Graph Equation Calculation for Image-Based Coordinate Systems
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Solution Overview
Problem
Conventional electronic devices cannot effectively study the relationship between a graph shape represented in an image and its corresponding graph equation, especially in relation to the actual size of the graph shape.
Innovation Solution
An electronic device with a display, graph graphic detection, rendering, line segment designation, point of origin setting, display range calculation, and graph equation calculation units, allowing users to detect graph shapes, set coordinates, input line segment lengths, and calculate graph equations based on user interactions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If merely a graph is rendered by connecting the plotted points based on the measured data, then the graph can be displayed, but the graph shape in the image and the graph equation expressed in line with the actual size of the graph shape cannot be studied in relation to each other
Solution Approach 1:
The system performs preliminary detection of graph graphics in the image and automatic setting of coordinate systems before graph equation calculation. The point of origin is automatically positioned at the lower left corner of the graph area, and the display range is pre-calculated based on graph position and size, enabling accurate equation derivation without manual coordinate setup
Solution Approach 2:
The system automatically detects graph graphics, determines their positions and sizes, sets coordinate systems, and calculates display ranges without requiring manual intervention. The electron device performs self-service by autonomously establishing the coordinate framework needed for accurate graph equation calculation
2Productivity
If a coordinate system is manually set to calculate graph equations, then the graph equation can be obtained, but the process becomes complex and time-consuming
Solution Approach 1:
The system automatically detects graph graphics and performs self-service by autonomously determining graph positions, sizes, and coordinate system parameters. This eliminates manual configuration steps and enables rapid graph equation calculation through automated coordinate system establishment
Solution Approach 2:
The manual mechanical process of setting coordinate systems is replaced by an automated image processing system that detects graph graphics and calculates coordinate parameters algorithmically, significantly improving calculation speed and reducing operational complexity
3Loss of information
If the graph is displayed without considering actual size, then the display is simple, but the relationship between graph shape and actual dimensions cannot be studied
Solution Approach 1:
The system performs preliminary detection of graph graphics to obtain position and size information before rendering. By pre-calculating the display range based on actual graph dimensions in the image, the system preserves actual size information while maintaining efficient display processing
Solution Approach 2:
The system adds a new dimension of information by incorporating actual size measurements into the graph display. Through automated detection and coordinate system establishment, real-world dimensions are mapped to the graphical representation, enabling size-related studies without significantly increasing processing complexity
Data Source
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AI summary
Disclosed is an electronic device including a display which displays an image, a graph graphic detection unit which detects a graph graphic matching any of predetermined graph shapes in the image, a graph rendering unit which renders a graph overlapping the graph graphic, a length input line segment designation unit which designates any one of line segments included in the image as a line segment subject to length input, a line segment length input unit which inputs a length of the line segment subject to length input, a point of origin setting unit which sets a point of origin of a coordinate system, a display range calculation unit which calculates a display range of the coordinate system, and a graph equation calculation unit which calculates a graph equation of the graph and displays a calculation result in the display.