Converting Y up to Y down coordinates

SledgeHammer01

My brain and my Google skills are sucking this late at night. Lets say I have a control height of 30 pixels Lets say my data range is -5 to 15 I want to normalize my coordinates, but flipped in Y up fashion. I.e. -5 is Y=29 on the screen, 15 is Y=0 Been googling transformation, coordinate systems, translation, etc. Lol, can't find a darn thing... I know this is simple math LOL. Only thing I'm coming up with this late at night is +5 all the points to get to a 0 origin, * 0.66 to scale and then 29 - that... but that can't be right...

Lost User

I am sure there is a proper mathematical way to do it, but this is what I figured out:

-5 to 15 = 0 to 20 is 21 'points'
0 to 29 is 30 pixels

thus

Y = ((y + 5) / 21 * 30) // transform 'points' to pixels
Y' = 29 - Y // flip down to up

OriginalGriff

Shouldn't that be done the other way round?

Y = ((y + 5) * 30) / 21 // transform 'points' to pixels

Since all the values are given as integers (and are likely to be integers at source) doing the division first will not give you a good result.

Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...

Lost User

Yes, but I tested it on my calculator and it worked fine. :laugh: Actually, it would be better to use float values since Windows forms accepts them as co-ordinates.

OriginalGriff

So it's even unit tested? Ship it then! :laugh: It would be better to use floats, but you know and I know how few people round here think of that... :sigh:

Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...

BillWoodruff

Thank you for my Sunday puzzle !

// version two, passes test of reversing the two sample ranges defined here
private Dictionary MapRangeValues(bool flipSign, List sourceRange, List mapToRange)
{
var dctTransform = new Dictionary();

double ratio = Convert.ToDouble(mapToRange.Max() - mapToRange.Min()) / (sourceRange.Max() - sourceRange.Min());

int offset = mapToRange\[0\] - sourceRange\[0\] + 1;

foreach (var sInt in sourceRange)
{
    int val = Convert.ToInt32(ratio\*sInt) + offset;
        //(sInt + offset));

    if (flipSign)
    {
        val = mapToRange.Max() - val - 1;
    }
    else
    {
        val--;
    }

    dctTransform.Add(sInt, val);
}

return dctTransform;

}

// some test data
private List DataRange = Enumerable.Range(-5, 21).ToList();

private List ControlRange = Enumerable.Range(0, 30).ToList();

// requires two TextBoxes on a Form ...
private void testTheSucker()
{
textBox1.Clear();
textBox2.Clear();

var result1 = MapRangeValues(true, DataRange, ControlRange);

var result2 = MapRangeValues(false, ControlRange, DataRange);

foreach (var kvp in result1)
{
    textBox1.Text += string.Format("{0}\\t{1}\\r\\n", kvp.Key, kvp.Value);
}

foreach (var kvp in result2)
{
    textBox2.Text += string.Format("{0}\\t{1}\\r\\n", kvp.Key, kvp.Value);
}

}

I am curious to see if this is as general purpose as I intend it to be: so, will test further. I am sure this can be improved (perhaps replaced with a few lines of Linq wizardry ?), and I'd welcome any feedback, corrections, ideas ! // first test results -5 29 -4 28 -3 26 -2 25 -1 23 0 22 1 21 2 19 3 18 4 16 5 15 6 13 7 12 8 10 9 9 10 8 11 6 12 5 13 3 14 2 15 0 // second test results 0 -5 1 -4 2 -4 3 -3 4 -2 5 -2 6 -1 7 0 8 1 9 1 10 2 11 3 12 3 13 4 14 5 15 5 16 6 17 7 18 7 19 8 20 9 21 9 22 10 23 11 24 12 25 12 26 13 27 14 28 14 29 15

«If you search in Google for 'no-one ever got fired for buying IBM:' the top-hit is the Wikipedia article on 'Fear, uncertainty and doubt'» What does that tell you about sanity in these times?

SledgeHammer01

Actually, this is in a WPF application, so by WPF convention, its an IEnumerable of doubles :). LOL, I guess my late at night answer was pretty close... I confused the whole 0 - 29 / 30 / 20 / 21 thing haha...

SledgeHammer01

Ah, so I was pretty close... I guess I shouldn't try to write code at 11pm LOL... got thrown off by the 0 / 1 0 - 29 = 30 points thing haha... when I woke up this morning, I was like what the hell was I thinking?

SledgeHammer01

Wow! You went all out :). Richards answer was kind of a 1 liner though :). Although he wasn't converting a list which you are... Thanks!

SledgeHammer01

Wait a sec here... I'm testing this out... Lets say I pass in 0 through 10 So 0 should transform to 29 and 10 should transform to 0 0 through 10 is 11 pixels ((0 + 0) / 11 * 30) = 0, 29 - 0 = 29, so that works ((10 + 0) / 11 * 30) = 27.27, 29 - 27.27 = 1.73 which doesn't work. even if I do the multiplication first, ((10 + 0) * 30 / 11) = 27.27

SledgeHammer01

Yeah, I think something is amiss...

		List<double> lst = new List<double>();

		lst.Add(0);
		lst.Add(3);
		lst.Add(7);
		lst.Add(10);

		double dMin = lst.Min();
		double dMax = lst.Max();

		double dHeight = 30;

		//double y = 0; // 29 is correct
		double y = 10; // 1.72 not correct

		double Y = ((y + Math.Abs(dMin)) \* dHeight) / (dMax - dMin + 1);
		Y = dHeight - 1 - Y;

		System.Diagnostics.Debug.WriteLine(Y);

With the -5 to 15 range, it gets closer, 0.43, so I guess that's a round off... if I truncate everything to ints, it comes out even worse, to 2 instead of 1.72.

SledgeHammer01

Hmm... seems more like this is the correct answer:

double Y = ((y + Math.Abs(dMin)) * (dHeight - 1)) / (dMax - dMin);
Y = dHeight - 1 - Y;

This works with:

//lst.Add(-5);
lst.Add(0);
lst.Add(3);
lst.Add(7);
lst.Add(10);
//lst.Add(15);

With the commented and uncommented values. dHeight = 30 (since the control is 30 pixels high, but the pixel range is 0 through 29) With the original formula, the 0 would get to 29 correctly, but the 10 would only go to 1.72. With the -5 / 15 range, it would go to 0.43. With this new formula, both ways got to 0 & 29.

SledgeHammer01

Ok, now I'm really confused... the min & max points are working now, but it seems like points in the middle are all wacky. If my control is 30 pixels high, the mid point is going to be 14, right? so if I give it 0, 3, 7, 10, my min & max is 0 & 10. So one would expect 5.5 to map to 14, but its mapping to 13.05 :confused:.

SledgeHammer01

NM... I think I'm on crack again... LOL... the new formula does work. If my range is 0 to 10, the mid point is 5. And the mid point on a control 30 pixels high, the pixel range is 0 to 29, so the mid point is 14.5 :).

Lost User

I've had many mornings like that.