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Math

moyack · 987

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Math
on: January 19, 2012, 02:57:58 PM
Category: Geometry, Variables
Language: vJASS
A library for math functions. Manages Matrix manipulation and more.

Code: jass
  1. library Math initializer Init
  2.  
  3. function R2I_n takes real r returns integer
  4.     local integer i = R2I(r)
  5.     if (r < I2R(i)+0.5) then
  6.         return i
  7.     else
  8.         return i+1
  9.     endif
  10. endfunction
  11.  
  12. struct VECTOR3
  13.     static VECTOR3 Zero
  14.     static VECTOR3 oneX
  15.     static VECTOR3 oneY
  16.     static VECTOR3 oneZ
  17.     real x
  18.     real y
  19.     real z
  20.    
  21.     static method New_0 takes nothing returns VECTOR3
  22.         local VECTOR3 this = VECTOR3.create()
  23.         set .x = 0
  24.         set .y = 0
  25.         set .z = 0
  26.         return this
  27.     endmethod
  28.    
  29.     static method New_1 takes real x, real y, real z returns VECTOR3
  30.         local VECTOR3 this = VECTOR3.create()
  31.         set .x = x
  32.         set .y = y
  33.         set .z = z
  34.         return this
  35.     endmethod
  36.    
  37.     static method New_2 takes VECTOR3 v returns VECTOR3
  38.         local VECTOR3 this = VECTOR3.create()
  39.         set .x = v.x
  40.         set .y = v.y
  41.         set .z = v.z
  42.         return this
  43.     endmethod
  44.    
  45.     method SetValues takes real x, real y, real z returns VECTOR3
  46.         set .x = x
  47.         set .y = y
  48.         set .z = z
  49.         return this
  50.     endmethod
  51.    
  52.     method Length takes nothing returns real
  53.         return SquareRoot(.x*.x+.y*.y+.z*.z)
  54.     endmethod
  55.    
  56.     method LengthSq takes nothing returns real
  57.         return .x*.x+.y*.y+.z*.z
  58.     endmethod
  59.    
  60.     method ToString takes nothing returns string
  61.         return "Vector3 id "+I2S(this) + "\nx = "+R2S(.x)+"   y = "+R2S(.y)+"   z = "+R2S(.z)
  62.     endmethod
  63.    
  64. endstruct
  65.  
  66. function Vec3Add takes VECTOR3 Output, VECTOR3 v1, VECTOR3 v2 returns VECTOR3
  67.     set Output.x = v1.x + v2.x
  68.     set Output.y = v1.y + v2.y
  69.     set Output.z = v1.z + v2.z
  70.     return Output
  71. endfunction
  72.  
  73. function Vec3Subtract takes VECTOR3 Output, VECTOR3 v1, VECTOR3 v2 returns VECTOR3
  74.     set Output.x = v1.x - v2.x
  75.     set Output.y = v1.y - v2.y
  76.     set Output.z = v1.z - v2.z
  77.     return Output
  78. endfunction
  79.    
  80. function Vec3Scale takes VECTOR3 Output, VECTOR3 v, real r returns VECTOR3
  81.     set Output.x = v.x * r
  82.     set Output.y = v.y * r
  83.     set Output.z = v.z * r
  84.     return Output
  85. endfunction
  86.    
  87. function Vec3Division takes VECTOR3 Output, VECTOR3 v, real r returns VECTOR3
  88.     set Output.x = v.x / r
  89.     set Output.y = v.y / r
  90.     set Output.z = v.z / r
  91.     return Output
  92. endfunction
  93.  
  94. function Vec3Length takes VECTOR3 v returns real
  95.     return SquareRoot(v.x*v.x+v.y*v.y+v.z*v.z)
  96. endfunction
  97.  
  98. function Vec3LengthSq takes VECTOR3 v returns real
  99.     return v.x*v.x+v.y*v.y+v.z*v.z
  100. endfunction
  101.  
  102. function Vec3Normalize takes VECTOR3 Output, VECTOR3 v returns VECTOR3
  103.     local real len = SquareRoot(v.x*v.x+v.y*v.y+v.z*v.z)
  104.     set Output.x = v.x/len
  105.     set Output.y = v.y/len
  106.     set Output.z = v.z/len
  107.     return Output
  108. endfunction
  109.  
  110. function Vec3Dot takes VECTOR3 v1, VECTOR3 v2 returns real
  111.     return v1.x*v2.x+v1.y*v2.y+v1.z*v2.z
  112. endfunction
  113.  
  114. function Vec3Cross takes VECTOR3 Output, VECTOR3 v1, VECTOR3 v2 returns VECTOR3
  115.     local real y  = v1.z * v2.x - v1.x * v2.z
  116.     local real z = v1.x * v2.y - v1.y * v2.x
  117.     set Output.x = v1.y * v2.z - v1.z * v2.y
  118.     set Output.y = y
  119.     set Output.z = z
  120.     return Output
  121. endfunction
  122.  
  123. function Vec3Transform_1 takes VECTOR3 Output, VECTOR3 v, MATRIX3 m returns VECTOR3
  124.     local real y = v.x*m.m12+v.y*m.m22+v.z*m.m32
  125.     local real z = v.x*m.m13+v.y*m.m23+v.z*m.m33
  126.     set Output.x = v.x*m.m11+v.y*m.m21+v.z*m.m31
  127.     set Output.y = y
  128.     set Output.z = z
  129.     return Output
  130. endfunction
  131.  
  132. function Vec3Transform_2 takes VECTOR3 Output, VECTOR3 v, MATRIX4 m returns VECTOR3
  133.     local real y = v.x*m.m12+v.y*m.m22+v.z*m.m32+m.m42
  134.     local real z = v.x*m.m13+v.y*m.m23+v.z*m.m33+m.m43
  135.     local real w = v.x*m.m14+v.y*m.m24+v.z*m.m34+m.m44
  136.     set Output.x = (v.x*m.m11+v.y*m.m21+v.z*m.m31+m.m41)/w
  137.     set Output.y = y/w
  138.     set Output.z = z/w
  139.     return Output
  140. endfunction
  141.  
  142.  
  143. struct MATRIX3
  144.     static MATRIX3 Zero
  145.     static MATRIX3 E
  146.     real m11
  147.     real m12
  148.     real m13
  149.     real m21
  150.     real m22
  151.     real m23
  152.     real m31
  153.     real m32
  154.     real m33
  155.    
  156.     static method New_0 takes nothing returns MATRIX3
  157.         local MATRIX3 this = MATRIX3.create()
  158.         set .m11 = 0
  159.         set .m12 = 0
  160.         set .m13 = 0
  161.         set .m21 = 0
  162.         set .m22 = 0
  163.         set .m23 = 0
  164.         set .m31 = 0
  165.         set .m32 = 0
  166.         set .m33 = 0
  167.         return this
  168.     endmethod
  169.    
  170.     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
  171.         local MATRIX3 this = MATRIX3.create()
  172.         set .m11 = r11
  173.         set .m12 = r12
  174.         set .m13 = r13
  175.         set .m21 = r21
  176.         set .m22 = r22
  177.         set .m23 = r23
  178.         set .m31 = r31
  179.         set .m32 = r32
  180.         set .m33 = r33
  181.         return this
  182.     endmethod
  183.    
  184.     static method New_2 takes MATRIX3 m returns MATRIX3
  185.         local MATRIX3 this = MATRIX3.create()
  186.         set .m11 = m.m11
  187.         set .m12 = m.m12
  188.         set .m13 = m.m13
  189.         set .m21 = m.m21
  190.         set .m22 = m.m22
  191.         set .m23 = m.m23
  192.         set .m31 = m.m31
  193.         set .m32 = m.m32
  194.         set .m33 = m.m33
  195.         return this
  196.     endmethod
  197.    
  198.     method SetValues takes real r11, real r12, real r13, real r21, real r22, real r23, real r31, real r32, real r33 returns MATRIX3
  199.         set .m11 = r11
  200.         set .m12 = r12
  201.         set .m13 = r13
  202.         set .m21 = r21
  203.         set .m22 = r22
  204.         set .m23 = r23
  205.         set .m31 = r31
  206.         set .m32 = r32
  207.         set .m33 = r33
  208.         return this
  209.     endmethod
  210.  
  211.     method ToString takes nothing returns string
  212.         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)
  213.     endmethod
  214.    
  215. endstruct
  216.  
  217. function Matrix3Multiply takes MATRIX3 Output, MATRIX3 M1, MATRIX3 M2 returns MATRIX3  
  218.     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)
  219. endfunction
  220.  
  221. function Matrix3Scaling takes MATRIX3 Output, real x, real y, real z returns MATRIX3
  222.     return Output.SetValues(x,0,0,0,y,0,0,0,z)
  223. endfunction
  224.  
  225. function Matrix3RotationX takes MATRIX3 Output, real a returns MATRIX3
  226.     return Output.SetValues(1,0,0,0,Cos(a),-Sin(a),0,Sin(a),Cos(a))
  227. endfunction
  228.  
  229. function Matrix3RotationY takes MATRIX3 Output, real a returns MATRIX3
  230.     return Output.SetValues(Cos(a),0,Sin(a),0,1,0,-Sin(a),0,Cos(a))
  231. endfunction
  232.  
  233. function Matrix3RotationZ takes MATRIX3 Output, real a returns MATRIX3
  234.     return Output.SetValues(Cos(a),-Sin(a),0,Sin(a),Cos(a),0,0,0,1)
  235. endfunction
  236.  
  237. function Matrix3RotationAxis takes MATRIX3 Output, VECTOR3 v, real a returns MATRIX3
  238.     local real cosa = Cos(a)
  239.     local real sina = Sin(a)
  240.     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)
  241. endfunction
  242.  
  243. function Matrix3RotationYawPitchRoll takes MATRIX3 Output, real Yaw, real Pitch, real Roll returns MATRIX3
  244.     local real cosa = Cos(Yaw)
  245.     local real sina = Sin(Yaw)
  246.     local real cosb = Cos(Pitch)
  247.     local real sinb = Sin(Pitch)
  248.     local real cosy = Cos(Roll)
  249.     local real siny = Sin(Roll)
  250.     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)
  251. endfunction
  252.  
  253. struct MATRIX4
  254.     static MATRIX4 Zero
  255.     static MATRIX4 E
  256.     real m11
  257.     real m12
  258.     real m13
  259.     real m14
  260.     real m21
  261.     real m22
  262.     real m23
  263.     real m24
  264.     real m31
  265.     real m32
  266.     real m33
  267.     real m34
  268.     real m41
  269.     real m42
  270.     real m43
  271.     real m44
  272.    
  273.     static method New_0 takes nothing returns MATRIX4
  274.         local MATRIX4 this = MATRIX4.create()
  275.         set .m11 = 0
  276.         set .m12 = 0
  277.         set .m13 = 0
  278.         set .m14 = 0
  279.         set .m21 = 0
  280.         set .m22 = 0
  281.         set .m23 = 0
  282.         set .m24 = 0
  283.         set .m31 = 0
  284.         set .m32 = 0
  285.         set .m33 = 0
  286.         set .m34 = 0
  287.         set .m41 = 0
  288.         set .m42 = 0
  289.         set .m43 = 0
  290.         set .m44 = 0
  291.         return this
  292.     endmethod
  293.    
  294.     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
  295.         local MATRIX4 this = MATRIX4.create()
  296.         set .m11 = r11
  297.         set .m12 = r12
  298.         set .m13 = r13
  299.         set .m14 = r14
  300.         set .m21 = r21
  301.         set .m22 = r22
  302.         set .m23 = r23
  303.         set .m24 = r24
  304.         set .m31 = r31
  305.         set .m32 = r32
  306.         set .m33 = r33
  307.         set .m34 = r34
  308.         set .m41 = r41
  309.         set .m42 = r42
  310.         set .m43 = r43
  311.         set .m44 = r44
  312.         return this
  313.     endmethod
  314.    
  315.     static method New_2 takes MATRIX4 m returns MATRIX4
  316.         local MATRIX4 this = MATRIX4.create()
  317.         set .m11 = m.m11
  318.         set .m12 = m.m12
  319.         set .m13 = m.m13
  320.         set .m14 = m.m14
  321.         set .m21 = m.m21
  322.         set .m22 = m.m22
  323.         set .m23 = m.m23
  324.         set .m24 = m.m24
  325.         set .m31 = m.m31
  326.         set .m32 = m.m32
  327.         set .m33 = m.m33
  328.         set .m34 = m.m34
  329.         set .m41 = m.m41
  330.         set .m42 = m.m42
  331.         set .m43 = m.m43
  332.         set .m44 = m.m44
  333.         return this
  334.     endmethod
  335.    
  336.     static method New_3 takes MATRIX3 m returns MATRIX4
  337.         local MATRIX4 this = MATRIX4.create()
  338.         set .m11 = m.m11
  339.         set .m12 = m.m12
  340.         set .m13 = m.m13
  341.         set .m14 = 0
  342.         set .m21 = m.m21
  343.         set .m22 = m.m22
  344.         set .m23 = m.m23
  345.         set .m24 = 0
  346.         set .m31 = m.m31
  347.         set .m32 = m.m32
  348.         set .m33 = m.m33
  349.         set .m34 = 0
  350.         set .m41 = 0
  351.         set .m42 = 0
  352.         set .m43 = 0
  353.         set .m44 = 1
  354.         return this
  355.     endmethod
  356.    
  357.     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
  358.         set .m11 = r11
  359.         set .m12 = r12
  360.         set .m13 = r13
  361.         set .m14 = r14
  362.         set .m21 = r21
  363.         set .m22 = r22
  364.         set .m23 = r23
  365.         set .m24 = r24
  366.         set .m31 = r31
  367.         set .m32 = r32
  368.         set .m33 = r33
  369.         set .m34 = r34
  370.         set .m41 = r41
  371.         set .m42 = r42
  372.         set .m43 = r43
  373.         set .m44 = r44
  374.         return this
  375.     endmethod
  376.  
  377.     method ToString takes nothing returns string
  378.         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)
  379.     endmethod
  380.    
  381. endstruct
  382.  
  383. function Matrix4Multiply takes MATRIX4 Output, MATRIX4 M1, MATRIX4 M2 returns MATRIX4
  384.     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)
  385. endfunction
  386.  
  387. private function Init takes nothing returns nothing
  388.    set VECTOR3.Zero = VECTOR3.New_0()
  389.    set VECTOR3.oneX = VECTOR3.New_1(1,0,0)
  390.    set VECTOR3.oneY = VECTOR3.New_1(0,1,0)
  391.    set VECTOR3.oneZ = VECTOR3.New_1(0,0,1)
  392.    set MATRIX3.Zero = MATRIX3.New_0()
  393.    set MATRIX3.E = MATRIX3.New_1(1,0,0,0,1,0,0,0,1)
  394.    set MATRIX4.Zero = MATRIX4.New_0()
  395.    set MATRIX4.E = MATRIX4.New_1(1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1)
  396. endfunction
  397.  
  398. endlibrary
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