Angles in turing

[Atherial]

Hey!
I was wondering if anyone could help guide me through the process of either finding an angle based on the angle of two vector positions, and or help me continue a line from a single position based on an angle.

In other words, I want to be able to have a single dot, say 0,0 that draws a line to another vector based on an angle.

The reason I cant figure this math out on my own is that I am in grade ten, and my math is next semester, while my computer studies class is this semester.
I have researched it a little on my own, and people say things along the lines of COS and SIN or whatever, but that is way over my head at this point.
Im programming in turing, but I figured 2 dimensional vectors are pretty much universal.

Thank you so much everyone, and Happy holidays to you all!
-Mackenzie

[Zren]

Quote:

continue a line from a single position based on an angle

Yay trig. SOH CAH TOA to the rescue.

http://mathworld.wolfram.com/SOHCAHTOA.html

(x1,y1) is the coordinates of the first point. We need to find (x2, y2) to draw the line.

x1 + adjacent = x2
y1 + opposite = y2

We don't know the length of the adjacent and opposite then, so we need to figure them out. We use the trigonometry equations (SOH CAH TOA) I linked to solve them.

sine(angle) = opposite / hypotenuse
cosine(angle) = adjacent / hypotenuse

We know the angle and the hypotenuse (aka the length of the line we're drawing). So we can rearrange that equation to solve for the unknown adjacent and opposite (move hypotenuse to the other side).

opposite = sine(angle) * hypotenuse
adjacent = cosine(angle) * hypotenuse

Which we can substitute into our earlier equations.

x1 + cosine(angle) * hypotenuse = x2
y1 + sine(angle) * hypotenuse = y2

Turing:

var x1, y1, x2, y2, angle, lengthOfLine : real angle := 45 % degrees lengthOfLine := 100 % hypotenuse % Point A x1 := maxx div 2 y1 := maxy div 2 % cosd and sind are functions to get the cosine/sine using degrees x2 := x1 + cosd (angle) * lengthOfLine y2 := y1 + sind (angle) * lengthOfLine Draw.Line (round (x1), round (y1), round (x2), round (y2), black)

[Zren]

Quote:

finding an angle based on the angle of two vector positions

There's a function called atan2 which can do this. And since Turing sucks, it doesn't come with it's own atan2 implementation. You'll need to write you're own (which is why I wrote the other answer first).

First, some more trig.

In this question, we know (x1, y1) and (x2, y2), but don't know the angle. We can find out the adjacent and opposite:

x1 + adjacent = x2
adjacent = x2 - x1

y1 + opposite = y2
opposite = y2 - y1

Now that we know them, we can use the TOA equation to solve for the angle.

tangent(angle) = opposite / adjacent
angle = arctangent(opposite / adjacent)

Turing:

x1 := 0 y1 := 0 x2 := 100 y2 := 100 angle := arctand((y2 - y1) / (x2 - x1)) put angle

However, using this method will break if x1 equals x2 since they will cancel out and you will divide by zero.

We need to set some conditions.


Image from: https://en.wikipedia.org/wiki/Atan2

Turing:

% atan2() implementation that returns degrees fcn atan2d (x : real, y : real) : real     if x > 0 then         result arctand (y / x)     elsif x < 0 and y >= 0 then         result arctand (y / x) + 180     elsif x < 0 and y < 0 then         result arctand (y / x) - 180     elsif x = 0 and y > 0 then         result 90     elsif x = 0 and y < 0 then         result -90     elsif x = 0 and y = 0 then         Error.Halt ("atan2(0, 0) = undefined")     end if end atan2d put atan2d (x2 - x1, y2 - y1)

You should note that you'll still need to check if both x and y are 0 before using this function (as it will raise an error).


And because I really love trig:

Turing:

var x1, y1, x2, y2, angle : real var mouseX, mouseY, mouseB : int % atan2() implementation that returns degrees fcn atan2d (x : real, y : real) : real     if x > 0 then         result arctand (y / x)     elsif x < 0 and y >= 0 then         result arctand (y / x) + 180     elsif x < 0 and y < 0 then         result arctand (y / x) - 180     elsif x = 0 and y > 0 then         result 90     elsif x = 0 and y < 0 then         result -90     elsif x = 0 and y = 0 then         Error.Halt ("atan2(0, 0) = undefined")     end if end atan2d View.Set ("offscreenonly") loop     % Input     Mouse.Where (mouseX, mouseY, mouseB)     % Logic     x1 := maxx div 2     y1 := maxy div 2     x2 := mouseX     y2 := mouseY     angle := atan2d (x2 - x1, y2 - y1)     % Draw     cls     Draw.Line (round (x1), round (y1), round (x2), round (y2), black)     put angle     View.Update() end loop

[Atherial]

Man oh man, that is the most detailed, on topic, and complete response I have ever seen, I wish I could donate more bits but that is all I have! Thank you thank you thank you!!!!

The second response works perfect and I adapted it to what I need, and it fit in absolutely perfectly. Thanks!

I did not even know what math to use nor did I know it was called trig.. But Im glad you could spread your love with me!
I didnt even know where to start either to be honest. Not only did you set me in the right direction, but you gave me a sample too! Thanks so so so much I cant thank you enough,
I wish I could repay you for your help!

However, with the first example in the first response, im confused as to how the variable xy plays a part, and also how to use it.
Please let me know if you have any additional information for this example to get it to function properly, its probably just me though.
I dont really know how this code works, but the second one is sosososo perfect.

Again, Thanks so much! Your response was an absolutely beautifully orchestrated answer, and you need more recognition for this beauty.

Thanks-
Mackenzie

[Zren]

Oh crap, that's a typo. xy is suppose to be y2. Edited the post.

[Atherial]

Oh okay, no worries at all.

So I tried a few Khan academy lessons, and with that page you added, I understand a little further now, but my mathematical abilities are still limited to a squared + b squared = c squared, but the information you provided me with is allowing me to slowly link this all together. Thanks!

So the length of the line is the hypotenuse, as you stated, however I cant seem to get the actual code to run now. Please forgive me if this is a silly mistake as it is late where I am, and I haven't had any caffeine today.

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I have attempted substituting the variable as a whole and just putting 100 in on its own, but I still get "Assigned value is the wrong type"

Turing:

% cosd and sind are functions to get the cosine/sine using degrees x2 := cosd(angle) * 100 y2 := sind(angle) * 100

Sorry for dragging this whole question on, but I just cant figure this one out. Once I get it functional I will post my finished project with this partition of code, as well as credit to your advice and response!

Means so much that you would take the time to answer.
Thank you,
Mackenzie


(Note, the finished project will hopefully be something along the lines of a worm styled game, depending on if I keep the self control to actually finish a project to where I would like to :p )

[Zren]

I kinda screwed up the first example. I forgot to add x1 and y1 when calculating x2 and y2.

You also need to use real numbers, not integers.

I edited it to contain this:

Turing:

var x1, y1, x2, y2, angle, lengthOfLine : real angle := 45 % degrees lengthOfLine := 100 % hypotenuse % Point A x1 := maxx div 2 y1 := maxy div 2 % cosd and sind are functions to get the cosine/sine using degrees x2 := x1 + cosd (angle) * lengthOfLine y2 := y1 + sind (angle) * lengthOfLine Draw.Line (round (x1), round (y1), round (x2), round (y2), black)

Which should be a properly running example.

[Atherial]

That works perfectly! Gonna mark this as solved and post my project once it is completed!

Thanks again!

[TokenHerbz]

beat me to it!!!! have bits Zren +++ yay!!