Projection/Modelview

Wm4::Matrix4f calcProjectionMatrix (Wm4::Vector3f eyePos, int screenIndex, float znear, float zfar)
{
  // Get coordinates of screen corners
  Wm4::Vector3f topLeft = screenCoordinates[screenIndex-1][0];
  Wm4::Vector3f topRight = screenCoordinates[screenIndex-1][1];
  Wm4::Vector3f bottomLeft = screenCoordinates[screenIndex-1][2];
  Wm4::Vector3f bottomRight = screenCoordinates[screenIndex-1][3];

  // Support vectors of Projection-plane
  Wm4::Vector3f support1 = topRight - topLeft;
  Wm4::Vector3f support2 = bottomLeft - topLeft;

  // Normal on Projection-plane
  Wm4::Vector3f normal = support2.Cross (support1);
  normal.Normalize();

  // Distance Screen/(0,0,0)
  float distance = topLeft.Dot(normal);

  // Distance Screen/Eye Position
  float eyeDistance = eyePos.Dot(normal) - distance;

  // Look-At-Point
  Wm4::Vector3f atPoint = eyePos - normal * eyeDistance;

  // Vector from topRight to topLeft
  Wm4::Vector3f tr_tl = topLeft-topRight;
  float tr_tl_length = tr_tl.Length();

  // Distance LookAt Point <-> right edge of Frustum on the Projection plane
  // calculated by projection of Vector topRight->atPoint onto the Vector
  // topRight->topLeft
  float rightP = tr_tl.Dot(atPoint-topRight) / tr_tl_length;

  // Distance LookAt Point <-> left edge of frustum
  float leftP = rightP - tr_tl_length;

  // Vector from topLeft to bottomLeft
  Wm4::Vector3f tl_bl = bottomLeft-topLeft;
  float tl_bl_length = tl_bl.Length();

  // Distance LookAt Point <-> upper edge of Frustum on the Projection plane
  // calculated by projection of Vector topLeft->atPoint onto the Vector
  // topLeft->bottomLeft
  float topP = tl_bl.Dot(atPoint-topLeft) / tl_bl_length;

  // Distance LookAt Point <-> bottom edge of frustum
  float bottomP = topP - tl_bl_length;

  // Distance LookAt Point<->right edge of frustum on near clipping plane
  float right = rightP * znear / eyeDistance;
  // Distance LookAt Point<->left edge of frustum on near clipping plane
  float left = leftP * znear / eyeDistance;;
  // Distance LookAt Point<->top edge of frustum on near clipping plane
  float top = topP * znear / eyeDistance;;
  // Distance LookAt Point<->bottom edge of frustum on near clipping plane
  float bottom = bottomP * znear / eyeDistance;;

  // Construction of Projection matrix
  // Basically a glFrustum call with left, right, bottom, top, znear
  // and zfar as Parameters

  //Right handed
  Wm4::Matrix4f m(
    2*znear/(right-left), 0.0f, (right+left)/(right-left), 0.0f,
    0.0f, 2*znear/(top-bottom), (top+bottom)/(top-bottom), 0.0f,
    0.0f, 0.0f, -(zfar+znear)/(zfar-znear), -2*zfar*znear/(zfar-znear),
    0.0f, 0.0f, -1.0f, 0.0f
  );

  m = m.Transpose();

  return m;

}


Wm4::Matrix4f getModelview(const Wm4::Vector3f& eyePos, int screenIndex)
{
  Wm4::Vector3f topLeft = screenCoordinates[screenIndex-1][0];
  Wm4::Vector3f topRight = screenCoordinates[screenIndex-1][1];
  Wm4::Vector3f bottomLeft = screenCoordinates[screenIndex-1][2];
  Wm4::Vector3f bottomRight = screenCoordinates[screenIndex-1][3];

  Wm4::Vector3f support1 = topRight - topLeft;
  Wm4::Vector3f support2 = bottomLeft - topLeft;

  Wm4::Vector3f normal = support2.Cross (support1);
  normal.Normalize();

  float distance = topLeft.Dot(normal);

  float eyeDistance = eyePos.Dot(normal) - distance;

  // LookAt point
  Wm4::Vector3f atPoint = eyePos - normal * eyeDistance;

  // Up-Vector
  Wm4::Vector3f upVector = topLeft - bottomLeft;
  upVector.Normalize();

  // Construction of ModelviewMatrix
  // Basically gluLookAt()-Function wth eyePos, atPoint and upVector

  // View Vector
  Wm4::Vector3f f = atPoint - eyePos;
  f.Normalize();

  // Supportvector orthogonal to up- and viewvector
  Wm4::Vector3f s = f.Cross(upVector);

  // Upvector
  Wm4::Vector3f u = s.Cross(f);

  Wm4::Matrix4f m(
     s[0],  s[1],  s[2], -(s[0]*eyePos[0] + s[1]*eyePos[1] + s[2]*eyePos[2]),
     u[0],  u[1],  u[2], -(u[0]*eyePos[0] + u[1]*eyePos[1] + u[2]*eyePos[2]),
    -f[0], -f[1], -f[2],  (f[0]*eyePos[0] + f[1]*eyePos[1] + f[2]*eyePos[2]),
    0.0f, 0.0f, 0.0f, 1.0f
  );

  m = m.Transpose();

  return m;
}