[JASS] Mathathics, spherical equation

[Dynasti]

[RAINBOW]Sphere Information[/RAINBOW]

 

[Element of Water]

I don't understand how that page helped at all, it didn't explain how to use the angles, just their posh names...

Isn't it
X = X+Speed*Cos(Phi)*Cos(Theta)
Y = Y+Speed*Cos(Phi)*Sin(Theta)
Z = Z+Speed*Cos(Phi)
?

Just using what I know about trigonometry, I might be wrong. But I'm sure to get the Z you need to use Phi, not Theta.

 

[Dynasti]

I'm not really sure.

I need to know how to use this equation for making spherical shield spell in wc3 ( or spherical motions )

 

[Element of Water]

Spherical shield spell? As in, a projectile comes within a spherical radius of you and it bounces off?

 

[Mechanical Man]

Isn't it
X = X+Speed*Cos(Phi)*Cos(Theta)
Y = Y+Speed*Cos(Phi)*Sin(Theta)
Z = Z+Speed*Cos(Phi)
?

No, because Z coordinate has a different trigonometrical function of Theta than X and Y (Phi is used for xy plane)

 

[Element of Water]

Please explain. I might learn something here.

 

[Mechanical Man]

Dynasti, but you tried if it works right?

 

[Dynasti]

I haven't tried yet, because not at a computer with wc3 atm.

Going to try it later

 

[Mechanical Man]

You don't need specifically wc3, you could also try it on a program with let's you program with visual outputs.


Anyway, I'm more used this way:
x = r*cos(φ)*cos(θ)
y = r*sin(φ)*cos(θ)
z = sin(θ)
where φ ranges from 0 to 2*π
and θ ranges from -π/2 to π/2

Thats because if you are only in xy plane, the θ=0 and z=0, which makes perfect sense as cos(θ)=1 and sin(θ)=0 thus you can ignore the functions with parameter θ.

http://en.wikipedia.org/wiki/Spherical_coordinates

 

[Dynasti]

Here is an example

function GetSphereLoc takes real x, real y, real z, real r, real xyAngle, real zAngle returns location
    local location loc = Location( x + r * Cos(zAngle) * Sin(xyAngle), y + r * Sin(zAngle) * Sin(xyAngle) )
    call SetLocationZ( loc, z + r * Cos(xyAngle) )

    return loc
endfunction

 

[Element of Water]

That's exactly what I said, except I got theta and phi muddled up. I thought theta was for x/y plane...

 

[Dynasti]

Well, I will test this tomorrow 12:00 ( GMT + 1 )

 

[Element of Water]

Lol, exactly noon GMT. You are precise.

 

[Dynasti]

Ok, I have tested it, does not work :/

Code

library SphereMotion

    globals
        private constant real FPS = 40.00
        
        private constant integer FlyId = 'Amrf'
        private constant integer DumId = 'n000'
    endglobals
    
    private struct Data
        unit Object
        
        real x0
        real y0
        real z0
        
        real zA = 0.0
        real xyA = 0.0
        
        real zV
        real xyV
        
        real r
        
        effect Art
        
        static integer array Sphere
        static integer TotalSpheres = 0
        
        static timer Timer = null
        
        static method Loop takes nothing returns nothing
            local Data dat
            local integer i = 0
            
            loop
                exitwhen i >= Data.TotalSpheres
                set dat = Data.Sphere[i]
                
                if GetWidgetLife(dat.Object) > .405 then
                    call SetUnitX(dat.Object, dat.x0 + (dat.r * Sin(dat.xyA) * Cos(dat.zA)))
                    call SetUnitY(dat.Object, dat.x0 + (dat.r * Sin(dat.xyA) * Sin(dat.zA)))
                    call SetUnitFlyHeight(dat.Object, dat.z0 + (dat.r * Cos(dat.xyA)), 0.0)
                    
                    set dat.zA = (dat.zA + dat.zV) * bj_RADTODEG
                    set dat.xyA = (dat.xyA + dat.xyV) * bj_RADTODEG
                    
                    if dat.zA > 360 then
                        set dat.zA = 0.0
                    elseif dat.zA < -360 then
                        set dat.zA = 0.0
                    else
                        set dat.zA = dat.zA * bj_DEGTORAD
                    endif
                    
                    if dat.xyA > 360 then
                        set dat.xyA = 0.0
                    elseif dat.xyA < -360 then
                        set dat.xyA = 0.0
                    else
                        set dat.xyA = dat.xyA * bj_DEGTORAD
                    endif
                else
                    call DestroyEffect(dat.Art)
                    set dat.Object = null
                    set dat.Art    = null
                    
                    call dat.destroy()
                    
                    set Data.TotalSpheres = Data.TotalSpheres - 1
                    set Data.Sphere[i] = dat.Sphere[Data.TotalSpheres]
                    
                    set i = i - 1
                endif
                
                set i = i + 1
            endloop
            
            if Data.TotalSpheres == 0 then
                call PauseTimer(Data.Timer)
            endif
        endmethod
        
        static method Start takes real x0, real y0, real z0, real r, real zA, real xyA, real zV, real xyV, string Art, real Time returns unit
            local Data dat = Data.allocate()
            
            set dat.x0 = x0
            set dat.y0 = y0
            set dat.z0 = z0 + r
            
            set dat.zA  = zA * bj_DEGTORAD
            set dat.xyA = xyA * bj_DEGTORAD
            set dat.zV  = (zV / FPS) * bj_DEGTORAD
            set dat.xyV = (xyV / FPS) * bj_DEGTORAD
            
            set dat.Object = CreateUnit(Player(PLAYER_NEUTRAL_AGGRESSIVE), DumId, x0, y0, 0)
            call UnitAddAbility(dat.Object, FlyId)
            call UnitRemoveAbility(dat.Object, FlyId)
            call SetUnitFlyHeight(dat.Object, z0, 0)
            
            set dat.Art = AddSpecialEffectTarget(Art, dat.Object, "origin")
            call SetUnitAnimationByIndex(dat.Object, 90)
            
            if Time > 0.0 then
                call UnitApplyTimedLife(dat.Object, 'BTLF', Time)
            endif
            
            if Data.TotalSpheres == 0 then
                call TimerStart(Data.Timer, 1.0/FPS, true, function Data.Loop)
            endif
            
            set Data.Sphere[Data.TotalSpheres] = dat
            set Data.TotalSpheres = Data.TotalSpheres + 1
            
            return dat.Object
        endmethod
    endstruct
    
    function CreateSphere takes real x0, real y0, real z0, real r, real zA, real xyA, real zV, real xyV, string Art, real Time, integer Parts, boolean Return returns group
        local group g = CreateGroup()
        local integer i = 0
        local real a = 360/Parts
        
        loop
            exitwhen i > Parts
            
            call GroupAddUnit(g, Data.Start(x0, y0, z0, r, zA, xyA + (a * i), zV, xyV, Art, Time))
            
            set i = i + 1
        endloop
        
        if Return then
            return g
        else
            call DestroyGroup(g)
            set g = null
            return g
        endif
    endfunction

endlibrary

 

[Mechanical Man]

Does it at least work in 2 dimensions? (θ is 0)

 

[Dynasti]

Does it at least work in 2 dimensions? (θ is 0)

no, the whole thing is somehow "fucked up". Just try the test map and hit esc to see, it just stops after some time

 

[Mechanical Man]

Then should be a problem somewhere else. I'm not a jass user, so could you please somehow highlight the movement code, using comments for example, so I can orientate better?

 

[Dynasti]

Mkay

Here is the movement

                    call SetUnitX(dat.Object, dat.x0 + (dat.r * Sin(dat.xyA) * Cos(dat.zA)))
                    call SetUnitY(dat.Object, dat.x0 + (dat.r * Sin(dat.xyA) * Sin(dat.zA)))
                    call SetUnitFlyHeight(dat.Object, dat.z0 + (dat.r * Cos(dat.xyA)), 0.0)

                    set dat.zA = (dat.zA + dat.zV) * bj_RADTODEG
                    set dat.xyA = (dat.xyA + dat.xyV) * bj_RADTODEG

                    if dat.zA > 360 then
                        set dat.zA = 0.0
                    elseif dat.zA < -360 then
                        set dat.zA = 0.0
                    else
                        set dat.zA = dat.zA * bj_DEGTORAD
                    endif

                    if dat.xyA > 360 then
                        set dat.xyA = 0.0
                    elseif dat.xyA < -360 then
                        set dat.xyA = 0.0
                    else
                        set dat.xyA = dat.xyA * bj_DEGTORAD
                    endif

 

[Mechanical Man]

Humm. Why are you constantly converting between radians and degrees? And I would swap sines and cosines for the xyA angle.

 

[Element of Water]

A tip about radians - 360 degrees equals 2pi radians. So instead of converting back and forth from radians and degrees, keep it all in radians and make those if blocks check if the angle is greater than 2*pi or smaller than -2*pi. Or for even higher efficiency, make a 2pi constant and use that.

 

[Dynasti]

Ok, updated it, but it still doesn't work :S

 

[Element of Water]

You don't create the timer

EDIT:
And there is a another problem, I made an init function which creates the timer and now my debug message displays, but the orbs go high into the air as soon as they are created and stay there...

EDIT:
Another problem: you use dat.x0 to set the unit's y position...

EDIT:
...yet ANOTHER problem - you never set dat.r...

EDIT:
And the trig is all screwed, but I can't really help you there... anyways this is my fixed version - it looks kinda cool, but it's not spherical. It's more American Football-Shaped.

 

[Dynasti]

Check out this beast

Just hit esc ingame

 

[Element of Water]

Ooh very nice. So the trig wasn't screwed? Weird. Anyways, yay, I fixed it for you .

 

[Dynasti]

Ok, fixed code abit, now it can support units :3

 

[Element of Water]

Nice, now what are you going to do with it? I'm intrigued now...

 

[Dynasti]

Nice, now what are you going to do with it? I'm intrigued now...

I think maybe making a user friendly spherical movement system, that you can use if you make a spell shield or something and you want a nice motion

 

[Element of Water]

OK cool. Now why should they use this which will lag if they use it a lot over custom models?

 

[Dynasti]

OK cool. Now why should they use this which will lag if they use it a lot over custom models?

Meh, does not lag, only if they spam 100 or more on one screen or sum.

Only lag that this code generates is sfx lag

 

[Element of Water]

I suppose... maybe you should make functions like angle cutoff point - so you can make like semi-spheres and stuff, like if you want a big dome on the ground... and I'd make an option so the missiles can damage units...

 

[Dynasti]

I suppose... maybe you should make functions like angle cutoff point - so you can make like semi-spheres and stuff, like if you want a big dome on the ground... and I'd make an option so the missiles can damage units...

i can do the dome, but the damage is up to the user.

It is easy, like pick every units in "yourspheregroup" and do damage every units in 50 range of picked unit

This would make more damage if there is more parts

 

[Element of Water]

But you will do the angle cutoff thing right?

 

[Dynasti]

But you will do the angle cutoff thing right?

I don't know how to do that :/

 

[Element of Water]

Lets say you have 2 cutoff points, 90 and 270. You would increase the angle by the velocity each interval, and if angle becomes greater than 270, multiply the velocity by -1, and if the angle becomes less than 90, multiply the velocity by -1. That way, you get a semi-circle motion, bouncing between those 2 angles.

 

[Dynasti]

Lets say you have 2 cutoff points, 90 and 270. You would increase the angle by the velocity each interval, and if angle becomes greater than 270, multiply the velocity by -1, and if the angle becomes less than 90, multiply the velocity by -1. That way, you get a semi-circle motion, bouncing between those 2 angles.

meh


Anyways, redid the system. It is now a Ellipsoid motion ( can be sphere ).
Where 'a' 'b' 'c' controls the size and shape of the ellipsoid.

if a = b = c you get a perfect sphere.

 

[Element of Water]

You should have it with a master radius and x, y and z scales rather than a, b and c, methinks.

 

[Dynasti]

You should have it with a master radius and x, y and z scales rather than a, b and c, methinks.

Meh, it is the same, just different names

Well I'l stick with abc because I use x0, y0 and z0 for position

 

[Element of Water]

yeah well the scales would be xS, yS, zS or something... they don't have to be x0, y0, z0...

 

[Dynasti]

yeah well the scales would be xS, yS, zS or something... they don't have to be x0, y0, z0...

EDIT!

Check out this new test attached a sphere group to an ellipsoid

 

[Element of Water]

Awsome! You could do something like attach 2 spheres to a sphere, each of those has 2 attached to it, each of those has 2 attached to it etc etc. And each one would be smaller than the last .

 

[Dynasti]

Awsome! You could do something like attach 2 spheres to a sphere, each of those has 2 attached to it, each of those has 2 attached to it etc etc. And each one would be smaller than the last .

lulz