Introduce conversion methods between Angle and Ratio

[mariuszhermansdorfer]

@angularsen, following your suggestions from #1337, here is an updated PR adding the conversion methods between Angle and Slope.

How do you suggest we proceed with creating strings like "1 in 2, 1 in 5, 1:2, 1:5" etc. ?

[mariuszhermansdorfer]

I could simply add the following method to Ratio.extra.cs:

        /// <summary>
        /// Converts the ratio to a string representing slope in a more detailed fraction format.
        /// </summary>
        /// <param name="cultureInfo">The culture info to format the string. If null, the current culture is used.</param>
        /// <returns>A string representing the slope in a detailed fraction format like "3 in 4" or "3 : 4".</returns>
        public string ToDetailedSlopeString(CultureInfo cultureInfo)
        {
            cultureInfo = cultureInfo ?? CultureInfo.CurrentCulture;

            // Find the closest fraction to represent the slope
            (int numerator, int denominator) = ConvertToFraction(this.DecimalFractions);

            string slopeFormat = cultureInfo.Name == "en-US" ? "{0} in {1}" : "{0} : {1}";

            return string.Format(cultureInfo, slopeFormat, numerator, denominator);
        }

        private (int, int) ConvertToFraction(double decimalFraction, int maxDenominator = 100)
        {
            if (decimalFraction == 0)
            {
                return (0, 1);
            }

            int sign = Math.Sign(decimalFraction);
            decimalFraction = Math.Abs(decimalFraction);

            int wholePart = (int)decimalFraction;
            decimalFraction -= wholePart;

            int lowerNumerator = 0, lowerDenominator = 1, upperNumerator = 1, upperDenominator = 1;

            while (lowerDenominator <= maxDenominator && upperDenominator <= maxDenominator)
            {
                int middleDenominator = lowerDenominator + upperDenominator;
                int middleNumerator = lowerNumerator + upperNumerator;

                if (middleDenominator > maxDenominator) break;

                double middleValue = (double)middleNumerator / middleDenominator;

                if (decimalFraction < middleValue)
                {
                    upperNumerator = middleNumerator;
                    upperDenominator = middleDenominator;
                }
                else if (decimalFraction > middleValue)
                {
                    lowerNumerator = middleNumerator;
                    lowerDenominator = middleDenominator;
                }
                else
                {
                    lowerNumerator = upperNumerator = middleNumerator;
                    lowerDenominator = upperDenominator = middleDenominator;
                    break;
                }
            }

            // Choose the fraction that is closer to the original decimalFraction
            double lowerDiff = decimalFraction - (double)lowerNumerator / lowerDenominator;
            double upperDiff = (double)upperNumerator / upperDenominator - decimalFraction;

            int finalNumerator, finalDenominator;

            if (lowerDiff < upperDiff)
            {
                finalNumerator = wholePart * lowerDenominator + lowerNumerator;
                finalDenominator = lowerDenominator;
            }
            else
            {
                finalNumerator = wholePart * upperDenominator + upperNumerator;
                finalDenominator = upperDenominator;
            }

            return (finalNumerator * sign, finalDenominator);
        }

[angularsen]

I don't know what the correct term is, but I'd expect something like ToRatioString() to output on the format 1:3 for 1 to 3 ratio.

This could be a method just like you proposed above.
Then create some unit tests to verify the behavior for a range of values.
For example, how does it work when the value is almost but not exactly 1:3, like 1:2.999 ? I assume it would be represented as 1000:2999? Or should there be some option to perform rounding? I'm not sure.

[angularsen]

There is some similar work here, for FeetInches.ToArchitecturalString():

UnitsNet/UnitsNet/CustomCode/Quantities/Length.extra.cs

Lines 238 to 314 in a95e33f

	/// <summary>
	/// Outputs feet and inches on the format: {feetValue}' - {inchesValueIntegral}[ / {inchesValueFractional}]"
	/// The inches are rounded to the nearest fraction of the fractionDenominator argument and reduced over the greatest common divisor.
	/// The fractional inch value is omitted if the numerator is 0 after rounding, or if the provided denominator is 1.
	/// </summary>
	/// <param name="fractionDenominator">The maximum precision to express the rounded inch fraction part. Use 1 to round to nearest integer, with no fraction.</param>
	/// <example>
	/// <code>
	/// var length = Length.FromFeetInches(3, 2.6);
	/// length.ToArchitecturalString(1) => 3' - 3"
	/// length.ToArchitecturalString(2) => 3' - 2 1/2"
	/// length.ToArchitecturalString(4) => 3' - 2 1/2"
	/// length.ToArchitecturalString(8) => 3' - 2 5/8"
	/// length.ToArchitecturalString(16) => 3' - 2 5/8"
	/// length.ToArchitecturalString(32) => 3' - 2 19/32"
	/// length.ToArchitecturalString(128) => 3' - 2 77/128"
	/// </code>
	/// </example>
	/// <exception cref="ArgumentOutOfRangeException">Denominator for fractional inch must be greater than zero.</exception>
	public string ToArchitecturalString(int fractionDenominator)
	{
	if (fractionDenominator < 1)
	{
	throw new ArgumentOutOfRangeException(nameof(fractionDenominator), "Denominator for fractional inch must be greater than zero.");
	}
	var inchTrunc = (int)Math.Truncate(Inches);
	var numerator = (int)Math.Round((Inches - inchTrunc) * fractionDenominator);
	if (numerator == fractionDenominator)
	{
	inchTrunc++;
	numerator = 0;
	}
	var inchPart = new System.Text.StringBuilder();
	if (inchTrunc != 0 || numerator == 0)
	{
	inchPart.Append(inchTrunc);
	}
	if (numerator > 0)
	{
	int GreatestCommonDivisor(int a, int b)
	{
	while (a != 0 && b != 0)
	{
	if (a > b)
	a %= b;
	else
	b %= a;
	}
	return a | b;
	}
	int gcd = GreatestCommonDivisor(numerator, fractionDenominator);
	if (inchPart.Length > 0)
	{
	inchPart.Append(' ');
	}
	inchPart.Append($"{numerator / gcd}/{fractionDenominator / gcd}");
	}
	inchPart.Append('"');
	if (Feet == 0)
	{
	return inchPart.ToString();
	}
	return $"{Feet}' - {inchPart}";
	}
	}

Maybe it can be reused or take inspiration from.

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