Math help for Angles

[kingkwong92]

Got a mean headache from trying to work this out.
I have a dagger (D) throw ability and a ninja star (S) throw ability.
Both a dummy units in a slide trigger.
Every 0.01 seconds they move a distance of speed(D) or speed(S).

I'm trying to make a trigger which detects when a dagger is within X range and if they also have a dagger or a ninja star, they will throw it and hit the incoming ninja star or dagger if it is coming from the front. I want to find the angle in which I have to throw the dagger or NS to intercept the incoming projectile. Is there any formula to predict the path of the projectile?

So far I have:
Point A = Position of thrown
Point B = Position of deflecting unit

Angle(AtoB) - Angle(A-facing) = Angle - Angle(B-A)
I havn't taken into account the speed of the projectiles. Atm I have no idea what I'm doing.
Any ideas???

 

[vypur85]

> Is there any formula to predict the path of the projectile?

Err.. Just acquire the angle between the target and the thrown object. And allow the new object to travel along that angle? Don't think any math formula is required here. That is, if I understand you correctly.

 

[kingkwong92]

The projectile moves in the direction it is facing.
Direction of travel = Facing angle
The dagger detects within 50 units range. Therefore the dagger can still hit even if
facing angle not equal to angle from unit to dagger
Eg. Dagger goes past unit but not directly aimed at the unit.

Also I want it to deflect any dagger that comes with range.

How do you upload an image? I could show you by drawing a diagram on paint

 

[KaerfNomekop]

So long as there are units within 50 range, check to see if their facing angle is within the required angle to deflect the dagger.

 

[kingkwong92]

I don't think I'm understood.
Eample: I have a unit (point A)
I draw a circle around the selected unit, this is the range in which a projectile is detected.
When a projectile enters the circle (point B)
If the dagger is heading straight towards the unit then Angle(A to B) equals facing of projectile.
However the projectile can also enter the circle but Angle(A to B) does not equal facing of projectile.

I want the unit to throw a projectile at Angle(X) which will then collide with the projectile at point(C). I need a formula which works out where point (C) is and use that to calculate the angle that the dagger must be thrown at.

 

[KaerfNomekop]

A Paint diagram would be helpful to understanding. This is doing my head in.

 

[kingkwong92]

How??? How do you add a pic???

 

[KaerfNomekop]

Upload it to the site.

 

[vypur85]

Uh. To be more precise...
Below every new post window, there's a 'Upload a File' button. That one...

I hope your image will be easy to understand. From your descriptions, they're kinda confusing but seemed to be something rather simple.

 

[kingkwong92]

-A projectile moves within the radius of detection of the hero at Point A.
-At that instant the hero throws a projectile that will intecept the incoming projectile at point B. (Blue line)
-I need to know how to calculate the path of the incoming projectile (Red line)and then get the angle in which I can throw my projectile. Also I have multiple projectiles with different speeds.
The projectiles will ricochete off each other.
Hope this is easier to understand. The maths is driving me crazy and I've drawn a million diagrams on paper to try work it out.

 

[kingkwong92]

Bump!!

 

[kingkwong92]

BumpBump!!

 

[xAnaMorphine]

I need to know how to calculate the path of the incoming projectile (Red line)

The red line is a straight line which has x and y coordinates
which subtends the circle around the hero.
Running a periodic trigger which records the x and y coordinates
of the projectile after entering the circle will help to determine the
position of the projectile.
Then you want to launch a projectile which faces the incoming projectile
which flys towards the estimated point where both straight line cross each
other. If that doesn't ring a bell let me try to explain it further.
Basically what you are looking for is the point of intersection between two
straight lines. Since you got the information about the intersection point
of the straight line and the circle you know how the straight line will continue.
I would use vectors to calculate the shortest distance between the hero and the
straight line which crosses the circle and then fire the projectile.
Hope that was somehow understandable.

 

[xAnaMorphine]

This should work...

g1: y=m*x+b
 
P1 (x from incoming projectile | y from incoming projectile)
P2 (x2 | y2)
 
m= (y2-y1)/(x2-x1)
 
b= y - m*x
b= (y from incoming projectile) - [(y2-y1)/(x2-x1)]* (x from incoming projectile)
 
---------------------
 
P3 (x3 from Hero | y3 from Hero)
 
m1= -1/m
 
g2: y=m1*x+b
 
b= (y3 from Hero) - (-1/m) * (x3 from Hero)
 
-------------------
 
Intersection between g1 and g2:
 
S: m*x+b = m1*x+b
S(sx | sy)
------------------
 
Euclidean distance between the
intersection Point S and the position of the Hero P3:
 
d(P,S)=sqrt(((x3-sx)^2) + ((y3-sy)^2))
 
(Just to prove it is the shortest distance.)
---------------
 
Launch projectile towards the intersection Point.

 

[kingkwong92]

How would this work if there are two different projectiles with different speeds.
Doesn't this just calculate a path perpendicular to the projectiles path?

 

[xAnaMorphine]

As for the different speeds it will get a little bit complicated.
I don't really know if there are any limits with the World Editor GUI but I think
something like this should work for the speed:

d(t)=(a/2)*t²+v*t+d0
 
while
d(t) is the place at the time "t",
a is the acceleration,
v the constant speed and
d0 the starting point.
 
In this particular example a is equal to 0 and we lookt at 2D vectors.
 
We need another function to determine the angle of the projectile:
 
v= q* (sin(alpha), cos(alpha))
 
while q is the speed of the projectile which should reflect the incoming projectile
 
if you solve the equations you get the intersection point...
 
 
http://en.wikipedia.org/wiki/Equations_of_motion

have fun ;/

 

[Imp Midna]

So, simply setting up an equation and solving it pretty much fails. Actually, i asked Wolfram matehmatica about the solution, but the Sin(x) and Cos(x) inside the direction vector makes it so complex that i cant even post it here.
So the trick to reduce it was setting the koordinate-system that way that the projectile is at (o|o) facing towards the x-achsis. You could get rid of the Sin(x) from the Hero-to-Intersept-Point line using the fact that the intersept-Point thus gotta be at y=0 and using Cos(x) = sqrt(1-Sin(x)^2).

Still, im not satisfied with what came out. Im just gonna show it to you:

where:
- rx is the difference of the x positions (X of Hero - X of Projectile)
- ry is the same with the y-positions
- v1 is the speed of the projectile
- v2 is the speed of the heros projectile
- t is the time till impact and also the way you find out the point where they are impacting (Point with offset t*speed in facing-angle degrees)

Now, the thing i marked green is the first thing you gotta care about. If this therm is <0, then you would take the sqrt of a negative number, which is not possible without i (and we dont use i). Thus, a projectile could possibly intercepted at 0 - 2 locations depending on what comes out.
Now what buggs me is the red part. Because it doesnt make sense. It would say that they can not intercept if the speed of the projectiles are the same, which pretty much makes no sense at all, because they can. Now, if you, for example, have two projectiles with a speed of 400 m/s, you could use 4.000.000m/s for v1 and 4.000.001 m/s for v2 and then divide the t that comes out by 10000 again, and you would get the correct position, but its still so god damned weird that i first decided not to share this "solution". Well, but now i do, dont ask me why. If thats enough for you, just implement it in such a way that you do this v2*10.000 + 1 stuff so it gives you the correct point again.

 

[xAnaMorphine]

Just wanted to update my previous posts;

• Erstelle Einheit
  • Events
  • Time - Every 10.00 seconds of game time
  • Conditions
  • Actions
  • Unit - Create 1 Footman for Player 2 (Blue) at (Center of Region 000 &lt;gen&gt;) facing Default building facing degrees
  • Set Anfangspunkt = (Position of (Last created unit))
  • Set X_Koordinate_Anfangspunkt = (X of Anfangspunkt)
  • Set Y_Koordinate_Anfangspunkt = (Y of Anfangspunkt)
  • Unit - Order (Last created unit) to Move To (Center of Region 001 &lt;gen&gt;)

Vektoren: (x-c)^2 = r^2, wobei x = Ortsvektoren auf dem Kreis und c = Ortsvektore des Mittelpunktes des Kreises
Gerade: x(t) = o + t * d, wobei o = der Ortsvektor eines beliebigen Punktes auf der Geraden ist und d = Richtungsvektor der Geraden
 
Da es sich um eine belibige Gerade handeln kann muss o neu definiert werden:
o'x = ox * cos(alpha) - oy * sin(alpha)
und
o'y= ox * sin(alpha) - oy * cos(alpha)

• Variablen
  • Events
  • Unit - A unit comes within 512.00 of Paladin 0001 &lt;gen&gt;
  • Conditions
  • Actions
  • Set Winkel = (Facing of (Triggering unit))
  • Set Radius = 256.00
  • Set Mittelpunkt = (Position of Paladin 0001 &lt;gen&gt;)
  • -------- Position des Footman beim eintreten in den Kreis --------
  • Set Schnittpunkt = (Position of (Triggering unit))
  • Set X_Koordinate = (X of Schnittpunkt)
  • Set Y_Koordinate = (Y of Schnittpunkt)
  • -------- Beliebige Position des Footman --------
  • Set X_Cos_Zwischenergebnis = (X_Koordinate x (Cos(Winkel)))
  • Set X_Sin_Zwischenergebnis = (X_Koordinate x (Sin(Winkel)))
  • Set Y_Cos_Zwischenergebnis = (Y_Koordinate x (Cos(Winkel)))
  • Set Y_Sin_Zwischenergebnis = (Y_Koordinate x (Sin(Winkel)))
  • -------- Beliebige Position (Anpassung der Koordinaten) --------
  • Set Neue_X_Koordinate = (X_Cos_Zwischenergebnis - Y_Sin_Zwischenergebnis)
  • Set Neue_Y_Koordinate = (X_Sin_Zwischenergebnis - Y_Cos_Zwischenergebnis)
  • -------- Punkt nach der Drehung --------
  • Set Neuer_Punkt = (Point(Neue_X_Koordinate, Neue_Y_Koordinate))
  • -------- Die Differenz der Punkte P und Q (Koordinaten) --------
  • Set Differenz_X = (Neue_X_Koordinate - X_Koordinate_Anfangspunkt)
  • Set Differenz_Y = (Neue_Y_Koordinate - Y_Koordinate_Anfangspunkt)
  • -------- Ermittlung der Hypotenuse --------
  • Set X_Hypotenuse_Zwischenergebnis = (Differenz_X x Differenz_X)
  • Set Y_Hypotenuse_Zwischenergebnis = (Differenz_Y x Differenz_Y)
  • Set Hypotenuse = (Square root((X_Hypotenuse_Zwischenergebnis + Y_Hypotenuse_Zwischenergebnis)))
  • -------- Berechnung --------
  • If (All Conditions are True) then do (Then Actions) else do (Else Actions)
  • If - Conditions
  • ((X_Koordinate Less than X_Koordinate_Anfangspunkt) and (Y_Koordinate Less than Y_Koordinate_Anfangspunkt)) or ((X_Koordinate Greater than X_Koordinate_Anfangspunkt) and (Y_Koordinate Greater than Y_Koordinate_Anfangspunkt))
  • Then - Actions
  • -------- Falls -r &lt;= x &lt;= r, dann liegt eine Kollision vor --------
  • Set X_Drehung_Kosinus = (Differenz_Y / Hypotenuse)
  • Set X_Drehung_Sinus = (Differenz_X / Hypotenuse)
  • Set X_Kosinus_Zwischenergebnis = (X_Koordinate x X_Drehung_Kosinus)
  • Set X_Sinus_Zwischenergebnis = (Y_Koordinate x X_Drehung_Sinus)
  • Set X_Koordinate_der_Drehung = (X_Kosinus_Zwischenergebnis - X_Sinus_Zwischenergebnis)
  • Else - Actions
  • -------- Falls -r &lt;= y &lt;= r, dann liegt eine Kollision vor --------
  • Set Y_Drehung_Kosinus = (Differenz_X / Hypotenuse)
  • Set Y_Drehung_Sinus = (Differenz_Y / Hypotenuse)
  • Set Y_Kosinus_Zwischenergebnis = (X_Koordinate x Y_Drehung_Sinus)
  • Set Y_Sinus_Zwischenergebnis = (Y_Koordinate x Y_Drehung_Kosinus)
  • -------- Gemeinsame Schnittpunkte zwischen Kreis und Gerade berechnen --------
  • -------- Wir berechnen Terme die mehrfach benötigt werden und setzen sie in eine Variable --------
  • -------- Term: d*c --------
  • Set X_Koordinate_von_D_und_C = (Differenz_X x (X of Mittelpunkt))
  • Set Y_Koordinate_von_D_und_C = (Differenz_Y x (Y of Mittelpunkt))
  • Set Term_D_und_C_zusammengefasst = (X_Koordinate_von_D_und_C + Y_Koordinate_von_D_und_C)
  • -------- Term: o*d --------
  • Set X_Koordinate_von_O_und_D = (X_Koordinate x Differenz_X)
  • Set Y_Koordinate_von_O_und_D = (Y_Koordinate x Differenz_Y)
  • Set Term_O_und_D_zusammengefasst = (X_Koordinate_von_O_und_D + Y_Koordinate_von_O_und_D)
  • -------- Term: d^2 --------
  • Set X_Koordinate_von_D_und_D = (Differenz_X x Differenz_X)
  • Set Y_Koordinate_von_D_und_D = (Differenz_Y x Differenz_Y)
  • Set Term_D_und_D_zusammengefasst = (X_Koordinate_von_D_und_D + Y_Koordinate_von_D_und_D)
  • -------- Term: d*c - o*d --------
  • Set Term_D_C_O_D = (Term_D_und_C_zusammengefasst - Term_O_und_D_zusammengefasst)
  • -------- Term: (d*c - o*d) / d^2 --------
  • Set Term_D_C_O_D_Durch_D2 = (Term_D_C_O_D / Term_D_und_D_zusammengefasst)
  • -------- Term: [(d*c - o*d) / d^2]^2 --------
  • Set Term_DCOD_Durch_D2_Quadriert = (Term_D_C_O_D_Durch_D2 x Term_D_C_O_D_Durch_D2)
  • -------- Term: o-c --------
  • Set X_Koordinate_von_O_und_C = (X_Koordinate - (X of Mittelpunkt))
  • Set Y_Koordinate_von_O_und_C = (Y_Koordinate - (Y of Mittelpunkt))
  • Set X_Koordinate_von_OC_Quadriert = (X_Koordinate_von_O_und_C x X_Koordinate_von_O_und_C)
  • Set Y_Koordinate_von_OC_Quadriert = (Y_Koordinate_von_O_und_C x Y_Koordinate_von_O_und_C)
  • Set Term_O_und_C_zusammengefasst = (X_Koordinate_von_OC_Quadriert + Y_Koordinate_von_OC_Quadriert)
  • -------- Term: r^2 --------
  • Set Radius_Quadriert = (Radius x Radius)
  • -------- Term: (o-c)^2 - r^2 --------
  • Set Term_OC2_R2 = (Term_O_und_C_zusammengefasst - Radius_Quadriert)
  • -------- Term: ((o-c)^2 - r^2) / d^2 --------
  • Set Term_OC2_R2_Durch_D2 = (Term_OC2_R2 / Term_D_und_D_zusammengefasst)
  • -------- Term: Differenz von [(d*c - o*d) / d^2]^2 und ((o-c)^2 - r^2) / d^2 --------
  • Set T1_Unter_Wurzel_Differenz = (Term_DCOD_Durch_D2_Quadriert - Term_OC2_R2_Durch_D2)
  • If (All Conditions are True) then do (Then Actions) else do (Else Actions)
  • If - Conditions
  • T1_Unter_Wurzel_Differenz Less than 0.00
  • Then - Actions
  • Game - Display to (All players) the text: Die Wurzel einer ne...
  • Else - Actions
  • -------- Wurzelziehen aus der Differenz --------
  • Set T1_Wurzel_Aus_Differenz = (Square root(T1_Unter_Wurzel_Differenz))
  • -------- T1 berechnen aus der Differenz der gezogenen Wurzel und (d*c - o*d) / d^2 --------
  • Set T1 = (Term_D_C_O_D_Durch_D2 - T1_Wurzel_Aus_Differenz)
  • Game - Display to (All players) the text: (Der Kreis wird berührt oder durchdrungen: + (String(T1)))

This is an example use which isn't perfect yet but it works.
It detects the unit and tracks the position.
For today I've got enough, will look into this tomorrow and finish it the next days

EDIT: Sorry for the german commentary but else I would loose track, will change it when it works how you demanded.

EDIT2: The system now fully detects the path of the unit

 

[xAnaMorphine]

Okay got it working now, here is the system.
Just play the map and check out the results, tell me if that's how you imagined.

For everyone who wants to look at the code I will post a pastebin right here
since my post else exceeds 10000 characters

http://pastebin.com/vRcmcffs

 

[kingkwong92]

Wow thank you so much guys. I kinda feel reallys tupid because I have to read the things you guys post up about 10 times before I can even understand a wee bit.

@xAnaMorphine:
I've just tested it and it works almost exactly the way that I want it too. Sometimes when the footman just enters the circle and leaves again, it is impossible for it to be intercepted but a shade still flies out to that point. It would be possible to intercept it if the velocity of the projectile is faster (in some cases).I would like it so if it is impossible to intercept then nothing happens. I normally like to know what I'm doing when adding stuff to a map but this just seems too complex for me. I might just have to copy and paste it. I didn't think it was as hard as I thought it was. Also could you please tell me why the speed of the shade keeps varying? Also why sometimes there are three other shades appearing and sometimes they don't.

EDIT!! I've also noticed that when I move the hero to the top-right or bottom-left, the shade moves to the wrong point. The footmans distance between lessens so therefore should be able to be intercepted.

@Imp Midna:
I really don't like the different velocity thing but I think xAnaMorphine's way works really well. Your way I can understand a wee bit more. I'll play around with both methods and see how they work out.