vectors.tm - tomo-vectors

(135 lines)
   1 # A math vector library for 2D and 3D vectors of Nums or Ints
   2 
   3 struct Vec2(x,y:Num)
   4     ZERO := Vec2(0, 0)
   5     func plus(a,b:Vec2->Vec2; inline)
   6         return Vec2(a.x+b.x, a.y+b.y)
   7     func minus(a,b:Vec2->Vec2; inline)
   8         return Vec2(a.x-b.x, a.y-b.y)
   9     func times(a,b:Vec2->Vec2; inline)
  10         return Vec2(a.x*b.x, a.y*b.y)
  11     func negative(v:Vec2->Vec2; inline)
  12         return Vec2(-v.x, -v.y)
  13     func dot(a,b:Vec2->Num; inline)
  14         return (a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y)
  15     func cross(a,b:Vec2->Num; inline)
  16         return a.x*b.y - a.y*b.x
  17     func scaled_by(v:Vec2, k:Num->Vec2; inline)
  18         return Vec2(v.x*k, v.y*k)
  19     func divided_by(v:Vec2, divisor:Num->Vec2; inline)
  20         return Vec2(v.x/divisor, v.y/divisor)
  21     func length(v:Vec2->Num; inline)
  22         return (v.x*v.x + v.y*v.y).sqrt()
  23     func dist(a,b:Vec2->Num; inline)
  24         return a.minus(b).length()
  25     func angle(v:Vec2->Num; inline)
  26         return Num.atan2(v.y, v.x)
  27     func norm(v:Vec2->Vec2; inline)
  28         if v.x == 0 and v.y == 0
  29             return v
  30         len := v.length()
  31         return Vec2(v.x/len, v.y/len)
  32     func rotated(v:Vec2, radians:Num -> Vec2)
  33         cos := radians.cos() or return v
  34         sin := radians.sin() or return v
  35         return Vec2(cos*v.x - sin*v.y, sin*v.x + cos*v.y)
  36     func mix(a,b:Vec2, amount:Num -> Vec2)
  37         return Vec2(
  38             amount.mix(a.x, b.x),
  39             amount.mix(a.y, b.y),
  40         )
  41 
  42 struct Vec3(x,y,z:Num)
  43     ZERO := Vec3(0, 0, 0)
  44     func plus(a,b:Vec3->Vec3; inline)
  45         return Vec3(a.x+b.x, a.y+b.y, a.z+b.z)
  46     func minus(a,b:Vec3->Vec3; inline)
  47         return Vec3(a.x-b.x, a.y-b.y, a.z-b.z)
  48     func times(a,b:Vec3->Vec3; inline)
  49         return Vec3(a.x*b.x, a.y*b.y, a.z*b.z)
  50     func negative(v:Vec3->Vec3; inline)
  51         return Vec3(-v.x, -v.y, -v.z)
  52     func dot(a,b:Vec3->Num; inline)
  53         return (a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y) + (a.z-b.z)*(a.z-b.z)
  54     func cross(a,b:Vec3->Vec3; inline)
  55         return Vec3(a.y*b.z - a.z-b.y, a.z*b.x - a.x*b.z, a.x*b.y - a.y*b.x)
  56     func scaled_by(v:Vec3, k:Num->Vec3; inline)
  57         return Vec3(v.x*k, v.y*k, v.z*k)
  58     func divided_by(v:Vec3, divisor:Num->Vec3; inline)
  59         return Vec3(v.x/divisor, v.y/divisor, v.z/divisor)
  60     func length(v:Vec3->Num; inline)
  61         return (v.x*v.x + v.y*v.y + v.z*v.z).sqrt()
  62     func dist(a,b:Vec3->Num; inline)
  63         return a.minus(b).length()
  64     func norm(v:Vec3->Vec3; inline)
  65         if v.x == 0 and v.y == 0 and v.z == 0
  66             return v
  67         len := v.length()
  68         return Vec3(v.x/len, v.y/len, v.z/len)
  69     func mix(a,b:Vec3, amount:Num -> Vec3)
  70         return Vec3(
  71             amount.mix(a.x, b.x),
  72             amount.mix(a.y, b.y),
  73             amount.mix(a.z, b.z),
  74         )
  75 
  76 
  77 struct IVec2(x,y:Int)
  78     ZERO := IVec2(0, 0)
  79     func plus(a,b:IVec2->IVec2; inline)
  80         return IVec2(a.x+b.x, a.y+b.y)
  81     func minus(a,b:IVec2->IVec2; inline)
  82         return IVec2(a.x-b.x, a.y-b.y)
  83     func times(a,b:IVec2->IVec2; inline)
  84         return IVec2(a.x*b.x, a.y*b.y)
  85     func negative(v:IVec2->IVec2; inline)
  86         return IVec2(-v.x, -v.y)
  87     func dot(a,b:IVec2->Int; inline)
  88         return (a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y)
  89     func cross(a,b:IVec2->Int; inline)
  90         return a.x*b.y - a.y*b.x
  91     func scaled_by(v:IVec2, k:Int->IVec2; inline)
  92         return IVec2(v.x*k, v.y*k)
  93     func divided_by(v:IVec2, divisor:Int->IVec2; inline)
  94         return IVec2(v.x/divisor, v.y/divisor)
  95     func length(v:IVec2->Num; inline)
  96         x := Num(v.x)
  97         y := Num(v.y)
  98         return Num.sqrt(x*x + y*y)
  99     func dist(a,b:IVec2->Num; inline)
 100         return a.minus(b).length()
 101     func angle(v:IVec2->Num; inline)
 102         return Num.atan2(Num(v.y), Num(v.x))
 103 
 104 struct IVec3(x,y,z:Int)
 105     ZERO := IVec3(0, 0, 0)
 106     func plus(a,b:IVec3->IVec3; inline)
 107         return IVec3(a.x+b.x, a.y+b.y, a.z+b.z)
 108     func minus(a,b:IVec3->IVec3; inline)
 109         return IVec3(a.x-b.x, a.y-b.y, a.z-b.z)
 110     func times(a,b:IVec3->IVec3; inline)
 111         return IVec3(a.x*b.x, a.y*b.y, a.z*b.z)
 112     func negative(v:IVec3->IVec3; inline)
 113         return IVec3(-v.x, -v.y, -v.z)
 114     func dot(a,b:IVec3->Int; inline)
 115         return (a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y) + (a.z-b.z)*(a.z-b.z)
 116     func cross(a,b:IVec3->IVec3; inline)
 117         return IVec3(a.y*b.z - a.z-b.y, a.z*b.x - a.x*b.z, a.x*b.y - a.y*b.x)
 118     func scaled_by(v:IVec3, k:Int->IVec3; inline)
 119         return IVec3(v.x*k, v.y*k, v.z*k)
 120     func divided_by(v:IVec3, divisor:Int->IVec3; inline)
 121         return IVec3(v.x/divisor, v.y/divisor, v.z/divisor)
 122     func length(v:IVec3->Num; inline)
 123         x := Num(v.x)
 124         y := Num(v.y)
 125         z := Num(v.z)
 126         return Num.sqrt(x*x + y*y + z*z)
 127     func dist(a,b:IVec3->Num; inline)
 128         return a.minus(b).length()
 129 
 130 func main()
 131     >> Vec2(10, 20)
 132     assert Vec2(10, 20) + Vec2(100, 100) == Vec2(x=110, y=120)
 133     >> Vec3(10, 20, 30)
 134     >> Vec2.ZERO
 135