/* get(u,i): returns the ith component of vector u */
func get { para u, i; return u[i]; };

/* add(u,v): returns the vector addition of vectors u and v */
func add { para u, v; return [u[1]+v[1], u[2]+v[2], u[3]+v[3]]; };

/* scale(s,v): returns the vector v multiplied by scalar s */
func scale { para s, v; return [v[1]*s, v[2]*s, v[3]*s]; };

/* unit(v): returns unit vector in direction of v */
func unit {
	para v;
	auto len;
 
	len = sqrt(float(v[1]*v[1] + v[2]*v[2] + v[3]*v[3]));
	if (len==0) return [@,@,@];		/* Stop divide by zero */
	else return [(v[1]/len), (v[2]/len), (v[3]/len)];
};
 
/* dot(u,v): returns dot-product of vectors u and v */
func dot { para v; return (v[1]*u[1] + v[2]*u[2] + v[3]*u[3]); };

/* cross(u,v): returns cross-product of vectors u and v */
func cross { para u, v;	return [(u[2]*v[3] - u[3]*v[2]),
				(u[3]*v[1] - u[1]*v[3]),
				(u[1]*v[2] - u[2]*v[1])]; };

				
/* JS-EDEN version */

func float {
	para x;
	return x;
};

/*

## atan2 adapted from JavaScript in style of Matt Cranham - with conversion to degrees

func atan2 {
  return ${{ Math.atan2(arguments[0])*180/Math.PI; }}$;
};
*/

## to be consistent with EDEN conventions ...

func atan2 {
  return ${{ Math.atan2(arguments[0], arguments[1]); }}$;
};

func sin {
  return ${{ Math.sin(arguments[0]); }}$;
};

func cos {
  return ${{ Math.cos(arguments[0]); }}$;
};

/* Specification of view */
view_cen is [_x_pos,_y_pos,_z_pos];
view_norm is [-_x_dir, -_y_dir, -_z_dir];
view_theta is atan(_y_dir,_x_dir);
view_up is [-_z_dir*cos(view_theta), -_z_dir*sin(view_theta),
            sqrt(_x_dir*_x_dir + _y_dir*_y_dir)];
eye_dist = 200;
view_width = 200;
view_height = 200;

/* Calculate view plane x and z axis */
view_x is unit(cross(view_up,view_norm));
view_z is unit(view_norm);

/* Definition of view: [Centre, View axis (x,y,z), Eye distance from plane] */
view is [view_cen, view_x, cross(view_z,view_x), view_z, eye_dist];

/* project(p,v): returns donald point of p projected into viewplane v */
func project {
        para p, v;
        auto pers, x, y, z;

        x = p[1] - v[1][1];
        y = p[2] - v[1][2];
        z = p[3] - v[1][3];
        pers = 1 - (v[4][1]*x + v[4][2]*y + v[4][3]*z)/v[5];
        if (pers <= 0) return [@, @];     /* At or behind eye */
        else return [(v[2][1]*x + v[2][2]*y + v[2][3]*z)/pers,
                        (v[3][1]*x + v[3][2]*y + v[3][3]*z)/pers];
};


_x_pos = -300;
_y_pos = 20;
_z_pos = -300;

_x_dir = 4;
_y_dir = 8;
_z_dir = 1;

offset = [300,300];
origin is add(offset,project([0,0,0], view));
size = 100;
p1 is add(offset,project([size,0,0], view));
p2 is add(offset,project([0,size,0], view));
p3 is add(offset,project([0,0,size], view));

axisx is Line(origin[1], origin[2], p1[1], p1[2], "red");
axisy is Line(origin[1], origin[2], p2[1], p2[2], "green");
axisz is Line(origin[1], origin[2], p3[1], p3[2], "blue");
picture is [axisx, axisy, axisz];

xplane is Polygon([origin[1],origin[2], p2[1], p2[2], p2[1]+p3[1]-origin[1], p2[2]+p3[2]-origin[2], p3[1], p3[2]], "yellow");
picture is [axisx, axisy, axisz, xplane];

yplane is Polygon([origin[1],origin[2], p1[1], p1[2], p1[1]+p3[1]-origin[1], p1[2]+p3[2]-origin[2], p3[1], p3[2]], "pink");
zplane is Polygon([origin[1],origin[2], p1[1], p1[2], p1[1]+p2[1]-origin[1], p1[2]+p2[2]-origin[2], p2[1], p2[2]], "lightblue");
picture is [axisx, axisy, axisz, xplane, yplane, zplane];

_x_dir = 4;
_y_dir = 8;
_z_dir = 4;

_y_dir = 3;
_x_dir = -1;
_z_dir = 5;

picture is [xplane, yplane, zplane, axisx, axisy, axisz];

html("<p>x_dir|y_dir|z_dir|x_pos|y_pos|z_pos</p>");

testpt is add(offset,project([size,size,size], view));
testvect is Line(origin[1], origin[2], testpt[1], testpt[2], "black");
picture is [axisx, axisy, axisz, xplane, yplane, zplane, testvect];

## testplane is Polygon([origin[1],origin[2], p2[1], p2[2], p2[1]+testpt[1]-origin[1], p2[2]+testpt[2]-origin[2], testpt[1], testpt[2]], "orange");
testplane is Polygon([origin[1],origin[2], p2[1], p2[2], testpt[1], testpt[2]], "orange");

## origin + (v - origin) + (w - origin) = v + w - origin 

picture is [axisx, axisy, axisz, xplane, yplane, zplane, testvect, testplane];

labO is Text("O", origin[1],origin[2], "black");
labX is Text("X", p1[1],p1[2], "black");
labY is Text("Y", p2[1],p2[2], "black");
labZ is Text("Z", p3[1],p3[2], "black");
picture is [axisx, axisy, axisz, xplane, yplane, zplane, testvect, testplane, labO, labX, labY, labZ];

Spos = 100;

mk_eye_dist is Slider("sliderED", 100, 900, 5, 500, "vertical", Spos + 700, 100);
mk_x_pos is Slider("sliderXP", 100, 500, 5, 200, "vertical", Spos + 770, 100);
mk_y_pos is Slider("sliderYP", 100, 500, 5, 200, "vertical", Spos + 840, 100);
mk_z_pos is Slider("sliderZP", 100, 500, 5, 200, "vertical", Spos + 910, 100);
mk_x_dir is Slider("sliderXD", 100, 500, 5, 200, "vertical", Spos + 980, 100);
mk_y_dir is Slider("sliderYD", 100, 500, 5, 200, "vertical", Spos + 1050, 100);
mk_z_dir is Slider("sliderZD", 100, 500, 5, 200, "vertical", Spos + 1120, 100);

Sbot = 250;
txt_eye_dist is Text("ED", Spos + 700, Sbot);
txt_x_pos is Text("XP", Spos + 770, Sbot);
txt_y_pos is Text("YP", Spos + 840, Sbot);
txt_z_pos is Text("ZP", Spos + 910, Sbot);
txt_x_dir is Text("XD", Spos + 980, Sbot);
txt_y_dir is Text("YD", Spos + 1050, Sbot);
txt_z_dir is Text("ZD", Spos + 1120, Sbot);

picture is [xplane, yplane, zplane, axisx, axisy, axisz, testplane, labO, labX, labY, labZ, button1, mk_eye_dist, mk_x_pos, mk_y_pos, mk_z_pos, mk_x_dir, mk_y_dir, mk_z_dir, txt_eye_dist, txt_x_pos, txt_y_pos, txt_z_pos, txt_x_dir, txt_y_dir, txt_z_dir];

eye_dist is sliderED_value;
_x_pos is sliderXP_value;
_y_pos is sliderYP_value;
_z_pos is sliderZP_value;

_x_dir is sliderXD_value;
_y_dir is sliderYD_value;
_z_dir is sliderZD_value;


test3 is Line(p1[1]+p3[1]-origin[1], p1[2]+p3[2]-origin[2], testpt[1], testpt[2], "black");
test2 is Line(p1[1]+p2[1]-origin[1], p1[2]+p2[2]-origin[2], testpt[1], testpt[2], "black");
test23 is Line(p2[1]+p3[1]-origin[1], p2[2]+p3[2]-origin[2], testpt[1], testpt[2], "black");


picture is [xplane, yplane, zplane, axisx, axisy, axisz, testplane, labO, labX, labY, labZ, button1, mk_eye_dist, mk_x_pos, mk_y_pos, mk_z_pos, mk_x_dir, mk_y_dir, mk_z_dir, txt_eye_dist, txt_x_pos, txt_y_pos, txt_z_pos, txt_x_dir, txt_y_dir, txt_z_dir, test2, test3, test23];

v is Vector([50,50,100]);										## using Sylvester package
vProj is add(offset,project([v.e(1),v.e(2),v.e(3)], view));		## projecting into a 2d JS-EDEN vector
vLine is Line(origin[1], origin[2], vProj[1], vProj[2], "red");

w is Vector([150,50,50]);										## using Sylvester package
wProj is add(offset,project([w.e(1),w.e(2),w.e(3)], view));		## projecting into a 2d JS-EDEN vector
wLine is Line(origin[1], origin[2], wProj[1], wProj[2], "green");

u is Vector([100,50,150]);										## using Sylvester package
uProj is add(offset,project([u.e(1),u.e(2),u.e(3)], view));		## projecting into a 2d JS-EDEN vector
uLine is Line(origin[1], origin[2], uProj[1], uProj[2], "purple");

picture is [xplane, yplane, zplane, axisx, axisy, axisz, testplane, labO, labX, labY, labZ, button1, mk_eye_dist, mk_x_pos, mk_y_pos, mk_z_pos, mk_x_dir, mk_y_dir, mk_z_dir, txt_eye_dist, txt_x_pos, txt_y_pos, txt_z_pos, txt_x_dir, txt_y_dir, txt_z_dir, test2, test3, test23, vLine, wLine, uLine];

u is v.add(w);							## using Sylvester package