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[sml3d] View of /trunk/sml3d/src/sml3d/base/vec2d.sml
 [sml3d] / trunk / sml3d / src / sml3d / base / vec2d.sml

# View of /trunk/sml3d/src/sml3d/base/vec2d.sml

Tue Jan 17 14:01:50 2012 UTC (7 years, 8 months ago) by jhr
File size: 2739 byte(s)
```  Working on new SML3d core library
```
```(* vec2d.sml
*
* COPYRIGHT (c) 2012 The SML3d Project (http://sml3d.cs.uchicago.edu)
*
* Operations on vectors in R^2 (double-precision version).
*)

structure Vec2d :> VEC2 where type flt = Double.flt
= struct

structure Flt = Double

type flt = Flt.flt

val epsilon = Flt.epsilon
val slerpTolerance : flt = 0.999

type vec2 = flt SML3dTypes.vec2
type vec3 = flt SML3dTypes.vec3

open Vec2

(* lift a 3D vector into homogeneous space *)
fun vector (x, y) : vec3 = (x, y, 0.0)
fun point (x, y) : vec3 = (x, y, 1.0)

val zero : vec2 = (0.0, 0.0)

val e1 : vec2 = (1.0, 0.0)
val e2 : vec2 = (0.0, 1.0)

fun toString (v : vec2) = concat[
"<", Flt.toString(#1 v), ",", Flt.toString(#2 v), ">"
]

fun neg ((x, y) : vec2) = (~x, ~y)

fun add ((x1, y1) : vec2, (x2, y2)) = (x1+x2, y1+y2)

fun sub ((x1, y1) : vec2, (x2, y2)) = (x1-x2, y1-y2)

fun mul ((x1, y1) : vec2, (x2, y2)) = (x1*x2, y1*y2)

fun scale (s, (x, y) : vec2) = (s*x, s*y)

fun abs (x, y) = (Flt.abs x, Flt.abs y)
fun min ((x1, y1), (x2, y2)) = (Flt.min(x1, x2), Flt.min(y1, y2))
fun max ((x1, y1), (x2, y2)) = (Flt.max(x1, x2), Flt.max(y1, y2))

fun dot ((x1, y1) : vec2, (x2, y2)) = (x1*x2 + y1*y2)

fun lerp (v1, t, v2) = adds (scale(1.0-t, v1), t, v2)

(* spherical interpolation between unit vectors *)
fun slerp (v1, t, v2) = let
val cosAngle = dot(v1, v2)
in
if (cosAngle < slerpTolerance)
then let
val angle = Flt.acos cosAngle
val recipSinAngle = 1.0 / Flt.sin angle
val scale1 = recipSinAngle * Flt.sin((1.0 - t) * angle)
val scale2 = recipSinAngle * Flt.sin(t * angle)
in
end
else lerp(v1, t, v2)
end

fun lengthSq v = dot(v, v)
fun length v = Flt.sqrt(lengthSq v)

fun distanceSq (u, v) = lengthSq (sub (u, v))
fun distance (u, v) = length (sub (u, v))

fun lengthAndDir v = let
val l = length v
in
if (l < epsilon)
then (l, v)
else (l, scale(1.0 / l, v))
end

fun normalize v = #2(lengthAndDir v)

fun clipLength (v, maxLen) = let
val lenSq = lengthSq v
in
if (lenSq < maxLen*maxLen)
then v
else scale(maxLen / Flt.sqrt lenSq, v)
end

fun parallelComponent {basis, v} = scale(dot(basis, v), basis)

fun perpendicularComponent {basis, v} = sub(v, parallelComponent {basis=basis, v=v})

(* rotate the vector by 90 degrees in the CW direction *)
fun perpCW (v : vec2) = (#2 v, ~(#1 v))
(* rotate the vector by 90 degrees in the CCW direction *)
fun perpCCW (v : vec2) = (~(#2 v), #1 v)

end
```