# Math Questions

Discussion in 'JASS Zone' started by tommerbob, Aug 15, 2011.

1. ### tommerbobMinecraft. :D

Ratings:
+110 / 0 / -0
I think I'm just gonna create a thread for all of my math questions I ever have in the future. I should pay more attention in math class. So here's my problem:

I'm trying to launch a projectile in a random direction from the point of origin:

JASS:
``````local projectile p  = 0
local real       ux = GetUnitX(d.orb)
local real       uy = GetUnitY(d.orb)
local real       tx = GetRandomReal(0, 360)
local real       ty = GetRandomReal(0, 360)

set p = projectile.create(ux,uy,50.00,Atan2((ty - uy),(tx - ux)))``````

(I'm using Kenny's Projectile system)

I thought the angle here:

JASS:
``Atan2((ty - uy),(tx - ux))``

should be random, but its not. The projectile is always going in the same direction. Thanks for help.

2. ### SolmyrActive Member

Ratings:
+30 / 0 / -0
`projectile.create(ux, uy, 50.00, GetRandomReal(0, 2 * bj_PI)) // You may want to pre-calculate 2 * bj_PI though.`

• Like x 1
3. ### Dirac22710180

Ratings:
+147 / 0 / -0
`Atan2(a,b)` takes radians, not angles.
`bj_PI/2`=90 degrees
`bj_PI`=180 degrees

4. ### tommerbobMinecraft. :D

Ratings:
+110 / 0 / -0
Okay, sorry I should have specified more. I need a random X/Y coordinate, to get the angle for

JASS:
`` projectile.create(ux,uy,50.00,Atan2((ty - uy),(tx - ux)))``

and I need the same random X/Y coordinate for this:

JASS:
``call p.projectArcing(tx, ty, p.posZ + 25.00, SHARD_SPEED, 0.08)``

5. ### Dirac22710180

Ratings:
+147 / 0 / -0
JASS:
``````local real randomAngle=GetRandomReal(0,bj_PI*2)
set x=ux+1000*Cos(randomAngle)
set y=uy+1000*Sin(randomAngle)``````

Is that what you want?

6. ### tommerbobMinecraft. :D

Ratings:
+110 / 0 / -0
perfecto. thanks 7. ### emjlr3Change can be a good thingStaff Member

Ratings:
+396 / 0 / -0
*6.28318=Pi*2

8. ### NoobImbaProYou can change this now in User CP.

Ratings:
+60 / 0 / -0
And Pi is equal to:

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788659361533818279682303019520353018529689957736225994138912497217752834791315155748572424541506959... Wikipedia FTW

9. ### SevionThe DIY Ninja

Ratings:
+423 / 0 / -0
Let's not post useless things, NoobImbaPro.

Realistically, in vJASS, Pi only needs to be accurate to the 4th decimal place. And actually, going up to the 2nd decimal place would be more than enough precision for anything vJASS related.

10. ### NoobImbaProYou can change this now in User CP.

Ratings:
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Why useless mate, I gave you the first 1100+ decimals of pi exactly
vJass can read a number with 6 decimals, but 3.1415 is accurate enough, even 3.14.

@tommerbob
give us another questions guy, we hope we help you understand many things that don't make sense to you

11. ### Nestharuso-o

Ratings:
+83 / 0 / -0
vjass can read a number with 20 decimals too.. they are stored in floats after all. However, to add/subtract things that are like 20 decimals, you have to do a trick because vjass value reading is weird (for numbers, not variables).

12. ### tommerbobMinecraft. :D

Ratings:
+110 / 0 / -0
I don't have any questions at the moment, but don't worry, I will in the future.

13. ### tommerbobMinecraft. :D

Ratings:
+110 / 0 / -0
Okay it didn't take me long to get lost in math again. Sorry for the double post.

I'm working on a "leap" spell. The unit jumps 600 distance toward his facing angle. I based it off a spell written by Dinowc, so I don't completely understand all of the math functions.

Problem: instead of jumping 600, he jumps like 3000.

Code:

JASS:
``````scope Leap initializer init

// Requirements:
//      NewGen
//      Timer Utils (TU)
//      Math Functions

// configurables:

globals
//========================================
private constant integer SPELL_ID = 'A01C' // raw code of Leap spell
private constant integer CROW_FORM = 'Amrf' // raw code of Crow Form

//========================================
private constant boolean INVULNERABLE = false // make unit invulnerable while in the air?
//========================================
private constant real INTERVAL = 0.03125
//========================================
private constant real MOVESPEED  = 800.
private constant real MAX_HEIGHT = 250.
private constant real JUMP_SPEED = 800. // wont affect much, but keep it at 800.

//========================================
private constant real DAMAGE_BASE = 20.
private constant real DAMAGE_LVL  = 10.
private constant real STR_BASE    = 2.
private constant real STR_LVL     = 0.25
private constant real INITIAL_AOE = 200.
private constant real AOE_PER_LVL = 0.

private constant attacktype ATTACK_TYPE = ATTACK_TYPE_HERO
private constant damagetype DAMAGE_TYPE = DAMAGE_TYPE_NORMAL

//========================================
// don't touch anything bellow:

private constant real MS = MOVESPEED * INTERVAL
endglobals

// Math functions:

globals
private constant real RADIANS = 0.0174

private real MaxX
private real MaxY
private real MinX
private real MinY
endglobals

private function PolarX takes real x, real dist, real angle returns real
return x + (dist * Cos(angle * RADIANS))
endfunction

private function PolarY takes real y, real dist, real angle returns real
return y + (dist * Sin(angle * RADIANS))
endfunction

private function GetParabolaZ takes real x, real d, real h returns real
return 4 * h * x * (d - x) / (d * d)
endfunction

private function distance takes real x1, real y1, real x2, real y2 returns real
local real dx = x2 - x1
local real dy = y2 - y1
return SquareRoot(dx * dx + dy * dy)
endfunction

private function AngleBetween takes real x1, real y1, real x2, real y2 returns real
return Rad2Deg(Atan2(y2 - y1, x2 - x1))
endfunction

private function SafeX takes real x returns real
if x < MaxX then
return x
else
return MaxX
endif

if x > MinX then
return x
else
return MinX
endif
endfunction

private function SafeY takes real y returns real
if y < MaxY then
return y
else
return MaxY
endif

if y > MinY then
return y
else
return MinY
endif
endfunction

//=========================================================

private function AOE takes integer level returns real
return INITIAL_AOE + ((level - 1) * AOE_PER_LVL)
endfunction

private function DAMAGE takes unit u, integer level returns real
return (DAMAGE_BASE + DAMAGE_LVL * (level - 1)) + ((STR_BASE + STR_LVL * (level - 1)) * GetHeroStr(u, true))
endfunction

private struct data
unit caster
real damage
real x
real d
real cos
real sin
integer level
timer t

static method create takes unit whichUnit, real tx, real ty returns data
local data d = data.allocate()

local real ux = GetUnitX(whichUnit)
local real uy = GetUnitY(whichUnit)
local real angle = GetUnitFacing(whichUnit)

set d.caster = whichUnit

set d.x = MS
set d.d = distance(ux, uy, tx, ty)

set d.cos = PolarX(0., MS, angle)
set d.sin = PolarY(0., MS, angle)

set d.level = GetUnitAbilityLevel(d.caster, SPELL_ID)
set d.damage = DAMAGE(d.caster, GetUnitAbilityLevel(d.caster, SPELL_ID))

set d.t = NewTimer()

call UnitRemoveAbility(d.caster, CROW_FORM)

call SetUnitInvulnerable(d.caster, INVULNERABLE)

if d.d < 100. then
set d.d = 100.
endif

call SetUnitAnimation(d.caster, "attack slam")
call SetUnitTimeScale(d.caster, 0.4)

return d
endmethod

method destroy takes nothing returns nothing
call ReleaseTimer(.t)
endmethod
endstruct

globals
private group G = CreateGroup()
private player P
private data D
endglobals

//=======================================================

private function filterFunc takes nothing returns boolean
local unit picked = GetFilterUnit()

if IsUnitEnemy(picked, P) and UnitAlive(picked) then
call UnitDamageTargetEx(D.caster, picked, D.damage, true, false, ATTACK_TYPE, DAMAGE_TYPE, WEAPON_TYPE_WHOKNOWS)
endif

set picked = null

return false
endfunction

//=======================================================

private function callback takes nothing returns nothing
local data d = GetTimerData(GetExpiredTimer())

local real xc = GetUnitX(d.caster)
local real yc = GetUnitY(d.caster)
local real angle = GetUnitFacing(d.caster)

if d.x <= d.d then

if d.x == MS then
call PauseUnit(d.caster, true)
endif

call SetUnitX(d.caster, SafeX(xc + d.cos))
call SetUnitY(d.caster, SafeY(yc + d.sin))

call SetUnitFlyHeight(d.caster, GetParabolaZ(d.x, d.d, MAX_HEIGHT), JUMP_SPEED)

set d.x = d.x + MS
else
if GetUnitAbilityLevel(d.caster, 'BSTN') == 0 and GetUnitAbilityLevel(d.caster, 'BPSE') == 0 then

set D = d
set P = GetOwningPlayer(d.caster)

call GroupEnumUnitsInRange(G, xc, yc, AOE(d.level), Filter(function filterFunc))

call PauseTimer(d.t)
else
call d.destroy()
endif

call PauseUnit(d.caster, false)
call SetUnitTimeScale(d.caster, 1.)
call QueueUnitAnimation(d.caster, "stand")
call SetUnitInvulnerable(d.caster, false)

call SetUnitFlyHeight(d.caster, 0., JUMP_SPEED)
endif
endfunction

private function actions takes nothing returns nothing
local unit caster = GetTriggerUnit()
local real angle = GetUnitFacing(caster)
local real ux = GetUnitX(caster)
local real uy = GetUnitX(caster)
local real tx    = ux + 600 * Cos(angle)
local real ty    = uy + 600 * Sin(angle)
local data d = data.create(caster, tx, ty)

call SetTimerData(d.t, d)

call TimerStart(d.t, INTERVAL, true, function callback)

set caster = null
endfunction

//=======================================================

private function conditions takes nothing returns boolean
return GetSpellAbilityId() == SPELL_ID
endfunction

private function init takes nothing returns nothing
local trigger t = CreateTrigger()
local integer i = 0

loop
call TriggerRegisterPlayerUnitEvent(t, Player(i), EVENT_PLAYER_UNIT_SPELL_EFFECT, null)
set i = i + 1
exitwhen i == MAX_PLAYERS - 1
endloop

set MaxX = GetRectMaxX(bj_mapInitialPlayableArea)-50.
set MaxY = GetRectMaxY(bj_mapInitialPlayableArea)-50.

set MinX = GetRectMinX(bj_mapInitialPlayableArea)+50.
set MinY = GetRectMinY(bj_mapInitialPlayableArea)+50.

set t = null
endfunction

endscope``````

14. ### SevionThe DIY Ninja

Ratings:
+423 / 0 / -0
Are you sure `GetUnitFacing` returns the angle in radians? I'm 99.99% sure that it returns it in degrees.

If that's the case, in your actions, do `local real angle = GetUnitFacing(caster) * bj_DEGTORAD`.

I haven't done vJASS in a while, but IIRC that is what you have to do with Cos/Sin. They take radians and GetUnitFacing returns degrees.

15. ### tommerbobMinecraft. :D

Ratings:
+110 / 0 / -0
Well the caster always moved in the correct direction, but always too far.

I changed the angle to:

JASS:
``local real angle = GetUnitFacing(caster) * bj_DEGTORAD``

and the caster now never moves in the correct direction, always to the right, the distance is still way too far.

I simplified the above code to cut down on space to make it easier to read through. Below should be just the necessary math functions/data that would screw this up:

JASS:
``````scope Leap initializer init

// Requirements:
//      NewGen
//      Timer Utils (TU)
//      Math Functions

// configurables:

globals

private constant real INTERVAL = 0.03125
//========================================
private constant real MOVESPEED  = 800.
private constant real MAX_HEIGHT = 250.
private constant real JUMP_SPEED = 800. // wont affect much, but keep it at 800.

// don't touch anything bellow:

private constant real MS = MOVESPEED * INTERVAL
endglobals

// Math functions:

globals
private constant real RADIANS = 0.0174

private real MaxX
private real MaxY
private real MinX
private real MinY
endglobals

private function PolarX takes real x, real dist, real angle returns real
return x + (dist * Cos(angle * RADIANS))
endfunction

private function PolarY takes real y, real dist, real angle returns real
return y + (dist * Sin(angle * RADIANS))
endfunction

private function GetParabolaZ takes real x, real d, real h returns real
return 4 * h * x * (d - x) / (d * d)
endfunction

private function distance takes real x1, real y1, real x2, real y2 returns real
local real dx = x2 - x1
local real dy = y2 - y1
return SquareRoot(dx * dx + dy * dy)
endfunction

private function AngleBetween takes real x1, real y1, real x2, real y2 returns real
return Rad2Deg(Atan2(y2 - y1, x2 - x1))
endfunction

private function SafeX takes real x returns real
if x < MaxX then
return x
else
return MaxX
endif

if x > MinX then
return x
else
return MinX
endif
endfunction

private function SafeY takes real y returns real
if y < MaxY then
return y
else
return MaxY
endif

if y > MinY then
return y
else
return MinY
endif
endfunction

private struct data
unit caster
real damage
real x
real d
real cos
real sin
integer level
timer t

static method create takes unit whichUnit, real tx, real ty returns data
local data d = data.allocate()

local real ux = GetUnitX(whichUnit)
local real uy = GetUnitY(whichUnit)
local real angle = GetUnitFacing(whichUnit)

set d.caster = whichUnit

set d.x = MS
set d.d = distance(ux, uy, tx, ty)

set d.cos = PolarX(0., MS, angle)
set d.sin = PolarY(0., MS, angle)

set d.t = NewTimer()

call UnitRemoveAbility(d.caster, CROW_FORM)

if d.d < 100. then
set d.d = 100.
endif

return d
endmethod

method destroy takes nothing returns nothing
call ReleaseTimer(.t)
endmethod
endstruct

globals
private group G = CreateGroup()
private player P
private data D
endglobals

private function callback takes nothing returns nothing
local data d = GetTimerData(GetExpiredTimer())

local real xc = GetUnitX(d.caster)
local real yc = GetUnitY(d.caster)
local real angle = GetUnitFacing(d.caster)

if d.x <= d.d then

if d.x == MS then
call PauseUnit(d.caster, true)
endif

call SetUnitX(d.caster, SafeX(xc + d.cos))
call SetUnitY(d.caster, SafeY(yc + d.sin))

call SetUnitFlyHeight(d.caster, GetParabolaZ(d.x, d.d, MAX_HEIGHT), JUMP_SPEED)

set d.x = d.x + MS
else
if GetUnitAbilityLevel(d.caster, 'BSTN') == 0 and GetUnitAbilityLevel(d.caster, 'BPSE') == 0 then

set D = d

call PauseTimer(d.t)
else
call d.destroy()
endif

call SetUnitFlyHeight(d.caster, 0., JUMP_SPEED)
endif
endfunction

private function actions takes nothing returns nothing
local unit caster = GetTriggerUnit()
local real angle = GetUnitFacing(caster)
local real ux = GetUnitX(caster)
local real uy = GetUnitX(caster)
local real tx    = ux + 600. * Cos(angle)
local real ty    = uy + 600. * Sin(angle)
local data d = data.create(caster, tx, ty)

call SetTimerData(d.t, d)
call TimerStart(d.t, INTERVAL, true, function callback)

set caster = null
endfunction

function init takes nothing returns nothing
set MaxX = GetRectMaxX(bj_mapInitialPlayableArea)-50.
set MaxY = GetRectMaxY(bj_mapInitialPlayableArea)-50.

set MinX = GetRectMinX(bj_mapInitialPlayableArea)+50.
set MinY = GetRectMinY(bj_mapInitialPlayableArea)+50.

endfunction

endscope``````

16. ### NoobImbaProYou can change this now in User CP.

Ratings:
+60 / 0 / -0
why don't you use my system?? AUMS

and see how I am doing all the stuff??

PS: You confuse radians with degrees, witch one will you use?? I prefer radians as emjlr3 does

17. ### tommerbobMinecraft. :D

Ratings:
+110 / 0 / -0
Well, no offense, but I won't use a system that 1) isn't approved or 2) isn't generally accepted by the community.

I'll look through it.

That just went through one ear and out the other.

18. ### Dirac22710180

Ratings:
+147 / 0 / -0
IMO leaps are quite easy, you can write one yourself if you have basic sliding knowledge and AceHart's jump parabola or even this crazy equation i have here

y = [(2a-4c)/(b^2)]*x^2 + [(4c-3a)/b]*x + a

a = Initial height of the proyectile
c = Max height of the proyectile
/////////////////////////////////////////////////////////
x = distance traveled
y = returns the height of the proyectile
b = input the distance between the start point and the end point here

19. ### NoobImbaProYou can change this now in User CP.

Ratings:
+60 / 0 / -0
I haven't meant to use it, just see how it does the whole thing.
Because it isn't approved does not mean that it is a crappy one.
It is the half system, that's why it isn't approved. When I mean the half I mean like Timer32 without T32x module

20. ### NoobImbaProYou can change this now in User CP.

Ratings:
+60 / 0 / -0
@Dirac

yeah it may seem as a crazy equation, but a simpler one may be better, like my equation:
y=ax-bx[SUP]2[/SUP]+c

with b = 4*height/distance[SUP]2[/SUP]
a = b*distance

and it's a normal physics parabola.

Where height is the max height of the projectile, where distance the distance the projectile/unit will do, x is the current distance from start point and y the requested height at that point. Oh and c the initial height. Is same with aceheart's but with less arithmetics