Graph Drawing Algorithm Integer Coordinate Alignment
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Solution Overview
Problem
Graphing scientific calculators and applications face challenges in correctly displaying graphs of functions with x-th power of negative integers, as they require integer values of x within the coordinate range, which existing methods fail to ensure accurately.
Innovation Solution
A method for determining coordinates of plot points for a graph drawing system, involving specifying minimum and maximum values of the drawing area, calculating a step width based on the coordinate width and display pixel width, and adjusting these values to ensure integer values of x within the coordinate range, thereby correctly plotting the function's graph.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If the coordinate range is set based on arbitrary minimum and maximum values, then the drawing area can be flexibly defined, but the graph may not correctly include all integer values of x required for functions with negative integer powers
Solution Approach 1:
The patent applies preliminary action by calculating and adjusting the coordinate range before graph plotting. The system determines the minimum and maximum coordinate values based on the step width calculation, ensuring that the coordinate range is pre-adjusted to include all necessary integer values of x before the graph is drawn, thus preventing missing integer points in the final graph
Solution Approach 2:
The patent changes parameters by dynamically adjusting the minimum and maximum coordinate values based on the calculated step width. The system modifies the coordinate range parameters (xmin, xmax) to ensure they are multiples of the step width, which guarantees that all integer values of x are included in the plotting range while maintaining flexibility in the drawing area definition
2Measurement precision
If the step width is calculated based on coordinate width and display pixel width, then the graph resolution is optimized for display, but the coordinate range may not align with integer values of x
Solution Approach 1:
The system performs preliminary calculation of the step width based on the display pixel width and coordinate width, then uses this step width to adjust the minimum and maximum coordinate values. This preliminary adjustment ensures that the coordinate range boundaries are aligned with the step width, which in turn ensures alignment with integer values of x while maintaining optimal display resolution
Solution Approach 2:
The patent changes the minimum and maximum coordinate parameters to be multiples of the calculated step width. This parameter adjustment maintains the graph display resolution optimized for the display device while ensuring that the coordinate range properly aligns with integer values of x, solving both requirements simultaneously
Data Source
AI summary
A method executed by a graph drawing system includes specifying minimum and maximum values of a drawing area in a first axis and a display pixel width along the first axis, determining a step width of a numerical value of the first axis based on a coordinate width along the first axis and the specified display pixel width, the coordinate width being obtained based on the specified minimum and maximum values, changing the minimum or maximum value based on the determined step width and the minimum or maximum value, and determining, based on at least the changed minimum or maximum value, the determined step width and a mathematical expression, coordinates of plot points of the graph, the coordinates including numerical values of variables.