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Trying to implement chart API in Java. But I am unsure of the mathematical formulas/concepts used in drawing each of the chart type. Can someone specify the mathematical concepts to be known for drawing each sort of the chart.

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Hm... very general question, so I can only answer equally general:

Take a look at gnuplot, which is a great mathematical plotting/charting api.

You can find out its concepts by looking at some plots and the manual, the corresponding formulas by reading the source code.

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