Math Questions

tommerbob · Aug 15, 2011

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.

Solmyr · Aug 15, 2011

[ljass]projectile.create(ux, uy, 50.00, GetRandomReal(0, 2 * bj_PI)) // You may want to pre-calculate 2 * bj_PI though.[/ljass]

Dirac · Aug 15, 2011

[ljass]Atan2(a,b)[/ljass] takes radians, not angles.
[ljass]bj_PI/2[/ljass]=90 degrees
[ljass]bj_PI[/ljass]=180 degrees

tommerbob · Aug 15, 2011

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)

Dirac · Aug 15, 2011

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?

tommerbob · Aug 16, 2011

perfecto. thanks

emjlr3 · Aug 19, 2011

*6.28318=Pi*2

NoobImbaPro · Aug 19, 2011

And Pi is equal to:

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788659361533818279682303019520353018529689957736225994138912497217752834791315155748572424541506959...

Wikipedia FTW

Sevion · Aug 19, 2011

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.

NoobImbaPro · Aug 19, 2011

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

Nestharus · Aug 19, 2011

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).

tommerbob · Aug 19, 2011

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

I don't have any questions at the moment, but don't worry, I will in the future.

tommerbob · Aug 19, 2011

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 = &#039;A01C&#039; // raw code of Leap spell
    private constant integer CROW_FORM = &#039;Amrf&#039; // 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&#039;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 &lt; MaxX then
        return x
    else
        return MaxX
    endif
    
    if x &gt; MinX then
        return x
    else
        return MinX
    endif
endfunction

private function SafeY takes real y returns real
    if y &lt; MaxY then
        return y
    else
        return MaxY
    endif
    
    if y &gt; 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 UnitAddAbility(d.caster, CROW_FORM)
        call UnitRemoveAbility(d.caster, CROW_FORM)
        
        call SetUnitInvulnerable(d.caster, INVULNERABLE)
        
        if d.d &lt; 100. then
            set d.d = 100.
        endif

        call SetUnitAnimation(d.caster, &quot;attack slam&quot;)
        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 &lt;= 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, &#039;BSTN&#039;) == 0 and GetUnitAbilityLevel(d.caster, &#039;BPSE&#039;) == 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, &quot;stand&quot;)
        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
    call TriggerAddCondition(t, Condition(function conditions))
    call TriggerAddAction(t, function actions)
    
    
    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

Sevion · Aug 20, 2011

Are you sure [ljass]GetUnitFacing[/ljass] 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 [ljass]local real angle = GetUnitFacing(caster) * bj_DEGTORAD[/ljass].

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.

tommerbob · Aug 20, 2011

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&#039;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 &lt; MaxX then
        return x
    else
        return MaxX
    endif
    
    if x &gt; MinX then
        return x
    else
        return MinX
    endif
endfunction

private function SafeY takes real y returns real
    if y &lt; MaxY then
        return y
    else
        return MaxY
    endif
    
    if y &gt; 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 UnitAddAbility(d.caster, CROW_FORM)
        call UnitRemoveAbility(d.caster, CROW_FORM)
        
        if d.d &lt; 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 &lt;= 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, &#039;BSTN&#039;) == 0 and GetUnitAbilityLevel(d.caster, &#039;BPSE&#039;) == 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

NoobImbaPro · Aug 20, 2011

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

tommerbob · Aug 20, 2011

NoobImbaPro said:
why don't you use my system?? AUMS

Well, no offense, but I won't use a system that 1) isn't approved or 2) isn't generally accepted by the community.

NoobImbaPro said:
and see how I am doing all the stuff??

I'll look through it.

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

That just went through one ear and out the other.

Dirac · Aug 20, 2011

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

NoobImbaPro · Aug 20, 2011

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

NoobImbaPro · Aug 23, 2011

@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

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