediary tool to bridge the gap between integer angle computations and fractional angle computations. The rotation matrices enable precise transformation of coordinates while the interpolation formula provides a efficient way to handle fractional components, resolving the contradiction between speed and precision.
2Measurement precision
If more loops are added to the CORDIC method to increase precision, then measurement precision is improved, but device complexity and computing resource requirements increase
Solution Approach 1:
By segmenting the angle computation into integer and fractional parts, the patent eliminates the need for multiple iterative loops. The integer portion is computed directly using rotation matrices while the fractional portion is handled through a single interpolation operation, significantly reducing computational complexity while maintaining high precision.
Solution Approach 2:
The patent changes the approach from iterative bit-by-bit computation (CORDIC) to a direct computation method using rotation matrices and interpolation. This parameter change in the computational method allows achieving high precision without increasing the number of loops or computational steps, thereby reducing device complexity.
3Productivity
If look-up tables are used to improve computation speed, then processing speed is improved, but measurement precision is reduced
Solution Approach 1:
The patent segments the angle into integer and fractional components, allowing the use of pre-computed rotation matrices for the integer portion (which provides exact results) while using interpolation only for the small fractional portion. This segmentation enables speed improvement through matrix operations while maintaining precision through the combination of exact and interpolated values.
Solution Approach 2:
The patent combines multiple computational approaches in a composite manner: rotation matrices for integer angles and interpolation formulas for fractional angles. This composite approach leverages the strengths of both methods - the speed of matrix operations and the precision of interpolation - to achieve both high speed and high precision simultaneously.
Data Source
AI summary
Disclosed herein an apparatus for determining estimating a measurement for a geometric dimension of an object, wherein the geometric dimension is at an angle to a predetermined reference geometric dimension of the object; comprising a processor, memory storing machine-executable code, and operating system supporting computer processes. The processor is configured to implement the machine-executable code to: receive data indicative of an input angle between the geometric dimension being measured and the reference geometric dimension; determine an integral angle and a fractional angle, respectively being an integral portion and a fractional portion of the input angle; determining trigonometric function values of the fractional angle; obtain determine a first rotation matrix for a first rotation from 0 degrees to the integral angle; determine a second rotation matrix for a second rotation by the fractional angle, based on the trigonometric function values of the fractional angle; determine trigonometric function values of the angle between the geometric dimensions on the basis of a combination of the first and second rotation matrices; estimate the measurement for the geometric dimension based on the trigonometric function values of the input angle and a measurement the predetermined reference geometric dimension.