Graph Drawing System with Continuity Detection
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Solution Overview
Problem
Existing graph drawing systems struggle to accurately represent functions with discontinuous points, often connecting non-continuous points with lines, leading to inaccurate graph representations.
Innovation Solution
A graph drawing system comprising an electronic device and a calculation server, where the server calculates drawing information including coordinates and continuity/discontinuity information, allowing the device to accurately plot and connect points based on the function, ensuring correct graph representation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If points are connected by lines sequentially changing coordinates with a predetermined step size, then the graph drawing process is simple and efficient, but discontinuous points may be incorrectly connected leading to inaccurate graph representation
Solution Approach 1:
The system performs preliminary analysis to determine continuity/discontinuity information before connecting points. The server calculates whether adjacent points should be connected by examining the function characteristics and point coordinates in advance, preventing incorrect connections before they occur.
Solution Approach 2:
The system uses continuity/discontinuity information as feedback to control the line connection process. By evaluating whether points are continuous and using this information to decide whether to draw connecting lines, the system ensures accurate graph representation while maintaining efficient processing.
2Speed
If the terminal performs all calculation and drawing operations locally, then the processing speed is fast, but the processing load on the user terminal increases
Solution Approach 1:
The system divides the graph drawing process into two segments: the server handles complex calculation operations including determining continuity/discontinuity information and calculating point coordinates, while the terminal handles simpler display operations. This segmentation reduces the processing load on the terminal while maintaining overall system speed.
Solution Approach 2:
The server acts as an intermediary that performs the heavy computational work. Instead of the terminal directly performing all calculations, it receives pre-calculated drawing information from the server, which includes all necessary data for accurate graph rendering without requiring the terminal to perform complex computations.
Data Source
AI summary
A graph drawing system includes an electronic device and a calculation server. A first processor of the electronic device transmits calculation inquiry data including information on a function entered by a user operation to the calculation server. A second processor of the calculation server calculates drawing information including coordinates of a plurality of drawing points represented by the function and plotted in a graph drawing area of the display, and continuity/discontinuity information indicating whether or not adjacent points of the drawing points should be connected to each other, based on the calculation inquiry data and transmits the drawing information to the electronic device. The first processor causes the display to display a graph corresponding to the function, based on the drawing information.