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View of /src/common/vec3f.sml

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Revision 14 - (download) (annotate)
Sat Feb 16 22:59:07 2008 UTC (11 years, 11 months ago) by jhr
Original Path: src/math/vec3f.sml
File size: 3788 byte(s)
  Adding 4D homogeneous vectors
(* vec3f.sml
 *
 * COPYRIGHT (c) 2006 John Reppy (http://www.cs.uchicago.edu/~jhr)
 * All rights reserved.
 *
 * Operations on vectors in R^3 (float version).
 *)

structure Vec3f : sig

    type float = FP.float

    type vec3f = {x : float, y : float, z : float}
    type vec4f = {x : float, y : float, z : float, w : float}

    val unpack : vec3f -> (float * float * float)
    val pack   : (float * float * float) -> vec3f
    val toList : vec3f -> float list

  (* functional update *)
    val setX : vec3f * float -> vec3f
    val setY : vec3f * float -> vec3f
    val setZ : vec3f * float -> vec3f

  (* lift a 3D vector into homogeneous space *)
    val vector : vec3f -> vec4f
    val point : vec3f -> vec4f

    val nth : vec3f * int -> float

    val zero : vec3f

  (* standard basis vectors *)
    val e1 : vec3f
    val e2 : vec3f
    val e3 : vec3f

    val toString : vec3f -> string

    val neg : vec3f -> vec3f
    val add : (vec3f * vec3f) -> vec3f
    val sub : (vec3f * vec3f) -> vec3f
    val mul : (vec3f * vec3f) -> vec3f

    val scale : (float * vec3f) -> vec3f

  (* adds (u, s, v) = u + s*v *)
    val adds : (vec3f * float * vec3f) -> vec3f

  (* lerp (u, t, v) = (1-t)*u + t*v; we assume that 0 <= t <= 1 *)
    val lerp : (vec3f * float * vec3f) -> vec3f

    val dot : (vec3f * vec3f) -> float
    val cross : (vec3f * vec3f) -> vec3f
    val normalize : vec3f -> vec3f
    val length : vec3f -> float
    val lengthSq : vec3f -> float		(* length squared *)
    val lengthAndDir : vec3f -> (float * vec3f)	(* length and normal vector *)
    val distanceSq : (vec3f * vec3f) -> float	(* distance squared *)

  (* iterators *)
    val map : (float -> 'a) -> vec3f -> {x : 'a, y : 'a, z : 'a}
    val app : (float -> unit) -> vec3f -> unit

  (* rays *)
    type rayf = {orig : vec3f, dir : vec3f}

    val rayToPoint : (rayf * float) -> vec3f

  end  = struct

    structure Math = Real32.Math

    type float = FP.float

    val epsilon : float = 1.0e~5

    type vec3f = float Vec3.vec3
    type vec4f = float Vec4.vec4

    open Vec3

  (* lift a 3D vector into homogeneous space *)
    fun vector {x, y, z} : vec4f = {x=x, y=y, z=z, w=0.0}
    fun point {x, y, z} : vec4f = {x=x, y=y, z=z, w=1.0}

    val zero : vec3f = {x=0.0, y = 0.0, z = 0.0}

    val e1 : vec3f = {x = 1.0, y = 0.0, z = 0.0}
    val e2 : vec3f = {x = 0.0, y = 1.0, z = 0.0}
    val e3 : vec3f = {x = 0.0, y = 0.0, z = 1.0}

    fun toString ({x, y, z} : vec3f) = concat[
	    "<", Real32.toString x, ",", Real32.toString y, ",", Real32.toString z, ">"
	  ]

    fun neg ({x, y, z} : vec3f) = {x = ~x, y = ~y, z = ~z}

    fun add ({x=x1, y=y1, z=z1} : vec3f, {x=x2, y=y2, z=z2}) =
	  {x=x1+x2, y=y1+y2, z=z1+z2}

    fun sub ({x=x1, y=y1, z=z1} : vec3f, {x=x2, y=y2, z=z2}) =
	  {x=x1-x2, y=y1-y2, z=z1-z2}

    fun mul ({x=x1, y=y1, z=z1} : vec3f, {x=x2, y=y2, z=z2}) =
	  {x=x1*x2, y=y1*y2, z=z1*z2}

    fun scale (s, {x, y, z} : vec3f) = {x = s*x, y = s*y, z = s*z}

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

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

    fun dot ({x=x1, y=y1, z=z1} : vec3f, {x=x2, y=y2, z=z2}) =
	  (x1*x2 + y1*y2 +z1*z2)

    fun cross ({x=x1, y=y1, z=z1} : vec3f, {x=x2, y=y2, z=z2}) = {
	    x = y1*z2 - z1*y2,
	    y = z1*x2 - x1*z2,
	    z = x1*y1 - y1*x2
	  }

    fun lengthSq (v : vec3f) = dot(v, v)

    fun length v = Math.sqrt(lengthSq v)

    fun distanceSq (u : vec3f, v) = lengthSq (sub (u, v))

    fun lengthAndDir (v as {x, y, z}) = 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)

  (* rays *)
    type rayf = {orig : vec3f, dir : vec3f}

    fun rayToPoint ({orig, dir}, s) = adds(orig, s, dir)

  end

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