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View of /trunk/sml3d/src/sml3d/base/vec3f.sml

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Revision 1260 - (download) (annotate)
Tue Jan 17 14:01:50 2012 UTC (7 years, 8 months ago) by jhr
File size: 2856 byte(s)
  Working on new SML3d core library
(* vec3f.sml
 *
 * COPYRIGHT (c) 2012 The SML3d Project (http://sml3d.cs.uchicago.edu)
 * All rights reserved.
 *
 * Operations on vectors in R^3 (float version).
 *)

structure Vec3f :> VEC3 where type flt = Float.flt =
  struct

    structure Flt = Float

    type flt = Flt.flt

    val epsilon = Flt.epsilon
    val slerpTolerance = 0.999

    type vec3 = flt SML3dTypes.vec3
    type vec4 = flt SML3dTypes.vec4

    open Vec3

  (* lift a 3D vector into homogeneous space *)
    fun vector (x, y, z) : vec4 = (x, y, z, 0.0)
    fun point (x, y, z) : vec4 = (x, y, z, 1.0)

    val zero : vec3 = (0.0, 0.0, 0.0)

    val e1 : vec3 = (1.0, 0.0, 0.0)
    val e2 : vec3 = (0.0, 1.0, 0.0)
    val e3 : vec3 = (0.0, 0.0, 1.0)

    fun toString ((x, y, z) : vec3) = concat[
	    "<", Flt.toString x, ",", Flt.toString y, ",", Flt.toString z, ">"
	  ]

    fun neg ((x, y, z) : vec3) = (~x, ~y, ~z)

    fun add ((x1, y1, z1) : vec3, (x2, y2, z2)) = (x1+x2, y1+y2, z1+z2)

    fun sub ((x1, y1, z1) : vec3, (x2, y2, z2)) = (x1-x2, y1-y2, z1-z2)

    fun mul ((x1, y1, z1) : vec3, (x2, y2, z2)) = (x1*x2, y1*y2, z1*z2)

    fun scale (s, (x, y, z) : vec3) = (s*x, s*y, s*z)

    fun adds (v1, s, v2) = add(v1, scale(s, v2))

    fun abs (x, y, z) = (Flt.abs x, Flt.abs y, Flt.abs z)
    fun min ((x1, y1, z1), (x2, y2, z2)) = (Flt.min(x1, x2), Flt.min(y1, y2), Flt.min(z1, z2))
    fun max ((x1, y1, z1), (x2, y2, z2)) = (Flt.max(x1, x2), Flt.max(y1, y2), Flt.max(z1, z2))

    fun dot ((x1, y1, z1) : vec3, (x2, y2, z2)) = (x1*x2 + y1*y2 +z1*z2)

    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
		  adds (scale(scale1, v1), scale1, v2)
		end
	      else lerp(v1, t, v2)
	  end

    fun cross ((x1, y1, z1) : vec3, (x2, y2, z2)) = (
	    y1*z2 - z1*y2,
	    z1*x2 - x1*z2,
	    x1*y2 - y1*x2
	  )

    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 (0.0, zero)
	      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})

  end

root@smlnj-gforge.cs.uchicago.edu
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