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# A math vector library for 2D and 3D vectors of Nums or Ints
struct Vec2(x,y:Num):
ZERO := Vec2(0, 0)
func plus(a,b:Vec2->Vec2; inline):
return Vec2(a.x+b.x, a.y+b.y)
func minus(a,b:Vec2->Vec2; inline):
return Vec2(a.x-b.x, a.y-b.y)
func times(a,b:Vec2->Vec2; inline):
return Vec2(a.x*b.x, a.y*b.y)
func negative(v:Vec2->Vec2; inline):
return Vec2(-v.x, -v.y)
func dot(a,b:Vec2->Num; inline):
return (a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y)
func cross(a,b:Vec2->Num; inline):
return a.x*b.y - a.y*b.x
func scaled_by(v:Vec2, k:Num->Vec2; inline):
return Vec2(v.x*k, v.y*k)
func divided_by(v:Vec2, divisor:Num->Vec2; inline):
return Vec2(v.x/divisor, v.y/divisor)
func length(v:Vec2->Num; inline):
return (v.x*v.x + v.y*v.y)!:sqrt()
func dist(a,b:Vec2->Num; inline):
return a:minus(b):length()
func angle(v:Vec2->Num; inline):
return Num.atan2(v.y, v.x)
func norm(v:Vec2->Vec2; inline):
if v.x == 0 and v.y == 0:
return v
len := v:length()
return Vec2(v.x/len, v.y/len)
func rotated(v:Vec2, radians:Num -> Vec2):
cos := radians:cos() or return v
sin := radians:sin() or return v
return Vec2(cos*v.x - sin*v.y, sin*v.x + cos*v.y)
func mix(a,b:Vec2, amount:Num -> Vec2):
return Vec2(
amount:mix(a.x, b.x),
amount:mix(a.y, b.y),
)
struct Vec3(x,y,z:Num):
ZERO := Vec3(0, 0, 0)
func plus(a,b:Vec3->Vec3; inline):
return Vec3(a.x+b.x, a.y+b.y, a.z+b.z)
func minus(a,b:Vec3->Vec3; inline):
return Vec3(a.x-b.x, a.y-b.y, a.z-b.z)
func times(a,b:Vec3->Vec3; inline):
return Vec3(a.x*b.x, a.y*b.y, a.z*b.z)
func negative(v:Vec3->Vec3; inline):
return Vec3(-v.x, -v.y, -v.z)
func dot(a,b:Vec3->Num; inline):
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)
func cross(a,b:Vec3->Vec3; inline):
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)
func scaled_by(v:Vec3, k:Num->Vec3; inline):
return Vec3(v.x*k, v.y*k, v.z*k)
func divided_by(v:Vec3, divisor:Num->Vec3; inline):
return Vec3(v.x/divisor, v.y/divisor, v.z/divisor)
func length(v:Vec3->Num; inline):
return (v.x*v.x + v.y*v.y + v.z*v.z)!:sqrt()
func dist(a,b:Vec3->Num; inline):
return a:minus(b):length()
func norm(v:Vec3->Vec3; inline):
if v.x == 0 and v.y == 0 and v.z == 0:
return v
len := v:length()
return Vec3(v.x/len, v.y/len, v.z/len)
func mix(a,b:Vec3, amount:Num -> Vec3):
return Vec3(
amount:mix(a.x, b.x),
amount:mix(a.y, b.y),
amount:mix(a.z, b.z),
)
struct IVec2(x,y:Int):
ZERO := IVec2(0, 0)
func plus(a,b:IVec2->IVec2; inline):
return IVec2(a.x+b.x, a.y+b.y)
func minus(a,b:IVec2->IVec2; inline):
return IVec2(a.x-b.x, a.y-b.y)
func times(a,b:IVec2->IVec2; inline):
return IVec2(a.x*b.x, a.y*b.y)
func negative(v:IVec2->IVec2; inline):
return IVec2(-v.x, -v.y)
func dot(a,b:IVec2->Int; inline):
return (a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y)
func cross(a,b:IVec2->Int; inline):
return a.x*b.y - a.y*b.x
func scaled_by(v:IVec2, k:Int->IVec2; inline):
return IVec2(v.x*k, v.y*k)
func divided_by(v:IVec2, divisor:Int->IVec2; inline):
return IVec2(v.x/divisor, v.y/divisor)
func length(v:IVec2->Num; inline):
x := Num(v.x)
y := Num(v.y)
return Num.sqrt(x*x + y*y)
func dist(a,b:IVec2->Num; inline):
return a:minus(b):length()
func angle(v:IVec2->Num; inline):
return Num.atan2(Num(v.y), Num(v.x))
struct IVec3(x,y,z:Int):
ZERO := IVec3(0, 0, 0)
func plus(a,b:IVec3->IVec3; inline):
return IVec3(a.x+b.x, a.y+b.y, a.z+b.z)
func minus(a,b:IVec3->IVec3; inline):
return IVec3(a.x-b.x, a.y-b.y, a.z-b.z)
func times(a,b:IVec3->IVec3; inline):
return IVec3(a.x*b.x, a.y*b.y, a.z*b.z)
func negative(v:IVec3->IVec3; inline):
return IVec3(-v.x, -v.y, -v.z)
func dot(a,b:IVec3->Int; inline):
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)
func cross(a,b:IVec3->IVec3; inline):
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)
func scaled_by(v:IVec3, k:Int->IVec3; inline):
return IVec3(v.x*k, v.y*k, v.z*k)
func divided_by(v:IVec3, divisor:Int->IVec3; inline):
return IVec3(v.x/divisor, v.y/divisor, v.z/divisor)
func length(v:IVec3->Num; inline):
x := Num(v.x)
y := Num(v.y)
z := Num(v.z)
return Num.sqrt(x*x + y*y + z*z)
func dist(a,b:IVec3->Num; inline):
return a:minus(b):length()
func main():
>> Vec2(10, 20)
>> Vec2(10, 20) + Vec2(100, 100)
= Vec2(x=110, y=120)
>> Vec3(10, 20, 30)
>> Vec2.ZERO
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