P3D.as

/*
 *  POINT3D CLASS  Copyright (c) Brandon Williams - 3/3/2001 - [email protected] - use freely with accreditation.
 *
 *
 *  CONSTRUCTOR:  point3d (px, py, pz, pcx, pcy, MC, psize, D)
 *
 *                       -- creates a new 3d point (can be used for 2d by making pz=0).  The arguements "px", "py",
 *                          and "pz" is the point's ordered triplet (x,y,z).  Arguements "pcx" and "pcy" is where on
 *                          the stage you want the origin to be.  Since (0,0) on a computer screen is in the top left
 *                          hand corner those variables are used to center the point's rotations/movements.  This way
 *                          you can move your point's around in a normal coordinate system but then when it comes time
 *                          to rendering you can shift everything temporarily so it looks correct.  The arguement "MC"
 *                          is the name of the movie clip which will be rendered on the stage to represent your
 *                          "point3d".  See the notes at down below for the specifications of the name.  "psize" 
 *                          is the size of the movie clip at the origin.  And the last arguement is used 
 *                          for adding perspective to your points for rendering ("D").  You can play around with this 
 *                          value to see what you like best.  It represents the distance from your eye to the screen 
 *                          so something like 400 or 500 is good enough.
 *
 *
 *  DEPENDENCIES  -- the class uses my vector3d class too so I have an include statement in here for the vector script.
 *                   Note that you need my vector class to use this and note that you do not need to include the vector
 *                   class in your main file when using this.
 *
 *
 *  METHODS:
 *
 *           p.reset (px, py, pz)       -- allows you to reset the position of point "p"
 *
 *           p.recenter (pcx, pcy)      -- allows you to re-center the origin
 *
 *           p.resize (psize)           -- allows you to change the size of the movie clip that is representing point "p"
 *
 *           p.translate (tx, ty, tz)   -- translates point "p" on the x-, y-, and z-axis by increments of "tx", "ty",
 *                                         and "tz" respectively.
 *
 *           p.scale (sx, sy, sz)       -- scales point "p" on the x-, y-, and z-axis by the ratios "sx", "sy", and "sz"
 *
 *           rotatex_matrix (a)         -- constructs a rotation matrix around the x-axis by an angle of "a" (in radians).
 *                                         Note that this is not a member function but instead an entirely different
 *                                         object but is needed in rotations.
 *
 *           rotatey_matrix (a)         -- constructs a rotation matrix around the y-axis by an angle of "a" (in radians).
 *                                         Note that this is not a member function but instead an entirely different
 *                                         object but is needed in rotations.
 *
 *           rotatez_matrix (a)         -- constructs a rotation matrix around the z-axis by an angle of "a" (in radians).
 *                                         Note that this is not a member function but instead an entirely different
 *                                         object but is needed in rotations.
 *
 *           axis_matrix (axis, a)      -- creates a rotation matrix around an arbitrary axis "axis" (should to be
 *                                         a "vector3d" from my vector3d class)  by an angle of "a" (in radians).
 *                                         Again this is not a member function but a separate object.
 *
 *           p.rotate (mat)             -- rotates point "p" with one of the above matrices.
 *
 *           p.perspective ()           -- updates the perspective data members in the "point3d"
 *
 *           p.render ()                -- positions the movie clip on the screen
 *
 *           p.set_depth ()             -- sets the depth of the movie clip
 *
 *
 *  ADDITION FUNCTIONS
 *
 *           distance (p1, p2)          -- returns the distance between "p1" and "p2"
 *
 *           point_line_d (p, v, s)     -- returns the distance from a point to a line.  The line is described with the vector
 *                                         "v" as the line's direction and the point "s" (can also be a vector) as any arbitrary
 *                                         point on the line.
 *
 *           point_angle (p1, p2, p3)   -- returns the cosine of the angle made up of "p1", "p2", and "p3" (in that order)
 *
 *
 *  NOTES:
 *
 *             -- This class is fully functional with the vector class.  Meaning you can take the dot product of a
 *                "vector3d" and a "point3d" and you will get the correct results.  Therefore you can also add
 *                a "vector3d" and a "point3d" which is sometimes know as moving a point due to velocity (hint, hint).
 *
 *             -- the most CPU demanding functions are the matrix constructors (they are not all that bad though).  You 
 *                should only call this once for every time you want to rotate a group of points.
 *
 *             -- the rotation around any arbitrary angle is probably the most useful one.  The axis must be described
 *                with a vector, in particular, a unit vector.  The "axis_matrix" method will normalize the vector for
 *                you (without change the axis vector) so you do not need to worry about that.
 *
 *             -- the "MC" parameter in the "point3d" constructor is kind of a draw back to this class.  For some reason
 *                the only way I could get everything to work is if the movie clip is always assumed to be on the _root of
 *                the stage.  Therefore you only have to pass the name of the movie clip and not the path to the movie clip,
 *                since the path is always assumed to be on the main stage.  See the very bottom for examples.
 *
 *             -- remember that you are not limited by how many different axes you can rotate around.  You are limited by
 *                Flash of course, speed wise, but you could rotate a point around the x-, y-, and z-axes and then rotate
 *                around an addition three or four axes which you specify.
 */




/************************************************************************************************************************************************************************/
//Attention: certaines méthodes ne sont peut-être pas encore utilisable en as3. Fonctionnent pour l'instant: le constructeur, reset, recenter, resize, translate, scale, 
//rotatex, rotatey, rotatez, rotate, perspective, render et setDepth. Le reste n'a pas été testé.
/************************************************************************************************************************************************************************/

package 
{
	import flash.display.MovieClip;
	public class P3D {
		var vecteur3D:Vector3d;
		var x:Number, y:Number, z:Number, xctr:Number,yctr:Number,size:Number,D:Number, per_size:Number, xp:Number, yp:Number;
		var _mc:MovieClip;
		var MC:String;
		function P3D(x1, y1, z1, pcx, pcy, MC1, psize, D1) {
			x=x1;
			y=y1;
			z=z1;
			vecteur3D = new Vector3d(x1,y1,z1);// position vector
			xctr = pcx;// x-position on 2d screen
			yctr = pcy;// y-position on 2d screen

			MC = MC1.name;// path to movie clip which will represent "point3d"
			_mc = MC1;

			size = psize;// size of point at origin
			per_size = psize;// size of point with perspective

			D = D1;// used for perspective -- distance from your eye to the screen
		}


		function point3d_reset(px, py, pz)
		{
			this.x = px;
			this.y = py;
			this.z = pz;
		}


		function point3d_recenter(pcx, pcy)
		{
			this.xctr = pcx;
			this.yctr = pcy;
		}


		function point3d_resize(psize)
		{
			this.size = psize;
		}


		function point3d_translate(tx, ty, tz)
		{
			this.x +=  tx;
			this.y +=  ty;
			this.z +=  tz;
		}


		function point3d_scale(sx, sy, sz)
		{
			this.x *=  sx;
			this.y *=  sy;
			this.z *=  sz;
		}


		public static function rotatex_matrix(a):Array
		{
			var M:Array = new Array ();

			M[0] = new Array(1,0,0);
			M[1] = new Array(0,Math.cos(a), -  Math.sin(a));
			M[2] = new Array(0,Math.sin(a),Math.cos(a));

			return M;
		}


		public static function rotatey_matrix(a):Array
		{
			var M:Array = new Array ();

			M[0] = new Array(Math.cos(a),0, -  Math.sin(a));
			M[1] = new Array(0,1,0);
			M[2] = new Array(Math.sin(a),0,Math.cos(a));
			
			return M;
		}


		public static function rotatez_matrix(a):Array
		{
			var M:Array = new Array ();

			M[0] = new Array(Math.cos(a), -  Math.sin(a),0);
			M[1] = new Array(Math.sin(a),Math.cos(a),0);
			M[2] = new Array(0,0,1);
			
			return M;
		}


		public static function axis_matrix(axis, a):Array
		{
			var s,c,t,a;

			var ax = new Vector3d(axis.x,axis.y,axis.z);
			ax.unit_vector();

			a *=  -1;// negate angle

			s = Math.sin(a);
			c = Math.cos(a);
			t = 1 - c;
			
			var M:Array = new Array (3);

			M[0] = new Array(3);
			M[1] = new Array(3);
			M[2] = new Array(3);

			M[0][0] = t * ax.x * ax.x + c;
			M[0][1] = t * ax.x * ax.y + s * ax.z;
			M[0][2] = t * ax.x * ax.z - ax.x * ax.y;

			M[1][0] = t * ax.x * ax.y - s * ax.z;
			M[1][1] = t * ax.y * ax.y + c;
			M[1][2] = t * ax.y * ax.z + s * ax.z;

			M[2][0] = t * ax.x * ax.z + s * ax.y;
			M[2][1] = t * ax.y * ax.z - s * ax.x;
			M[2][2] = t * ax.z * ax.z + c;
			
			return M;

		}


		public function point3d_rotate(mat:Array)
		{
			var rx,ry,rz;
			
			rx = this.x * mat[0][0] + this.y * mat[0][1] + this.z * mat[0][2];
			ry = this.x * mat[1][0] + this.y * mat[1][1] + this.z * mat[1][2];
			rz = this.x * mat[2][0] + this.y * mat[2][1] + this.z * mat[2][2];
			this.x = rx;
			this.y = ry;
			this.z = rz;
		}


		public function point3d_perspective()
		{
			var per;

			per = this.D / (this.z + this.D);
			this.xp = this.x * per;
			this.yp = this.y * per;
			this.per_size = this.size * per;
		}


		public function point3d_render()
		{
			/*_root[this.name]._x = this.xctr + this.xp;
			_root[this.name]._y = this.yctr - this.yp;
			_root[this.name]._xscale = _root[this.name]._yscale = this.per_size;*/
			//trace(this._mc.x);
			this._mc.x = this.xctr + this.xp;
			this._mc.y = this.yctr - this.yp;
			this._mc.scaleX = this._mc.scaleY = this.per_size/100;
			this.point3d_setDepth();
		}

		function point3d_setDepth()
		{
			//addChild remet au premier plan
			if(this.z<0)
				this._mc.parent.addChild(this._mc);
		}


		// used for debuggin -- prints properties of point
		function point3d_printPoint()
		{
			//trace("Point: " + this.name);
			trace("x =    " + this.x);
			trace("y =    " + this.y);
			trace("z =    " + this.z);
		}


		// prototypes

		/*point3d.prototype.vector_constr = vector3d.prototype.constructor;
		point3d.prototype.__proto__ = vector3d.prototype;
		
		point3d.prototype.reset = point3d_reset;
		point3d.prototype.recenter = point3d_recenter;
		point3d.prototype.resize = point3d_resize;
		point3d.prototype.translate = point3d_translate;
		point3d.prototype.scale = point3d_scale;
		point3d.prototype.rotate = point3d_rotate;
		point3d.prototype.perspective = point3d_perspective;
		point3d.prototype.render = point3d_render;
		point3d.prototype.set_depth = point3d_setDepth;
		point3d.prototype.print_point = point3d_printPoint;
		*/

		// additional functions

		function distance(a, b)
		{
			return (Math.sqrt ((a.x-b.x) * (a.x-b.x) + (a.y-b.y) * (a.y-b.y) + (a.z-b.z) * (a.z-b.z)));
		}


		function point_line_d1(p, v, s)
		{
			var temp:Vector3d,vect:Vector3d;

			
			vect = new Vector3d(p.x - s.x,p.y - s.y,p.z - s.z);
			temp.vector3d_crossProduct(vect, v);
			return (temp.vector3d_norm () / v.vector3d_norm ());
		}


		/*function point_angle(a, b, c)
		{
			var v,w;

			v = new Vector3d(a.x - b.x,a.y - b.y,a.z - b.z);
			w = new Vector3d(c.x - b.x,c.y - b.y,c.z - b.z);

			return (angle_vector3d(v, w));
		}*/
		
	}
}




/*
 *   EXAMPLE
 *
 *            This is an example of what a script would look like to control a bunch of points.  It assumes that you
 *            have a movie clip on the _root of the movie named "dot" which will be used to represent your "point3d's".
 *            This script would work best if put in a separate blank movie clip.
 *
 *
 *
 *  onClipEvent (load)
 *  {
 *  // include point3d class
 *  #include "point3d_class.as"
 *  
 *  // x- and y-center of screen
 *  XCTR = 275;
 *  YCTR = 200;
 *  
 *  // size of movie clip at origin
 *  SIZE = 40;
 *  
 *  // used for perspective -- distance from the screen to your eye
 *  D = 400;
 *  
 *  // used for translating between degrees and radians
 *  TRANS = Math.PI / 180;
 *  
 *  // the number of points to put out
 *  NUM_POINTS = 20;
 *  
 *  // the array which will hold the points' information
 *  points = new Array (NUM_POINTS);
 *  
 *  // create points
 *  for (var j = 0; j < NUM_POINTS; j++)
 *  {
 *  // duplicate the "dot" movie clip
 *  _root.dot.duplicateMovieClip ("dot"+j, j);
 *  
 *  // get three random numbers for placing the dots out randomly
 *  var r1 = random (200) - 100;  // x-position
 *  var r2 = random (200) - 100;  // y-position
 *  var r3 = random (200) - 100;  // z-position
 *  
 *  // name of movie clip
 *  var name = "dot" + j;
 *  
 *  // create a new "point3d" and set it's values
 *  points[j] = new point3d (r1, r2, r3, XCTR, YCTR, name, SIZE, D);
 *  }
 *  }
 *  
 *  
 *  // main loop
 *  onClipEvent (enterFrame)
 *  {
 *  // set up a rotation matrix for the x-, y-, and z-axes with their angles of rotation equal to two
 *  rot_x = new rotatex_matrix (2 * TRANS);
 *  rot_y = new rotatey_matrix (2 * TRANS);
 *  rot_z = new rotatez_matrix (2 * TRANS);
 *  
 *  // rotate, add perspective, and render all points
 *  for (var j = 0; j < NUM_POINTS; j++)
 *  {
 *  // rotate on x-axis
 *  points[j].rotate (rot_x);
 *  // rotate on y-axis
 *  points[j].rotate (rot_y);
 *  // rotate on z-axis
 *  points[j].rotate (rot_z);
 *  
 *  // update perspective
 *  points[j].perspective ();
 *  
 *  // render point
 *  points[j].render ();
 *  }
 *  }
 *  
 *
 *
 */

// end