#include <stdio.h>
	// yes, I know stdio.h is not good C++, but I like the *printf( )
#include <stdlib.h>
#include <ctype.h>

#define _USE_MATH_DEFINES
#include <math.h>

#ifdef WIN32
#include <windows.h>
#pragma warning(disable:4996)
#endif

#include <GL/gl.h>
#include <GL/glu.h>
#include "glut.h"
#include "glui.h"

//	This is a sample OpenGL / GLUT / GLUI program
//
//	The objective is to draw a 3d object and change the color of the axes
//		with radio buttons
//
//	The left mouse button allows rotation
//	The middle mouse button allows scaling
//	The glui window allows:
//		1. The 3d object to be transformed
//		2. The projection to be changed
//		3. The color of the axes to be changed
//		4. The axes to be turned on and off
//		5. The transformations to be reset
//		6. The program to quit
//
//	Author:			Joe Graphics
//
//  Latest update:	March 26, 2015

// constants:
//
// NOTE: There are a bunch of good reasons to use const variables instead
// of #define's.  However, Visual C++ does not allow a const variable
// to be used as an array size or as the case in a switch( ) statement.  So in
// the following, all constants are const variables except those which need to
// be array sizes or cases in switch( ) statements.  Those are #defines.
//


// title of these windows:

const char *WINDOWTITLE = { "OpenGL / GLUT / GLUI Sample -- Joe Graphics" };
const char *GLUITITLE   = { "User Interface Window" };


// what the glui package defines as true and false:

const int GLUITRUE  = { true  };
const int GLUIFALSE = { false };


// the escape key:

#define ESCAPE		0x1b


// initial window size:

const int INIT_WINDOW_SIZE = { 600 };


// size of the box:

const float BOXSIZE = { 2.f };



// multiplication factors for input interaction:
//  (these are known from previous experience)

const float ANGFACT = { 1. };
const float SCLFACT = { 0.005f };


// able to use the left mouse for either rotation or scaling,
// in case have only a 2-button mouse:

enum LeftButton
{
	ROTATE,
	SCALE
};


// minimum allowable scale factor:

const float MINSCALE = { 0.05f };


// active mouse buttons (or them together):

const int LEFT   = { 4 };
const int MIDDLE = { 2 };
const int RIGHT  = { 1 };


// which projection:

enum Projections
{
	ORTHO,
	PERSP
};


// which button:

enum ButtonVals
{
	RESET,
	QUIT
};


// window background color (rgba):

const float BACKCOLOR[ ] = { 0., 0., 0., 0. };


// line width for the axes:

const GLfloat AXES_WIDTH   = { 3. };


// the color numbers:
// this order must match the radio button order

enum Colors
{
	RED,
	YELLOW,
	GREEN,
	CYAN,
	BLUE,
	MAGENTA,
	WHITE,
	BLACK
};


// the color definitions:
// this order must match the radio button order

const GLfloat Colors[ ][3] = 
{
	{ 1., 0., 0. },		// red
	{ 1., 1., 0. },		// yellow
	{ 0., 1., 0. },		// green
	{ 0., 1., 1. },		// cyan
	{ 0., 0., 1. },		// blue
	{ 1., 0., 1. },		// magenta
	{ 1., 1., 1. },		// white
	{ 0., 0., 0. },		// black
};


// fog parameters:

const GLfloat FOGCOLOR[4] = { .0, .0, .0, 1. };
const GLenum  FOGMODE     = { GL_LINEAR };
const GLfloat FOGDENSITY  = { 0.30f };
const GLfloat FOGSTART    = { 1.5 };
const GLfloat FOGEND      = { 4. };


// non-constant global variables:

int	ActiveButton;			// current button that is down
GLuint	AxesList;			// list to hold the axes
int	AxesOn;					// != 0 means to draw the axes
int	DebugOn;				// != 0 means to print debugging info
int	DepthCueOn;				// != 0 means to use intensity depth cueing
GLUI *	Glui;				// instance of glui window
int	GluiWindow;				// the glut id for the glui window
int	LeftButton;				// either ROTATE or SCALE
GLuint	BoxList;			// object display list
int	MainWindow;				// window id for main graphics window
GLfloat	RotMatrix[4][4];	// set by glui rotation widget
float	Scale, Scale2;		// scaling factors
int	WhichColor;				// index into Colors[ ]
int	WhichProjection;		// ORTHO or PERSP
int	Xmouse, Ymouse;			// mouse values
float	Xrot, Yrot;			// rotation angles in degrees
float	TransXYZ[3];		// set by glui translation widgets


// function prototypes:

void	Animate( );
void	Buttons( int );
void	Display( );
void	DoRasterString( float, float, float, char * );
void	DoStrokeString( float, float, float, float, char * );
float	ElapsedSeconds( );
void	InitGlui( );
void	InitGraphics( );
void	InitLists( );
void	Keyboard( unsigned char, int, int );
void	MouseButton( int, int, int, int );
void	MouseMotion( int, int );
void	Reset( );
void	Resize( int, int );
void	Visibility( int );

void	Arrow( float [3], float [3] );
void	Cross( float [3], float [3], float [3] );
float	Dot( float [3], float [3] );
float	Unit( float [3], float [3] );
void	Axes( float );
void	HsvRgb( float[3], float [3] );

// main program:

int
main( int argc, char *argv[ ] )
{
	// turn on the glut package:
	// (do this before checking argc and argv since it might
	// pull some command line arguments out)

	glutInit( &argc, argv );


	// setup all the graphics stuff:

	InitGraphics( );


	// create the display structures that will not change:

	InitLists( );


	// init all the global variables used by Display( ):
	// this will also post a redisplay
	// it is important to call this before InitGlui( )
	// so that the variables that glui will control are correct
	// when each glui widget is created

	Reset( );


	// setup all the user interface stuff:

	InitGlui( );


	// draw the scene once and wait for some interaction:
	// (this will never return)

	glutMainLoop( );


	// this is here to make the compiler happy:

	return 0;
}


// this is where one would put code that is to be called
// everytime the glut main loop has nothing to do
//
// this is typically where animation parameters are set
//
// do not call Display( ) from here -- let glutMainLoop( ) do it

void
Animate( )
{
	// put animation stuff in here -- change some global variables
	// for Display( ) to find:



	// force a call to Display( ) next time it is convenient:

	glutSetWindow( MainWindow );
	glutPostRedisplay( );
}



// glui buttons callback:

void
Buttons( int id )
{
	switch( id )
	{
		case RESET:
			Reset( );
			Glui->sync_live( );
			glutSetWindow( MainWindow );
			glutPostRedisplay( );
			break;

		case QUIT:
			// gracefully close the glui window:
			// gracefully close out the graphics:
			// gracefully close the graphics window:
			// gracefully exit the program:

			Glui->close( );
			glutSetWindow( MainWindow );
			glFinish( );
			glutDestroyWindow( MainWindow );
			exit( 0 );
			break;

		default:
			fprintf( stderr, "Don't know what to do with Button ID %d\n", id );
	}

}


// draw the complete scene:

void
Display( )
{
	if( DebugOn != 0 )
	{
		fprintf( stderr, "Display\n" );
	}


	// set which window we want to do the graphics into:

	glutSetWindow( MainWindow );


	// erase the background:

	glDrawBuffer( GL_BACK );
	glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT );
	glEnable( GL_DEPTH_TEST );


	// specify shading to be flat:

	glShadeModel( GL_FLAT );


	// set the viewport to a square centered in the window:

	GLsizei vx = glutGet( GLUT_WINDOW_WIDTH );
	GLsizei vy = glutGet( GLUT_WINDOW_HEIGHT );
	GLsizei v = vx < vy ? vx : vy;			// minimum dimension
	GLint xl = ( vx - v ) / 2;
	GLint yb = ( vy - v ) / 2;
	glViewport( xl, yb,  v, v );


	// set the viewing volume:
	// remember that the Z clipping  values are actually
	// given as DISTANCES IN FRONT OF THE EYE
	// USE gluOrtho2D( ) IF YOU ARE DOING 2D !

	glMatrixMode( GL_PROJECTION );
	glLoadIdentity( );
	if( WhichProjection == ORTHO )
		glOrtho( -3., 3.,     -3., 3.,     0.1, 1000. );
	else
		gluPerspective( 90., 1.,	0.1, 1000. );


	// place the objects into the scene:

	glMatrixMode( GL_MODELVIEW );
	glLoadIdentity( );


	// set the eye position, look-at position, and up-vector:
	// IF DOING 2D, REMOVE THIS -- OTHERWISE ALL YOUR 2D WILL DISAPPEAR !

	gluLookAt( 0., 0., 3.,     0., 0., 0.,     0., 1., 0. );


	// translate the objects in the scene:
	// note the minus sign on the z value
	// this is to make the appearance of the glui z translate
	// widget more intuitively match the translate behavior
	// DO NOT TRANSLATE IN Z IF YOU ARE DOING 2D !

	glTranslatef( (GLfloat)TransXYZ[0], (GLfloat)TransXYZ[1], -(GLfloat)TransXYZ[2] );


	// rotate the scene:
	// DO NOT ROTATE (EXCEPT ABOUT Z) IF YOU ARE DOING 2D !

	glRotatef( (GLfloat)Yrot, 0., 1., 0. );
	glRotatef( (GLfloat)Xrot, 1., 0., 0. );
	glMultMatrixf( (const GLfloat *) RotMatrix );


	// uniformly scale the scene:

	glScalef( (GLfloat)Scale, (GLfloat)Scale, (GLfloat)Scale );
	GLfloat scale2 = 1. + Scale2;		// because glui translation starts at 0.
	if( scale2 < MINSCALE )
		scale2 = MINSCALE;
	glScalef( (GLfloat)scale2, (GLfloat)scale2, (GLfloat)scale2 );


	// set the fog parameters:
	// DON'T NEED THIS IF DOING 2D !

	if( DepthCueOn != 0 )
	{
		glFogi( GL_FOG_MODE, FOGMODE );
		glFogfv( GL_FOG_COLOR, FOGCOLOR );
		glFogf( GL_FOG_DENSITY, FOGDENSITY );
		glFogf( GL_FOG_START, FOGSTART );
		glFogf( GL_FOG_END, FOGEND );
		glEnable( GL_FOG );
	}
	else
	{
		glDisable( GL_FOG );
	}


	// possibly draw the axes:

	if( AxesOn != 0 )
	{
		glColor3fv( &Colors[WhichColor][0] );
		glCallList( AxesList );
	}


	// set the color of the object:

	glColor3fv( Colors[WhichColor] );


	// draw the current object:

	glCallList( BoxList );


	// draw some gratuitous text that just rotates on top of the scene:

	glDisable( GL_DEPTH_TEST );
	glColor3f( 0., 1., 1. );
	DoRasterString( 0., 1., 0., "Text That Moves" );


	// draw some gratuitous text that is fixed on the screen:
	//
	// the projection matrix is reset to define a scene whose
	// world coordinate system goes from 0-100 in each axis
	//
	// this is called "percent units", and is just a convenience
	//
	// the modelview matrix is reset to identity as we don't
	// want to transform these coordinates

	glDisable( GL_DEPTH_TEST );
	glMatrixMode( GL_PROJECTION );
	glLoadIdentity( );
	gluOrtho2D( 0., 100.,     0., 100. );
	glMatrixMode( GL_MODELVIEW );
	glLoadIdentity( );
	glColor3f( 1., 1., 1. );
	DoRasterString( 5., 5., 0., "Text That Doesn't" );


	// swap the double-buffered framebuffers:

	glutSwapBuffers( );


	// be sure the graphics buffer has been sent:
	// note: be sure to use glFlush( ) here, not glFinish( ) !

	glFlush( );
}


// use glut to display a string of characters using a raster font:

void
DoRasterString( float x, float y, float z, char *s )
{
	char c;			// one character to print

	glRasterPos3f( (GLfloat)x, (GLfloat)y, (GLfloat)z );
	for( ; ( c = *s ) != '\0'; s++ )
	{
		glutBitmapCharacter( GLUT_BITMAP_TIMES_ROMAN_24, c );
	}
}


// use glut to display a string of characters using a stroke font:

void
DoStrokeString( float x, float y, float z, float ht, char *s )
{
	char c;			// one character to print

	glPushMatrix( );
		glTranslatef( (GLfloat)x, (GLfloat)y, (GLfloat)z );
		float sf = ht / ( 119.05 + 33.33 );
		glScalef( (GLfloat)sf, (GLfloat)sf, (GLfloat)sf );
		for( ; ( c = *s ) != '\0'; s++ )
		{
			glutStrokeCharacter( GLUT_STROKE_ROMAN, c );
		}
	glPopMatrix( );
}


// return the number of seconds since the start of the program:

float
ElapsedSeconds( )
{
	// get # of milliseconds since the start of the program:

	int ms = glutGet( GLUT_ELAPSED_TIME );

	// convert it to seconds:

	return (float)ms / 1000.;
}


// initialize the glui window:

void
InitGlui( )
{
	GLUI_Panel *panel;
	GLUI_RadioGroup *group;
	GLUI_Rotation *rot;
	GLUI_Translation *trans, *scale;


	// setup the glui window:

	glutInitWindowPosition( INIT_WINDOW_SIZE + 50, 0 );
	Glui = GLUI_Master.create_glui( (char *) GLUITITLE );


	Glui->add_statictext( (char *) GLUITITLE );
	Glui->add_separator( );

	Glui->add_checkbox( "Axes", &AxesOn );

	Glui->add_checkbox( "Perspective", &WhichProjection );

	Glui->add_checkbox( "Intensity Depth Cue", &DepthCueOn );

	panel = Glui->add_panel(  "Axes Color" );
		group = Glui->add_radiogroup_to_panel( panel, &WhichColor );
			Glui->add_radiobutton_to_group( group, "Red" );
			Glui->add_radiobutton_to_group( group, "Yellow" );
			Glui->add_radiobutton_to_group( group, "Green" );
			Glui->add_radiobutton_to_group( group, "Cyan" );
			Glui->add_radiobutton_to_group( group, "Blue" );
			Glui->add_radiobutton_to_group( group, "Magenta" );
			Glui->add_radiobutton_to_group( group, "White" );
			Glui->add_radiobutton_to_group( group, "Black" );

	panel = Glui->add_panel( "Object Transformation" );

		rot = Glui->add_rotation_to_panel( panel, "Rotation", (float *) RotMatrix );

		// allow the object to be spun via the glui rotation widget:

		rot->set_spin( 1.0 );


		Glui->add_column_to_panel( panel, GLUIFALSE );
		scale = Glui->add_translation_to_panel( panel, "Scale",  GLUI_TRANSLATION_Y , &Scale2 );
		scale->set_speed( 0.005f );

		Glui->add_column_to_panel( panel, GLUIFALSE );
		trans = Glui->add_translation_to_panel( panel, "Trans XY", GLUI_TRANSLATION_XY, &TransXYZ[0] );
		trans->set_speed( 0.05f );

		Glui->add_column_to_panel( panel, GLUIFALSE );
		trans = Glui->add_translation_to_panel( panel, "Trans Z",  GLUI_TRANSLATION_Z , &TransXYZ[2] );
		trans->set_speed( 0.05f );

	Glui->add_checkbox( "Debug", &DebugOn );


	panel = Glui->add_panel( "", GLUIFALSE );

	Glui->add_button_to_panel( panel, "Reset", RESET, (GLUI_Update_CB) Buttons );

	Glui->add_column_to_panel( panel, GLUIFALSE );

	Glui->add_button_to_panel( panel, "Quit", QUIT, (GLUI_Update_CB) Buttons );


	// tell glui what graphics window it needs to post a redisplay to:

	Glui->set_main_gfx_window( MainWindow );


	// set the graphics window's idle function if needed:

	GLUI_Master.set_glutIdleFunc( NULL );
}


// initialize the glut and OpenGL libraries:
//	also setup display lists and callback functions

void
InitGraphics( )
{
	// setup the display mode:
	// ( *must* be done before call to glutCreateWindow( ) )
	// ask for color, double-buffering, and z-buffering:

	glutInitDisplayMode( GLUT_RGBA | GLUT_DOUBLE | GLUT_DEPTH );


	// set the initial window configuration:

	glutInitWindowPosition( 0, 0 );
	glutInitWindowSize( INIT_WINDOW_SIZE, INIT_WINDOW_SIZE );


	// open the window and set its title:

	MainWindow = glutCreateWindow( WINDOWTITLE );
	glutSetWindowTitle( WINDOWTITLE );


	// setup the clear values:

	glClearColor( BACKCOLOR[0], BACKCOLOR[1], BACKCOLOR[2], BACKCOLOR[3] );


	// setup the callback functions:

	// DisplayFunc -- redraw the window
	// ReshapeFunc -- handle the user resizing the window
	// KeyboardFunc -- handle a keyboard input
	// MouseFunc -- handle the mouse button going down or up
	// MotionFunc -- handle the mouse moving with a button down
	// PassiveMotionFunc -- handle the mouse moving with a button up
	// VisibilityFunc -- handle a change in window visibility
	// EntryFunc	-- handle the cursor entering or leaving the window
	// SpecialFunc -- handle special keys on the keyboard
	// SpaceballMotionFunc -- handle spaceball translation
	// SpaceballRotateFunc -- handle spaceball rotation
	// SpaceballButtonFunc -- handle spaceball button hits
	// ButtonBoxFunc -- handle button box hits
	// DialsFunc -- handle dial rotations
	// TabletMotionFunc -- handle digitizing tablet motion
	// TabletButtonFunc -- handle digitizing tablet button hits
	// MenuStateFunc -- declare when a pop-up menu is in use
	// TimerFunc -- trigger something to happen a certain time from now
	// IdleFunc -- what to do when nothing else is going on

	glutSetWindow( MainWindow );
	glutDisplayFunc( Display );
	glutReshapeFunc( Resize );
	glutKeyboardFunc( Keyboard );
	glutMouseFunc( MouseButton );
	glutMotionFunc( MouseMotion );
	glutPassiveMotionFunc( NULL );
	glutVisibilityFunc( Visibility );
	glutEntryFunc( NULL );
	glutSpecialFunc( NULL );
	glutSpaceballMotionFunc( NULL );
	glutSpaceballRotateFunc( NULL );
	glutSpaceballButtonFunc( NULL );
	glutButtonBoxFunc( NULL );
	glutDialsFunc( NULL );
	glutTabletMotionFunc( NULL );
	glutTabletButtonFunc( NULL );
	glutMenuStateFunc( NULL );
	glutTimerFunc( 0, NULL, 0 );

	// DO NOT SET THE GLUT IDLE FUNCTION HERE !!
	// glutIdleFunc( NULL );
	// let glui take care of it in InitGlui( )
}


// initialize the display lists that will not change:
// (a display list is a way to store opengl commands in
//  memory so that they can be played back efficiently at a later time
//  with a call to glCallList( )

void
InitLists( )
{
	float dx = BOXSIZE / 2.;
	float dy = BOXSIZE / 2.;
	float dz = BOXSIZE / 2.;

	// create the object:

	BoxList = glGenLists( 1 );
	glNewList( BoxList, GL_COMPILE );

		glBegin( GL_QUADS );

			glColor3f( 0., 0., 1. );
			glNormal3f( 0., 0.,  1. );
				glVertex3f( -dx, -dy,  dz );
				glVertex3f(  dx, -dy,  dz );
				glVertex3f(  dx,  dy,  dz );
				glVertex3f( -dx,  dy,  dz );

			glNormal3f( 0., 0., -1. );
				glTexCoord2f( 0., 0. );
				glVertex3f( -dx, -dy, -dz );
				glTexCoord2f( 0., 1. );
				glVertex3f( -dx,  dy, -dz );
				glTexCoord2f( 1., 1. );
				glVertex3f(  dx,  dy, -dz );
				glTexCoord2f( 1., 0. );
				glVertex3f(  dx, -dy, -dz );

			glColor3f( 1., 0., 0. );
			glNormal3f(  1., 0., 0. );
				glVertex3f(  dx, -dy,  dz );
				glVertex3f(  dx, -dy, -dz );
				glVertex3f(  dx,  dy, -dz );
				glVertex3f(  dx,  dy,  dz );

			glNormal3f( -1., 0., 0. );
				glVertex3f( -dx, -dy,  dz );
				glVertex3f( -dx,  dy,  dz );
				glVertex3f( -dx,  dy, -dz );
				glVertex3f( -dx, -dy, -dz );

			glColor3f( 0., 1., 0. );
			glNormal3f( 0.,  1., 0. );
				glVertex3f( -dx,  dy,  dz );
				glVertex3f(  dx,  dy,  dz );
				glVertex3f(  dx,  dy, -dz );
				glVertex3f( -dx,  dy, -dz );

			glNormal3f( 0., -1., 0. );
				glVertex3f( -dx, -dy,  dz );
				glVertex3f( -dx, -dy, -dz );
				glVertex3f(  dx, -dy, -dz );
				glVertex3f(  dx, -dy,  dz );

		glEnd( );

	glEndList( );


	// create the axes:

	AxesList = glGenLists( 1 );
	glNewList( AxesList, GL_COMPILE );
		glLineWidth( AXES_WIDTH );
			Axes( 1.5 );
		glLineWidth( 1. );
	glEndList( );
}


// the keyboard callback:

void
Keyboard( unsigned char c, int x, int y )
{
	if( DebugOn != 0 )
		fprintf( stderr, "Keyboard: '%c' (0x%0x)\n", c, c );

	switch( c )
	{
		case 'o':
		case 'O':
			WhichProjection = ORTHO;
			break;

		case 'p':
		case 'P':
			WhichProjection = PERSP;
			break;

		case 'q':
		case 'Q':
		case ESCAPE:
			Buttons( QUIT );	// will not return here
			break;			// happy compiler

		case 'r':
		case 'R':
			LeftButton = ROTATE;
			break;

		case 's':
		case 'S':
			LeftButton = SCALE;
			break;

		default:
			fprintf( stderr, "Don't know what to do with keyboard hit: '%c' (0x%0x)\n", c, c );
	}


	// synchronize the GLUI display with the variables:

	Glui->sync_live( );


	// force a call to Display( ):

	glutSetWindow( MainWindow );
	glutPostRedisplay( );
}


// called when the mouse button transitions down or up:

void
MouseButton( int button, int state, int x, int y )
{
	int b = 0;			// LEFT, MIDDLE, or RIGHT

	if( DebugOn != 0 )
		fprintf( stderr, "MouseButton: %d, %d, %d, %d\n", button, state, x, y );

	
	// get the proper button bit mask:

	switch( button )
	{
		case GLUT_LEFT_BUTTON:
			b = LEFT;		break;

		case GLUT_MIDDLE_BUTTON:
			b = MIDDLE;		break;

		case GLUT_RIGHT_BUTTON:
			b = RIGHT;		break;

		default:
			b = 0;
			fprintf( stderr, "Unknown mouse button: %d\n", button );
	}


	// button down sets the bit, up clears the bit:

	if( state == GLUT_DOWN )
	{
		Xmouse = x;
		Ymouse = y;
		ActiveButton |= b;		// set the proper bit
	}
	else
	{
		ActiveButton &= ~b;		// clear the proper bit
	}
}


// called when the mouse moves while a button is down:

void
MouseMotion( int x, int y )
{
	if( DebugOn != 0 )
		fprintf( stderr, "MouseMotion: %d, %d\n", x, y );


	int dx = x - Xmouse;		// change in mouse coords
	int dy = y - Ymouse;

	if( ( ActiveButton & LEFT ) != 0 )
	{
		switch( LeftButton )
		{
			case ROTATE:
				Xrot += ( ANGFACT*dy );
				Yrot += ( ANGFACT*dx );
				break;

			case SCALE:
				Scale += SCLFACT * (float) ( dx - dy );
				if( Scale < MINSCALE )
					Scale = MINSCALE;
				break;
		}
	}


	if( ( ActiveButton & MIDDLE ) != 0 )
	{
		Scale += SCLFACT * (float) ( dx - dy );

		// keep object from turning inside-out or disappearing:

		if( Scale < MINSCALE )
			Scale = MINSCALE;
	}

	Xmouse = x;			// new current position
	Ymouse = y;

	glutSetWindow( MainWindow );
	glutPostRedisplay( );
}


// reset the transformations and the colors:
// this only sets the global variables --
// the glut main loop is responsible for redrawing the scene

void
Reset( )
{
	ActiveButton = 0;
	AxesOn = GLUITRUE;
	DebugOn = GLUIFALSE;
	DepthCueOn = GLUIFALSE;
	LeftButton = ROTATE;
	Scale  = 1.0;
	Scale2 = 0.0;		// because we add 1. to it in Display( )
	WhichColor = WHITE;
	WhichProjection = PERSP;
	Xrot = Yrot = 0.;
	TransXYZ[0] = TransXYZ[1] = TransXYZ[2] = 0.;

	                  RotMatrix[0][1] = RotMatrix[0][2] = RotMatrix[0][3] = 0.;
	RotMatrix[1][0]                   = RotMatrix[1][2] = RotMatrix[1][3] = 0.;
	RotMatrix[2][0] = RotMatrix[2][1]                   = RotMatrix[2][3] = 0.;
	RotMatrix[3][0] = RotMatrix[3][1] = RotMatrix[3][3]                   = 0.;
	RotMatrix[0][0] = RotMatrix[1][1] = RotMatrix[2][2] = RotMatrix[3][3] = 1.;
}


// called when user resizes the window:

void
Resize( int width, int height )
{
	if( DebugOn != 0 )
		fprintf( stderr, "ReSize: %d, %d\n", width, height );

	// don't really need to do anything since window size is
	// checked each time in Display( ):

	glutSetWindow( MainWindow );
	glutPostRedisplay( );
}


// handle a change to the window's visibility:

void
Visibility ( int state )
{
	if( DebugOn != 0 )
		fprintf( stderr, "Visibility: %d\n", state );

	if( state == GLUT_VISIBLE )
	{
		glutSetWindow( MainWindow );
		glutPostRedisplay( );
	}
	else
	{
		// could optimize by keeping track of the fact
		// that the window is not visible and avoid
		// animating or redrawing it ...
	}
}




///////////////////////////////////////   HANDY UTILITIES:  //////////////////////////

// size of wings as fraction of length:

#define WINGS	0.10


// axes:

#define X	1
#define Y	2
#define Z	3


// x, y, z, axes:

static float axx[3] = { 1., 0., 0. };
static float ayy[3] = { 0., 1., 0. };
static float azz[3] = { 0., 0., 1. };


void
Arrow( float tail[3], float head[3] )
{
	float u[3], v[3], w[3];		// arrow coordinate system

	// set w direction in u-v-w coordinate system:

	w[0] = head[0] - tail[0];
	w[1] = head[1] - tail[1];
	w[2] = head[2] - tail[2];


	// determine major direction:

	int axis = X;
	float mag = fabs( w[0] );
	if(  fabs( w[1] )  > mag  )
	{
		axis = Y;
		mag = fabs( w[1] );
	}
	if(  fabs( w[2] )  > mag  )
	{
		axis = Z;
		mag = fabs( w[2] );
	}


	// set size of wings and turn w into a Unit vector:

	float d = WINGS * Unit( w, w );


	// draw the shaft of the arrow:

	glBegin( GL_LINE_STRIP );
		glVertex3fv( tail );
		glVertex3fv( head );
	glEnd( );

	// draw two sets of wings in the non-major directions:

	float x, y, z;

	if( axis != X )
	{
		Cross( w, axx, v );
		(void) Unit( v, v );
		Cross( v, w, u  );
		x = head[0] + d * ( u[0] - w[0] );
		y = head[1] + d * ( u[1] - w[1] );
		z = head[2] + d * ( u[2] - w[2] );
		glBegin( GL_LINE_STRIP );
			glVertex3fv( head );
			glVertex3f( x, y, z );
		glEnd( );
		x = head[0] + d * ( -u[0] - w[0] );
		y = head[1] + d * ( -u[1] - w[1] );
		z = head[2] + d * ( -u[2] - w[2] );
		glBegin( GL_LINE_STRIP );
			glVertex3fv( head );
			glVertex3f( x, y, z );
		glEnd( );
	}


	if( axis != Y )
	{
		Cross( w, ayy, v );
		(void) Unit( v, v );
		Cross( v, w, u  );
		x = head[0] + d * ( u[0] - w[0] );
		y = head[1] + d * ( u[1] - w[1] );
		z = head[2] + d * ( u[2] - w[2] );
		glBegin( GL_LINE_STRIP );
			glVertex3fv( head );
			glVertex3f( x, y, z );
		glEnd( );
		x = head[0] + d * ( -u[0] - w[0] );
		y = head[1] + d * ( -u[1] - w[1] );
		z = head[2] + d * ( -u[2] - w[2] );
		glBegin( GL_LINE_STRIP );
			glVertex3fv( head );
			glVertex3f( x, y, z );
		glEnd( );
	}



	if( axis != Z )
	{
		Cross( w, azz, v );
		(void) Unit( v, v );
		Cross( v, w, u  );
		x = head[0] + d * ( u[0] - w[0] );
		y = head[1] + d * ( u[1] - w[1] );
		z = head[2] + d * ( u[2] - w[2] );
		glBegin( GL_LINE_STRIP );
			glVertex3fv( head );
			glVertex3f( x, y, z );
		glEnd( );
		x = head[0] + d * ( -u[0] - w[0] );
		y = head[1] + d * ( -u[1] - w[1] );
		z = head[2] + d * ( -u[2] - w[2] );
		glBegin( GL_LINE_STRIP );
			glVertex3fv( head );
			glVertex3f( x, y, z );
		glEnd( );
	}
}



float
Dot( float v1[3], float v2[3] )
{
	return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
}



void
Cross( float v1[3], float v2[3], float vout[3] )
{
	float tmp[3];

	tmp[0] = v1[1]*v2[2] - v2[1]*v1[2];
	tmp[1] = v2[0]*v1[2] - v1[0]*v2[2];
	tmp[2] = v1[0]*v2[1] - v2[0]*v1[1];

	vout[0] = tmp[0];
	vout[1] = tmp[1];
	vout[2] = tmp[2];
}



float
Unit( float vin[3], float vout[3] )
{
	float dist = vin[0]*vin[0] + vin[1]*vin[1] + vin[2]*vin[2];

	if( dist > 0.0 )
	{
		dist = sqrt( dist );
		vout[0] = vin[0] / dist;
		vout[1] = vin[1] / dist;
		vout[2] = vin[2] / dist;
	}
	else
	{
		vout[0] = vin[0];
		vout[1] = vin[1];
		vout[2] = vin[2];
	}

	return dist;
}



// the stroke characters 'X' 'Y' 'Z' :

static float xx[ ] = {
		0.f, 1.f, 0.f, 1.f
	      };

static float xy[ ] = {
		-.5f, .5f, .5f, -.5f
	      };

static int xorder[ ] = {
		1, 2, -3, 4
		};


static float yx[ ] = {
		0.f, 0.f, -.5f, .5f
	      };

static float yy[ ] = {
		0.f, .6f, 1.f, 1.f
	      };

static int yorder[ ] = {
		1, 2, 3, -2, 4
		};


static float zx[ ] = {
		1.f, 0.f, 1.f, 0.f, .25f, .75f
	      };

static float zy[ ] = {
		.5f, .5f, -.5f, -.5f, 0.f, 0.f
	      };

static int zorder[ ] = {
		1, 2, 3, 4, -5, 6
		};


// fraction of the length to use as height of the characters:

const float LENFRAC = 0.10f;


// fraction of length to use as start location of the characters:

const float BASEFRAC = 1.10f;


//	Draw a set of 3D axes:
//	(length is the axis length in world coordinates)

void
Axes( float length )
{
	glBegin( GL_LINE_STRIP );
		glVertex3f( length, 0., 0. );
		glVertex3f( 0., 0., 0. );
		glVertex3f( 0., length, 0. );
	glEnd( );
	glBegin( GL_LINE_STRIP );
		glVertex3f( 0., 0., 0. );
		glVertex3f( 0., 0., length );
	glEnd( );

	float fact = LENFRAC * length;
	float base = BASEFRAC * length;

	glBegin( GL_LINE_STRIP );
		for( int i = 0; i < 4; i++ )
		{
			int j = xorder[i];
			if( j < 0 )
			{
				
				glEnd( );
				glBegin( GL_LINE_STRIP );
				j = -j;
			}
			j--;
			glVertex3f( base + fact*xx[j], fact*xy[j], 0.0 );
		}
	glEnd( );

	glBegin( GL_LINE_STRIP );
		for( int i = 0; i < 5; i++ )
		{
			int j = yorder[i];
			if( j < 0 )
			{
				
				glEnd( );
				glBegin( GL_LINE_STRIP );
				j = -j;
			}
			j--;
			glVertex3f( fact*yx[j], base + fact*yy[j], 0.0 );
		}
	glEnd( );

	glBegin( GL_LINE_STRIP );
		for( int i = 0; i < 6; i++ )
		{
			int j = zorder[i];
			if( j < 0 )
			{
				
				glEnd( );
				glBegin( GL_LINE_STRIP );
				j = -j;
			}
			j--;
			glVertex3f( 0.0, fact*zy[j], base + fact*zx[j] );
		}
	glEnd( );

}


// function to convert HSV to RGB
//
// Reference:  Foley, van Dam, Feiner, Hughes,
//		"Computer Graphics Principles and Practices,"

void
HsvRgb( float hsv[3], float rgb[3] )
{
	float r, g, b;			// red, green, blue

	// guarantee valid input:

	float h = hsv[0] / 60.;
	while( h >= 6. )	h -= 6.;
	while( h <  0. ) 	h += 6.;

	float s = hsv[1];
	if( s < 0. )
		s = 0.;
	if( s > 1. )
		s = 1.;

	float v = hsv[2];
	if( v < 0. )
		v = 0.;
	if( v > 1. )
		v = 1.;


	// if sat==0, then is a gray:

	if( s == 0.0 )
	{
		rgb[0] = rgb[1] = rgb[2] = v;
		return;
	}


	// get an rgb from the hue itself:
	
	float i = floor( h );
	float f = h - i;
	float p = v * ( 1. - s );
	float q = v * ( 1. - s*f );
	float t = v * ( 1. - ( s * (1.-f) ) );

	switch( (int) i )
	{
		case 0:
			r = v;	g = t;	b = p;
			break;
	
		case 1:
			r = q;	g = v;	b = p;
			break;
	
		case 2:
			r = p;	g = v;	b = t;
			break;
	
		case 3:
			r = p;	g = q;	b = v;
			break;
	
		case 4:
			r = t;	g = p;	b = v;
			break;
	
		case 5:
			r = v;	g = p;	b = q;
			break;
	}


	rgb[0] = r;
	rgb[1] = g;
	rgb[2] = b;
}