Calculate Endpoint from Bearing

[Julen_I]

I can’t help with that, I can’t even open your project on Windows.

Julen

[Robert_Weaver]

I’m glad to see that it’s working for you, but I’m somewhat puzzled that it works with the direction of rotation of the angle the same as that of the bearing. Traditional angles are measured counterclockwise from the x axis, while bearing is measured clockwise from the y axis.

[Julen_I]

Since the y axis is reversed, it’s like if we were looking at the reference system from behind (or, as if the entire reference system could rotate around the x axis and it had fallen downwards), so we see a counterclockwise angle as clockwise.

I hope that makes some sense. Anyway, the reason is our reference system is not the usual one (in which y increases when moving to the north).

Julen

[Robert_Weaver]

@Julen_I

ey = 40 - 30 cos(180º) = 40 - 30 (-1) = 40 + 30 = 70
ex = 50 + 30* sin (180º) = 50 + 30*0 = 50
(50, 70)

Why are you subtracting the second term in the example calculation for ey when your formula is
ey = sy + Distance * sin(Angle) ?

[Julen_I]

I am using the cosine there. The cosine of angles larger than 90º (so those pointing downwards if that angle is the bearing) is negative, but ey > sy if bearing > 90º, so that minus sign is required.

Again, this is all because of the uncommon reference system and way to measure the angle.

And concerning the sine/cosine, usually you would use the sine for the y axis when the angle has its origin on the horizontal axis, but the bearing has its origin on the vertical axis, so the cosine needs to be used for the vertical axis and the sine for the horizontal axis.

The cosine and sine have the following property:
cosine alpha = sine (alpha + 90 º)
and there is a phase difference of 90 º between the angle as we would usually measure it (starting from the x axis) and the bearing.

Julen

[Robert_Weaver]

So, are you saying that your formula should always be:
ey = sy - Distance * sin(Angle)
always with the minus sign (which is different from what you originally posted)?
It seems to me that the sign keeps being changed ad hoc to make the result fit.

The reason why I provided my earlier formula:
Angle = (90-Bearing)*Pi/180
was in order to convert the bearing into a traditional representation of angle that everyone is familiar with: one that is referenced to the x axis, and increases in a counterclockwise direction.

[Julen_I]

@Robert_Weaver

(which is different from what you originally posted)?

I originally posted that because:

@Robert_Weaver

When referred to as a “Bearing” the convention is to measure the angle clockwise from North.

@Julen_I

Thank you Robert, I didn’t know that.

In that case the use of sine and cosine in your first post was correct, Martin (assuming you are using the default x axis orientation). Sorry for the confusion.

And in my original post I said…

@Julen_I

but that depends on how you define the angle.

and

@Julen_I

but again it depends on how your system is defined.

Once I learnt the meaning of bearing I never again changed the minus sign. Have you tried the expressions Martin posted orginally (which are the correct ones) and also yours with a few examples?

Like

@Julen_I

ey = 40 - 30 cos(180º) = 40 - 30 (-1) = 40 + 30 = 70
ex = 50 + 30* sin (180º) = 50 + 30*0 = 50
(50, 70)

In your expressions that would result in
Angle = 90 º -180 º = - 90 º
ex = 50 + 30 * cos (-90) = 50 + 30 * 0 = 50
ey = 40 + 30 * sin (-90) = 40 + 30 * (-1) = 10
(50, 10), which is not correct.

Try with other initial points and bearings

@Robert_Weaver

with: one that is referenced to the x axis, and increases in a counterclockwise direction.

And you did that conversion right, but you are not taking into account the downwards direction of the y axis.

Julen

[Robert_Weaver]

Okay thanks. I missed the “downwards direction of the y axis” part.
Though, I can’t help but think that such a non standard convention is going to cause more problems as time goes on.