Overfloater

I learned this “trick” some time ago, while reading the source code for the MooTools JavaScript framework (version 1.1, I think).

I used this “trick” not so long ago, when developing the Spacetree visualization for the JavaScript InfoVis Toolkit library.

When clicking a node, the Spacetree visualization unselects all tree nodes and then selects the nodes in between the root node and the selected node. This can be implemented as a recursive function, since we have to iterate through the clicked node and its ancestors to set those nodes as selected.

I defined an anonymous recursive function that receives a node and a special value as formal parameters, and sets the selected property from this node and its ancestors to the specified value:

  (function(node, val) {
      if(node == null) return;
      node.selected = val;
      return arguments.callee(node.parent, val);
  })

arguments.callee holds a reference to the defined function.
You can check that by copying this code:

  (function(text) {
    alert(arguments.callee);
    alert(text);
  })("some text");

and running it in your Firefox console.

Unfortunately, our anonymous recursive function needs to be called more than once, since we first need to unselect previous selected nodes, and then to select the nodes in between the clicked node and the root node.
Similar to the “return this” trick to chain method calls, we can add “return arguments.callee” to chain function calls.

  (function(node, val) {
      if(node == null) return arguments.callee;
      node.selected = val;
      return arguments.callee(node.parent, val);
  })

This way, we can call our function multiple times. I’ll first pass the previous clicked node in order to unselect the previous selected path, and then I’ll pass the new clicked node in order to select our new path:

  (function(node, val) {
      if(node == null) return arguments.callee;
      node.selected = val;
      return arguments.callee(node.parent, val);
  })(nodePrev, false)(nodeNew, true);

What’s more interesting though, it’s trying to do the same thing in another language, like Lisp or OCaml.
Who knows, you might sumble upon the Y combinator.

Update 10/2009: The project is currently hosted at GitHub.
Update 01/2009: Created a new hoc3.zip file and some documentation.

A while ago Radiohead published their House of Cards video data in form of CSV files. Each CSV file contains information about the 3D position of the points for each frame.

I wrote a couple of previous posts that covered how to render and save that data with OpenGL and OCaml and also how to customize camera movement in OpenGL.

This post shows how to customize particle animations for Radiohead’s House of Cards video.
A proof of concept for camera movement + particle animation is shown in this youtube video:

If you want to generate the video, you have to download Radiohead’s HoC music video data here. Also, you can download the source code for this project here.

This small project is organized in a way that is easy to add new features, camera animations and particle transformations in order to easily code new videos with different effects using the HoC data.

Radiohead’s HoC data is a set of CSV files. Those files are rendered in OpenGL with OCaml and then saved in bmp or jpeg files to be merged into a video using ffmpeg. If you want to know more about this you should probably read part 1 of this “trilogy”.

The Camera Model class allows you to make custom camera movements that can be handled and defined in a Timeline object in the main.ml file. If you like to know more about this, you can read part 2 of this “trilogy”.

This last post shows how to customize particle interpolation and movement by using the Particle Model class, the ParticleTrans module and the Timeline object.

Particle Model

The particle_model class handles particle animations.
Somewhat like the camera class, particle_model stores the initial frame and the last frame along with some extra information about the timing of the animation.
The particle_model then performs an interpolation from the initial_frame to the last_frame, rendering the state of the transformation in the draw function.

A possible interface for the particle model could be something like this:

class particle_model :
  object
    (* starting frame *)
    val mutable start_frame : VertexType.depth_vertex list
    (* ending frame *)
    val mutable last_frame : VertexType.depth_vertex list
    (* currently loaded frame *)
    val mutable loaded_frame : VertexType.depth_vertex list
    (* if setted to true, it will load a new frame for each
    step of the animation *)
    val mutable refresh_frames : bool
    (* same as the camera_model -check that post *)
    val mutable time : float
    val mutable total_frames : float
    val mutable transition : Transition.trans * Transition.ease
    (* extend start_frame or last_frame in order to
    have same number of points *)
    method balance : unit
    (* equivalent to the camera methods *)
    method step : unit
    method draw : float -> unit
    (* set the type of the animation you want
    to perform *)
    method set_animation :
      float ->
      bool * bool *
      (ParticleTrans.transformation * float *
       (Transition.trans * Transition.ease)) ->
      unit
  end

Particle animations have a special type, that ressembles the camera model transition type.
This type is defined as follows:

type animation_op =
    ParticleTrans.transformation * float *
    (Transition.trans * Transition.ease)

Just to make a comparison, the camera model transition type is:

type camera_op_list = (camera_op list) * float * (trans * ease)

This type can be divided into three main parts:

• The float value is the total number of frames the animation will use.
• The (trans * ease) value allows you to customize different type of transitions, from Linear, None to Quad, EaseInOut. More information about this is in the camera_model post.
• ParticleTrans.transformation is a function that applies a transformation to a frame. You can define custom functions in that module and then apply them to the visualization.
  I only defined a couple of functions, but you can define any other animation you like. You just have to define a function that receives a frame as input and returns a frame as output.
  The interface for ParticleTrans is:

  type transformation =
  	| Idle
  	| Project of float * float * float
  	| Random
  
  val idle : 'a -> 'a
  
  val project :
    transformation ->
    VertexType.depth_vertex list ->
  	VertexType.depth_vertex list
  
  val random : VertexType.depth_vertex list ->
  	VertexType.depth_vertex list
  
  val get_trans :
    transformation ->
    VertexType.depth_vertex list ->
  	VertexType.depth_vertex list

Putting it all together

The timeline object (described in the previous post) holds information about the camera and particle transformations beeing applied at each stage of the animation.
This class-less object is defined in the main.ml file and looks like this:

let timeline =
  object (self)
    val mutable frame = 0.
    val camera_timeline = [
    (* operations defined in the
    camera model post *)
    ]

    val particle_timeline = [
      (* frame number,  (invert, refresh frames, instruction) *)
      (1., (true, true, (Random, 120., (Elastic, EaseOut))));
      (420., (false, false, (Random, 50., (Quad, EaseOut))));
      (471., (false, true, (Idle, 80., (Quad, EaseIn))))
      ]

    method get_frame = frame

    method tick =
      frame <- frame +. 1.;
      self#update_camera;
      self#update_animation

    method update_camera =
      try
        let camera_anim = List.assoc frame camera_timeline in
          cam#set_animations camera_anim;
        with
          | Not_found -> ()

    method update_animation =
      try
        let anim = List.assoc frame particle_timeline in
          part#set_animation frame anim;
      with
          | Not_found -> ()
end

The particle_timeline and camera_timeline variables hold the transformations to be performed at different stages of the animation.

Download and Use

You can download the project here.
You can compile the project by typing:

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 particleTrans.ml particle.ml main.ml -o main

Any comment about the Video or the OpenGL/OCaml implementation is very welcome!

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:

• [ Translate from to ]
• [ Rotate from to rotation_axis ]
• [ Translate ...; Rotate ... ]

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!