```/// LSU EE 4702-1 (Fall 2016), GPU Programming
//
/// Homework 1 --- SOLUTION
//
///
/// Instructions
//
//
//  Edit this file only. Contact the instructor if you believe that
//  code in other files, such as hw01-graphics.cc needs to be edited.
//
//  Answers to questions that don't require writing code (for
//  example, a question like "Explain why...") can be put in this
//  file as comments or can be submitted separately (on paper or view
//  E-mail).
//
//  that's not obvious or to describe what the code is based on (if
//  it's not yours).
//
//  There is no need to use comments to mark your code.
//
//  Try to clean up your code by removing any commented-out
//  variations.

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

/// What Code Does

// Simulates a string of beads over a platform. The string is modeled
// as point masses connected by springs with a long relaxed
// length. 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.)
//
//  '1'    Set up scene 1.
//  '2'    Set up scene 2.
//  '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.
//  '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 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 <math.h>
#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;

bool contact;                 // Can be used for special effects.

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

#include "hw01-graphics.cc"

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

opt_globe = true;
globe.position = pCoor(15.2,12,-18.5);
opt_globe_charge = 250;
variable_control.insert(opt_globe_charge,"Globe's Electric Charge");

distance_relaxed = 15.0 / chain_length;
opt_spring_constant = 1000;
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_time_step_easy = false;

opt_air_resistance = 0.001;
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");

init_graphics();

ball_setup_2();
}

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

/// Initialize Simulation
//
void
World::ball_setup_1()
{
/// Arrange balls horizontally

// Desired position of top ball.
//
pCoor top_pos(15.2, distance_relaxed * ( chain_length + 1 ), -18.5);

// Desired distance between adjacent balls.
//
pVect ball_separation(distance_relaxed, 0, 0);

for ( int i=0; i<chain_length; i++ )
{
Ball* const ball = &balls[i];
ball->position = top_pos - i * ball_separation;

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

}

void
World::ball_setup_2()
{
/// Arrange balls in direction dir.

/// HOMEWORK 1: Solutions to Problems 1 and 2 here.

// Desired position of top ball.
//
pCoor top_pos(15.2, distance_relaxed * ( chain_length + 1 ), -18.5);

// Randomly chosen normal vector.
//
pNorm dir( drand48() - 0.5, -drand48() * 0.5, drand48() - 0.5 );

/// SOLUTION --- PROBLEM 1
//
//  Use unit vector dir and distance_relaxed to compute a vector
//  giving the desired ball-to-ball spacing.
//
pVect ball_to_ball = distance_relaxed * dir;

for ( int i=0; i<chain_length; i++ )
{
Ball* const ball = &balls[i];

/// SOLUTION --- PROBLEM 1, continued.
//
//  Use ball_to_ball to find difference between top ball and
//  desired position of i'th ball.
//
pVect top_to_ball = i * ball_to_ball;
//
//  And use this to find the position of the i'th ball.
//
ball->position = top_pos + top_to_ball;

/// SOLUTION --- PROBLEM 2
//
//  To obtain smooth rotation, the velocity direction must be
//  orthogonal to the axis of rotation (the y axis in this case)
//  and orthogonal to a vector connecting the ball to the axis
//  of rotation.
//
pVect rot_axis(0,-1,0);  // From problem description.
//
//  So that all the balls rotate smoothly, the magnitude of the
//  velocity must be proportional to the distance between the
//  ball and the closest point on the axis. The distance from
//  the axis is dist = i * distance_relaxed * cos(theta), where
//  theta is the smallest angle between dir and rot_axis.
//  Fortunately, the magnitude of cross( rot_axis, top_to_ball )
//  is dist, so the cross product provides both the correct
//  direction and the correct magnitude.
//
ball->velocity = 0.8 * cross( rot_axis, top_to_ball );

ball->mass = 4/3.0 * M_PI * pow(ball->radius,3);
ball->contact = false;
}

}

void
World::ball_setup_3()
{
float delta_theta = 2 * M_PI / chain_length;

const float circum = chain_length * distance_relaxed;
const float circ_radius = circum / ( 2 * M_PI );

// Given:
pNorm n(0,1,1);
pCoor C(15.2,17.8,-18.5);

// Compute:
pNorm ax(C,P);  // ax is a normal vector from C to P.
pNorm ay = cross(ax,n);
float r = ax.magnitude;

// Construct points on circle:
//  for ( float theta = 0; theta < 2 * M_PI; theta += delta_theta )
for ( int i=0; i<chain_length; i++ )
{
const float theta = i * delta_theta;

pCoor pos = C + r * cos(theta) * ax + r * sin(theta) * ay;
// Do something with pos..

Ball* const ball = &balls[i];
ball->position = pos;

ball->velocity = pVect(0,0,0);
ball->radius = ( i == chain_length - 1 ? 0.6 : 0.3 ) * distance_relaxed;
ball->mass = 4/3.0 * M_PI * pow(ball->radius,3);
ball->contact = false;
}

}

void
World::ball_setup_4()
{
}

void
World::ball_setup_5()
{
}

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

/// HOMEWORK 1: Solution to Problem 3 in this routine.

//
/// Compute force and update velocity of each ball.
//
for ( int i=0; i<chain_length; i++ )
{
Ball* const ball = &balls[i];

// Skip locked balls.
//
if ( opt_head_lock && i == 0 || opt_tail_lock && i == chain_length - 1 )
{
ball->velocity = pVect(0,0,0);
continue;
}

pVect force(0,0,0);

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

/// SOLUTION --- PROBLEM 3
//
//  Find the direction between the globe and the ball. The
//  repulsion force will be in this direction.
//
pNorm gdist(globe.position,ball->position);
//
//  Compute the magnitude of the repulsion force. Note that
//  the pNorm::mag_sq member is being used to avoid re-computing
//  the square of the distance (magnitude).
//
const float eforce = opt_globe_charge * ball->mass / gdist.mag_sq;
//
//  Apply the force.
//
if ( opt_globe ) force += eforce * gdist;

// Spring Force from Neighbor Balls
//
for ( int n_idx: { i-1, i+1 } )
{
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 );

// Get distance between balls using pNorm member magnitude.
//
const float distance_between_balls = ball_to_neighbor.magnitude;

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

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

// 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;

force += spring_constant * spring_stretch * ball_to_neighbor;
}

// 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.
//
ball->velocity += ( force / ball->mass ) * delta_t;

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

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

for ( int i=0; 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 || 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;

const double time_step_duration = 0.0001;

// Compute amount by which to advance simulation state for this frame.
//
const double duration =
opt_single_time_step ? 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_full(time_step_duration);
world_time += 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;
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);
}
```