3D Graph Visualization for Complex Function Analysis
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Solution Overview
Problem
Current educational technologies lack effective methods for visually representing complex functions in a way that clearly illustrates the relationship between real and imaginary parts of complex numbers, hindering students' understanding of these concepts.
Innovation Solution
A method and system that utilize a computer to generate and display two three-dimensional graphs, one representing the real part function and the other the imaginary part function of a complex function, allowing users to visualize the relationship between four variables through an interactive interface on a client terminal connected to a server device, enabling accurate representation and interpretation of complex functions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If traditional two-dimensional graphing methods are used for complex functions, then the implementation is simple, but the ability to clearly illustrate relationships between real and imaginary parts is insufficient
Solution Approach 1:
The patent transitions from two-dimensional graph representation to three-dimensional graph representation to visualize complex functions. By adding the z-axis to represent the imaginary part while keeping x and y axes for real parts, the system can simultaneously display relationships between multiple variables (real part input, imaginary part input, real part output, imaginary part output) in a single visual space, thereby preserving complete information about complex function relationships without losing any dimensional data.
2Measurement precision
If four variables of complex function are displayed separately, then each variable is clearly shown, but the overall relationship understanding becomes difficult
Solution Approach 1:
The patent merges the representation of four separate variables (real part input x, imaginary part input y, real part output u, imaginary part output v) into a unified three-dimensional coordinate system. By mapping these variables to spatial coordinates where x and y form the base plane and z represents the imaginary output component, the system allows users to grasp the overall complex function relationship through a single integrated visual representation while maintaining precise variable differentiation through coordinate labels and mathematical expressions.
3Measurement precision
If complex functions are represented using mathematical expressions only, then the precision is high, but the visual understanding is limited
Solution Approach 1:
The patent introduces three-dimensional graphs as an intermediary representation between mathematical expressions and human visual understanding. The system generates 3D graphical visualizations from complex function mathematical expressions, where the graphs serve as a mediator that translates abstract mathematical relationships into intuitive spatial forms. Users can first view the mathematical expression for precision, then switch to the 3D graph for visual comprehension, with the graph acting as a bridge that preserves the exact mathematical relationships while making them visually accessible.
Data Source
AI summary
A computer performs generating, on the basis of mathematical expression information indicating a complex function, first display information on a first three-dimensional graph that indicates a relationship between a first variable indicating a real part of a first complex number input to the complex function indicated by the mathematical expression information, a second variable indicating an imaginary part of the first complex number, and a third variable indicating a real part of a second complex number output from the complex function, generating, on the basis of the mathematical expression information, second display information on a second three-dimensional graph that indicates a relationship between the first variable, the second variable, and a fourth variable indicating an imaginary part of the second complex number, and outputting display information including the first display information and the second display information.