Pie Chart Rendering via Horizontal Line Segments
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Solution Overview
Problem
In a client-server environment, generating pie charts to illustrate data on a web page is inefficient when the client is offline, as web browsers typically handle only rectangular elements and lack built-in methods for creating non-rectangular shapes like pie slices.
Innovation Solution
A method using JavaScript to construct pie charts from horizontal lines on a web page without relying on a server, employing the Bresenham circle scan algorithm to determine end points of horizontal lines forming the pie chart, allowing for efficient creation and display of pie charts in any JavaScript-enabled browser.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If pie charts are generated using traditional client-server architecture, then the pie chart can be displayed on the web page, but the generation process becomes inefficient when the client is offline and requires server involvement
Solution Approach 1:
The patent implements self-service by enabling the client to generate pie charts independently using JavaScript code that calculates slice coordinates and renders the chart directly in the browser, eliminating the need for server involvement and enabling offline operation while maintaining generation efficiency
2Ease of manufacture
If pie charts are created using web technologies (HTML, CSS), then the pie chart can be displayed in the browser, but the process becomes complex because web technologies only provide built-in methods for rectangular elements
Solution Approach 1:
The patent replaces the mechanical constraint of rectangular web elements with a mathematical approach using JavaScript to calculate circular coordinates and render pie slices, substituting the rigid web technology framework with flexible computational geometry
3Manufacturing precision
If pie charts are constructed by computing coordinates of each point, then the pie chart can be accurately rendered, but the computation becomes excessively complex and time-consuming
Solution Approach 1:
The patent applies segmentation by dividing the pie chart into discrete slices and further segmenting each slice into horizontal lines, calculating only the essential endpoint coordinates for each line segment rather than every point, thereby maintaining rendering accuracy while dramatically reducing computational complexity
Solution Approach 2:
The patent uses partial action by calculating only the necessary endpoint coordinates of horizontal lines that define each pie slice rather than computing all intermediate points, achieving sufficient precision for accurate rendering without the excessive computation of complete coordinate sets
Data Source
AI summary
A method for drawing pie charts illustrating comparative data on the display of a client computer in a client-server environment with horizontal parallel lines each having a height of one pixel. A circular or elliptical pie is first defined in an array of endpoints of a set of horizontal lines from which the pie is constructed. Each slice of the pie is assigned a start angle and a stop angle as a function of the datum that it represents and its proximity to other slices. Pixels on the horizontal lines forming the pie are then tested to define segments of the horizontal lines for inclusion in the slices. The pixels of each line segment are illuminated on the display to form an image of a pie with each slice proportional in area to its respective datum.