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Using OCaml to visualize Radiohead's HoC music video (part 2)

Posted in: ocaml , visualization , opengl
This post is about performing advanced camera movement in OpenGL. We'll use the same Radiohead's HoC dataset we used in the previous post. Once again, the quality of the youtube video is pretty lame. You can right click here and save link as... to download a high quality version of the video (~100MB). I strongly recommend you to see the high quality video :)

Camera Instructions

Camera movement is made of Translations and/or Rotations. We want to provide our camera model with instructions of the type: As the last example shows, multiple transformations can be done at the same time (translations and rotations). The definition for a transformation type is: 
type camera_op = 
  | Translate of Gl.point3 * Gl.point3  
  | Rotate of float * float * Gl.vect3
A camera instruction is a list of these operations (camera_op) and a number specifying the number of frames this transformation should take (i.e the duration of the transformation). So, for example, this instruction: ( [ Translate( (100., 100., 100.), (0., 0., 0.) ) ], 300. ) translates the camera from (100, 100, 100) to (0, 0, 0) in 300 frames, that is in 10 seconds (at 30 frames per second). Translation is done by simple interpolation. The interpolation formula for translating from A to B is something like this: A + (B - A) * delta with delta in (0, 1).

Transitions

It would be nice if camera movement, besides being linear, could also perform other advanced transitions, like the ones used in Fx.Transitions by Mootools. Some of these transitions are: Quadratic, EaseIn, EaseOut, EaseInOut, Back, Sine, etc... These effects are achieved by applying functions to the delta value, changing the way it increases or descreases its value. A possible interface for a Transition module is: 
type trans = Linear | Quart
type ease = None | EaseOut | EaseIn | EaseInOut

val linear : 'a -> 'a
val quart : float -> float

val ease_in : ('a -> 'b) -> 'a -> 'b
val ease_out : (float -> float) -> float -> float
val ease_in_out : (float -> float) -> float -> float

val get_transition : trans -> float -> float
val get_ease : ease -> (float -> float) -> float -> float

val get_animation : trans -> ease -> float -> float
By using Transition.get_animation Quad EaseInOut delta we can change the timing of our animation from this: into this: Our camera instructions are then defined as: 
type camera_op_list = (camera_op list) * float * (trans * ease)
For example: ( [ Translate( (100., 100., 100.), (0., 0., 0.) ) ], 300. (Quad, EaseOut))

The Camera Model

A possible interface for the camera model is: 
class camera_model :
  object
    val mutable animations : camera_op list
    val mutable time : float
    val mutable total_frames : float
    val mutable transition : Transition.trans * Transition.ease

    method get_time : float
    method step : unit
    method draw : unit
    method translate : Gl.point3 -> Gl.point3 -> float -> unit
    method rotate : float -> float -> Gl.vect3 -> float -> unit
    method set_animations :
      camera_op list * float * (trans * ease) -> unit
  end
The camera_model instance variables contain the destructured camera_op_list type elements: animations, total_frames and transition. We also provide individual methods for handling translations and rotations. These methods simply compute a delta value, apply the interpolation and then call GlMat.translate3 or GlMat.rotate3. The 40 line implementation looks like this: 
class camera_model =
 object (self)
  val mutable total_frames = 0.
  val mutable time = 0.
  val mutable transition = (Linear, None)
  val mutable animations = []
  
  method get_time = time
  
  method set_animations ans =
    let (x, y, z) = ans in
      animations <- x;
      total_frames <- y;
      transition <- z;
      time <- 0.
  
  method step =
    if time < total_frames then
      time <- time +. 1.

  method translate start last delta =
    let (trans, ease) = transition in
    let delta_val = Transition.get_animation trans ease delta in 
    let (x, y, z) = start in
    let (x', y', z') = last in
    let DVertex(a, b, c, d) = Interpolate.cartesian 
                                (DVertex(x, y, z, 0.)) 
                                (DVertex(x', y', z', 0.)) 
                                delta_val
    in
      GlMat.translate3 (a, b, c)
  
  method rotate start last vec delta =
    let (trans, ease) = transition in
    let delta_val = Transition.get_animation trans ease delta in
    let ang = Interpolate.cartesian_float start last delta_val in
    GlMat.rotate3 ang vec 
    

    method draw =
      let delta = time /. total_frames in
        List.iter (fun anim ->
          match anim with
            | Translate(start, last) -> 
               self#translate start last delta
            | Rotate(start, last, vec) -> 
               self#rotate start last vec delta ) animations
end

Timeline

Now that we have our camera model, we need a "timeline" object that can pass intructions to the camera at different stages of the animation. We define a class-less object timeline that holds a list of camera transformations to be executed at a specific frame of the animation: 
let timeline = 
  object (self)
    val mutable frame = 0.
    (* Starting frame number, camera_instructions *)
    val camera_timeline = [
      (1.,   (* camera_instructions *));
      (310., (* camera_instructions *));
      (631., (* camera_instructions *) ]
      
    method get_frame = frame
    
    method tick =
      frame <- frame +. 1.;
      self#update_camera;
    
    method update_camera =
      try
        let camera_anim = List.assoc frame camera_timeline in
          cam#set_animations camera_anim;
        with
          | Not_found -> ()
end

Download and Use

This is all I've done to handle camera movement. I'm not an advanced OpenGL/OCaml developer, so any comment/suggestion about my understanding of OCaml/OpenGL is very welcome. You can download the source here. You can compile the source with: 
ocamlc -g str.cma -I +camlimages ci_core.cma ci_jpeg.cma ci_bmp.cma 
-I +lablGL lablglut.cma lablgl.cma interpolate.ml transition.ml 
camera.ml loader.ml main.ml -o main
Last part of this "trilogy" will be about particle transformations in OpenGL. Hope you enjoyed it!
« Using OCaml to visualize Radiohead's HoC music video (part 1)
Using OCaml to visualize Radiohead's HoC music video (part 3) »
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