some math help^^

[darkbeer]

Hey,
I just wanted to make my own jump system, so i tried to code it, but unfortunately i don't get how to calculate the height of a unit while its jumping.

Heres the code I use:

library JumpSystem
    
    globals
        integer JumpTotal = 0
        timer JumpTimer = CreateTimer()
        JumpStruct array JumpAr
    endglobals
    
    struct JumpStruct
        unit u
        real dist
        real x
        real speed
        real height
        real angle
        location target
        boolean destroypls
    endstruct        
    
    constant function GetJumpPeriode takes nothing returns real
        return 0.03
    endfunction
    
    function EndJump takes unit u returns nothing
        call SetUnitPathing(u, true)
        call UnitRemoveAbility(u, 'Amrf')
    endfunction
    
    function JumpLoop takes nothing returns nothing
        local JumpStruct dat = JumpStruct.create()
        local integer i = 0
        local location loc
        local location Offset
        local real height
        local real PosZ
        
        call DisplayTextToForce(GetPlayersAll(), "aa")
        
        loop
            exitwhen i == JumpTotal
            set dat = JumpAr<i>
            if dat.destroypls == true then
                call dat.destroy()
                set JumpAr<i> = JumpAr[JumpTotal - 1]
                set JumpTotal = JumpTotal - 1
                set i = i - 1
            else
                set loc = GetUnitLoc(dat.u)
                set Offset = PolarProjectionBJ(loc, dat.speed, dat.angle)
                call SetUnitPositionLoc(dat.u, Offset)
                set PosZ = GetLocationZ(Offset)
                if dat.x &lt;= dat.dist/2 then
                set height =( SquareRoot( dat.height * dat.height - (dat.dist/2 - dat.x) * (dat.dist/2 - dat.x))) //these are the things that give me problems^^
                else
                set height = ( SquareRoot( dat.height * dat.height - (dat.x - dat.dist/2) * (dat.x - dat.dist/2))) //these are the things that give me problems^^
                endif
                call SetUnitFlyHeight(dat.u, height, 0 )
                set dat.x = dat.x + dat.speed
                if dat.x &gt;= dat.dist then
                    set dat.destroypls = true
                    call EndJump(dat.u)
                endif
                call RemoveLocation(Offset)
                set Offset = null
            endif
            set i = i + 1
        endloop
        
        if JumpTotal == 0 then
            call PauseTimer(JumpTimer)
        endif
        
    endfunction
    
    function StartJump takes unit u, real height, real time, location target returns nothing
        local location loc = GetUnitLoc(u)
        local real dist = DistanceBetweenPoints(loc, target)
        local JumpStruct dat = JumpStruct.create()
        
        set dat.target = target
        set dat.u = u
        set dat.dist = dist
        set dat.x = 0
        set dat.speed = dist / time * GetJumpPeriode()
        set dat.height = height
        set dat.destroypls = false
        set dat.angle = AngleBetweenPoints(loc, target)
        
        set JumpAr[JumpTotal] = dat
        
        call SetUnitPathing(u, false)
        call UnitAddAbility(u, &#039;Amrf&#039;)
        
        if JumpTotal == 0 then
            call TimerStart(JumpTimer, GetJumpPeriode(), true, function JumpLoop)
        endif
        
        set JumpTotal = JumpTotal + 1
        
        call RemoveLocation(loc)
        set loc = null
    endfunction
endlibrary

function Trig_Jump_System_Actions takes nothing returns nothing
endfunction

//===========================================================================
function InitTrig_Jump_System takes nothing returns nothing
    local trigger t = CreateTrigger(  )
    call TriggerAddAction( gg_trg_Jump_System, function Trig_Jump_System_Actions )
    set t = null
endfunction
</i></i>

Hope someone got any ideas about it, ill also try to make it dynamic so it the height will adept to the ground level when jumping over a canyon or sth. like that.

thankfull for any suggestions

 

[TheDamien]

Motion with constant acceleration:

set y = v0*t + 0.5*a*t*t + y0

y is the position of the body.
y0 is the body's initial position.
t is the time passed.
a is the acceleration (gravity, in this case).
v is the current velocity (not used yet).

We can assume t is always 1 if you use y instead of y0 as initial position and v instead of v0. You get, roughly:

set y = v + 0.5*a + y
set v = v + a

 

[darkbeer]

Thx,
kind of stupid to make it look a circle instead of using physik^^, so i tried to make itusing the constant acceleration, i thought that is the formula:

s = v(0) * t - 0.5 * a * t ^ 2

hm v(0) should be SquareRoot(2 * a * s) or am i wrong?

so i made a new code using that formula, but it doesnt work properly since the unit flys higher and higher instead of falling down -.-

heres new code:

library JumpSystem
    
    globals
        real gravity = 10
        integer JumpTotal = 0
        timer JumpTimer = CreateTimer()
        JumpStruct array JumpAr
    endglobals
    
    struct JumpStruct
        real totaltime
        real time
        unit u
        real dist
        real x
        real speed
        real height
        real angle
        location target
        boolean destroypls
    endstruct        
    
    constant function GetJumpPeriode takes nothing returns real
        return 0.03
    endfunction
    
    function EndJump takes unit u returns nothing
        call SetUnitPathing(u, true)
        call UnitRemoveAbility(u, 'Amrf')
    endfunction
    
    function JumpLoop takes nothing returns nothing
        local JumpStruct dat = JumpStruct.create()
        local integer i = 0
        local location loc
        local location Offset
        local real height
        local real PosZ
        local real v0
        
        call DisplayTextToForce(GetPlayersAll(), "aa")
        
        loop
            exitwhen i == JumpTotal
            set dat = JumpAr<i>
            if dat.destroypls == true then
                call dat.destroy()
                set JumpAr<i> = JumpAr[JumpTotal - 1]
                set JumpTotal = JumpTotal - 1
                set i = i - 1
            else
                set loc = GetUnitLoc(dat.u)
                set dat.time = dat.time + GetJumpPeriode()
                set Offset = PolarProjectionBJ(loc, dat.speed, dat.angle)
                call SetUnitPositionLoc(dat.u, Offset)
                set PosZ = GetLocationZ(Offset)
                set v0 = SquareRoot(2 * gravity * dat.height) // &lt;-- somewhere here is the problem
                set height = v0 * dat.time - 0.5 * gravity * dat.time // &lt;-- somewhere here is the problem
                call BJDebugMsg(R2S(v0 * dat.time))
                call BJDebugMsg(R2S(0.5 * gravity * dat.time * dat.time))
                call SetUnitFlyHeight(dat.u, height, 0 )
                set dat.x = dat.x + dat.speed
                if dat.x &gt;= dat.dist then
                    set dat.destroypls = true
                    call EndJump(dat.u)
                endif
                call RemoveLocation(Offset)
                set Offset = null
            endif
            set i = i + 1
        endloop
        
        if JumpTotal == 0 then
            call PauseTimer(JumpTimer)
        endif
        
    endfunction
    
    function StartJump takes unit u, real height, real time, location target returns nothing
        local location loc = GetUnitLoc(u)
        local real dist = DistanceBetweenPoints(loc, target)
        local JumpStruct dat = JumpStruct.create()
        
        set dat.target = target
        set dat.u = u
        set dat.dist = dist
        set dat.x = 0
        set dat.speed = dist / time * GetJumpPeriode()
        set dat.height = height
        set dat.destroypls = false
        set dat.angle = AngleBetweenPoints(loc, target)
        set dat.time = 0
        set dat.totaltime = time
        
        set JumpAr[JumpTotal] = dat
        
        call SetUnitPathing(u, false)
        call UnitAddAbility(u, &#039;Amrf&#039;)
        
        if JumpTotal == 0 then
            call TimerStart(JumpTimer, GetJumpPeriode(), true, function JumpLoop)
        endif
        
        set JumpTotal = JumpTotal + 1
        
        call RemoveLocation(loc)
        set loc = null
    endfunction
endlibrary

function Trig_Jump_System_Actions takes nothing returns nothing
endfunction

//===========================================================================
function InitTrig_Jump_System takes nothing returns nothing
    local trigger t = CreateTrigger(  )
    call TriggerAddAction( gg_trg_Jump_System, function Trig_Jump_System_Actions )
    set t = null
endfunction

</i></i>

and well, i dont know what to do with a, in real life its the gravity, so i tryed to set it to a constant as well^^

 

[TheDamien]

You don't need to be able to calculate v0, as you will not be using that equation.

Here is the basic calculation for height (which is y) and v (which is velocity), per firing of the timer. You would set v to the force of the jump in your "StartJump" function.

set y = v + 0.5*a + y
set v = v + a

I have made a demo map for you to look at, it is attached to this post.

 

[darkbeer]

First of all thanks for your effort,

unfortunately your formula isnt the thing i was searching for, i want to make my jump spell depending on time and distance, so i can change them^^

I already did the normal movement, i just need to calculate the current height depending on the time.

therefore i thought ill isolate g in this formula:

g = gravity acceleration
v(0) = z start speed
t = total time
h = jump height

2h = v(0) * t - 0.5 * g * t ^ 2 // t and h are given, t is the total time

so it is: g = (2 * v(0) * t - 4 * h)/ t ^2

now i just need to get v(0)

but i dont get how yet^^, heres the a second formula for v:

v = v(0) - g*t, // now at the highest point, v should be zero and t = half the total time required for the jump.

So v(0) should be g * t / 2, as Damien said.

So v(0) = h / t, and g = -2 * h / t ^2

But that doesnt work, can anyone tell me where the mistake is?

 

[TheDamien]

t = duration of jump
a = acceleration (gravity)
dist = distance of jump
deg = direction of jump in degrees

The initial z velocity of the jump is t*(a/-2) (this does not take into account height variation).

The x velocity during the jump is SinBJ(deg)*dist/t

The y velocity during the jump is CosBJ(deg)*dist/t

 

[darkbeer]

Hm, if this keeps on i will go crazy -.-,

i just can't find my mistake: [Edit: Found it ]

here are my formulas:

Given:
H is the maximum height the unit reaches during its jump.
T is the total time required for the jump

Formulas:
h(t) = v(0) * t - 0.5 * g * t ^ 2
v = v(0) - g * t

h(t) will be z of unit
t is the current time of the jump

Required:
v(0) initial speed
g: gravity in real life

h(t) = v(0) * t - 0.5 * g * t ^ 2
v = v(0) - g * t

Now: the highest point should be when t = T / 2
and v there must be 0

So it is v(0) = g * T/2.

So we get: h(t) = g * T/2 * t - g/2 * t ^ 2

okay the highest point should be at half of the total time:

H = g * T/ 2 * T/ 2 - g / 2 * T/2 * T/2

-> H = g * T ^ 2 / 4 - g * T ^ 2 / 8

-> H = g * T ^ 2 / 8

-> g = 8 * H / T ^ 2

-> v(0) = 4 * H / T

-.- Calculation error from me, works now on same ground level

Now i want to implent the different terrain heights, so units can jump up cliffs and over canyons.

any suggestions how to make it look real?

 

[TheDamien]

You don't need to know the height halfway through the jump. The demo map I uploaded has jumping over different terrain heights and a much simpler implementation.

 

[darkbeer]

Allright, thx a lot damien

Allthought i used my own formula in the end, i know yours is much simpler and probably better^^
but i just wanted to do it in my own way, using physik from school xD

heres my temporary code: (If anyone is interested in it^^) // implents jumping over different terrain heights

library JumpSystem
    globals
        private integer JumpTotal = 0
        private timer JumpTimer = CreateTimer()
        private JumpStruct array JumpAr
    endglobals
    
    struct JumpStruct
        real totaltime
        real time
        unit u
        real speed
        real height
        real vz
        real vecz
        real g
        real z
        real angle
        boolean destroypls
    endstruct        
    
    private constant function GetJumpPeriode takes nothing returns real
        return 0.03
    endfunction
    
    private function EndJump takes unit u returns nothing
        call SetUnitPathing(u, true)
        call SetUnitFlyHeight(u, 0, 0)
    endfunction
    
    function JumpLoop takes nothing returns nothing
        local JumpStruct dat = JumpStruct.create()
        local integer i = 0
        local location loc
        local location Offset
        local real height
        local real PosZ
        
        loop
            exitwhen i == JumpTotal
            set dat = JumpAr<i>
            if dat.destroypls == true then
                call dat.destroy()
                set JumpAr<i> = JumpAr[JumpTotal - 1]
                set JumpTotal = JumpTotal - 1
                set i = i - 1
            else
                set loc = GetUnitLoc(dat.u)
                set dat.time = dat.time + GetJumpPeriode()
                set Offset = PolarProjectionBJ(loc, dat.speed, dat.angle)
                call SetUnitPositionLoc(dat.u, Offset)
                set PosZ = GetLocationZ(Offset)
                set height = dat.z + dat.vz * dat.time - 0.5 * dat.g * dat.time * dat.time - PosZ - dat.vecz * dat.time * dat.time
                call SetUnitFlyHeight(dat.u, height, 0 )
                if dat.time &gt;= dat.totaltime then
                    set dat.destroypls = true
                    call EndJump(dat.u)
                endif
                call RemoveLocation(Offset)
                set Offset = null
            endif
            set i = i + 1
        endloop
        
        if JumpTotal == 0 then
            call PauseTimer(JumpTimer)
        endif
        
    endfunction
    
    function StartJump takes unit u, real height, real time, location target returns nothing
        local location loc = GetUnitLoc(u)
        local real dist = DistanceBetweenPoints(loc, target)
        local JumpStruct dat = JumpStruct.create()
        local real vz
        
        set dat.u = u
        set dat.z = GetLocationZ(loc)
        set dat.vecz = (dat.z - GetLocationZ(target)) / time / time
        set dat.vz = 4 * height / time
        set dat.g = 8 * height / time / time
        set dat.speed = dist / time * GetJumpPeriode()
        set dat.height = height
        set dat.destroypls = false
        set dat.angle = AngleBetweenPoints(loc, target)
        set dat.time = 0
        set dat.totaltime = time
        
        set JumpAr[JumpTotal] = dat
        
        call SetUnitPathing(u, false)
        call UnitAddAbility(u, &#039;Amrf&#039;)
        call SetUnitFlyHeight(u, 0.01, 0)
        call UnitRemoveAbility(u, &#039;Amrf&#039;)
        
        if JumpTotal == 0 then
            call TimerStart(JumpTimer, GetJumpPeriode(), true, function JumpLoop)
        endif
        
        set JumpTotal = JumpTotal + 1
        
        call RemoveLocation(loc)
        set loc = null
    endfunction
endlibrary

//===========================================================================
function InitTrig_Jump_System takes nothing returns nothing
endfunction

</i></i>

guess i will remove the locations as far as possible and make a few little changes, but it works^^

THX @ damien