Vector

[Anitarf]

This is a set of function intended for spatial geometric calculations. They can be used as a basis for projectile movement, collision detection and other similar operations in 3D space. The functions operate with "vector objects" - integers that represent the index of a vector in a set of arrays. Those arrays store the three coordinates of a vector. The system can do many vector operations, from addition to projection, as well as getting terrain normals and collision detection. These functions were first used in my and iNfraNe's Blizzard's sports map contest entry Dwarven Downhill.

Update: I have finished making a vJass version of this system. Vectors are implemented as a struct and all the operations that can be done with them have been greatly optimized. The vector methods should now be several times faster than the old functions. The post still contains the original non-vJass map if anyone needs it.

Vector:

library Vector

//*****************************************************************
//*  VECTOR LIBRARY
//*
//*  written by: Anitarf
//*
//*  The library contains a struct named vector, which represents a
//*  point in 3D space. As such, it has three real members, one for
//*  each coordinate: x, y, z. It also has the following methods:
//*
//*        static method create takes real x, real y, real z returns vector
//*  Creates a new vector with the given coordinates.
//*
//*        method getLength takes nothing returns real
//*  Returns the length of the vector it is called on.
//*
//*        static method sum takes vector augend, vector addend returns vector
//*  Returns the sum of two vectors as a new vector.
//*
//*        method add takes vector addend returns nothing
//*  Similar to sum, except that it doesn't create a new vector for the result,
//*  but changes the vector it is called on by adding the "added" to it.
//*
//*        static method difference takes vector minuend, vector subtrahend returns vector
//*  Returns the difference between two vectors as a new vector.
//*
//*        method subtract takes vector subtrahend returns nothing
//*  Similar to difference, except that it doesn't create a new vector for the result,
//*  but changes the vector it is called on by subtracting the "subtrahend" from it.
//*
//*        method scale takes real factor returns nothing
//*  Scales the vector it is called on by the given factor.
//*
//*        method setLength takes real length returns nothing
//*  Sets the length of the vector it is called on to the given value, maintaining its orientation.
//*
//*        static method dotProduct takes vector a, vector b returns real
//*  Calculates the dot product (also called scalar product) of two vectors.
//*
//*        static method crossProduct takes vector a, vector b returns vector
//*  Calculates the cross product (also called vector product) of two vectors
//*  and returns it as a new vector.
//*
//*        static method tripleProductScalar takes vector a, vector b, vector c returns real
//*  Calculates the triple scalar product of three vectors.
//*
//*        static method tripleProductVector takes vector a, vector b, vector c returns vector
//*  Calculates the triple vector product of three vectors and returns it as a new vector.
//*
//*
//*        static method projectionVector takes vector projected, vector direction returns vector
//*  Calculates the projection of the vector "projected" onto the vector "direction"
//*  and returns it as a new vector.
//*  Returns null if the vector "direction" has a length of 0.
//*
//*        method projectVector takes vector direction returns nothing
//*  Projects the vector it is called on onto the vector "direction".
//*  Does nothing if the vector "direction" has a length of 0.
//*
//*        static method projectionPlane takes vector projected, vector normal returns vector
//*  Calculates the projection of the vector "projected" onto a plane defined by
//*  its normal vector and returns it as a new vector.
//*  Returns null if the vector "normal" has a length of 0.
//*
//*        method projectPlane takes vector normal returns nothing
//*  Projects the vector it is called on onto a plane defined by its normal vector.
//*  Does nothing if the vector "normal" has a length of 0.
//*
//*        static method getAngle takes vector a, vector b returns real
//*  Returns the angle between two vectors, in radians, returns a value between 0 and pi.
//*  Returns 0.0 if any of the vectors are 0 units long.
//*
//*        method rotate takes vector axis, real angle returns nothing
//*  Rotates the vector it is called on around the axis defined by the vector "axis"
//*  by the given angle, which should be input in radians.
//*  Does nothing if axis is 0 units long.
//*
//*
//*        static method createTerrainPoint takes real x, real y returns vector
//*  Creates a vector to the given terrain coordinate, taking its z height into account.
//*
//*        method getTerrainPoint takes real x, real y returns nothing
//*  Sets the vector it is called on to the given terrain coordinate, taking its z height into account.
//*
//*        static method createTerrainNormal takes real x, real y, real sampleRadius returns vector
//*  Creates the normal vector of the terrain at given coordinates. "sampleRadius" defines
//*  how far apart the reference points will be, if they are further apart, the result will
//*  be an impression of smoother terrain; normaly the value should be between 0 and 128.
//*
//*        method getTerrainNormal takes real x, real y, real sampleRadius returns nothing
//*  Sets the vector it is called on to the normal of the terrain at given coordinates.
//*
//*
//*        method isInCylinder takes vector cylinderOrigin, vector cylinderHeight, real cylinderRadius returns boolean
//*  Determines if a point is within a given cylinder. The cylinder's origin vector points
//*  to the center of one of the two paralel circular sides, and the height vector points
//*  from the origin point to the center of the other of the two paralel circular sides.
//*  Returns false if the point is not in the cylinder or if the vector cylinderHeight is 0 units long.
//*
//*        method isInCone takes vector coneOrigin, vector coneHeight, real coneRadius returns boolean
//*  Determines if a point is within a given cone. The cone's origin vector points to the
//*  center of the circular side, and the height vector points from the origin point to
//*  the tip of the cone.
//*  Returns false if the point is not in the cylinder or if the vector coneHeight is 0 units long.
//*
//*        method isInSphere takes vector sphereOrigin, real sphereRadius returns boolean
//*  Determines if a point is within a give sphere. The sphere's origin vector points to the
//*  center of the sphere.
//*  Returns false if the point is not in the sphere.
//*****************************************************************

    struct vector
        real x
        real y
        real z
        
        static method create takes real x, real y, real z returns vector
            local vector v = vector.allocate()
            set v.x=x
            set v.y=y
            set v.z=z
            return v
        endmethod
        
        method getLength takes nothing returns real
          return SquareRoot(.x*.x + .y*.y + .z*.z)
        endmethod
        
        static method sum takes vector augend, vector addend returns vector
            local vector v = vector.allocate()
            set v.x = augend.x+addend.x
            set v.y = augend.y+addend.y
            set v.z = augend.z+addend.z
            return v
        endmethod
        method add takes vector addend returns nothing
            set this.x=this.x+addend.x
            set this.y=this.y+addend.y
            set this.z=this.z+addend.z
        endmethod
        
        static method difference takes vector minuend, vector subtrahend returns vector
            local vector v = vector.allocate()
            set v.x = minuend.x-subtrahend.x
            set v.y = minuend.y-subtrahend.y
            set v.z = minuend.z-subtrahend.z
            return v
        endmethod
        method subtract takes vector subtrahend returns nothing
            set this.x=this.x-subtrahend.x
            set this.y=this.y-subtrahend.y
            set this.z=this.z-subtrahend.z
        endmethod
        
        method scale takes real factor returns nothing
            set this.x=this.x*factor
            set this.y=this.y*factor
            set this.z=this.z*factor
        endmethod
        
        method setLength takes real length returns nothing
            local real l = SquareRoot(.x*.x + .y*.y + .z*.z)
            if l == 0.0 then
                debug call BJDebugMsg("vector.setLength error: The length of the vector is 0.0!")
                return
            endif
            set l = length/l
            set this.x = this.x*l
            set this.y = this.y*l
            set this.z = this.z*l
        endmethod
        
        static method dotProduct takes vector a, vector b returns real
            return (a.x*b.x+a.y*b.y+a.z*b.z)
        endmethod
        
        static method crossProduct takes vector a, vector b returns vector
            local vector v = vector.allocate()
            set v.x = a.y*b.z - a.z*b.y
            set v.y = a.z*b.x - a.x*b.z
            set v.z = a.x*b.y - a.y*b.x
            return v
        endmethod

        static method tripleProductScalar takes vector a, vector b, vector c returns real
            return ((a.y*b.z - a.z*b.y)*c.x+(a.z*b.x - a.x*b.z)*c.y+(a.x*b.y - a.y*b.x)*c.z)
        endmethod

        static method tripleProductVector takes vector a, vector b, vector c returns vector
            local vector v = vector.allocate()
            local real n = a.x*c.x+a.y*c.y+a.z*c.z
            local real m = a.x*b.x+a.y*b.y+a.z*b.z
            set v.x = b.x*n-c.x*m
            set v.y = b.y*n-c.y*m
            set v.z = b.z*n-c.z*m
            return v
        endmethod

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

        static method projectionVector takes vector projected, vector direction returns vector
            local vector v = vector.allocate()
            local real l = direction.x*direction.x+direction.y*direction.y+direction.z*direction.z
            if l == 0.0 then
                call v.destroy()
                debug call BJDebugMsg("vector.projectionVector error: The length of the direction vector is 0.0!")
                return 0
            endif
            set l = (projected.x*direction.x+projected.y*direction.y+projected.z*direction.z) / l
            set v.x = direction.x*l
            set v.y = direction.y*l
            set v.z = direction.z*l
            return v
        endmethod
        method projectVector takes vector direction returns nothing
            local real l = direction.x*direction.x+direction.y*direction.y+direction.z*direction.z
            if l == 0.0 then
                debug call BJDebugMsg("vector.projectVector error: The length of the direction vector is 0.0!")
                return
            endif
            set l = (this.x*direction.x+this.y*direction.y+this.z*direction.z) / l
            set this.x = direction.x*l
            set this.y = direction.y*l
            set this.z = direction.z*l
        endmethod

        static method projectionPlane takes vector projected, vector normal returns vector
            local vector v = vector.allocate()
            local real l = normal.x*normal.x+normal.y*normal.y+normal.z*normal.z
            if l == 0.0 then
                call v.destroy()
                debug call BJDebugMsg("vector.projectionPlane error: The length of the normal vector is 0.0!")
                return 0
            endif
            set l = (projected.x*normal.x+projected.y*normal.y+projected.z*normal.z) / l
            set v.x = projected.x - normal.x*l
            set v.y = projected.y - normal.y*l
            set v.z = projected.z - normal.z*l
            return v
        endmethod
        method projectPlane takes vector normal returns nothing
            local real l = normal.x*normal.x+normal.y*normal.y+normal.z*normal.z
            if l == 0.0 then
                debug call BJDebugMsg("vector.projectPlane error: The length of the normal vector is 0.0!")
                return
            endif
            set l = (this.x*normal.x+this.y*normal.y+this.z*normal.z) / l
            set this.x = this.x - normal.x*l
            set this.y = this.y - normal.y*l
            set this.z = this.z - normal.z*l
        endmethod

        static method getAngle takes vector a, vector b returns real
            local real l = SquareRoot(a.x*a.x + a.y*a.y + a.z*a.z)*SquareRoot(b.x*b.x + b.y*b.y + b.z*b.z)
            if l == 0 then
                debug call BJDebugMsg("vector.getAngle error: The length of at least one of the vectors is 0.0!")
                return 0.0
            endif
            return Acos((a.x*b.x+a.y*b.y+a.z*b.z)/l) //angle is returned in radians
        endmethod
        
        method rotate takes vector axis, real angle returns nothing //angle is taken in radians
            local real xx
            local real xy
            local real xz
            local real yx
            local real yy
            local real yz
            local real zx
            local real zy
            local real zz
            local real al = axis.x*axis.x+axis.y*axis.y+axis.z*axis.z //axis length^2
            local real f
            local real c = Cos(angle)
            local real s = Sin(angle)
            if al == 0.0 then
                debug call BJDebugMsg("vector.rotate error: The length of the axis vector is 0.0!")
                return
            endif
            set f = (this.x*axis.x+this.y*axis.y+this.z*axis.z) / al
            set zx = axis.x*f
            set zy = axis.y*f
            set zz = axis.z*f //axis component of rotated vector
            set xx = this.x-zx
            set xy = this.y-zy
            set xz = this.z-zz //component of vector perpendicular to axis
            set al = SquareRoot(al)
            set yx = (axis.y*xz - axis.z*xy)/al
            set yy = (axis.z*xx - axis.x*xz)/al //y same length as x by using cross product and dividing with axis length
            set yz = (axis.x*xy - axis.y*xx)/al //x,y - coordinate system in which we rotate
            set this.x=xx*c+yx*s+zx
            set this.y=xy*c+yy*s+zy
            set this.z=xz*c+yz*s+zz
        endmethod
        
// ================================================================

        private static location loc = Location(0.0,0.0)

        static method createTerrainPoint takes real x, real y returns vector
            local vector v = vector.allocate()
            call MoveLocation(vector.loc,x,y)
            set v.x=x
            set v.y=y
            set v.z=GetLocationZ(loc)
            return v
        endmethod
        method getTerrainPoint takes real x, real y returns nothing
            call MoveLocation(vector.loc,x,y)
            set this.x=x
            set this.y=y
            set this.z=GetLocationZ(loc)
        endmethod

        static method createTerrainNormal takes real x, real y, real sampleRadius returns vector
            local vector v = vector.allocate()
            local real zx
            local real zy
            call MoveLocation(vector.loc, x-sampleRadius, y)
            set zx=GetLocationZ(vector.loc)
            call MoveLocation(vector.loc, x+sampleRadius, y)
            set zx=zx-GetLocationZ(vector.loc)
            call MoveLocation(vector.loc, x, y-sampleRadius)
            set zy=GetLocationZ(vector.loc)
            call MoveLocation(vector.loc, x, y+sampleRadius)
            set zy=zy-GetLocationZ(vector.loc)
            set sampleRadius=2*sampleRadius
            set v.x = zx*sampleRadius
            set v.y = zy*sampleRadius
            set v.z = sampleRadius*sampleRadius
            return v
        endmethod
        method getTerrainNormal takes real x, real y, real sampleRadius returns nothing
            local real zx
            local real zy
            call MoveLocation(vector.loc, x-sampleRadius, y)
            set zx=GetLocationZ(vector.loc)
            call MoveLocation(vector.loc, x+sampleRadius, y)
            set zx=zx-GetLocationZ(vector.loc)
            call MoveLocation(vector.loc, x, y-sampleRadius)
            set zy=GetLocationZ(vector.loc)
            call MoveLocation(vector.loc, x, y+sampleRadius)
            set zy=zy-GetLocationZ(vector.loc)
            set sampleRadius=2*sampleRadius
            set this.x = zx*sampleRadius
            set this.y = zy*sampleRadius
            set this.z = sampleRadius*sampleRadius
        endmethod

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

        method isInCylinder takes vector cylinderOrigin, vector cylinderHeight, real cylinderRadius returns boolean
            local real l

            local real x = this.x-cylinderOrigin.x
            local real y = this.y-cylinderOrigin.y
            local real z = this.z-cylinderOrigin.z
            if x*cylinderHeight.x+y*cylinderHeight.y+z*cylinderHeight.z < 0.0 then //point below cylinder
                return false
            endif
            
            set x = x-cylinderHeight.x
            set y = y-cylinderHeight.y
            set z = z-cylinderHeight.z
            if x*cylinderHeight.x+y*cylinderHeight.y+z*cylinderHeight.z > 0.0 then //point above cylinder
                return false
            endif
            
            set l = cylinderHeight.x*cylinderHeight.x+cylinderHeight.y*cylinderHeight.y+cylinderHeight.z*cylinderHeight.z
            if l == 0.0 then
                debug call BJDebugMsg("vector.isInCylinder error: The length of the cylinderHeight vector is 0.0!")
                return false
            endif
            set l = (x*cylinderHeight.x+y*cylinderHeight.y+z*cylinderHeight.z) / l
            set x = x - cylinderHeight.x*l
            set y = y - cylinderHeight.y*l
            set z = z - cylinderHeight.z*l
            if x*x+y*y+z*z > cylinderRadius*cylinderRadius then //point outside cylinder
                return false
            endif
            
            return true
        endmethod

        method isInCone takes vector coneOrigin, vector coneHeight, real coneRadius returns boolean
            local real l

            local real x = this.x-coneOrigin.x
            local real y = this.y-coneOrigin.y
            local real z = this.z-coneOrigin.z
            if x*coneHeight.x+y*coneHeight.y+z*coneHeight.z < 0.0 then //point below cone
                return false
            endif
            
            set l = coneHeight.x*coneHeight.x+coneHeight.y*coneHeight.y+coneHeight.z*coneHeight.z
            if l == 0.0 then
                debug call BJDebugMsg("vector.isInCone error: The length of the coneHeight vector is 0.0!")
                return false
            endif
            set l = (x*coneHeight.x+y*coneHeight.y+z*coneHeight.z) / l
            set x = x - coneHeight.x*l
            set y = y - coneHeight.y*l
            set z = z - coneHeight.z*l
            if SquareRoot(x*x+y*y+z*z) > coneRadius*(1.0-l) then //point outside cone
                return false
            endif
            
            return true
        endmethod

        method isInSphere takes vector sphereOrigin, real sphereRadius returns boolean
            if sphereRadius*sphereRadius < ((this.x-sphereOrigin.x)*(this.x-sphereOrigin.x)+(this.y-sphereOrigin.y)*(this.y-sphereOrigin.y)+(this.z-sphereOrigin.z)*(this.z-sphereOrigin.z)) then
                return false
            endif
            return true
        endmethod
    endstruct

endlibrary
library VectorLib requires Vector // For backwards compatibility.
endlibrary

[karukef]

Extremely useful. Thanks a lot for making this for everyone to use!

Just looked it over, and it even has TerrainNormal, that's smooth :)

Had lot's of fun watching the bouncy ball forever and ever. Well, until it's always growing momentum med it bounce itself out of existance, dunno where it went. At one point it slid along the ground, painting it with 100+ bounce art effect. But in general, very smooth.

[PipeDream]

Finally you submit this! The demonstration is beautiful. Approved.

Constant accelerations produces parabolas. That very simple integration method will always increase or decrease energy since it can only exactly reproduce lines. If you flip the order of adding velocity/acceleration to position/velocity you'll see it decay instead of grow. Since the solution is exactly a parabola you can use an explicit formula.
But if you want to be generic to non constant acceleration you can get the same exact integration of constant acceleration with a tiny bit more complexity:

JASS:

    local integer k1v //unoptimized Runge Kutta 2
    local integer k1x //Takes a trial half sized step
    local integer k2v //computes derivatives in middle of interval
    local integer k2x //uses those values to step from beginning to end

    set k1v = VectorAmplify(vectors[4],BouncyPeriod()*.5)
    set k1x = VectorAmplify(vectors[3],BouncyPeriod()*.5)

    set k2v = VectorAmplify(vectors[4],BouncyPeriod()) //recompute acceleration if it's time or position dependent
    set k2x = VectorSum(k1v,vectors[3])
    call VectorScale(k2x,BouncyPeriod())
 
    call VectorAdd(vectors[2],k2x)
    call VectorAdd(vectors[3],k2v)
    
    call VectorDestroy(k1v)
    call VectorDestroy(k1x)
    call VectorDestroy(k2v)
    call VectorDestroy(k2x)

And remove the scale of BouncyPeriod() from the initial state. This is a somewhat less interesting demonstration since it doesn't grow in energy and because of that the skidding karukef mentions occurs more frequently.

In general for spells the lack of conservation in the simple integrator is not a problem, but it will become one as you increase the time step. .01 is smaller than what is necessary for visually smooth. With this integrator you can safely increase to a less aggressive .03-.05.

[Anitarf]

Originally Posted by PipeDream

That very simple integration method will always increase or decrease energy since it can only exactly reproduce lines. If you flip the order of adding velocity/acceleration to position/velocity you'll see it decay instead of grow.

Yes, I noticed that, but I didn't want to overdo things for the purpose of a sample. I just decreased the period from 0.02 to 0.01 and hoped nobody would be bored enough to watch the ball long enough to see it bounce out of the arena.

This is a somewhat less interesting demonstration since it doesn't grow in energy and because of that the skidding karukef mentions occurs more frequently.

That can be fixed by increasing the starting velocity. The skidding occurs when the ball lands on a wall close to the ground and bounces out with a near flat velocity. The chances of that happening reduce consderably with longer bounces.

In general for spells the lack of conservation in the simple integrator is not a problem, but it will become one as you increase the time step. .01 is smaller than what is necessary for visually smooth. With this integrator you can safely increase to a less aggressive .03-.05.

Mostly, I think spells won't even want to conserve the speed, few objects bounce perfectly so I imagine users would want to scale down the speed with every bounce anyway.

But in the end, it's up to the users to decide how to utilize these functions, for simple projectile parabola approximations or more detailed and complex physical models.

[Toadcop]

Anitarf - cool =) as for me your map (on the contest) was the best (after my XGM-Soccer ;) ) real nice physic but have some problems with camera + how i remember you have a constant vector for "pushing" it was 0 degree... or not i don't remeber you must make it more terrain orintainted and not constant !

PS the only real sys what i respect... because of usage of GetLocationZ(). my TPC use it for Z correction.

Anitarf - i all ready use it in my TPC =) for create more reallystic "bounces" but really the hole sys is to simple (i mean your example) but it's not areal problem + the performance is great !

PS the best system which i have ever seen ! (non my sys =) )
+10000 rep :D !!!

[ArchWorm]

Anitarf, let me introduce Toadcop. He made a system, Toadcop's projectile creator. I don't feel like searching for it, I remember seeing a link at Infrane's PS. And his system allows to create dynamically moving projectiles with effects such as bounce, and other stuff...
I must admit that your sys is easier than TPC, I will not judge is it better, but it's easier.
Toadcop, anytime you need help with english, drop me a PM.

[iNfraNe]

This system is not made for moving objects dynamically. This is for is using mathematical vectors, the demo map just has a moving ball to demonstrate the use.
While this system is VERY usefull it is not a dynamically moving system on its own. My system uses these functions to calculate stuff.

[ArchWorm]

iNfraNe, I see, but I said it about geometrical base of these systems.

[xombie]

ArchWorm look a poopie!
I noticed that by VECTOR he means SCALAR. A vector is a magnitude and direction combined, whilst a scalar is simply magnitude. For clarity, what he is doing is creating an x,y,Ø vector, and a 'z' scalar (for height).

I will be releasing one of this humdingers not to compete with this one, but simply to polish up my math skills. GJ on this system I love the idea.

Ø = Theta (angle)

Edit: When going through it I was so confused how he incorporated height with vectors, but now I see they are just scalars.
Edit: Oops sorry, I see the vectors now. This point has just been proven useless 'hoorah'

[PipeDream]

A vector is not a magnitude and direction, it's something you can add with other vectors and scale. E.g., the real number line is a vector space, but the vectors have only one component. The scalars are the things you scale the vectors with, they can be either real or complex numbers. This package implements a three dimensional real vector space. All three components are part of the vector, but "x","y" and "z" are scalars, as they prescribe how much unit vector to scale and add to the mix.

The vectors this system implements can be represented as magnitude and direction. For these two concepts you need a little more structure than the addition/scaling a vector space gives you. Once you add a dot product that maps two vectors to a scalar you can measure lengths and angles and think about a magnitude/direction representation. In practice you don't use that for actual computations since it's a nightmarish mess.

[xombie]

I don't even know why I bothered doubting him lol, I should have automatically known he was right.

------------------------------------------------------------------------------------------------------------------------

I haven't gotten around to learning anything 3D in mathematics or physics (I'm in grade 12, and I take AP Calculus -- basically means 1st year university calculus), my knowledge in the area of this is very scarce, and would appreciate learning. I've figured out a rough outline using a pen and paper on how this goes about working, but I would appreciate it if you or Anitarf could PM me a simple but thorough explanation of everything that is going on in this system. I could try to talk to Anitarf sometime on BNet but things like this intrigue me and I'd like to learn more.

PS.

Until then I'm going to be thoroughly looking through the map getting a better understanding of it - something I should be learning in school but hey! school sucks and doesn't teach you jack.

Edit: Oh shit double-post, I'll fix this.
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JASS:

function BouncyBallCreate takes nothing returns nothing
    local integer array vectors
    local timer t
    set udg_BouncyBall = CreateUnit(Player(0), 'ewsp', 0.0,0.0,0.0)

  //  make it possible to change the unit's flyheight
    call UnitAddAbility(udg_BouncyBall, 'Amrf')
    call UnitRemoveAbility(udg_BouncyBall, 'Amrf')

  //  create the unit's position vector
    set vectors[1]=VectorCreate(0.0,0.0,100.0)

  //  create the unit's starting speed vector
    set vectors[2]=VectorCreate(GetRandomReal(-100.0, 100.0)*BouncyPeriod(),GetRandomReal(-100.0, 100.0)*BouncyPeriod(),500.0*BouncyPeriod())

  //  create the gravity acceleration vector
    set vectors[3]=VectorCreate(0.0, 0.0, -800.0*BouncyPeriod()*BouncyPeriod())

  //  to avoid having too many variables, we store these vectors into another vector
    set vectors[4]=VectorCreate(I2R(vectors[1]), I2R(vectors[2]), I2R(vectors[3]))
    call SetUnitUserData(udg_BouncyBall, vectors[4])

    set t = CreateTimer()
    call TimerStart(t, BouncyPeriod(), true, function BouncyBallMove )
endfunction

After taking a look at your VectorCreate() function, it seems that you create 4 different vectors, and the 4th one is simply a clone of the first three. Would this not create DOUBLE the vector that you originally intended?

In your fourth vector creation, what do you convert the values to integers for? Also, more specifically than before: In your setting of vectors[1] you give the 'z' a value of 100.00. Later, in vectors[2], you create ANOTHER vector, equal to 5. Then, again, in vectors[3], you add an acceleration of gravity. I'm completely lost as to what you are doing here.

[iNfraNe]

Actually, the 4th vector is being used as a storing method for the other 3. The beauty of this system is that it can link 3 reals to 1 integer. So what the 4th does is link the other 3 vectors to it, so they can be selected trough 1 integer. It actually, unlike the other 3, has nothing mathematical about it.

on an offtopic note: your signature function would crash the WE since its lacking a return statement.

[Anitarf]

What you were looking at is the initialization function. It just creates the three basic vectors that the bouncy ball needs: one to determine it's position, what's it's offset from the origin of the map; another to determine it's speed, how much does it move in one time unit; another to determine it's acceleration, how much does the speed change in one time unit. The fourth one has nothing to do with physics but is used as a data structure. Under it's "coordinates" it stores the IDs of the before mentioned 3 vectors.

Then you have a periodic timer that calls the function that moves the ball every time unit.

[MaD[Lion]]

this system totally owns :D

[oninuva]

So I guess you need to know JASS to use it?