Nice Label Algorithm for Charts with minimum ticks

问题:

I need to calculate the Ticklabels and the Tickrange for charts manually.

I know the "standard" algorithm for nice ticks (see http://books.google.de/books?id=fvA7zLEFWZgC&pg=PA61&lpg=PA61&redir_esc=y#v=onepage&q&f=false) and I also know this Java implementation.

The problem is, that with this algorithm, the ticks are "too smart". That means, The algorithm decides how much ticks should be displayed. My requirement is, that there are always 5 Ticks, but these should of course be "pretty". The naive approach would be to get the maximum value, divide with 5 and multiply with the ticknumber. The values here are - of course - not optimal and the ticks are pretty ugly.

Does anyone know a solution for the problem or have a hint for a formal algorithm description?

回答1:

You should be able to use the Java implementation with minor corrections.

Change maxticks to 5.

Change the calculate mehod to this:

private void calculate() {
        this.range = niceNum(maxPoint - minPoint, false);
        this.tickSpacing = niceNum(range / (maxTicks - 1), true);
        this.niceMin =
            Math.floor(minPoint / tickSpacing) * tickSpacing;
        this.niceMax = this.niceMin + tickSpacing * (maxticks - 1); // Always display maxticks
    }

Disclaimer: Note that I haven't tested this, so you may have to tweak it to make it look good. My suggested solution adds extra space at the top of the chart to always make room for 5 ticks. This may look ugly in some cases.

回答2:

I am the author of "Algorithm for Optimal Scaling on a Chart Axis". It used to be hosted on trollop.org, but I have recently moved domains/blogging engines. Anyhow, I'll post the contents here for easier access.

I've been working on an Android charting application for an assignment and ran into a bit of an issue when it came to presenting the chart in a nicely scaled format. I spent a some time trying to create this algorithm on my own and came awfully close, but in the end I found a pseudo-code example in a book called "Graphics Gems, Volume 1" by Andrew S. Glassner. An excellent description of the problem is given in the chapter on "Nice Numbers for Graph Labels":

When creating a graph by computer, it is desirable to label the x and y axes with "nice" numbers: simple decimal numbers. For example, if the data range is 105 to 543, we'd probably want to plot the range from 100 to 600 and put tick marks every 100 units. Or if the data range is 2.04 to 2.16, we'd probably plot a range from 2.00 to 2.20 with a tick spacing of 0.05. Humans are good at choosing such "nice" numbers, but simplistic algorithms are not. The naïve label-selection algorithm takes the data range and divides it into n equal intervals, but this usually results in ugly tick labels. We here describe a simple method for generating nice graph labels.

The primary observation is that the "nicest" numbers in decimal are 1, 2, and 5, and all power-of-ten multiples of these numbers. We will use only such numbers for the tick spacing, and place tick marks at multiples of the tick spacing...

I used the pseudo-code example in this book to create the following class in Java:

public class NiceScale {

  private double minPoint;
  private double maxPoint;
  private double maxTicks = 10;
  private double tickSpacing;
  private double range;
  private double niceMin;
  private double niceMax;

  /**
   * Instantiates a new instance of the NiceScale class.
   *
   * @param min the minimum data point on the axis
   * @param max the maximum data point on the axis
   */
  public NiceScale(double min, double max) {
    this.minPoint = min;
    this.maxPoint = max;
    calculate();
  }

  /**
   * Calculate and update values for tick spacing and nice
   * minimum and maximum data points on the axis.
   */
  private void calculate() {
    this.range = niceNum(maxPoint - minPoint, false);
    this.tickSpacing = niceNum(range / (maxTicks - 1), true);
    this.niceMin =
      Math.floor(minPoint / tickSpacing) * tickSpacing;
    this.niceMax =
      Math.ceil(maxPoint / tickSpacing) * tickSpacing;
  }

  /**
   * Returns a "nice" number approximately equal to range Rounds
   * the number if round = true Takes the ceiling if round = false.
   *
   * @param range the data range
   * @param round whether to round the result
   * @return a "nice" number to be used for the data range
   */
  private double niceNum(double range, boolean round) {
    double exponent; /** exponent of range */
    double fraction; /** fractional part of range */
    double niceFraction; /** nice, rounded fraction */

    exponent = Math.floor(Math.log10(range));
    fraction = range / Math.pow(10, exponent);

    if (round) {
      if (fraction < 1.5)
        niceFraction = 1;
      else if (fraction < 3)
        niceFraction = 2;
      else if (fraction < 7)
        niceFraction = 5;
      else
        niceFraction = 10;
    } else {
      if (fraction <= 1)
        niceFraction = 1;
      else if (fraction <= 2)
        niceFraction = 2;
      else if (fraction <= 5)
        niceFraction = 5;
      else
        niceFraction = 10;
    }

    return niceFraction * Math.pow(10, exponent);
  }

  /**
   * Sets the minimum and maximum data points for the axis.
   *
   * @param minPoint the minimum data point on the axis
   * @param maxPoint the maximum data point on the axis
   */
  public void setMinMaxPoints(double minPoint, double maxPoint) {
    this.minPoint = minPoint;
    this.maxPoint = maxPoint;
    calculate();
  }

  /**
   * Sets maximum number of tick marks we're comfortable with
   *
   * @param maxTicks the maximum number of tick marks for the axis
   */
  public void setMaxTicks(double maxTicks) {
    this.maxTicks = maxTicks;
    calculate();
  }
}

We can then make use of the above code like this:

NiceScale numScale = new NiceScale(-0.085, 0.173);

System.out.println("Tick Spacing:\t" + numScale.getTickSpacing());
System.out.println("Nice Minimum:\t" + numScale.getNiceMin());
System.out.println("Nice Maximum:\t" + numScale.getNiceMax());

Which will then output nicely formatted numbers for use in whatever application for which you need to create pretty scales. =D

Tick Spacing: 0.05
Nice Minimum: -0.1
Nice Maximum: 0.2

回答3:

I have converted above java code to Python as per my requirement.

 import math

  class NiceScale:
    def __init__(self, minv,maxv):
        self.maxTicks = 6
        self.tickSpacing = 0
        self.lst = 10
        self.niceMin = 0
        self.niceMax = 0
        self.minPoint = minv
        self.maxPoint = maxv
        self.calculate()

    def calculate(self):
        self.lst = self.niceNum(self.maxPoint - self.minPoint, False)
        self.tickSpacing = self.niceNum(self.lst / (self.maxTicks - 1), True)
        self.niceMin = math.floor(self.minPoint / self.tickSpacing) * self.tickSpacing
        self.niceMax = math.ceil(self.maxPoint / self.tickSpacing) * self.tickSpacing

    def niceNum(self, lst, rround):
        self.lst = lst
        exponent = 0 # exponent of range */
        fraction = 0 # fractional part of range */
        niceFraction = 0 # nice, rounded fraction */

        exponent = math.floor(math.log10(self.lst));
        fraction = self.lst / math.pow(10, exponent);

        if (self.lst):
            if (fraction < 1.5):
                niceFraction = 1
            elif (fraction < 3):
                niceFraction = 2
            elif (fraction < 7):
                niceFraction = 5;
            else:
                niceFraction = 10;
        else :
            if (fraction <= 1):
                niceFraction = 1
            elif (fraction <= 2):
                niceFraction = 2
            elif (fraction <= 5):
                niceFraction = 5
            else:
                niceFraction = 10

        return niceFraction * math.pow(10, exponent)

    def setMinMaxPoints(self, minPoint, maxPoint):
          self.minPoint = minPoint
          self.maxPoint = maxPoint
          self.calculate()

    def setMaxTicks(self, maxTicks):
        self.maxTicks = maxTicks;
        self.calculate()

a=NiceScale(14024, 17756)
print "a.lst ", a.lst
print "a.maxPoint ", a.maxPoint
print "a.maxTicks ", a.maxTicks
print "a.minPoint ", a.minPoint
print "a.niceMax ", a.niceMax
print "a.niceMin ", a.niceMin
print "a.tickSpacing ", a.tickSpacing

回答4:

Here is the same thing in Objective C

YFRNiceScale.h

#import <Foundation/Foundation.h>

@interface YFRNiceScale : NSObject

@property (nonatomic, readonly) CGFloat minPoint;
@property (nonatomic, readonly) CGFloat maxPoint;
@property (nonatomic, readonly) CGFloat maxTicks;
@property (nonatomic, readonly) CGFloat tickSpacing;
@property (nonatomic, readonly) CGFloat range;
@property (nonatomic, readonly) CGFloat niceRange;
@property (nonatomic, readonly) CGFloat niceMin;
@property (nonatomic, readonly) CGFloat niceMax;


- (id) initWithMin: (CGFloat) min andMax: (CGFloat) max;
- (id) initWithNSMin: (NSDecimalNumber*) min andNSMax: (NSDecimalNumber*) max;

@end

YFRNiceScale.m

#import "YFRNiceScale.h"

@implementation YFRNiceScale

@synthesize minPoint = _minPoint;
@synthesize maxPoint = _maxPoint;
@synthesize maxTicks = _maxTicks;
@synthesize tickSpacing = _tickSpacing;
@synthesize range = _range;
@synthesize niceRange = _niceRange;
@synthesize niceMin = _niceMin;
@synthesize niceMax = _niceMax;

- (id)init {
    self = [super init];
    if (self) {

    }
    return self;
}

- (id) initWithMin: (CGFloat) min andMax: (CGFloat) max {

    if (self) {
        _maxTicks = 10;
        _minPoint = min;
        _maxPoint = max;
        [self calculate];
    }
    return [self init];
}

- (id) initWithNSMin: (NSDecimalNumber*) min andNSMax: (NSDecimalNumber*) max {

    if (self) {
        _maxTicks = 10;
        _minPoint = [min doubleValue];
        _maxPoint = [max doubleValue];
        [self calculate];
    }
    return [self init];
}


/**
 * Calculate and update values for tick spacing and nice minimum and maximum
 * data points on the axis.
 */

- (void) calculate {
    _range = [self niceNumRange: (_maxPoint-_minPoint) roundResult:NO];
    _tickSpacing = [self niceNumRange: (_range / (_maxTicks - 1)) roundResult:YES];
    _niceMin = floor(_minPoint / _tickSpacing) * _tickSpacing;
    _niceMax = ceil(_maxPoint / _tickSpacing) * _tickSpacing;

    _niceRange = _niceMax - _niceMin;
}


/**
 * Returns a "nice" number approximately equal to range Rounds the number if
 * round = true Takes the ceiling if round = false.
 *
 * @param range
 *            the data range
 * @param round
 *            whether to round the result
 * @return a "nice" number to be used for the data range
 */
- (CGFloat) niceNumRange:(CGFloat) aRange roundResult:(BOOL) round {
    CGFloat exponent;
    CGFloat fraction;
    CGFloat niceFraction;

    exponent = floor(log10(aRange));
    fraction = aRange / pow(10, exponent);

    if (round) {
        if (fraction < 1.5) {
            niceFraction = 1;
        } else if (fraction < 3) {
            niceFraction = 2;
        } else if (fraction < 7) {
            niceFraction = 5;
        } else {
            niceFraction = 10;
        }

    } else {
        if (fraction <= 1) {
            niceFraction = 1;
        } else if (fraction <= 2) {
            niceFraction = 2;
        } else if (fraction <= 5) {
            niceFraction = 2;
        } else {
            niceFraction = 10;
        }
    }

    return niceFraction * pow(10, exponent);
}

- (NSString*) description {
    return [NSString stringWithFormat:@"NiceScale [minPoint=%.2f, maxPoint=%.2f, maxTicks=%.2f, tickSpacing=%.2f, range=%.2f, niceMin=%.2f, niceMax=%.2f]", _minPoint, _maxPoint, _maxTicks, _tickSpacing, _range, _niceMin, _niceMax ];
}

@end

Usage:

YFRNiceScale* niceScale = [[YFRNiceScale alloc] initWithMin:0 andMax:500];
NSLog(@"Nice: %@", niceScale);

回答5:

I found this thread while writing some php, so now the same code is available in php too!

class CNiceScale {

  private $minPoint;
  private $maxPoint;
  private $maxTicks = 10;
  private $tickSpacing;
  private $range;
  private $niceMin;
  private $niceMax;

  public function setScale($min, $max) {
    $this->minPoint = $min;
    $this->maxPoint = $max;
    $this->calculate();
  }

  private function calculate() {
    $this->range = $this->niceNum($this->maxPoint - $this->minPoint, false);
    $this->tickSpacing = $this->niceNum($this->range / ($this->maxTicks - 1), true);
    $this->niceMin = floor($this->minPoint / $this->tickSpacing) * $this->tickSpacing;
    $this->niceMax = ceil($this->maxPoint / $this->tickSpacing) * $this->tickSpacing;
  }

  private function niceNum($range, $round) {
    $exponent; /** exponent of range */
    $fraction; /** fractional part of range */
    $niceFraction; /** nice, rounded fraction */

    $exponent = floor(log10($range));
    $fraction = $range / pow(10, $exponent);

    if ($round) {
      if ($fraction < 1.5)
        $niceFraction = 1;
      else if ($fraction < 3)
        $niceFraction = 2;
      else if ($fraction < 7)
        $niceFraction = 5;
      else
        $niceFraction = 10;
    } else {
      if ($fraction <= 1)
        $niceFraction = 1;
      else if ($fraction <= 2)
        $niceFraction = 2;
      else if ($fraction <= 5)
        $niceFraction = 5;
      else
        $niceFraction = 10;
    }

    return $niceFraction * pow(10, $exponent);
  }

  public function setMinMaxPoints($minPoint, $maxPoint) {
    $this->minPoint = $minPoint;
    $this->maxPoint = $maxPoint;
    $this->calculate();
  }

  public function setMaxTicks($maxTicks) {
    $this->maxTicks = $maxTicks;
    $this->calculate();
  }

  public function getTickSpacing() {
    return $this->tickSpacing;
  }

  public function getNiceMin() {
    return $this->niceMin;
  }

  public function getNiceMax() {
    return $this->niceMax;
  }

}

回答6:

I needed this algorithm converted to C#, so here it is...

public static class NiceScale {

    public static void Calculate(double min, double max, int maxTicks, out double range, out double tickSpacing, out double niceMin, out double niceMax) {
        range = niceNum(max - min, false);
        tickSpacing = niceNum(range / (maxTicks - 1), true);
        niceMin = Math.Floor(min / tickSpacing) * tickSpacing;
        niceMax = Math.Ceiling(max / tickSpacing) * tickSpacing;
    }

    private static double niceNum(double range, bool round) {
        double pow = Math.Pow(10, Math.Floor(Math.Log10(range)));
        double fraction = range / pow;

        double niceFraction;
        if (round) {
            if (fraction < 1.5) {
                niceFraction = 1;
            } else if (fraction < 3) {
                niceFraction = 2;
            } else if (fraction < 7) {
                niceFraction = 5;
            } else {
                niceFraction = 10;
            }
        } else {
            if (fraction <= 1) {
                niceFraction = 1;
            } else if (fraction <= 2) {
                niceFraction = 2;
            } else if (fraction <= 5) {
                niceFraction = 5;
            } else {
                niceFraction = 10;
            }
        }

        return niceFraction * pow;
    }

}

回答7:

Here is a javascript version:

var minPoint;
var maxPoint;
var maxTicks = 10;
var tickSpacing;
var range;
var niceMin;
var niceMax;

/**
 * Instantiates a new instance of the NiceScale class.
 *
 *  min the minimum data point on the axis
 *  max the maximum data point on the axis
 */
function niceScale( min, max) {
    minPoint = min;
    maxPoint = max;
    calculate();
    return {
        tickSpacing: tickSpacing,
        niceMinimum: niceMin,
        niceMaximum: niceMax
    };
}



/**
 * Calculate and update values for tick spacing and nice
 * minimum and maximum data points on the axis.
 */
function calculate() {
    range = niceNum(maxPoint - minPoint, false);
    tickSpacing = niceNum(range / (maxTicks - 1), true);
    niceMin =
      Math.floor(minPoint / tickSpacing) * tickSpacing;
    niceMax =
      Math.ceil(maxPoint / tickSpacing) * tickSpacing;
}

/**
 * Returns a "nice" number approximately equal to range Rounds
 * the number if round = true Takes the ceiling if round = false.
 *
 *  localRange the data range
 *  round whether to round the result
 *  a "nice" number to be used for the data range
 */
function niceNum( localRange,  round) {
    var exponent; /** exponent of localRange */
    var fraction; /** fractional part of localRange */
    var niceFraction; /** nice, rounded fraction */

    exponent = Math.floor(Math.log10(localRange));
    fraction = localRange / Math.pow(10, exponent);

    if (round) {
        if (fraction < 1.5)
            niceFraction = 1;
        else if (fraction < 3)
            niceFraction = 2;
        else if (fraction < 7)
            niceFraction = 5;
        else
            niceFraction = 10;
    } else {
        if (fraction <= 1)
            niceFraction = 1;
        else if (fraction <= 2)
            niceFraction = 2;
        else if (fraction <= 5)
            niceFraction = 5;
        else
            niceFraction = 10;
    }

    return niceFraction * Math.pow(10, exponent);
}

/**
 * Sets the minimum and maximum data points for the axis.
 *
 *  minPoint the minimum data point on the axis
 *  maxPoint the maximum data point on the axis
 */
function setMinMaxPoints( localMinPoint,  localMaxPoint) {
    minPoint = localMinPoint;
    maxPoint = localMaxoint;
    calculate();
}

/**
 * Sets maximum number of tick marks we're comfortable with
 *
 *  maxTicks the maximum number of tick marks for the axis
 */
function setMaxTicks(localMaxTicks) {
    maxTicks = localMaxTicks;
    calculate();
}

Enjoy!

回答8:

Since everybody and his dog is posting a translation to other popular languages, here is my version for the Nimrod programming language. I also added handling of cases where the amount of ticks is less than two:

import math, strutils

const
  defaultMaxTicks = 10

type NiceScale = object
  minPoint: float
  maxPoint: float
  maxTicks: int
  tickSpacing: float
  niceMin: float
  niceMax: float

proc ff(x: float): string =
  result = x.formatFloat(ffDecimal, 3)

proc `$`*(x: NiceScale): string =
  result = "Input minPoint: " & x.minPoint.ff &
    "\nInput maxPoint: " & x.maxPoint.ff &
    "\nInput maxTicks: " & $x.maxTicks &
    "\nOutput niceMin: " & x.niceMin.ff &
    "\nOutput niceMax: " & x.niceMax.ff &
    "\nOutput tickSpacing: " & x.tickSpacing.ff &
    "\n"

proc calculate*(x: var NiceScale)

proc init*(x: var NiceScale; minPoint, maxPoint: float;
    maxTicks = defaultMaxTicks) =
  x.minPoint = minPoint
  x.maxPoint = maxPoint
  x.maxTicks = maxTicks
  x.calculate

proc initScale*(minPoint, maxPoint: float;
    maxTicks = defaultMaxTicks): NiceScale =
  result.init(minPoint, maxPoint, maxTicks)

proc niceNum(scaleRange: float; doRound: bool): float =
  var
    exponent: float ## Exponent of scaleRange.
    fraction: float ## Fractional part of scaleRange.
    niceFraction: float ## Nice, rounded fraction.

  exponent = floor(log10(scaleRange));
  fraction = scaleRange / pow(10, exponent);

  if doRound:
    if fraction < 1.5:
      niceFraction = 1
    elif fraction < 3:
      niceFraction = 2
    elif fraction < 7:
      niceFraction = 5
    else:
      niceFraction = 10
  else:
    if fraction <= 1:
      niceFraction = 1
    elif fraction <= 2:
      niceFraction = 2
    elif fraction <= 5:
      niceFraction = 5
    else:
      niceFraction = 10

  return niceFraction * pow(10, exponent)

proc calculate*(x: var NiceScale) =
  assert x.maxPoint > x.minPoint, "Wrong input range!"
  assert x.maxTicks >= 0, "Sorry, can't have imaginary ticks!"
  let scaleRange = niceNum(x.maxPoint - x.minPoint, false)
  if x.maxTicks < 2:
    x.niceMin = floor(x.minPoint)
    x.niceMax = ceil(x.maxPoint)
    x.tickSpacing = (x.niceMax - x.niceMin) /
      (if x.maxTicks == 1: 2.0 else: 1.0)
  else:
    x.tickSpacing = niceNum(scaleRange / (float(x.maxTicks - 1)), true)
    x.niceMin = floor(x.minPoint / x.tickSpacing) * x.tickSpacing
    x.niceMax = ceil(x.maxPoint / x.tickSpacing) * x.tickSpacing

when isMainModule:
  var s = initScale(57.2, 103.3)
  echo s

This is the comment stripped version. Full one can be read at GitHub integrated into my project.

回答9:

This is the Swift version:

class NiceScale {
    private var minPoint: Double
    private var maxPoint: Double
    private var maxTicks = 10
    private(set) var tickSpacing: Double = 0
    private(set) var range: Double = 0
    private(set) var niceMin: Double = 0
    private(set) var niceMax: Double = 0

    init(min: Double, max: Double) {
        minPoint = min
        maxPoint = max
        calculate()
    }

    func setMinMaxPoints(min: Double, max: Double) {
        minPoint = min
        maxPoint = max
        calculate()
    }

    private func calculate() {
        range = niceNum(maxPoint - minPoint, round: false)
        tickSpacing = niceNum(range / Double((maxTicks - 1)), round: true)
        niceMin = floor(minPoint / tickSpacing) * tickSpacing
        niceMax = floor(maxPoint / tickSpacing) * tickSpacing
    }

    private func niceNum(range: Double, round: Bool) -> Double {
        let exponent = floor(log10(range))
        let fraction = range / pow(10, exponent)
        let niceFraction: Double

        if round {
            if fraction <= 1.5 {
                niceFraction = 1
            } else if fraction <= 3 {
                niceFraction = 2
            } else if fraction <= 7 {
                niceFraction = 5
            } else {
                niceFraction = 10
            }
        } else {
            if fraction <= 1 {
                niceFraction = 1
            } else if fraction <= 2 {
                niceFraction = 2
            } else if fraction <= 5 {
                niceFraction = 5
            } else {
                niceFraction = 10
            }
        }

        return niceFraction * pow(10, exponent)
    }
}

回答10:

Here's the C++ version. As a bonus you get a function that returns the minimum number of decimal points to display the tick labels on the axis.

The header file:

class NiceScale 
{   public:

    float minPoint;
    float maxPoint;
    float maxTicks;
    float tickSpacing;
    float range;
    float niceMin;
    float niceMax;

    public:
    NiceScale()
    {   maxTicks = 10;
    }

    /**
    * Instantiates a new instance of the NiceScale class.
    *
    * @param min the minimum data point on the axis
    * @param max the maximum data point on the axis
    */
    NiceScale(float min, float max) 
    {   minPoint = min;
        maxPoint = max;
        calculate();
    }

    /**
    * Calculate and update values for tick spacing and nice
    * minimum and maximum data points on the axis.
    */
    void calculate() ;

    /**
    * Returns a "nice" number approximately equal to range Rounds
    * the number if round = true Takes the ceiling if round = false.
    *
    * @param range the data range
    * @param round whether to round the result
    * @return a "nice" number to be used for the data range
    */
    float niceNum(float range, boolean round) ;

    /**
    * Sets the minimum and maximum data points for the axis.
    *
    * @param minPoint the minimum data point on the axis
    * @param maxPoint the maximum data point on the axis
    */
    void setMinMaxPoints(float minPoint, float maxPoint) ;

    /**
    * Sets maximum number of tick marks we're comfortable with
    *
    * @param maxTicks the maximum number of tick marks for the axis
    */
    void setMaxTicks(float maxTicks) ;
    int decimals(void);
};

And the CPP file:

/**
* Calculate and update values for tick spacing and nice
* minimum and maximum data points on the axis.
*/
void NiceScale::calculate() 
{
    range = niceNum(maxPoint - minPoint, false);
    tickSpacing = niceNum(range / (maxTicks - 1), true);
    niceMin = floor(minPoint / tickSpacing) * tickSpacing;
    niceMax = ceil(maxPoint / tickSpacing) * tickSpacing;
}

/**
* Returns a "nice" number approximately equal to range 
  Rounds the number if round = true Takes the ceiling if round = false.
*
* @param range the data range
* @param round whether to round the result
* @return a "nice" number to be used for the data range
*/
float NiceScale::niceNum(float range, boolean round) 
{   float exponent; /** exponent of range */
    float fraction; /** fractional part of range */
    float niceFraction; /** nice, rounded fraction */

    exponent = floor(log10(range));
    fraction = range / pow(10.f, exponent);

    if (round) 
    {   if (fraction < 1.5)
            niceFraction = 1;
        else if (fraction < 3)
            niceFraction = 2;
        else if (fraction < 7)
            niceFraction = 5;
        else
            niceFraction = 10;
    } 
    else 
    {   if (fraction <= 1)
            niceFraction = 1;
        else if (fraction <= 2)
            niceFraction = 2;
        else if (fraction <= 5)
            niceFraction = 5;
        else
            niceFraction = 10;
    }

    return niceFraction * pow(10, exponent);
}

/**
* Sets the minimum and maximum data points for the axis.
*
* @param minPoint the minimum data point on the axis
* @param maxPoint the maximum data point on the axis
*/
void NiceScale::setMinMaxPoints(float minPoint, float maxPoint) 
{
    this->minPoint = minPoint;
    this->maxPoint = maxPoint;
    calculate();
}

/**
* Sets maximum number of tick marks we're comfortable with
*
* @param maxTicks the maximum number of tick marks for the axis
*/
void NiceScale::setMaxTicks(float maxTicks) 
{
    this->maxTicks = maxTicks;
    calculate();
}

// minimum number of decimals in tick labels
// use in sprintf statement:
// sprintf(buf, "%.*f", decimals(), tickValue);
int NiceScale::decimals(void)
{
    float logTickX = log10(tickSpacing);
    if(logTickX >= 0)
        return 0;
    return (int)(abs(floor(logTickX)));
}

回答11:

This is the VB.NET version.

Public Class NiceScale

Private minPoint As Double
Private maxPoint As Double
Private maxTicks As Double = 10
Private tickSpacing
Private range As Double
Private niceMin As Double
Private niceMax As Double

Public Sub New(min As Double, max As Double)
    minPoint = min
    maxPoint = max
    calculate()
End Sub

Private Sub calculate()
    range = niceNum(maxPoint - minPoint, False)
    tickSpacing = niceNum(range / (maxTicks - 1), True)
    niceMin = Math.Floor(minPoint / tickSpacing) * tickSpacing
    niceMax = Math.Ceiling(maxPoint / tickSpacing) * tickSpacing
End Sub

Private Function niceNum(range As Double, round As Boolean) As Double
    Dim exponent As Double '/** exponent of range */
    Dim fraction As Double '/** fractional part of range */
    Dim niceFraction As Double '/** nice, rounded fraction */

    exponent = Math.Floor(Math.Log10(range))
    fraction = range / Math.Pow(10, exponent)

    If round Then
        If (fraction < 1.5) Then
            niceFraction = 1
        ElseIf (fraction < 3) Then
            niceFraction = 2
        ElseIf (fraction < 7) Then
            niceFraction = 5
        Else
            niceFraction = 10
        End If
    Else
        If (fraction <= 1) Then
            niceFraction = 1
        ElseIf (fraction <= 2) Then
            niceFraction = 2
        ElseIf (fraction <= 5) Then
            niceFraction = 5
        Else
            niceFraction = 10
        End If
    End If

    Return niceFraction * Math.Pow(10, exponent)
End Function

Public Sub setMinMaxPoints(minPoint As Double, maxPoint As Double)
    minPoint = minPoint
    maxPoint = maxPoint
    calculate()
End Sub

Public Sub setMaxTicks(maxTicks As Double)
    maxTicks = maxTicks
    calculate()
End Sub

Public Function getTickSpacing() As Double
    Return tickSpacing
End Function

Public Function getNiceMin() As Double
    Return niceMin
End Function

Public Function getNiceMax() As Double
    Return niceMax
End Function

End Class

回答12:

Here it is in TypeScript!

/**
 * Calculate and update values for tick spacing and nice
 * minimum and maximum data points on the axis.
 */
function calculateTicks(maxTicks: number, minPoint: number, maxPoint: number): [number, number, number] {
    let range = niceNum(maxPoint - minPoint, false);
    let tickSpacing = niceNum(range / (maxTicks - 1), true);
    let niceMin = Math.floor(minPoint / tickSpacing) * tickSpacing;
    let niceMax = Math.ceil(maxPoint / tickSpacing) * tickSpacing;
    let tickCount = range / tickSpacing;
    return [tickCount, niceMin, niceMax];
}

/**
 * Returns a "nice" number approximately equal to range Rounds
 * the number if round = true Takes the ceiling if round = false.
 *
 * @param range the data range
 * @param round whether to round the result
 * @return a "nice" number to be used for the data range
 */
function niceNum(range: number, round: boolean): number {
    let exponent: number;
    /** exponent of range */
    let fraction: number;
    /** fractional part of range */
    let niceFraction: number;
    /** nice, rounded fraction */

    exponent = Math.floor(Math.log10(range));
    fraction = range / Math.pow(10, exponent);

    if (round) {
        if (fraction < 1.5)
            niceFraction = 1;
        else if (fraction < 3)
            niceFraction = 2;
        else if (fraction < 7)
            niceFraction = 5;
        else
            niceFraction = 10;
    } else {
        if (fraction <= 1)
            niceFraction = 1;
        else if (fraction <= 2)
            niceFraction = 2;
        else if (fraction <= 5)
            niceFraction = 5;
        else
            niceFraction = 10;
    }

    return niceFraction * Math.pow(10, exponent);
}

回答13:

Here's the Kotlin version!

import java.lang.Math.*

/**
 * Instantiates a new instance of the NiceScale class.
 *
 * @param min Double The minimum data point.
 * @param max Double The maximum data point.
 */
class NiceScale(private var minPoint: Double, private var maxPoint: Double) {

    private var maxTicks = 15.0
    private var range: Double = 0.0
    var niceMin: Double = 0.0
    var niceMax: Double = 0.0
    var tickSpacing: Double = 0.0

    init {
        calculate()
    }

    /**
     * Calculate and update values for tick spacing and nice
     * minimum and maximum data points on the axis.
     */
    private fun calculate() {
        range = niceNum(maxPoint - minPoint, false)
        tickSpacing = niceNum(range / (maxTicks - 1), true)
        niceMin = floor(minPoint / tickSpacing) * tickSpacing
        niceMax = ceil(maxPoint / tickSpacing) * tickSpacing
    }

    /**
     * Returns a "nice" number approximately equal to range. Rounds
     * the number if round = true. Takes the ceiling if round = false.
     *
     * @param range Double The data range.
     * @param round Boolean Whether to round the result.
     * @return Double A "nice" number to be used for the data range.
     */
    private fun niceNum(range: Double, round: Boolean): Double {
        /** Exponent of range  */
        val exponent: Double = floor(log10(range))
        /** Fractional part of range  */
        val fraction: Double
        /** Nice, rounded fraction  */
        val niceFraction: Double

        fraction = range / pow(10.0, exponent)

        niceFraction = if (round) {
            when {
                fraction < 1.5 -> 1.0
                fraction < 3 -> 2.0
                fraction < 7 -> 5.0
                else -> 10.0
            }
        } else {
            when {
                fraction <= 1 -> 1.0
                fraction <= 2 -> 2.0
                fraction <= 5 -> 5.0
                else -> 10.0
            }
        }

        return niceFraction * pow(10.0, exponent)
    }

    /**
     * Sets the minimum and maximum data points.
     *
     * @param minPoint Double The minimum data point.
     * @param maxPoint Double The maximum data point.
     */
    fun setMinMaxPoints(minPoint: Double, maxPoint: Double) {
        this.minPoint = minPoint
        this.maxPoint = maxPoint
        calculate()
    }

    /**
     * Sets maximum number of tick marks we're comfortable with.
     *
     * @param maxTicks Double The maximum number of tick marks.
     */
    fun setMaxTicks(maxTicks: Double) {
        this.maxTicks = maxTicks
        calculate()
    }
}

回答14:

Here'a better organized C# code.

public class NiceScale
{

    public double NiceMin { get; set; }
    public double NiceMax { get; set; }
    public double TickSpacing { get; private set; }

    private double _minPoint;
    private double _maxPoint;
    private double _maxTicks = 5;
    private double _range;

    /**
     * Instantiates a new instance of the NiceScale class.
     *
     * @param min the minimum data point on the axis
     * @param max the maximum data point on the axis
     */
    public NiceScale(double min, double max)
    {
        _minPoint = min;
        _maxPoint = max;
        Calculate();
    }

    /**
     * Calculate and update values for tick spacing and nice
     * minimum and maximum data points on the axis.
     */
    private void Calculate()
    {
        _range = NiceNum(_maxPoint - _minPoint, false);
        TickSpacing = NiceNum(_range / (_maxTicks - 1), true);
        NiceMin = Math.Floor(_minPoint / TickSpacing) * TickSpacing;
        NiceMax = Math.Ceiling(_maxPoint / TickSpacing) * TickSpacing;
    }

    /**
     * Returns a "nice" number approximately equal to range Rounds
     * the number if round = true Takes the ceiling if round = false.
     *
     * @param range the data range
     * @param round whether to round the result
     * @return a "nice" number to be used for the data range
     */
    private double NiceNum(double range, bool round)
    {
        double exponent; /** exponent of range */
        double fraction; /** fractional part of range */
        double niceFraction; /** nice, rounded fraction */

        exponent = Math.Floor(Math.Log10(range));
        fraction = range / Math.Pow(10, exponent);

        if (round) {
            if (fraction < 1.5)
                niceFraction = 1;
            else if (fraction < 3)
                niceFraction = 2;
            else if (fraction < 7)
                niceFraction = 5;
            else
                niceFraction = 10;
        } else {
            if (fraction <= 1)
                niceFraction = 1;
            else if (fraction <= 2)
                niceFraction = 2;
            else if (fraction <= 5)
                niceFraction = 5;
            else
                niceFraction = 10;
        }

        return niceFraction * Math.Pow(10, exponent);
    }

    /**
     * Sets the minimum and maximum data points for the axis.
     *
     * @param minPoint the minimum data point on the axis
     * @param maxPoint the maximum data point on the axis
     */
    public void SetMinMaxPoints(double minPoint, double maxPoint)
    {
        _minPoint = minPoint;
        _maxPoint = maxPoint;
        Calculate();
    }

    /**
     * Sets maximum number of tick marks we're comfortable with
     *
     * @param maxTicks the maximum number of tick marks for the axis
     */
    public void SetMaxTicks(double maxTicks)
    {
        _maxTicks = maxTicks;
        Calculate();
    }
}