Draw string with normalized scientific notation (superscripted )

Question

I want to draw following string in my game

To compare, there are 10^75 particles in the universe.

where 10⁷⁵ is formatted in a normalized scientific notation (as we've been doing in school).

I use SpriteBatch.DrawString method, but I cannot figure out a nite solution. There are a few trivial ones:

• Draw two strings where the second string's got a smaller font or is scaled.
• Draw an image.

I've been looking at UTF tables, but seems it's not possible.

Do I have to have special font for this task?

Answer 1

I'm not familiar with XNA but in a Silverlight project where I had to do the same thing I ended up constructing scientific notation numbers from superscript characters.

You don't need a special font, just a Unicode font which has the superscript characters used below.

Heres the code to map digits 0-9 to the appropriate character:

    private static string GetSuperscript(int digit)
    {
        switch (digit)
        {
            case 0:
                return "\x2070";

            case 1:
                return "\x00B9";

            case 2:
                return "\x00B2";

            case 3:
                return "\x00B3";

            case 4:
                return "\x2074";

            case 5:
                return "\x2075";

            case 6:
                return "\x2076";

            case 7:
                return "\x2077";

            case 8:
                return "\x2078";

            case 9:
                return "\x2079";

            default:
                return string.Empty;
        }
    }

And this converts your original double into scientific notation

    public static string FormatAsPowerOfTen(double? value, int decimals)
    {
        if(!value.HasValue)
        {
            return string.Empty;
        }

        var exp = (int)Math.Log10(value.Value);

        var fmt = string.Format("{{0:F{0}}}x10{{1}}", decimals);

        return string.Format(fmt, value / Math.Pow(10, exp), FormatExponentWithSuperscript(exp));
    }

    private static string FormatExponentWithSuperscript(int exp)
    {
        var sb = new StringBuilder();

        bool isNegative = false;

        if(exp < 0)
        {
            isNegative = true;
            exp = -exp;
        }

        while (exp != 0)
        {
            sb.Insert(0, GetSuperscript(exp%10));

            exp = exp/10;
        }

        if(isNegative)
        {
            sb.Insert(0, "-");
        }

        return sb.ToString();
    }

So now you should be able to use FormatAsPowerOfTen(123400, 2) resulting in 1.23x10⁵.

Answer 2

I have tweaked the answer of @Phil at some locations, and like to share my version with you.

    public static string FormatAsPowerOfTen(this double? value, int decimals)
    {
        if (!value.HasValue)
            return string.Empty;
        else
            return FormatAsPowerOfTen(value.Value, decimals);
    }

    public static string FormatAsPowerOfTen(this double value, int decimals)
    {
        const string Mantissa = "{{0:F{0}}}";

        // Use Floor to round negative numbers so, that the number will have one digit before the decimal separator, rather than none.
        var exp = Convert.ToInt32(Math.Floor(Math.Log10(value)));

        string fmt = string.Format(Mantissa, decimals);

        // Do not show 10^0, as this is not commonly used in scientific publications.
        if (exp != 0)
             fmt = string.Concat(fmt, " × 10{1}"); // Use unicode multiplication sign, rather than x.

        return string.Format(fmt, value / Math.Pow(10, exp), FormatExponentWithSuperscript(exp));
    }

    private static string FormatExponentWithSuperscript(int exp)
    {
        bool isNegative = false;
        var sb = new StringBuilder();

        if (exp < 0)
        {
            isNegative = true;
            exp = -exp;
        }

        while (exp != 0)
        {
            sb.Insert(0, GetSuperscript(exp % 10));
            exp = exp / 10;
        }

        if (isNegative)
            sb.Insert(0, '⁻'); //Use unicode SUPERSCRIPT minus

        return sb.ToString();
    }

Also, note that, due to font substitution, this method may give you ugly results for combinations of 1,2 and 3 with other digits in an exponent. 0 and 4-9 were added in unicode and are missing from many fonts. You should make sure you are using a font that supports all digits, like Arial Unicode MS, Cambria, Calibri, Consolas or Lucida Sans Unicode.