```/// LSU EE 4702-1 (Fall 2015), GPU Programming
//
/// Homework 2 -- SOLUTION
//

/// Instructions
//
//  Assignment: http://www.ece.lsu.edu/koppel/gpup/2015/hw02.pdf
//  Solution: http://www.ece.lsu.edu/koppel/gpup/2015/hw02_sol.pdf

/// Purpose
//
//   Demonstrate simulation of point masses connected by springs.

/// What Code Does

// Simulates balls connected by springs over a platform. Balls and
// springs can be initialized in different arrangements (called
// scenes). Currently scene 1 is a simple string of beads, and scenes
// 2, 3, and 4 are trusses. The platform consists of tiles, some are
// purple-tinted mirrors (showing a reflection of the ball), the
// others show the course syllabus.

///  Keyboard Commands
//
/// Object (Eye, Light, Ball) Location or Push
//   Arrows, Page Up, Page Down
//        Move object or push ball, depending on mode.
//        With shift key pressed, motion is 5x faster.
//   'e': Move eye.
//   'l': Move light.
//   'b': Move head (first) ball. (Change position but not velocity.)
//
/// Eye Direction
//   Home, End, Delete, Insert
//   Turn the eye direction.
//   Home should rotate eye direction up, End should rotate eye
//   down, Delete should rotate eye left, Insert should rotate eye
//   right.  The eye direction vector is displayed in the upper left.

/// Simulation Options
//  (Also see variables below.)
//
//  'v'    Cycle through display of links/balls (SKEL) and triangles (SKIN).
//  'w'    Twirl balls around axis formed by head and tail.
//  '1'    Set up scene 1.
//  '2'    Set up scene 2.
//  '3'    Set up scene 3.
//  'p'    Pause simulation. (Press again to resume.)
//  ' '    (Space bar.) Advance simulation by 1/30 second.
//  'S- '  (Shift-space bar.) Advance simulation by one time step.
//  'h'    Freeze position of first (head) ball. (Press again to release.)
//  't'    Freeze position of last (tail) ball. (Press again to release.)
//  's'    Stop balls.
//  'g'    Turn gravity on and off.
//  'y'    Toggle value of opt_tryout1. Intended for experiments and debugging.
//  'Y'    Toggle value of opt_tryout2. Intended for experiments and debugging.
//  'F11'  Change size of green text (in upper left).
//  'F12'  Write screenshot to file.

/// Variables
//   Selected program variables can be modified using the keyboard.
//   Use "Tab" to cycle through the variable to be modified, the
//   name of the variable is displayed next to "VAR" on the bottom
//   line of green text.

//  'Tab' Cycle to next variable.
//  '`'   Cycle to previous variable.
//  '+'   Increase variable value.
//  '-'   Decrease variable value.
//
//  VAR Spring Constant - Set spring constant.
//  VAR Time Step Duration - Set physics time step.
//  VAR Air Resistance - Set air resistance.
//  VAR Light Intensity - The light intensity.
//  VAR Gravity - Gravitational acceleration. (Turn on/off using 'g'.)

#define GL_GLEXT_PROTOTYPES
#define GLX_GLXEXT_PROTOTYPES

#include <GL/gl.h>
#include <GL/glext.h>
#include <GL/glx.h>
#include <GL/glxext.h>
#include <GL/glu.h>
#include <GL/freeglut.h>

#include <gp/util.h>
#include <gp/glextfuncs.h>
#include <gp/coord.h>
#include <gp/pstring.h>
#include <gp/misc.h>
#include <gp/gl-buffer.h>
#include <gp/texture-util.h>
#include <gp/colors.h>

#include "util-containers.h"
#include "shapes.h"

///
/// Main Data Structures
///
//
// class World: All data about scene.

class World;

// Object Holding Ball State
//
class Ball {
public:
Ball():velocity(pVect(0,0,0)),locked(false),
color(color_lsu_spirit_gold),contact(false){};
pCoor position;
pVect velocity;

float mass;
float mass_min; // Mass below which simulation is unstable.

bool locked;

pVect force;
pColor color;
bool contact;                 // When true, ball rendered in gray.
float spring_constant_sum;    // Used to compute minimum mass.

void push(pVect amt);
void translate(pVect amt);
void stop();
void freeze();
};

public:
distance_relaxed(pDistance(b1->position,b2->position)), snapped(false),
natural_color(color_lsu_spirit_purple),color(color_lsu_spirit_purple){}
Link(Ball *b1, Ball *b2, pColor colorp):ball1(b1),ball2(b2),
distance_relaxed(pDistance(b1->position,b2->position)), snapped(false),
natural_color(colorp),color(colorp){}
Ball* const ball1;
Ball* const ball2;
float distance_relaxed;
bool snapped;
pColor natural_color;
pColor color;
};

// Declare containers and iterators for Balls and Links.
// (See util_container.h.)
//
typedef pVectorI<Ball> Balls;
typedef pVectorI_Iter<Ball> BIter;

/// SOLUTION -- Problem 2

struct Strip {
Strip(Balls& b, pColor colour):balls(b),color(colour){}
Strip(pColor colour):color(colour){}
Balls balls;
pColor color;
};

typedef pVectorI<Strip> Strips;
typedef pVectorI_Iter<Strip> SIter;

/// Homework 2 All Problems
//
//   Use this class to define variables and member functions.
//   Don't modify hw02-graphics.cc.
//
class My_Piece_Of_The_World {
public:

/// SOLUTION -- Problem 1
//
float link_stressed_thd;  // Amount of stretch to be considered stressed.

pColor color_stressed;

/// SOLUTION -- Problem 2

Strips strips;

};

struct Truss_Info {

// See make_truss for a description of what the members are for.

// Inputs
PStack<pCoor> base_coors;  // Coordinates of first set of balls.
pVect unit_length;
int num_units;

// Output
Balls balls;

/// SOLUTION -- Problem 2
//
Strips strips;
};

#include "hw02-graphics.cc"

void
World::init()
{
mp.color_stressed = pColor(1,0,0); // Red, what else?

/// SOLUTION -- Problem 1
//
// Define thresholds at which a link will be considered stressed and
// will snap.

chain_length = 14;

opt_time_step_duration = 0.0003;
variable_control.insert(opt_time_step_duration,"Time Step Duration");

distance_relaxed = 15.0 / chain_length;
opt_spring_constant = 15000;
variable_control.insert(opt_spring_constant,"Spring Constant");

opt_gravity_accel = 9.8;
opt_gravity = true;
gravity_accel = pVect(0,-opt_gravity_accel,0);
variable_control.insert(opt_gravity_accel,"Gravity");

opt_air_resistance = 0.04;
variable_control.insert(opt_air_resistance,"Air Resistance");

world_time = 0;
time_step_count = 0;
last_frame_wall_time = time_wall_fp();
frame_timer.work_unit_set("Steps / s");

ball_eye = NULL;
opt_view = 3;
opt_ride = false;

init_graphics();

ball_setup_1();
lock_update();
}

Ball*
World::make_marker(pCoor position, pColor color)
{
Ball* const ball = new Ball;
ball->position = position;
ball->locked = true;
ball->velocity = pVect(0,0,0);
ball->mass = 0;
ball->contact = false;
ball->color = color;
return ball;
}

void
World::lock_update()
{
// This routine called when options like opt_head_lock might have
// changed.

// Update locked status.
//
if ( tail_ball ) tail_ball->locked = opt_tail_lock;

// Re-compute minimum mass needed for stability.
//
for ( BIter ball(balls); ball; ) ball->spring_constant_sum = 0;
const double dtis = pow( opt_time_step_duration, 2 );
{
b1->spring_constant_sum += opt_spring_constant;
b2->spring_constant_sum += opt_spring_constant;
}
for ( BIter ball(balls); ball; )
ball->mass_min = ball->spring_constant_sum * dtis;
}

void
World::balls_twirl()
{
if ( !head_ball || !tail_ball ) return;

for ( BIter ball(balls); ball; )
{
const float dist_along_axis = dot(b_to_top,axis);
const float lsq = b_to_top.mag_sq() - dist_along_axis * dist_along_axis;
if ( lsq <= 1e-5 ) { ball->velocity = pVect(0,0,0); continue; }
const float dist_to_axis = sqrt(lsq);
pNorm rot_dir = cross(b_to_top,axis);
ball->velocity += 10 * dist_to_axis * rot_dir;
}
}

void
World::objects_erase()
{
ball_eye = NULL;
balls.erase();

/// SOLUTION -- Problem 2
mp.strips.clear();
}

///
/// Physical Simulation Code
///

/// Initialize Simulation
//

void
World::ball_setup_1()
{
// Arrange and size balls to form a pendulum.

pCoor first_pos(13.4,17.8,-9.2);
pVect delta_pos = pVect(distance_relaxed,0,0);

// Remove objects from the simulated objects lists, balls and links.
// The delete operator is used on objects in the lists.
//
objects_erase();

for ( int i=0; i<chain_length; i++ )
{
// Construct a new ball and add it to the simulated objects list (balls).
//
Ball* const ball = balls += new Ball;

// Initialize position and other information.
//
ball->position = first_pos + i * delta_pos;
ball->locked = false;
ball->velocity = pVect(0,0,0);
ball->mass = 4/3.0 * M_PI * pow(ball->radius,3);
ball->contact = false;

// If it's not the first ball link it to the previous ball.
if ( i > 0 ) links += new Link( ball, balls[i-1] );
}

// The balls pointed to by head_ball and tail_ball can be manipulated
// using the user interface (by pressing 'h' or 't', for example).
// Set these variables.
//
tail_ball = balls[balls-1];

opt_tail_lock = false;   // Tail ball can move freely.
}

void
World::make_truss(Truss_Info *truss_info)
{
/// Construct a truss based on members of truss_info.
//

//            <---- num_units (=9) ----------->
//  j
//  0         O---O---O---O---O---O---O---O---O     ^
//            |   |   |   |   |   |   |   |   |     |
//  1         O---O---O---O---O---O---O---O---O   num_sides (=3)
//            |   |   |   |   |   |   |   |   |     |
//  2         O---O---O---O---O---O---O---O---O     v
//
//      i ->  0   1   2   3   4   5   6   7   8
//
//  Note: Not all links are shown in the diagram above.

/// Truss_Info Inputs
//
//  truss_info->num_units
//    The number of sections in the truss (see diagram above).
//
//  truss_info->base_coors
//    A list containing num_sides coordinates, the coordinates of
//    balls at i=0 (see diagram above). (num_sides is the number of
//    elements in this list.)  These coordinates should all be
//    in the same plane.
//
//  truss_info->unit_length
//    A vector pointing from the ball at (i,j) to the ball at (i+1,j).
//
/// Truss_Info Outputs
//
//  truss_info->balls
//    A list that should be filled with the balls making up the truss.
//
//    A list that should be filled with the links making up the truss.

const int num_sides = truss_info->base_coors.occ();
const int num_units = truss_info->num_units;

// Lists to hold balls and links created for truss.
//
Balls& bprep = truss_info->balls;

// Create balls for truss.
//
for ( int i=0; i<num_units; i++ )
for ( pCoor bcoor; truss_info->base_coors.iterate(bcoor); )
{
Ball* const ball = bprep += new Ball;
ball->position = bcoor + i * truss_info->unit_length;
ball->locked = false;
ball->velocity = pVect(0,0,0);
ball->mass = 4/3.0 * M_PI * pow(ball->radius,3);
ball->contact = false;
}

/// SOLUTION -- Problem 2
//
//  Prepare an array holding pointers to balls in the order needed
//  to construct a triangle strip.
//
for ( int j=0; j<num_sides; j++ )
{
Strip* const strip = new Strip(color_chocolate);
truss_info->strips += strip;
for ( int i=0; i<num_units; i++ )
{
const int idx = j + num_sides * i;

// Compute the index of the ball at (i, (j-1) mod num_sides ).
//
const int pn_idx = idx + ( j == 0 ? num_sides - 1 : -1 );

// Add the ball corresponding to (i,j).
//
strip->balls += bprep[idx];
strip->balls += bprep[pn_idx];
}
}

//
for ( int i=0; i<num_units; i++ )
for ( int j=0; j<num_sides; j++ )
{
const int idx = j + num_sides * i;

// Retrieve the ball corresponding to (i,j).
//
Ball* const ball = bprep[idx];

// Compute the index of the ball at (i, (j-1) mod num_sides ).
//
const int pn_idx = idx + ( j == 0 ? num_sides - 1 : -1 );

// Insert link to neighbor ball with name i.
//
lprep += new Link( ball, bprep[pn_idx], color_gray );

// Insert links to balls with same i that are not neighbors.
//
if ( j == i % num_sides )
for ( int k = 2; k < num_sides-1; k++ )
( ball, bprep[ idx + (k+j)%num_sides - j ], color_white );

if ( i == 0 ) continue;

// Insert link to ball at (i-1,j).
//
lprep +=
new Link( ball, bprep[idx-num_sides], color_lsu_official_purple );

// Insert link to ball at (i-1, j-1 mod num_sides ).
//
lprep += new Link( ball, bprep[pn_idx-num_sides], color_green );
}
}

void
World::ball_setup_2()
{
pCoor first_pos(13.4,17.8,-9.2);
const float spacing = distance_relaxed;
pVect delta_pos = pVect(spacing*0.05,-spacing,0);
pNorm loc_y = delta_pos;
pNorm loc_x = pVect(0,0,1);
pNorm loc_z = cross(loc_y,loc_x);

// Erase the existing balls and links.
//
objects_erase();

Truss_Info truss_info;

truss_info.num_units = chain_length;
truss_info.unit_length = delta_pos;

const int sides = 4;

for ( int j=0; j<sides; j++ )
{
const double angle = double(j)/sides*2*M_PI;
pCoor chain_first_pos =
first_pos
+ 0.5 * spacing * cos(angle) * loc_x
+ 0.5 * spacing * sin(angle) * loc_z;

truss_info.base_coors += chain_first_pos;
}

make_truss(&truss_info);

// Insert links to balls at either end.
//
head_ball = balls += new Ball;
for ( int j=0; j<sides; j++ )

tail_ball = balls += new Ball;
tail_ball->position = first_pos + chain_length * delta_pos;

const int bsize = truss_info.balls.size();

for ( int j=0; j<sides; j++ )
color_chocolate );

for ( BIter ball(balls); ball; )
{
ball->locked = false;
ball->velocity = pVect(0,0,0);
ball->mass = 4/3.0 * M_PI * pow(ball->radius,3);
ball->contact = false;
}

balls += truss_info.balls;

/// SOLUTION -- Problem 2
mp.strips += truss_info.strips;

opt_tail_lock = false;
}

void
World::ball_setup_3()
{
pCoor first_pos(13.4,17.8,-9.2);
const float spacing = distance_relaxed;
pVect delta_pos = pVect(spacing*0.05,-spacing,0);
pNorm delta_dir = delta_pos;
pNorm tan_dir = pVect(0,0,1);
pNorm um_dir = cross(tan_dir,delta_dir);

// Erase the existing balls and links.
//
objects_erase();

Truss_Info truss_info;

truss_info.num_units = chain_length;
truss_info.unit_length = delta_pos;

const int sides = 4;

for ( int j=0; j<sides; j++ )
{
const double angle = double(j)/sides*2*M_PI;
pCoor chain_first_pos =
first_pos
+ 0.5 * spacing * cos(angle) * tan_dir
+ 0.5 * spacing * sin(angle) * um_dir;

truss_info.base_coors += chain_first_pos;
}

make_truss(&truss_info);

const int idx_center = chain_length / 2 * sides;

for ( int i=0; i<sides; i++ )
{
Truss_Info ti;
ti.num_units = chain_length / 2;
const int idx_1 = idx_center + ( i == 0 ? sides - 1 : i - 1 );
const int idx_2 = idx_center + i;

Ball* const b0 = truss_info.balls[idx_1];
Ball* const b1 = truss_info.balls[idx_1 - sides];
Ball* const b2 = truss_info.balls[idx_2 - sides];
Ball* const b3 = truss_info.balls[idx_2];
ti.base_coors += b0->position;
ti.base_coors += b1->position;
ti.base_coors += b2->position;
ti.base_coors += b3->position;

make_truss(&ti);
balls += ti.balls;

/// SOLUTION -- Problem 2
mp.strips += ti.strips;

int tsz = ti.balls.size();

if ( i == 2 )
{
ball_eye = ti.balls[tsz-2];
ball_down = ti.balls[tsz-1];
}
else if ( i == 1 )
{
ball_gaze = ti.balls[tsz/2];
}

}

// Insert links to balls at either end.
//
head_ball = balls += new Ball;
for ( int j=0; j<sides; j++ )

tail_ball = balls += new Ball;
tail_ball->position = first_pos + chain_length * delta_pos;

const int bsize = truss_info.balls.size();

for ( int j=0; j<sides; j++ )
color_chocolate );

for ( BIter ball(balls); ball; )
{
ball->locked = false;
ball->velocity = pVect(0,0,0);
ball->mass = 4/3.0 * M_PI * pow(ball->radius,3);
ball->contact = false;
}

balls += truss_info.balls;
mp.strips += truss_info.strips;

opt_tail_lock = false;
}

void
World::ball_setup_4()
{
}

void
World::ball_setup_5()
{
}

/// Advance Simulation State by delta_t Seconds
//
void
World::time_step_cpu(double delta_t)
{
time_step_count++;

// Smoothly move ball in response to user input.
//
{
}

for ( BIter ball(balls); ball; )
ball->force = ball->mass * gravity_accel;

{
/// Problem 1 and 3 solutions go here, and other places.

/// SOLUTION -- Problem 1
//

// Spring Force from Neighbor Balls
//

// Construct a normalized (Unit) Vector from ball to neighbor.
//
pNorm ball_to_neighbor(ball1->position,ball2->position);

const float distance_between_balls = ball_to_neighbor.magnitude;

// Compute the speed of ball towards neighbor_ball.
//
pVect delta_v = ball2->velocity - ball1->velocity;
float delta_s = dot( delta_v, ball_to_neighbor );

// Compute by how much the spring is stretched (positive value)
// or compressed (negative value).
//
const float spring_stretch =

/// SOLUTION -- Problem 1
//

// First, check if link is at least stressed.
//
if ( link->distance_relaxed > 0.001 // Don't bother with very short links.
&& distance_between_balls
{
// Take appropriate action if snap threshold exceeded.
//
if ( distance_between_balls

// Find an amount by which to blend link's original color
// and stressed color.
//
const float factor =
/ ( mp.link_snap_thd - 1 );
+ factor * mp.color_stressed;
}
else
{
}

// Determine whether spring is gaining energy (whether its length
// is getting further from its relaxed length).
//
const bool gaining_e = ( delta_s > 0.0 ) == ( spring_stretch > 0 );

// Use a smaller spring constant when spring is loosing energy,
// a quick and dirty way of simulating energy loss due to spring
// friction.
//
const float spring_constant =
gaining_e ? opt_spring_constant : opt_spring_constant * 0.7;

ball1->force += spring_constant * spring_stretch * ball_to_neighbor;
ball2->force -= spring_constant * spring_stretch * ball_to_neighbor;
}

///
/// Update Position of Each Ball
///

for ( BIter ball(balls); ball; )
{
/// Problem 3 solution goes here, and other places.

if ( ball->locked )
{
ball->velocity = pVect(0,0,0);
continue;
}

// Update Velocity
//
// This code assumes that force on ball is constant over time
// step. This is clearly wrong when balls are moving with
// respect to each other because the springs are changing
// length. This inaccuracy will make the simulation unstable
// when spring constant is large for the time step.
//
const float mass = max( ball->mass, ball->mass_min );

pVect delta_v = ( ball->force / mass ) * delta_t;

if ( platform_collision_possible(ball->position) && ball->position.y < 0 )
{

// Use a high spring constant for the platform. To damp energy
// use a smaller constant when ball is moving away from the
// platform.
//
const float spring_constant_plat =
ball->velocity.y < 0 ? 100000 : 50000;

const float force_up = -ball->position.y * spring_constant_plat;
const float delta_v_up = force_up / mass * delta_t;

/// SOLUTION -- Problem 3
//
// Use delta_v_op to compute a frictional force, and from
// that a delta_v_surf. If delta_v_surf is so large that it
// would reverse the direction of the ball then just stop
// the ball.

const float fric_coefficient = 0.1;

// The amount of lateral frictional force is based on the
// separation force (the force pushing the ball up).
//
const float fric_force_mag = fric_coefficient * force_up;

// Compute the velocity of the ball along the surface.
//
pNorm surface_v(ball->velocity.x,0,ball->velocity.z);

// Compute the change in velocity due to the frictional force.
//
const float delta_v_surf = fric_force_mag / mass * delta_t;

// Check whether the change in velocity would reverse the direction.
//
if ( delta_v_surf > surface_v.magnitude )
{
// Here the frictional change in velocity that was
// computed would reverse the direction of the
// ball. That really can't happen, the ball would just
// stop (in the x and z directions). So set delta_v so
// that it stops the ball.
//
delta_v =
pVect(-ball->velocity.x,delta_v.y,-ball->velocity.z);
}
else
{
// The change in velocity will slow the ball down, so
// apply it.
//
delta_v -= delta_v_surf * surface_v;
}
delta_v.y += delta_v_up;
}

ball->velocity += delta_v;

// Air Resistance
//
const double fs = pow(1+opt_air_resistance,-delta_t);
ball->velocity *= fs;

// Update Position
//
// Assume that velocity is constant.
//
ball->position += ball->velocity * delta_t;

}
}

bool
World::platform_collision_possible(pCoor pos)
{
// Assuming no motion in x or z axes.
//
return pos.x >= platform_xmin && pos.x <= platform_xmax
&& pos.z >= platform_zmin && pos.z <= platform_zmax;
}

/// External Modifications to State
//
//   These allow the user to play with state while simulation
//   running.

// Move the ball.
//
void Ball::translate(pVect amt) {position += amt;}

// Add velocity to the ball.
//
void Ball::push(pVect amt) {velocity += amt;}

// Set the velocity to zero.
//
void Ball::stop() {velocity = pVect(0,0,0); }

// Set the velocity and rotation (not yet supported) to zero.
//
void Ball::freeze() {velocity = pVect(0,0,0); }

void World::balls_translate(pVect amt)
{ for ( BIter ball(balls); ball; ) ball->translate(amt); }
void World::balls_push(pVect amt)
{ for ( BIter ball(balls); ball; ) ball->push(amt); }
void World::balls_stop()
{ for ( BIter ball(balls); ball; ) ball->stop(); }
void World::balls_freeze(){balls_stop();}

void
World::render_my_piece()
{
/// SOLUTION -- Problem 2.

// Declare arrays used to hold vertex coordinates and normals.
//
pCoor *coord_buffer = NULL;
pVect *norm_buffer = NULL;
int buffer_elts = 0;  // Number of elements in currently allocated array.

// Iterate over each strip (truss side).
//
for ( SIter strip(mp.strips); strip; )
{
const int elts = strip->balls;

// If arrays are not large enough for this truss allocate more
// storage.
//
if ( elts > buffer_elts )
{
buffer_elts = elts;
coord_buffer =
(pCoor*) realloc(coord_buffer,elts*sizeof(coord_buffer[0]));
norm_buffer =
(pVect*) realloc(norm_buffer,elts*sizeof(norm_buffer[0]));
}

// Copy ball positions into vertex coordinate array.
//
for ( int i=0; i<elts; i++ )
coord_buffer[i] = strip->balls[i]->position;

// Compute normals and copy them into normal array.
//
for ( int i=0; i<elts-2; i+=2 )
{
// Consider coordinates i to i+3. For each one construct a
// normal based on its two neighbors and add the normal to
// norm_buffer. When the loop finishes an element of
// norm_buffer will be the sum of two normals.
//
pVect vlateral0(coord_buffer[i],coord_buffer[i+1]);
pVect vlateral1(coord_buffer[i+2],coord_buffer[i+3]);
pVect vleft(coord_buffer[i],coord_buffer[i+2]);
pVect vright(coord_buffer[i+1],coord_buffer[i+3]);
pNorm nleft0(cross(vlateral0,vleft));
pNorm nright0(cross(vlateral0,vright));
pNorm nleft1(cross(vlateral1,vleft));
pNorm nright1(cross(vlateral1,vright));
if ( i == 0 )
{
norm_buffer[0] = nleft0;
norm_buffer[1] = nright0;
}
norm_buffer[i] += nleft0;
norm_buffer[i+1] += nright0;
norm_buffer[i+2] = nleft1;
norm_buffer[i+3] = nright1;
if ( i == elts - 3 )
{
norm_buffer[i+2] += nleft1;
norm_buffer[i+3] += nright1;
}
}

// Render the strip.
//
glEnableClientState(GL_VERTEX_ARRAY);
glVertexPointer(3, GL_FLOAT, sizeof(pCoor), coord_buffer);
glEnableClientState(GL_NORMAL_ARRAY);
glNormalPointer(GL_FLOAT, 0, norm_buffer);
glColor3fv(strip->color);
glDrawArrays(GL_TRIANGLE_STRIP, 0, elts);
glDisableClientState(GL_NORMAL_ARRAY);
glDisableClientState(GL_VERTEX_ARRAY);
}

free(coord_buffer);
free(norm_buffer);
}

void
World::frame_callback()
{
// This routine called whenever window needs to be updated.

const double time_now = time_wall_fp();

if ( !opt_pause || opt_single_frame || opt_single_time_step )
{

// Amount of time since the user saw the last frame.
//
const double wall_delta_t = time_now - last_frame_wall_time;

// Compute amount by which to advance simulation state for this frame.
//
const double duration =
opt_single_time_step ? opt_time_step_duration :
opt_single_frame ? 1/30.0 :
wall_delta_t;

const double world_time_target = world_time + duration;

while ( world_time < world_time_target )
{
time_step_cpu(opt_time_step_duration);
world_time += opt_time_step_duration;
}

// Reset these, just in case they were set.
//
opt_single_frame = opt_single_time_step = false;
}

last_frame_wall_time = time_now;

if ( opt_ride && ball_eye )
{
pNorm b_eye_down(ball_eye->position,ball_down->position);
pVect b_eye_up = -b_eye_down;
pCoor eye_pos = ball_eye->position + 2.2 * ball_eye->radius * b_eye_up;
pNorm b_eye_direction(eye_pos,ball_gaze->position);

pNorm b_eye_left = cross(b_eye_direction,b_eye_up);
pMatrix_Translate center_eye(-eye_pos);
pMatrix rotate; rotate.set_identity();
for ( int i=0; i<3; i++ ) rotate.rc(0,i) = b_eye_left.elt(i);
for ( int i=0; i<3; i++ ) rotate.rc(1,i) = b_eye_up.elt(i);
for ( int i=0; i<3; i++ ) rotate.rc(2,i) = -b_eye_direction.elt(i);
modelview = rotate * center_eye;
pMatrix reflect; reflect.set_identity(); reflect.rc(1,1) = -1;
transform_mirror = modelview * reflect * invert(modelview);
}

render();
}

int
main(int argv, char **argc)
{
pOpenGL_Helper popengl_helper(argv,argc);
World world(popengl_helper);

popengl_helper.rate_set(30);
popengl_helper.display_cb_set(world.frame_callback_w,&world);
}
```