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Revision 210 - (download) (annotate)
Tue Jun 17 03:29:03 2008 UTC (11 years, 3 months ago) by jhr
File size: 10520 byte(s)
  Added rotations.
(* matrix4d.sml
 *
 * COPYRIGHT (c) 2008 John Reppy (http://cs.uchicago.edu/~jhr)
 * All rights reserved.
 *
 * Double-precision 4x4 matrices
 *)

structure Matrix4d : sig

    type mat4d

    type double = SML3dTypes.double
    type vec3d = SML3dTypes.vec3d
    type vec4d = SML3dTypes.vec4d

    val mat : {
	    m11 : double, m12 : double, m13 : double, m14 : double,
	    m21 : double, m22 : double, m23 : double, m24 : double,
	    m31 : double, m32 : double, m33 : double, m34 : double,
	    m41 : double, m42 : double, m43 : double, m44 : double
	  } -> mat4d

  (* standard matrices *)
    val identity : mat4d			(* identity matrix *)
    val isoscale : double -> mat4d		(* isotropic scaling *)
    val scale    : vec3d -> mat4d		(* anisotropic scaling *)
    val rotateX  : double -> mat4d		(* rotation around X axis (in degrees) *)
    val rotateY  : double -> mat4d		(* rotation around Y axis (in degrees) *)
    val rotateZ  : double -> mat4d		(* rotation around Z axis (in degrees) *)
    val rotate   : double * vec3d -> mat4d	(* rotation around an axis (in degrees) *)

    val perspective : {fov : double, aspect : double, near : double, far : double} -> mat4d

    val mxv : mat4d * vec4d -> vec4d
    val vxm : vec4d * mat4d -> vec4d
    val mxm : mat4d * mat4d -> mat4d

    val transpose : mat4d -> mat4d

    val inverse : mat4d -> mat4d option

  (* returns matrix as flat vector in column-major order *)
    val toVector : mat4d -> double Vector.vector

  end = struct

    type double = SML3dTypes.double
    type vec3d = SML3dTypes.vec3d
    type vec4d = SML3dTypes.vec4d

    val epsilond : double = 1.0e~7

  (* represented in column-major order, since that is what OpenGL LoadMatrix
   * expects.
   *)
    datatype mat4d = M of double Vector.vector

    fun ! (a : double Vector.vector, (r, c)) = Unsafe.Vector.sub(a, 4*c + r - 5)
    infix !

    fun new {m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33, m34, m41, m42, m43, m44} =
	  M(Vector.fromList [
	      m11, m21, m31, m41, m12, m22, m32, m42, m13, m23, m33, m43, m14, m24, m34, m44
	    ])

    val mat = new

    val identity = new{
	    m11 = 1.0, m12 = 0.0, m13 = 0.0, m14 = 0.0,
	    m21 = 0.0, m22 = 1.0, m23 = 0.0, m24 = 0.0,
	    m31 = 0.0, m32 = 0.0, m33 = 1.0, m34 = 0.0,
	    m41 = 0.0, m42 = 0.0, m43 = 0.0, m44 = 1.0
	  }

    fun isoscale s = new{
	    m11 = s,   m12 = 0.0, m13 = 0.0, m14 = 0.0,
	    m21 = 0.0, m22 = s,   m23 = 0.0, m24 = 0.0,
	    m31 = 0.0, m32 = 0.0, m33 = s,   m34 = 0.0,
	    m41 = 0.0, m42 = 0.0, m43 = 0.0, m44 = 1.0
	  }

    fun scale {x, y, z} = new{
	    m11 = x,   m12 = 0.0, m13 = 0.0, m14 = 0.0,
	    m21 = 0.0, m22 = y,   m23 = 0.0, m24 = 0.0,
	    m31 = 0.0, m32 = 0.0, m33 = z,   m34 = 0.0,
	    m41 = 0.0, m42 = 0.0, m43 = 0.0, m44 = 1.0
	  }

    fun translate {x, y, z} = new{
	    m11 = 1.0, m12 = 0.0, m13 = 0.0, m14 = x,
	    m21 = 0.0, m22 = 1.0, m23 = 0.0, m24 = y,
	    m31 = 0.0, m32 = 0.0, m33 = 1.0, m34 = z,
	    m41 = 0.0, m42 = 0.0, m43 = 0.0, m44 = 1.0
	  }

  (* rotation around X axis (in degrees) *)
    fun rotateX angle = let
	  val angle = Double.toRadians angle
	  val s = Double.sin angle
	  val c = Double.cos angle
	  in
	    new {
		m11 = 1.0, m12 = 0.0, m13 = 0.0, m14 = 0.0,
		m21 = 0.0, m22 = c,   m23 = ~s,	 m24 = 0.0,
		m31 = 0.0, m32 = s,   m33 = c,   m34 = 0.0,
		m41 = 0.0, m42 = 0.0, m43 = 0.0, m44 = 1.0
	      }
	  end

  (* rotation around Y axis (in degrees) *)
    fun rotateY angle = let
	  val angle = Double.toRadians angle
	  val s = Double.sin angle
	  val c = Double.cos angle
	  in
	    new {
		m11 = c,   m12 = 0.0, m13 = s,   m14 = 0.0,
		m21 = 0.0, m22 = 1.0, m23 = 0.0, m24 = 0.0,
		m31 = ~s,  m32 = 0.0, m33 = c,   m34 = 0.0,
		m41 = 0.0, m42 = 0.0, m43 = 0.0, m44 = 1.0
	      }
	  end

  (* rotation around Z axis (in degrees) *)
    fun rotateZ angle = let
	  val angle = Double.toRadians angle
	  val s = Double.sin angle
	  val c = Double.cos angle
	  in
	    new {
		m11 = c,   m12 = ~s,  m13 = 0.0, m14 = 0.0,
		m21 = s,   m22 = c,   m23 = 0.0, m24 = 0.0,
		m31 = 0.0, m32 = 0.0, m33 = 1.0, m34 = 0.0,
		m41 = 0.0, m42 = 0.0, m43 = 0.0, m44 = 1.0
	      }
	  end

  (* rotation around an axis (in degrees) *)
    fun rotate (angle, {x, y, z}) = let
	  val angle = Double.toRadians angle
	  val s = Double.sin angle
	  val c = Double.cos angle
	  val c' = 1.0 - c
	  in
	    new {
		m11 = x*x*c'+c,   m12 = x*y*c'-z*s, m13 = x*z*c'+y*s, m14 = 0.0,
		m21 = y*x*c'+z*s, m22 = y*y*c'+c,   m23 = y*z*c'-x*s, m24 = 0.0,
		m31 = x*z*c'-y*s, m32 = y*z*c'+x*s, m33 = z*z*c'+c,   m34 = 0.0,
		m41 = 0.0,        m42 = 0.0,        m43 = 0.0,        m44 = 1.0
	      }
	  end

  (* construct the OpenGL perspective projection matrix *)
    fun perspective {fov, aspect, near, far} = let
	  val f = 1.0 / Double.tan ((fov * Double.M_PI) / 360.0)
	  val d' = 1.0 / (near - far)
	  in
	    new {
		m11 = f / aspect, m12 = 0.0,	m13 = 0.0,	     m14 = 0.0,
		m21 = 0.0,	  m22 = f,	m23 = 0.0,	     m24 = 0.0,
		m31 = 0.0,	  m32 = 0.0,	m33 = d'*(near+far), m34 = 2.0*d'*near*far,
		m41 = 0.0,	  m42 = 0.0,	m43 = ~1.0,	     m44 = 0.0
	      }
	  end

  (* multiply a matrix times a column vector *)
    fun mxv (M mat, {x, y, z, w}) = let
	  fun m arg = mat ! arg
	  in {
	    x = m(1,1) * x + m(1,2) * y + m(1,3) * z + m(1,4) * w,
	    y = m(2,1) * x + m(2,2) * y + m(2,3) * z + m(2,4) * w,
	    z = m(3,1) * x + m(3,2) * y + m(3,3) * z + m(3,4) * w,
	    w = m(4,1) * x + m(4,2) * y + m(4,3) * z + m(4,4) * w
	  } end
    
  (* multiply a row vector times a matrix *)
    fun vxm ({x, y, z, w}, M mat) = let
	  fun m arg = mat ! arg
	  in {
	    x = m(1,1) * x + m(2,1) * y + m(3,1) * z + m(4,1) * w,
	    y = m(1,2) * x + m(2,2) * y + m(3,2) * z + m(4,2) * w,
	    z = m(1,3) * x + m(2,3) * y + m(3,3) * z + m(4,3) * w,
	    w = m(1,4) * x + m(2,4) * y + m(3,4) * z + m(4,4) * w
	  } end

  (* matrix transpose *)
    fun transpose (M mat) = let
	  fun m arg = mat ! arg
	  in
	    new {
		m11 = m(1,1), m12 = m(2,1), m13 = m(3,1), m14 = m(4,1),
		m21 = m(1,2), m22 = m(2,2), m23 = m(3,2), m24 = m(4,2),
		m31 = m(1,3), m32 = m(2,3), m33 = m(3,3), m34 = m(4,3),
		m41 = m(1,4), m42 = m(2,4), m43 = m(3,4), m44 = m(4,4)
	      }
	  end

  (* matrix multiplication *)
    fun mxm (M aMat, M bMat) = let
	  fun a arg = aMat ! arg
	  fun b arg = bMat ! arg
	  in
	    new {
		m11 = a(1,1) * b(1,1) + a(1,2) * b(2,1) + a(1,3) * b(3,1) + a(1,4) * b(4,1),
		m12 = a(1,1) * b(1,2) + a(1,2) * b(2,2) + a(1,3) * b(3,2) + a(1,4) * b(4,2),
		m13 = a(1,1) * b(1,3) + a(1,2) * b(2,3) + a(1,3) * b(3,3) + a(1,4) * b(4,3),
		m14 = a(1,1) * b(1,4) + a(1,2) * b(2,4) + a(1,3) * b(3,4) + a(1,4) * b(4,4),
		m21 = a(2,1) * b(1,1) + a(2,2) * b(2,1) + a(2,3) * b(3,1) + a(2,4) * b(4,1),
		m22 = a(2,1) * b(1,2) + a(2,2) * b(2,2) + a(2,3) * b(3,2) + a(2,4) * b(4,2),
		m23 = a(2,1) * b(1,3) + a(2,2) * b(2,3) + a(2,3) * b(3,3) + a(2,4) * b(4,3),
		m24 = a(2,1) * b(1,4) + a(2,2) * b(2,4) + a(2,3) * b(3,4) + a(2,4) * b(4,4),
		m31 = a(3,1) * b(1,1) + a(3,2) * b(2,1) + a(3,3) * b(3,1) + a(3,4) * b(4,1),
		m32 = a(3,1) * b(1,2) + a(3,2) * b(2,2) + a(3,3) * b(3,2) + a(3,4) * b(4,2),
		m33 = a(3,1) * b(1,3) + a(3,2) * b(2,3) + a(3,3) * b(3,3) + a(3,4) * b(4,3),
		m34 = a(3,1) * b(1,4) + a(3,2) * b(2,4) + a(3,3) * b(3,4) + a(3,4) * b(4,4),
		m41 = a(4,1) * b(1,1) + a(4,2) * b(2,1) + a(4,3) * b(3,1) + a(4,4) * b(4,1),
		m42 = a(4,1) * b(1,2) + a(4,2) * b(2,2) + a(4,3) * b(3,2) + a(4,4) * b(4,2),
		m43 = a(4,1) * b(1,3) + a(4,2) * b(2,3) + a(4,3) * b(3,3) + a(4,4) * b(4,3),
		m44 = a(4,1) * b(1,4) + a(4,2) * b(2,4) + a(4,3) * b(3,4) + a(4,4) * b(4,4)
	      }
	  end

    fun inverse (M mat) = let
	  fun m arg = (mat ! arg)
	(* 2x2 subdeterminants *)
	  val tbt34C12 = m(3,1)*m(4,2) - m(3,2)*m(4,1)
	  val tbt34C13 = m(3,1)*m(4,3) - m(3,3)*m(4,1)
	  val tbt34C14 = m(3,1)*m(4,4) - m(3,4)*m(4,1)
	  val tbt34C23 = m(3,2)*m(4,3) - m(3,3)*m(4,2)
	  val tbt34C24 = m(3,2)*m(4,4) - m(3,4)*m(4,2)
	  val tbt34C34 = m(3,3)*m(4,4) - m(3,4)*m(4,3)
	(* 2x2 subdeterminants *)
	  val tbt24C12 = m(2,1)*m(4,2) - m(2,2)*m(4,1)
	  val tbt24C13 = m(2,1)*m(4,3) - m(2,3)*m(4,1)
	  val tbt24C14 = m(2,1)*m(4,4) - m(2,4)*m(4,1)
	  val tbt24C23 = m(2,2)*m(4,3) - m(2,3)*m(4,2)
	  val tbt24C24 = m(2,2)*m(4,4) - m(2,4)*m(4,2)
	  val tbt24C34 = m(2,3)*m(4,4) - m(2,4)*m(4,3)
	(* 2x2 subdeterminants *)
	  val tbt23C12 = m(2,1)*m(3,2) - m(2,2)*m(3,1)
	  val tbt23C13 = m(2,1)*m(3,3) - m(2,3)*m(3,1)
	  val tbt23C14 = m(2,1)*m(3,4) - m(2,4)*m(3,1)
	  val tbt23C23 = m(2,2)*m(3,3) - m(2,3)*m(3,2)
	  val tbt23C24 = m(2,2)*m(3,4) - m(2,4)*m(3,2)
	  val tbt23C34 = m(2,3)*m(3,4) - m(2,4)*m(3,3)
	(* 3x3 subdeterminants *)
	  val sd11 = m(2,2)*tbt34C34 - m(2,3)*tbt34C24 + m(2,4)*tbt34C23
	  val sd12 = m(2,1)*tbt34C34 - m(2,3)*tbt34C14 + m(2,4)*tbt34C13
	  val sd13 = m(2,1)*tbt34C24 - m(2,2)*tbt34C14 + m(2,4)*tbt34C12
	  val sd14 = m(2,1)*tbt34C23 - m(2,2)*tbt34C13 + m(2,3)*tbt34C12
	(* 3x3 subdeterminants *)
	  val sd21 = m(1,2)*tbt34C34 - m(1,3)*tbt34C24 + m(1,4)*tbt34C23
	  val sd22 = m(1,1)*tbt34C34 - m(1,3)*tbt34C14 + m(1,4)*tbt34C13
	  val sd23 = m(1,1)*tbt34C24 - m(1,2)*tbt34C14 + m(1,4)*tbt34C12
	  val sd24 = m(1,1)*tbt34C23 - m(1,2)*tbt34C13 + m(1,3)*tbt34C12
	(* 3x3 subdeterminants *)
	  val sd31 = m(1,2)*tbt24C34 - m(1,3)*tbt24C24 + m(1,4)*tbt24C23
	  val sd32 = m(1,1)*tbt24C34 - m(1,3)*tbt24C14 + m(1,4)*tbt24C13
	  val sd33 = m(1,1)*tbt24C24 - m(1,2)*tbt24C14 + m(1,4)*tbt24C12
	  val sd34 = m(1,1)*tbt24C23 - m(1,2)*tbt24C13 + m(1,3)*tbt24C12
	(* 3x3 subdeterminants *)
	  val sd41 = m(1,2)*tbt23C34 - m(1,3)*tbt23C24 + m(1,4)*tbt23C23
	  val sd42 = m(1,1)*tbt23C34 - m(1,3)*tbt23C14 + m(1,4)*tbt23C13
	  val sd43 = m(1,1)*tbt23C24 - m(1,2)*tbt23C14 + m(1,4)*tbt23C12
	  val sd44 = m(1,1)*tbt23C23 - m(1,2)*tbt23C13 + m(1,3)*tbt23C12
	(* determinant *)
	  val det = m(1,1)*sd11 - m(1,2)*sd12 + m(1,3)*sd13 - m(1,4)*sd14
	  in
	    if ((det > ~epsilond) andalso (det < epsilond))
	      then NONE
	      else let
		val detInv = 1.0 / det
		in
		  SOME(new {
		      m11 = sd11*detInv,
		      m21 = ~sd12*detInv,
		      m31 = sd13*detInv,
		      m41 = ~sd14*detInv,
		      m12 = ~sd21*detInv,
		      m22 = sd22*detInv,
		      m32 = ~sd23*detInv,
		      m42 = sd24*detInv,
		      m13 = sd31*detInv,
		      m23 = ~sd32*detInv,
		      m33 = sd33*detInv,
		      m43 = ~sd34*detInv,
		      m14 = ~sd41*detInv,
		      m24 = sd42*detInv,
		      m34 = ~sd43*detInv,
		      m44 = sd44*detInv
		    })
		end
	  end

    fun toVector (M v) = v

  end

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