Question

Help figuring formula to get Hour and Minute of clock by angle

Asked by: stormist

I'm working on a software program with a clock control. I have the angle calculated where 1-30 degrees is 2 o clock, 31-60 degrees is 1 and so on in counter clockwise direction. So to list them all

Time/Degrees

12/ 61-90
1/31-60
2/1-30
3/331-360
4/301-330
5/271-300
6/241-270
7/211-240
8/181-210
9/151-180
10/121-150
11/61-90

What would be a formula if given the angle you could find the hour?

What would be the formula to find out which minute the minute hand is pointing to if given the angle of it?

And if possible, how would you find the correct angle of the minute hand if given the angle of the hour hand on this degree setup?

Thanks a ton to any math whizzes, this is not homework I promise. Its a real issue I'm dealing with on a .NET control.

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Asked On: 2009-09-12 at 17:59:12ID24727413
Topics: Algorithms
,; Probability & Statistics
,; Math & Science
Participating Experts: 3
Points: 500
Comments: 19

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Answers

by: billprewPosted on 2009-09-12 at 18:24:37ID: 25318596

Something like this will get the hour (h) based on the angle samples you gave:

i=truncate(angle/30)
if i>1 then h=14-i else h=2-i

For the minute hand I'd want to see some sample data like you gave for the hour, but it could be similar to the hour and look like:

i=truncate(angle/6)
if i>1 then h=70-i else h=10-i

I don't understand the third part of your question.

Why did you set zero degrees at 2:00 rather that 12:00, seems odd.

~bp

by: aburrPosted on 2009-09-12 at 19:24:13ID: 25318728

something seem to be wrong with 11 O'clock

by: aburrPosted on 2009-09-12 at 19:27:50ID: 25318742

"What would be the formula to find out which minute the minute hand is pointing to if given the angle of it?"

What does the minute hand make an angle with?
do you start with the angle that the minute hand makes with the vertical? or with the direction from center to 2? Or the angle it makes with the hour hand?

by: aburrPosted on 2009-09-12 at 19:48:38ID: 25318774

"What would be the formula to find out which minute the minute hand is pointing to if given the angle of it?"
--
If by angel you mean the counterclockwise angle that the minute hand makes with a vertical the relation is
time (in minutes) = 60 - angle/6

by: stormistPosted on 2009-09-12 at 22:41:15ID: 25319086

The hour code worked great. The minute code gave weird results but like you said the zero degrees starting at 2 is odd and makes this more difficult. It comes from the method below. Do you see any way to fix it where 12 would be 0 degrees and then it would continue clockwise to 360?

To clarify on my last question. If a user were to drag the hour hand halfway between the 2 and 3, using angle-to- hour formula we know they want the hour to be 2'Oclock but at that degree (assuming the method below were working correctly and 12'oclock was 0 degrees and moved onward clockwise, say they clicked on 76 degrees when they clicked halfway between 2-3) what degree should the minute hand be set out to properly reflect the time when the hour hand is at that degree. (halfway between 2 and 3)

Thank you very much for your time and replies.

 /// <summary>
        /// gets Angle from mouse position
        /// </summary>
        /// <param name="xy">Mouse Position</param>
        /// <param name="origin">Center of circle</param>
        /// <returns>angle</returns>
        private float XYToDegrees(Point xy, Point origin)
        {
            double angle = 0.0;
 
            if (xy.Y < origin.Y)
            {
                if (xy.X > origin.X)
                {
                    angle = (double)(xy.X - origin.X) / (double)(origin.Y - xy.Y);
                    angle = Math.Atan(angle);
                    angle = 90.0 - angle * 180.0 / Math.PI;
                }
                else if (xy.X < origin.X)
                {
                    angle = (double)(origin.X - xy.X) / (double)(origin.Y - xy.Y);
                    angle = Math.Atan(-angle);
                    angle = 90.0 - angle * 180.0 / Math.PI;
                }
            }
            else if (xy.Y > origin.Y)
            {
                if (xy.X > origin.X)
                {
                    angle = (double)(xy.X - origin.X) / (double)(xy.Y - origin.Y);
                    angle = Math.Atan(-angle);
                    angle = 270.0 - angle * 180.0 / Math.PI;
                }
                else if (xy.X < origin.X)
                {
                    angle = (double)(origin.X - xy.X) / (double)(xy.Y - origin.Y);
                    angle = Math.Atan(angle);
                    angle = 270.0 - angle * 180.0 / Math.PI;
                }
            }
            return (float)angle;
        }

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by: thehagmanPosted on 2009-09-13 at 00:20:58ID: 25319291

Well, if billprew's formula

i=truncate(angle/30)
if i>1 then h=14-i else h=2-i

worked for h, then it can be slghtly rewritten as follows:

t = 2.0 - angle/30.0
if t < 1.0 then t = t + 12.0
h = truncate(t)

This should still give the same hour, but we can add a line to calculate the minutes from the rest:

m = truncate(60*(t-h))

by: billprewPosted on 2009-09-13 at 07:41:28ID: 25320359

Using a modified version of your procedure shown below, this should return the angle of the mouse position relative to the origin, with 0 degrees at the top (12:00), and 180 degrees at the bottom (6:00). This makes the calculation of the hours or minutes from degrees simpler as:

h=truncate(angle/30)
if h<1 then h=h+12

m=truncate(angle/6)

I think you also need to add code to you routine to handle the case where X and/or Y equal the origin X or origin Y, since those are special cases and some can cause division by zero.

~bp

/// <summary>
/// gets Angle from mouse position
/// </summary>
/// <param name="xy">Mouse Position</param>
/// <param name="origin">Center of circle</param>
/// <returns>angle</returns>
private float XYToDegrees(Point xy, Point origin)
{
    double angle = 0.0;
    double base = 0.0;
 
    if (xy.Y < origin.Y)
        base = 180.0;
    else if (xy.Y > origin.Y)
        if (xy.X > origin.X)
            base = 0.0;
        else if (xy.X < origin.X)
            base = 360.0;
 
    angle = (double)(xy.X - origin.X) / (double)(xy.Y - origin.Y);
    angle = Math.Atan(-angle);
    angle = (angle + base) * 180.0 / Math.PI;
 
    return (float)angle;
}

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by: billprewPosted on 2009-09-13 at 07:42:23ID: 25320362

Oops, cut and paste error in the above, correct one line to:

angle = Math.Atan(angle);

~bp

by: stormistPosted on 2009-09-13 at 11:37:33ID: 25321269

This method seems to be returning some weird stuff.
I copied it below with the correction you stated plus base renamed to based since base is reserved in C#

10314 at 12
10225 at 3

20625 at 6

20564 at 8

  /// gets Angle from mouse position
        /// </summary>
        /// <param name="xy">Mouse Position</param>
        /// <param name="origin">Center of circle</param>
        /// <returns>angle</returns>
        private float XYToDegrees(Point xy, Point origin)
        {
            double angle = 0.0;
            double based = 0.0;
 
            if (xy.Y < origin.Y)
                based = 180.0;
            else if (xy.Y > origin.Y)
                if (xy.X > origin.X)
                    based = 0.0;
                else if (xy.X < origin.X)
                    based = 360.0;
 
            angle = (double)(xy.X - origin.X) / (double)(xy.Y - origin.Y);
            angle = Math.Atan(angle);
            angle = (angle + based) * 180.0 / Math.PI;
 
            return (float)angle;
        }

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by: billprewPosted on 2009-09-13 at 12:55:02ID: 25321486

My bad, I had worked it out on paper, then messed it up in updating your code. Try this change.

angle = (angle * 180.0 / Math.PI) + based;

~bp

by: stormistPosted on 2009-09-13 at 13:30:45ID: 25321603

I assumed you mean't to change the last line on angle =. Did so and got 0 degrees at 6'oclock, and incrementation to 360 counterclockwise. If some kind of mirror effect could be applied it would be working correctly I think?

Any idea what the problem could be?

Thanks so much for your continued assistance.

by: billprewPosted on 2009-09-13 at 13:55:59ID: 25321688

Well, not sure what is going on here, unless what I'm thinking of on paper isn't matching the coordinates you are using. I'm attaching an Excel sheet with a number of test cases, and the calculations that should be occurring in your routine now. The Excel sheet seems to give the results I am expecting.

The first four columns should make sense, they are just the origin X and Y, and the data point X and Y. Then I calculated the "based" value as you should be. Then I calculated the angle in radians for these points. Next I convert to degrees (angle*180/PI). Lastly I add to the "biased" value. I am seeing values as I would have expected in the sheet.

~bp

EE24727413.xls
- 20 KB
Test data in Excel

by: billprewPosted on 2009-09-13 at 14:16:30ID: 25321756

I created a quick test in Java and the algorithm seems to work, so I must be visualizing things different than you maybe? Here's the program to test the same data as Excel, and the results after it.

~bp

public class ee {
    public static void main (String[] args) {
        System.out.printf("%f\n", XYToDegrees(0,  0,  1,  1));
        System.out.printf("%f\n", XYToDegrees(0,  0,  -1, 1));
        System.out.printf("%f\n", XYToDegrees(0,  0,  1,  -1));
        System.out.printf("%f\n", XYToDegrees(0,  0,  -1, -1));
        System.out.printf("%f\n", XYToDegrees(0,  0,  2,  1));
        System.out.printf("%f\n", XYToDegrees(0,  0,  -2, 1));
        System.out.printf("%f\n", XYToDegrees(0,  0,  2,  -1));
        System.out.printf("%f\n", XYToDegrees(0,  0,  -2, -1));
        System.out.printf("%f\n", XYToDegrees(0,  0,  1,  2));
        System.out.printf("%f\n", XYToDegrees(0,  0,  -1, 2));
        System.out.printf("%f\n", XYToDegrees(0,  0,  1,  -2));
        System.out.printf("%f\n", XYToDegrees(0,  0,  -1, -2));
        System.out.printf("%f\n", XYToDegrees(10, 10, 15, 15));
        System.out.printf("%f\n", XYToDegrees(10, 10, 5,  15));
        System.out.printf("%f\n", XYToDegrees(10, 10, 15, 5));
        System.out.printf("%f\n", XYToDegrees(10, 10, 5,  5));
        System.out.printf("%f\n", XYToDegrees(10, 10, 20, 15));
        System.out.printf("%f\n", XYToDegrees(10, 10, 0,  15));
        System.out.printf("%f\n", XYToDegrees(10, 10, 20, 5));
        System.out.printf("%f\n", XYToDegrees(10, 10, 0,  5));
        System.out.printf("%f\n", XYToDegrees(10, 10, 15, 20));
        System.out.printf("%f\n", XYToDegrees(10, 10, 5,  20));
        System.out.printf("%f\n", XYToDegrees(10, 10, 15, 0));
        System.out.printf("%f\n", XYToDegrees(10, 10, 5,  0));
    }
 
    public static float XYToDegrees(float ox, float oy, float x, float y)
    {
        double angle = 0.0;
        double base = 0.0;
 
        if (y < oy)
            base = 180.0;
        else if (y > oy)
            if (x > ox)
                base = 0.0;
            else if (x < ox)
                base = 360.0;
 
        angle = (double)(x - ox) / (double)(y - oy);
        angle = Math.atan(angle);
        angle = (angle * 180.0 / Math.PI) + base;
 
        return (float)angle;
    }
}
 
 
45.000000
315.000000
135.000000
225.000000
63.434948
296.565063
116.565048
243.434952
26.565052
333.434937
153.434952
206.565048
45.000000
315.000000
135.000000
225.000000
63.434948
296.565063
116.565048
243.434952
26.565052
333.434937
153.434952
206.565048

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by: stormistPosted on 2009-09-13 at 14:47:13ID: 25321879

Could it be something to do with the fact that as I go from left to right on my clock face the mouse position returned on the X axis increases (as expected) but when I go up on the Y axis, the Y cordinate decreases. When I go down, the Y Cordinate increases. Shouldn't the Y axis go up and my mouse goes up and vice versa? I'm just using the point returned from my mouse click event..

by: stormistPosted on 2009-09-13 at 14:55:30ID: 25321931

From Cordinate system being utilized, here are the values of X/Y at various points on the clock. (approx)

Clock Angle:

X: 69 Y: 23 Angle 180 12'oclock
X: 112 Y: 66 Angle 93.9 3'oclock
X: 91 Y: 105 Angle 31.4 5'oclock
X: 47 Y: 106 Angle 329.2 7 o clock
X: 27 Y 66 Angle 265 9 'oclock
X: 48 Y: 32 Angle 209 11'oclock

Perhaps that is the discrepancy? Never does the coordinate system used in the control go into the negative.

by: billprewPosted on 2009-09-13 at 15:00:32ID: 25321956

Ah yes, that will pose a problem, let me think about how that needs to be addressed. I should have picked up on that earlier, typical coordinate systems used for the computer screen mouse are based off of 0,0 being in the upper left, and then increasing in positive values from there.

~bp

by: billprewPosted on 2009-09-13 at 15:18:52ID: 25322027

Okay, see if this works better. I also added the logic to handle the 4 multiples of 90.

~bp

/// gets Angle from mouse position
/// </summary>
/// <param name="xy">Mouse Position</param>
/// <param name="origin">Center of circle</param>
/// <returns>angle</returns>
private float XYToDegrees(Point xy, Point origin)
{
    double angle = 0.0;
    double based = 0.0;
 
    if (xy.Y == origin.Y)
        if (xy.X > origin.X)
            angle = 90.0;
        else 
            return 270.0;
 
    if (xy.X == origin.X)
        if (xy.Y > origin.Y)
            angle = 180.0;
        else 
            return 0.0;
 
    if (xy.Y > origin.Y)
        based = 180.0;
    else 
        if (xy.X > origin.X)
            based = 0.0;
        else
            based = 360.0;
 
    angle = (double)(xy.X - origin.X) / (double)(xy.Y - origin.Y);
    angle = Math.Atan(angle);
    angle = based - (angle * 180.0 / Math.PI);
 
    return (float)angle;
}

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by: billprewPosted on 2009-09-13 at 15:20:01ID: 25322031

Oops, a couple of typos there, should be this.

~bp

/// gets Angle from mouse position
/// </summary>
/// <param name="xy">Mouse Position</param>
/// <param name="origin">Center of circle</param>
/// <returns>angle</returns>
private float XYToDegrees(Point xy, Point origin)
{
    double angle = 0.0;
    double based = 0.0;
 
    if (xy.Y == origin.Y)
        if (xy.X > origin.X)
            return 90.0;
        else 
            return 270.0;
 
    if (xy.X == origin.X)
        if (xy.Y > origin.Y)
            return 180.0;
        else 
            return 0.0;
 
    if (xy.Y > origin.Y)
        based = 180.0;
    else 
        if (xy.X > origin.X)
            based = 0.0;
        else
            based = 360.0;
 
    angle = (double)(xy.X - origin.X) / (double)(xy.Y - origin.Y);
    angle = Math.Atan(angle);
    angle = based - (angle * 180.0 / Math.PI);
 
    return (float)angle;
}

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by: stormistPosted on 2009-09-13 at 15:40:41ID: 25322131

Brilliant! Works great!! Was beginning to think I was seeing numbers backwards or something =)

Thanks a ton! Here is a follow-up question I just posted:
http://www.experts-exchange.com/Programming/Algorithms/Q_24728287.html

20120131-EE-VQP-002

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Help figuring formula to get Hour and Minute of clock by angle

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Business Clients

In the Press

In the Press

In the Press