how to determine a correct domain for a range of n

问题:

I want to create a line graph but the range of numbers are different sometimes its like :

1,2,5,8,10

and sometimes its like :

-5 , -1 , 4 , 5, 15 , 8 ,20 ,...

by studying excel and openoffice I understand that they can indicate a range something like :

minNumber - k to maxNumber + k

and they divide the Y axis into equal area.

is there any specific formula for doing these things ?

回答1:

When I looked at this problem I found that commercial products do a nice job of extending the range just enough to achieve pleasingly nice round numbers for their tick marks. If this is something you are interested in, take a look at this C# code that I wrote to try out different algorithms:

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace TickPicker
{
    class TickPicker
    {
        double tickLow;
        double tickHigh;
        double tickUnit;
        double tickCount;
        //static double[] targetUnits = { 1, 2, 5, 10 };
        static double[] targetUnits = { 1, 2, 2.5, 5, 10 };
        static int[] roundFactors = { 1, 5, 4, 2, 1 };
        //static double[] targetUnits = { 1, 1.5, 2.5, 5, 10 };
        //static double[] targetUnits = { 1, 1.25, 2, 2.5, 5, 10 };
        //static double[] targetUnits = { 1, 1.25, 1.5, 2, 2.5, 5, 10 };
        //static double[] targetUnits = { 1, 1.25, 2, 5, 10 };
        //static double[] targetUnits = { 1, 1.25, 1.5, 2, 5, 10 };
        static double[] targetLogs = arrayLog(targetUnits);

        TickPicker(double low, double high, int tickCountGoal)
        {
            double range = high - low;
            double divGoal = range / (tickCountGoal - 2);
            double logGoal = Math.Log10(divGoal);
            double powerFactor = Math.Floor(logGoal);
            logGoal = logGoal - powerFactor;
            int closestIndex = findClosest(targetLogs, logGoal);
            tickUnit = targetUnits[closestIndex] * (Math.Pow(10, powerFactor));
            // Ensure the actual range encompasses the intended range
            // The roundFactor discourages the .5 on the low and high range
            int roundFactor = roundFactors[closestIndex];
            tickLow = Math.Floor(low / tickUnit / roundFactor) * tickUnit * roundFactor;
            tickHigh = Math.Ceiling(high / tickUnit / roundFactor) * tickUnit * roundFactor;
            tickCount = (tickHigh - tickLow) / tickUnit;
        }

        static double[] arrayLog(double[] inputs)
        {
            double[] retVal = new double[inputs.Length];
            int x = 0;
            foreach (double input in inputs)
            {
                retVal[x] = Math.Log10(inputs[x]);
                x++;
            }
            return retVal;
        }

        static int findClosest(double[] candidates, double input)
        {
            int low = 0;
            for(int i = 1; i < candidates.Length && input > candidates[i]; i++)
            {
                low = i;
            }
            int high = low + 1;
            return candidates[high] - input < input - candidates[low] ? high : low;
        }

        static void testPicker(double low, double high, int tickCountGoal)
        {
            TickPicker picker = new TickPicker(low, high, tickCountGoal);
            System.Console.WriteLine("[{0}:{1}]/{2} gives [{3}:{4}] with {5} ticks of {6} units each.", low, high, tickCountGoal, picker.tickLow, picker.tickHigh, picker.tickCount, picker.tickUnit);
        }

        static void Main(string[] args)
        {
            testPicker(4.7, 39.2, 13);
            testPicker(4.7, 39.2, 16);
            testPicker(4.7, 39.2, 19);
            testPicker(4.7, 39.2, 21);
            testPicker(4.7, 39.2, 24);
            testPicker(1967, 2011, 20);
            testPicker(1967, 2011, 10);
            testPicker(2.71, 3.14, 5);
            testPicker(.0568, 13, 20);
        }
    }
}

回答2:

I think you mean minNumber and not meanNumber.

The formula is close to what you say. Your range is maxNumber - minNumber. If you want some space on either side add 2k, where k is the space for either side. You know your graph is Y pixels wide. Y/range is how many pixels there are per unit for your graph.

You basically apply this adjustment while drawing the graph. Apply a shift based on your min, and then a strech based on your pixel/unit.

So Drawing point X means you are actually drawing at ((X - min) / pixels per unit).

回答3:

I'm not 100% convinced that this is a programming question (although there are a decent handful of graphing libraries one could use), but the general idea would be this.

You have these points coming in, let's say -5. That's the 0th value we've received, so for an x value of 0, we place -5 on the y-axis. We repeat for -1, 4, etc.

So, you'd get a list looking something like this (figuratively):

X   |    Y
0   |   -5
1   |   -1
2   |   4
3   |   5
4   |   15

The result is a scatterplot (not a line), but there are tools in Excel to get that for you.

[EDIT] To get it as an actual function, you could use the following form:

y-y_1=m(x-x_1)

Where m = (y_2-y_1)/(x_2-x_1), y_2 is your highest y-value, y_1 is your lowest, x_2 is your highest x-value, and x_1 is your lowest.