Decoding hexadecimal format

Question

I have this string in hexadecimal: "0000803F00000000000000B4B410D1A90000803FB41051B500000034B41051350000803F000000000000000000C05B400000000000C06B400000000000D07440"

and I know what it contains:

(1, 0, -1.192093e-007),

(-9.284362e-014, 1, -7.788287e-007),

(1.192093e-007, 7.788287e-007, 1),

(111, 222, 333).

And yes, it is a tranform matrix!

Decoding the first 72 characters (8 chars per number) was trivial, you only need to split by 8 and use IEEE floating point format ie. 0x0000803F = 1.0f

So we still have "000000000000000000C05B400000000000C06B400000000000D07440" that contains the fourth vector but I never saw such kind of numeric codification.

Any though on this?

Answer 1

It looks like these are 8-byte IEEE floating point numbers, starting at byte 40. So the layout is:

• Bytes 0-11: first vector, 3 single-precision numbers
• Bytes 12-23: second vector, 3 single-precision numbers
• Bytes 25-35: third vector, 3 single-precision numbers
• Bytes 36-39: Unused? (Padding?)
• Bytes 40-63: fourth vector, 3 double-precision numbers

The code below shows an example of parsing this in C#. The output of the code is:

(1, 0, -1.192093E-07)
(-9.284362E-14, 1, -7.788287E-07)
(1.192093E-07, 7.788287E-07, 1)
(111, 222, 333)

Sample code:

using System;

class Program
{
    static void Main(string[] args)
    {
        string text = "0000803F00000000000000B4B410D1A90000803FB41051B500000034B41051350000803F000000000000000000C05B400000000000C06B400000000000D07440";
        byte[] bytes = ParseHex(text);

        for (int i = 0; i < 3; i++)
        {
            float x = BitConverter.ToSingle(bytes, i * 12);
            float y = BitConverter.ToSingle(bytes, i * 12 + 4);
            float z = BitConverter.ToSingle(bytes, i * 12 + 8);
            Console.WriteLine($"({x}, {y}, {z})");
        }

        // Final vector
        {
            double x = BitConverter.ToDouble(bytes, 40);
            double y = BitConverter.ToDouble(bytes, 48);
            double z = BitConverter.ToDouble(bytes, 56);
            Console.WriteLine($"({x}, {y}, {z})");
        }
    }

    // From https://stackoverflow.com/a/854026/9574109
    public static byte[] ParseHex(string hex)
    {
        int offset = hex.StartsWith("0x") ? 2 : 0;
        if ((hex.Length % 2) != 0)
        {
            throw new ArgumentException("Invalid length: " + hex.Length);
        }
        byte[] ret = new byte[(hex.Length-offset)/2];

        for (int i=0; i < ret.Length; i++)
        {
            ret[i] = (byte) ((ParseNybble(hex[offset]) << 4) 
                             | ParseNybble(hex[offset+1]));
            offset += 2;
        }
        return ret;
    }        

    static int ParseNybble(char c)
    {
        if (c >= '0' && c <= '9')
        {
            return c-'0';
        }
        if (c >= 'A' && c <= 'F')
        {
            return c-'A'+10;
        }
        if (c >= 'a' && c <= 'f')
        {
            return c-'a'+10;
        }
        throw new ArgumentException("Invalid hex digit: " + c);
    }
}