WC3 JASS.com
"The Jass Vault" plus vJASS and Zinc

library Math initializer Init

 

function R2I_n takes real r returns integer

    local integer i = R2I(r)

    if (r < I2R(i)+0.5) then

        return i

    else

        return i+1

    endif

 

struct VECTOR3

    static VECTOR3 Zero

    static VECTOR3 oneX

    static VECTOR3 oneY

    static VECTOR3 oneZ

    real x

    real y

    real z

   

    static method New_0 takes nothing returns VECTOR3

        local VECTOR3 this = VECTOR3.create()

        set .x = 0

        set .y = 0

        set .z = 0

        return this

    endmethod

   

    static method New_1 takes real x, real y, real z returns VECTOR3

        local VECTOR3 this = VECTOR3.create()

        set .x = x

        set .y = y

        set .z = z

        return this

    endmethod

   

    static method New_2 takes VECTOR3 v returns VECTOR3

        local VECTOR3 this = VECTOR3.create()

        set .x = v.x

        set .y = v.y

        set .z = v.z

        return this

    endmethod

   

    method SetValues takes real x, real y, real z returns VECTOR3

        set .x = x

        set .y = y

        set .z = z

        return this

    endmethod

   

    method Length takes nothing returns real

        return SquareRoot(.x*.x+.y*.y+.z*.z)

    endmethod

   

    method LengthSq takes nothing returns real

        return .x*.x+.y*.y+.z*.z

    endmethod

   

    method ToString takes nothing returns string

        return "Vector3 id "+I2S(this) + "\nx = "+R2S(.x)+"   y = "+R2S(.y)+"   z = "+R2S(.z)

    endmethod

   

 

function Vec3Add takes VECTOR3 Output, VECTOR3 v1, VECTOR3 v2 returns VECTOR3

    set Output.x = v1.x + v2.x

    set Output.y = v1.y + v2.y

    set Output.z = v1.z + v2.z

    return Output

 

function Vec3Subtract takes VECTOR3 Output, VECTOR3 v1, VECTOR3 v2 returns VECTOR3

    set Output.x = v1.x - v2.x

    set Output.y = v1.y - v2.y

    set Output.z = v1.z - v2.z

    return Output

   

function Vec3Scale takes VECTOR3 Output, VECTOR3 v, real r returns VECTOR3

    set Output.x = v.x * r

    set Output.y = v.y * r

    set Output.z = v.z * r

    return Output

   

function Vec3Division takes VECTOR3 Output, VECTOR3 v, real r returns VECTOR3

    set Output.x = v.x / r

    set Output.y = v.y / r

    set Output.z = v.z / r

    return Output

 

function Vec3Length takes VECTOR3 v returns real

    return SquareRoot(v.x*v.x+v.y*v.y+v.z*v.z)

 

function Vec3LengthSq takes VECTOR3 v returns real

    return v.x*v.x+v.y*v.y+v.z*v.z

 

function Vec3Normalize takes VECTOR3 Output, VECTOR3 v returns VECTOR3

    local real len = SquareRoot(v.x*v.x+v.y*v.y+v.z*v.z)

    set Output.x = v.x/len

    set Output.y = v.y/len

    set Output.z = v.z/len

    return Output

 

function Vec3Dot takes VECTOR3 v1, VECTOR3 v2 returns real

    return v1.x*v2.x+v1.y*v2.y+v1.z*v2.z

 

function Vec3Cross takes VECTOR3 Output, VECTOR3 v1, VECTOR3 v2 returns VECTOR3

    local real y  = v1.z * v2.x - v1.x * v2.z

    local real z = v1.x * v2.y - v1.y * v2.x

    set Output.x = v1.y * v2.z - v1.z * v2.y

    set Output.y = y

    set Output.z = z

    return Output

 

function Vec3Transform_1 takes VECTOR3 Output, VECTOR3 v, MATRIX3 m returns VECTOR3

    local real y = v.x*m.m12+v.y*m.m22+v.z*m.m32

    local real z = v.x*m.m13+v.y*m.m23+v.z*m.m33

    set Output.x = v.x*m.m11+v.y*m.m21+v.z*m.m31

    set Output.y = y

    set Output.z = z

    return Output

 

function Vec3Transform_2 takes VECTOR3 Output, VECTOR3 v, MATRIX4 m returns VECTOR3

    local real y = v.x*m.m12+v.y*m.m22+v.z*m.m32+m.m42

    local real z = v.x*m.m13+v.y*m.m23+v.z*m.m33+m.m43

    local real w = v.x*m.m14+v.y*m.m24+v.z*m.m34+m.m44

    set Output.x = (v.x*m.m11+v.y*m.m21+v.z*m.m31+m.m41)/w

    set Output.y = y/w

    set Output.z = z/w

    return Output

 

 

struct MATRIX3

    static MATRIX3 Zero

    static MATRIX3 E

    real m11

    real m12

    real m13

    real m21

    real m22

    real m23

    real m31

    real m32

    real m33

   

    static method New_0 takes nothing returns MATRIX3

        local MATRIX3 this = MATRIX3.create()

        set .m11 = 0

        set .m12 = 0

        set .m13 = 0

        set .m21 = 0

        set .m22 = 0

        set .m23 = 0

        set .m31 = 0

        set .m32 = 0

        set .m33 = 0

        return this

    endmethod

   

    static method New_1 takes real r11, real r12, real r13, real r21, real r22, real r23, real r31, real r32, real r33 returns MATRIX3

        local MATRIX3 this = MATRIX3.create()

        set .m11 = r11

        set .m12 = r12

        set .m13 = r13

        set .m21 = r21

        set .m22 = r22

        set .m23 = r23

        set .m31 = r31

        set .m32 = r32

        set .m33 = r33

        return this

    endmethod

   

    static method New_2 takes MATRIX3 m returns MATRIX3

        local MATRIX3 this = MATRIX3.create()

        set .m11 = m.m11

        set .m12 = m.m12

        set .m13 = m.m13

        set .m21 = m.m21

        set .m22 = m.m22

        set .m23 = m.m23

        set .m31 = m.m31

        set .m32 = m.m32

        set .m33 = m.m33

        return this

    endmethod

   

    method SetValues takes real r11, real r12, real r13, real r21, real r22, real r23, real r31, real r32, real r33 returns MATRIX3

        set .m11 = r11

        set .m12 = r12

        set .m13 = r13

        set .m21 = r21

        set .m22 = r22

        set .m23 = r23

        set .m31 = r31

        set .m32 = r32

        set .m33 = r33

        return this

    endmethod

 

    method ToString takes nothing returns string

        return "Matrux3 id "+I2S(this)+"\n"+R2S(.m11)+"  "+R2S(.m12)+"  "+R2S(.m13)+"\n"+R2S(.m21)+"  "+R2S(.m22)+"  "+R2S(.m23)+"\n"+R2S(.m31)+"  "+R2S(.m32)+"  "+R2S(.m33)

    endmethod

   

 

function Matrix3Multiply takes MATRIX3 Output, MATRIX3 M1, MATRIX3 M2 returns MATRIX3 

    return Output.SetValues(M1.m11*M2.m11 + M1.m21*M2.m12 + M1.m31*M2.m13,M1.m12*M2.m11 + M1.m22*M2.m12 + M1.m32*M2.m13,M1.m13*M2.m11 + M1.m23*M2.m12 + M1.m33*M2.m13,M1.m11*M2.m21 + M1.m21*M2.m22 + M1.m31*M2.m23,M1.m12*M2.m21 + M1.m22*M2.m22 + M1.m32*M2.m23,M1.m13*M2.m21 + M1.m23*M2.m22 + M1.m33*M2.m23,M1.m11*M2.m31 + M1.m21*M2.m32 + M1.m31*M2.m33,M1.m12*M2.m31 + M1.m22*M2.m32 + M1.m32*M2.m33,M1.m13*M2.m31 + M1.m23*M2.m32 + M1.m33*M2.m33)

 

function Matrix3Scaling takes MATRIX3 Output, real x, real y, real z returns MATRIX3

    return Output.SetValues(x,0,0,0,y,0,0,0,z)

 

function Matrix3RotationX takes MATRIX3 Output, real a returns MATRIX3

    return Output.SetValues(1,0,0,0,Cos(a),-Sin(a),0,Sin(a),Cos(a))

 

function Matrix3RotationY takes MATRIX3 Output, real a returns MATRIX3

    return Output.SetValues(Cos(a),0,Sin(a),0,1,0,-Sin(a),0,Cos(a))

 

function Matrix3RotationZ takes MATRIX3 Output, real a returns MATRIX3

    return Output.SetValues(Cos(a),-Sin(a),0,Sin(a),Cos(a),0,0,0,1)

 

function Matrix3RotationAxis takes MATRIX3 Output, VECTOR3 v, real a returns MATRIX3

    local real cosa = Cos(a)

    local real sina = Sin(a)

    return Output.SetValues(cosa + (1-cosa)*v.x*v.x,(1-cosa)*v.x*v.y-sina*v.z,(1-cosa)*v.x*v.z + sina*v.y,(1-cosa)*v.y*v.x + sina*v.z,cosa + (1-cosa)*v.y*v.y,(1-cosa)*v.y*v.z-sina*v.x,(1-cosa)*v.z*v.x-sina*v.y,(1-cosa)*v.z*v.y + sina*v.x,cosa + (1-cosa)*v.z*v.z)

 

function Matrix3RotationYawPitchRoll takes MATRIX3 Output, real Yaw, real Pitch, real Roll returns MATRIX3

    local real cosa = Cos(Yaw)

    local real sina = Sin(Yaw)

    local real cosb = Cos(Pitch)

    local real sinb = Sin(Pitch)

    local real cosy = Cos(Roll)

    local real siny = Sin(Roll)

    return Output.SetValues(cosa*cosb,cosa*sinb*siny-sina*cosy,cosa*sinb*cosy + sina*siny,sina*cosb,sina*sinb*siny + cosa*cosy,sina*sinb*cosy-cosa*siny,-sinb,cosb*siny,cosb*cosy)

 

struct MATRIX4

    static MATRIX4 Zero

    static MATRIX4 E

    real m11

    real m12

    real m13

    real m14

    real m21

    real m22

    real m23

    real m24

    real m31

    real m32

    real m33

    real m34

    real m41

    real m42

    real m43

    real m44

   

    static method New_0 takes nothing returns MATRIX4

        local MATRIX4 this = MATRIX4.create()

        set .m11 = 0

        set .m12 = 0

        set .m13 = 0

        set .m14 = 0

        set .m21 = 0

        set .m22 = 0

        set .m23 = 0

        set .m24 = 0

        set .m31 = 0

        set .m32 = 0

        set .m33 = 0

        set .m34 = 0

        set .m41 = 0

        set .m42 = 0

        set .m43 = 0

        set .m44 = 0

        return this

    endmethod

   

    static method New_1 takes real r11, real r12, real r13, real r14, real r21, real r22, real r23, real r24, real r31, real r32, real r33, real r34, real r41, real r42, real r43, real r44 returns MATRIX4

        local MATRIX4 this = MATRIX4.create()

        set .m11 = r11

        set .m12 = r12

        set .m13 = r13

        set .m14 = r14

        set .m21 = r21

        set .m22 = r22

        set .m23 = r23

        set .m24 = r24

        set .m31 = r31

        set .m32 = r32

        set .m33 = r33

        set .m34 = r34

        set .m41 = r41

        set .m42 = r42

        set .m43 = r43

        set .m44 = r44

        return this

    endmethod

   

    static method New_2 takes MATRIX4 m returns MATRIX4

        local MATRIX4 this = MATRIX4.create()

        set .m11 = m.m11

        set .m12 = m.m12

        set .m13 = m.m13

        set .m14 = m.m14

        set .m21 = m.m21

        set .m22 = m.m22

        set .m23 = m.m23

        set .m24 = m.m24

        set .m31 = m.m31

        set .m32 = m.m32

        set .m33 = m.m33

        set .m34 = m.m34

        set .m41 = m.m41

        set .m42 = m.m42

        set .m43 = m.m43

        set .m44 = m.m44

        return this

    endmethod

   

    static method New_3 takes MATRIX3 m returns MATRIX4

        local MATRIX4 this = MATRIX4.create()

        set .m11 = m.m11

        set .m12 = m.m12

        set .m13 = m.m13

        set .m14 = 0

        set .m21 = m.m21

        set .m22 = m.m22

        set .m23 = m.m23

        set .m24 = 0

        set .m31 = m.m31

        set .m32 = m.m32

        set .m33 = m.m33

        set .m34 = 0

        set .m41 = 0

        set .m42 = 0

        set .m43 = 0

        set .m44 = 1

        return this

    endmethod

   

    method SetValues takes real r11, real r12, real r13, real r14, real r21, real r22, real r23, real r24, real r31, real r32, real r33, real r34, real r41, real r42, real r43, real r44 returns MATRIX4

        set .m11 = r11

        set .m12 = r12

        set .m13 = r13

        set .m14 = r14

        set .m21 = r21

        set .m22 = r22

        set .m23 = r23

        set .m24 = r24

        set .m31 = r31

        set .m32 = r32

        set .m33 = r33

        set .m34 = r34

        set .m41 = r41

        set .m42 = r42

        set .m43 = r43

        set .m44 = r44

        return this

    endmethod

 

    method ToString takes nothing returns string

        return "Matrux4 id "+I2S(this)+"\n"+R2S(.m11)+"  "+R2S(.m12)+"  "+R2S(.m13)+"  "+R2S(.m14)+"\n"+R2S(.m21)+"  "+R2S(.m22)+"  "+R2S(.m23)+"  "+R2S(.m24)+"\n"+R2S(.m31)+"  "+R2S(.m32)+"  "+R2S(.m33)+"  "+R2S(.m34)+"\n"+R2S(.m41)+"  "+R2S(.m42)+"  "+R2S(.m43)+"  "+R2S(.m44)

    endmethod

   

 

function Matrix4Multiply takes MATRIX4 Output, MATRIX4 M1, MATRIX4 M2 returns MATRIX4

    return Output.SetValues(M1.m11*M2.m11 + M1.m21*M2.m12 + M1.m31*M2.m13 + M1.m41*M2.m14,M1.m12*M2.m11 + M1.m22*M2.m12 + M1.m32*M2.m13 + M1.m42*M2.m14,M1.m13*M2.m11 + M1.m23*M2.m12 + M1.m33*M2.m13 + M1.m43*M2.m14,M1.m14*M2.m11 + M1.m24*M2.m12 + M1.m34*M2.m13 + M1.m44*M2.m14,M1.m11*M2.m21 + M1.m21*M2.m22 + M1.m31*M2.m23 + M1.m41*M2.m24,M1.m12*M2.m21 + M1.m22*M2.m22 + M1.m32*M2.m23 + M1.m42*M2.m24,M1.m13*M2.m21 + M1.m23*M2.m22 + M1.m33*M2.m23 + M1.m43*M2.m24,M1.m14*M2.m21 + M1.m24*M2.m22 + M1.m34*M2.m23 + M1.m44*M2.m24,M1.m11*M2.m31 + M1.m21*M2.m32 + M1.m31*M2.m33 + M1.m41*M2.m34,M1.m12*M2.m31 + M1.m22*M2.m32 + M1.m32*M2.m33 + M1.m42*M2.m34,M1.m13*M2.m31 + M1.m23*M2.m32 + M1.m33*M2.m33 + M1.m43*M2.m34,M1.m14*M2.m31 + M1.m24*M2.m32 + M1.m34*M2.m33 + M1.m44*M2.m34,M1.m11*M2.m41 + M1.m21*M2.m42 + M1.m31*M2.m43 + M1.m41*M2.m44,M1.m12*M2.m41 + M1.m22*M2.m42 + M1.m32*M2.m43 + M1.m42*M2.m44,M1.m13*M2.m41 + M1.m23*M2.m42 + M1.m33*M2.m43 + M1.m43*M2.m44,M1.m14*M2.m41 + M1.m24*M2.m42 + M1.m34*M2.m43 + M1.m44*M2.m44)

 

private function Init takes nothing returns nothing

   set VECTOR3.Zero = VECTOR3.New_0()

   set VECTOR3.oneX = VECTOR3.New_1(1,0,0)

   set VECTOR3.oneY = VECTOR3.New_1(0,1,0)

   set VECTOR3.oneZ = VECTOR3.New_1(0,0,1)

   set MATRIX3.Zero = MATRIX3.New_0()

   set MATRIX3.E = MATRIX3.New_1(1,0,0,0,1,0,0,0,1)

   set MATRIX4.Zero = MATRIX4.New_0()

   set MATRIX4.E = MATRIX4.New_1(1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1)