```/// LSU EE 4702-1 (Fall 2012), GPU Programming
//

/// Homework 1 -- SOLUTION
//
// See http://www.ece.lsu.edu/koppel/gpup/2012/hw01.pdf for instructions.

// \$Id:\$

/// Purpose
//
//   Demonstrate simulation of string modeled as point masses and springs

/// What Code Does

// Simulates a string bouncing over a platform. The string is modeled
// as point masses connected by springs with motion damped by air
// resistance. The platform consists of tiles, some are purple-tinted
// mirrors (showing a reflection of the ball), the others show the
// course syllabus. The ball and the shape of the platform can be
// manipulated by the user.

///  Keyboard Commands
//
/// Object (Eye, Light, Ball) Location or Push
//   Arrows, Page Up, Page Down
//   Will move object or push ball, depending on mode:
//   'e': Move eye.
//   'l': Move light.
//   'b': Move ball. (Change position but not velocity.)
//   'B': Push ball. (Add 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.)
//
//  'p'    Pause simulation. (Press again to resume.)
//  'k'    Freeze position of end of string. (Press again to release.)
//  's'    Stop ball.
//  'S'    Freeze ball. (Set velocity of all vertices to zero.)
//  'g'    Turn gravity on and off.
//  'f'    Toggle between flat and curved platform.
//  '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 Light Intensity - The light intensity.
//  VAR Gravity - Gravitational acceleration. (Turn on/off using 'g'.)
//  VAR Platform Depth - Adjust depth of curved platform. (On/off suing 'f'.)

#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 "shapes.h"

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

class World;

// Object Holding Ball State
//
class Ball {
public:
pCoor position;
pVect velocity;
float mass, mass_inv;
void push(pVect amt);
void translate(pVect amt);
void stop();
void freeze();
};

#include "hw1-graphics.cc"

void
World::init()
{
chain_length = 20;
balls = new Ball[chain_length];

distance_relaxed = 0.2;
opt_spring_constant = 20;
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");

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

init_graphics();

ball_init();
}

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

/// Initialize Simulation
//
void
World::ball_init()
{
// Set initial position to a visibly interesting point.
//
pCoor next_pos(2.1,12,-20.8);

for ( int i=0; i<chain_length; i++ )
{
Ball* const ball = &balls[i];
ball->position = next_pos;
ball->velocity = pVect(0,0,0);
ball->mass = i == 0 ? 10 : 1;

next_pos += pVect(1,0,0);
}

}

/// Advance Simulation State by delta_t Seconds
//
void
World::time_step_cpu(double delta_t)
{
//
/// Compute force and update velocity of each ball.
//
for ( int i=1; i<chain_length; i++ )
{
Ball* const ball = &balls[i];

pVect force(0,0,0);

// Gravitational Force
//
force += ball->mass * gravity_accel;

// Spring Force from Neighbor Balls
//
for ( int n_idx = i-1; n_idx <= i+1; n_idx += 2 )
{
if ( n_idx < 0 ) continue;
if ( n_idx == chain_length ) break;

Ball* const neighbor_ball = &balls[n_idx];

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

// SOLUTION
const float distance_relaxed =

// Compute how much the spring is stretched.
//
const float spring_stretch =
ball_to_neighbor.magnitude - distance_relaxed;

// SOLUTION
const float spring_constant =
spring_stretch < 0 ? 10 * opt_spring_constant : opt_spring_constant;

force += spring_constant * spring_stretch * ball_to_neighbor;
}

// Air Resistance
//
const float air_resistance = 0.02;
pVect ar_force  = -pow(1.0 - air_resistance,delta_t) * ball->velocity;
force += ar_force;

// 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
// which tight springs (large opt_spring_constant) and long time
// steps (large delta_t).
//
ball->velocity += ( force / ball->mass ) * delta_t;
}

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

// Skip first ball if head_lock option true.
//
const int ball_first_idx = opt_head_lock ? 1 : 0;

for ( int i=ball_first_idx; i<chain_length; i++ )
{
Ball* const ball = &balls[i];

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

// Possible Collision with Platform
//

// Skip if collision impossible.
//
if ( !platform_collision_possible(ball->position) ) continue;
if ( ball->position.y >= 0 ) continue;

// Snap ball position to surface.
//
ball->position.y = 0;

// Reflect y (vertical) component of velocity, with a reduction
// due to energy lost in the collision.
//
if ( ball->velocity.y < 0 )
ball->velocity.y = - 0.9 * ball->velocity.y;
}
}

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,int b){balls[b].translate(amt);}
void World::balls_push(pVect amt,int b){balls[b].push(amt);}
void World::balls_translate(pVect amt)
{ for(int i=0;i<chain_length;i++)balls[i].translate(amt);}
void World::balls_push(pVect amt)
{ for(int i=0;i<chain_length;i++)balls[i].push(amt);}
void World::balls_stop()
{ for(int i=0;i<chain_length;i++)balls[i].stop();}
void World::balls_freeze(){balls_stop();}

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

const double time_now = time_wall_fp();

if ( opt_pause || world_time == 0 )
{
/// Don't change simulation state.
//
world_time = time_now;
}
else
{
/// Advance simulation state by wall clock time.
//
const double delta_t = time_now - world_time;
time_step_cpu(delta_t);
world_time += delta_t;
}

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);
}

```