```/// LSU EE 4702-1 (Fall 2017), GPU Programming
//
/// Homework 1 -- SOLUTION
//
//  For solution search for SOLUTION in this file.

/// Instructions
//
//  Read the assignment: http://www.ece.lsu.edu/koppel/gpup/2017/hw01.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. 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.)
//   'B': Push head ball. (Add velocity.)
//
/// Eye Direction, View, and Screenshot Options
//
//  'Home', 'End', 'Delete', 'Insert'
//         Change the eye direction.
//         Home rotates eye direction up, End rotates eye
//         down, Delete rotates eye to the left, Insert rotates eye
//         to the right.
//         The eye direction vector is displayed in the upper left.
//
//  'Ctrl' '+'  or  'Ctrl' '=',  and  'Ctrl' '-'  or  'Ctrl' '_',
//         Increase and decrease green text size.
//  'F12'  Write screenshot to file.

/// Simulation Options
//  (Also see variables below.)
//
//  'w'    Twirl balls around axis formed by head and tail. (Prob 2 soln).
//  '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.

/// 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/shader.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),persistant(false),
color(color_lsu_spirit_gold),contact(false){};
pCoor position;
pVect velocity;

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

bool locked;
bool persistant;  // Don't delete it when resetting scenes.

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();
};

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

// Declare containers and iterators for Balls and Links.
// (See util_container.h.)
//
typedef pVectorI<Link> Links;
typedef pVectorI<Ball> Balls;
typedef pVector<pCoor> pCoors;
typedef pVector<pVect> pVects;

#include "hw01-graphics.cc"

void
World::init()
{
chain_length = 14;

opt_height = 1;
variable_control.insert_linear(opt_height,"Volcano height (opt_height)",0.04);

opt_e = 0.3;
variable_control.insert(opt_e,"Volcano exponent (opt_e)");

opt_layers = 8;
variable_control.insert(opt_layers,"Volcano num layers (opt_layers)",1,2);

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");

init_graphics();

pCoor marker_pos(13.4,15.8,-9.2);
balls += marker_red = make_marker(marker_pos,color_red);
marker_pos.y += 2 * marker_red->radius;
balls += marker_blue = make_marker(marker_pos,color_blue);
marker_pos.y += 2 * marker_red->radius;
balls += marker_khaki = make_marker(marker_pos,color_khaki);

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->radius = 0.2;
ball->mass = 0;
ball->contact = false;
ball->color = color;
ball->persistant = true;
return ball;
}

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

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

// Re-compute minimum mass needed for stability.
//
for ( Ball *ball: balls ) ball->spring_constant_sum = 0;
const double dtis = pow( opt_time_step_duration, 2 );
for ( Link *link: links )
{
Ball* const b1 = link->ball1;
Ball* const b2 = link->ball2;
b1->spring_constant_sum += opt_spring_constant;
b2->spring_constant_sum += opt_spring_constant;
}
for ( Ball *ball: balls )
ball->mass_min = ball->spring_constant_sum * dtis;
}

void
World::render_p0()
{
/// Use this code for minor experiments, or leave it unchanged.

// Make sure that this scene set the thing_1 positions.
if ( !thing_1_apex ) return;

pCoor apex = thing_1_apex->position;
pCoor base = thing_1_base->position;
vector<pCoor> ring;
for ( Ball *b: thing_1_ring ) ring.push_back(b->position);

glColorMaterial(GL_FRONT,GL_AMBIENT_AND_DIFFUSE);
glMaterialfv(GL_BACK,GL_AMBIENT_AND_DIFFUSE,color_gray);

glBegin(GL_TRIANGLES);

for ( pCoor circ: ring )
{
pNorm norm = cross(apex,circ,base);

glColor3fv(color_red);

glNormal3fv(norm);
glVertex3fv(apex);
glVertex3fv(base);
glVertex3fv(circ);

}
glEnd();
}

void
World::render_p1()
{
/// Put Problem 1 solution in this routine.

// Make sure that this scene set the thing_1 positions.
if ( !thing_1_apex ) return;

pCoor apex = thing_1_apex->position;
pCoor base = thing_1_base->position;
vector<pCoor> ring;
for ( Ball *b: thing_1_ring ) ring.push_back(b->position);

glColorMaterial(GL_FRONT,GL_AMBIENT_AND_DIFFUSE);
glMaterialfv(GL_BACK,GL_AMBIENT_AND_DIFFUSE,color_gray);

/// SOLUTION:
//  Remove glBegin.

for ( int i=0; i<3; i++ )
{
pCoor circ = ring[i];

pNorm norm = cross(apex,circ,base);

// Compute the center of the triangle ..
//
pVect ab(apex,base);
pVect ac(apex,circ);
pCoor mid = apex + ( ab + ac ) / 3;

// .. and drop a marker there.
//
switch ( i ) {
case 0: marker_red->position = mid; break;
case 1: marker_blue->position = mid; break;
case 2: marker_khaki->position = mid; break;
}

glColor3fv(color_red);

/// SOLUTION
//
//  Compute vertices of triangle hole.

pNorm ma(mid,apex);
pNorm mb(mid,base);
pNorm mc(mid,circ);
pCoor a2 = mid + 0.5 * ma.magnitude * ma;
pCoor b2 = mid + 0.5 * mb.magnitude * mb;
pCoor c2 = mid + 0.5 * mc.magnitude * mc;

// Draw triangle strip.

glBegin(GL_TRIANGLE_STRIP);

glNormal3fv(norm);
glVertex3fv(a2);
glVertex3fv(apex);
glVertex3fv(b2);
glVertex3fv(base);
glVertex3fv(c2);
glVertex3fv(circ);
glVertex3fv(a2);
glVertex3fv(apex);

glEnd();

}
}

void
World::render_p2()
{
// Make sure that this scene set the thing_1 positions.
if ( !thing_1_apex ) return;

pCoor apex = thing_1_apex->position;
pCoor base = thing_1_base->position;
vector<pCoor> ring;
for ( Ball *b: thing_1_ring ) ring.push_back(b->position);

glColorMaterial(GL_FRONT,GL_AMBIENT_AND_DIFFUSE);
glMaterialfv(GL_BACK,GL_AMBIENT_AND_DIFFUSE,color_gray);

for ( int i=0; i<3; i++ )
{
pCoor circ = ring[i];

pNorm norm = cross(apex,circ,base);

// Compute the center of the triangle ..
//
pVect ab(apex,base);
pVect ac(apex,circ);
pCoor mid = apex + ( ab + ac ) / 3;

// .. and drop a marker there.
//
switch ( i ) {
case 0: marker_red->position = mid; break;
case 1: marker_blue->position = mid; break;
case 2: marker_khaki->position = mid; break;
}

glColor3fv(color_red);

/// SOLUTION

// Compute vectors from vertices to triangle center (mid).
//
pVect am(apex,mid);
pVect bm(base,mid);
pVect cm(circ,mid);

float t_stop = 0.9;
float delta_t = t_stop / opt_layers;

// Use an array to conveniently obtain adjacent vertices of triangle
// using loop iterator, j.
//
pCoor coors[4] = {apex,base,circ,apex};

// Iterate over sides of volcano.
//
for ( int j=0; j<3; j++ )
{
pCoor p0 = coors[j];
pCoor q0 = coors[j+1];
pVect pm(p0,mid);
pVect qm(q0,mid);

// Use a triangle strip for the path up the volcano.

glBegin(GL_TRIANGLE_STRIP);
glColor3fv(color_red);

for ( int k = 0;  k <= opt_layers;  k++ )
{
float t = k * delta_t;
pVect up = t * opt_height * norm;
float frac = pow(t,opt_e);

// Compute points on lines going up volcano.
//
pCoor p = p0 + up + frac * pm;
pCoor q = q0 + up + frac * qm;

// Compute derivative of parametric line function,
// and evaluate it at each point to get vectors along surface.
//
pVect dupdt = opt_height * norm;
float dfracdt = t ? opt_e * pow(t,opt_e-1) : 0;
pVect dpdt = dupdt + dfracdt * pm;
pVect dqdt = dupdt + dfracdt * qm;

// Take cross product to find normal.
//
pNorm n = cross(dpdt,dqdt);

glNormal3fv(n);
glVertex3fv(p);
glVertex3fv(q);
}

glEnd();
}
}
}

void
World::objects_erase()
{
thing_1_apex = NULL;
thing_1_ring.clear();
thing_1_pseudo.clear();
Balls save;
for ( auto b: balls ) if ( b->persistant ) save += b; else delete b;
balls = move(save);
links.erase();
chain_starts.clear();
}

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

/// Initialize Simulation
//

void
World::ball_setup_1()
{
// Arrange and size balls to form a cable suspended between two fixed points.

pCoor first_pos(7.2,7.8,-20.2);

pVect head_to_tail(25,0,3.33333);
const int len = 5;
pVect delta_pos = head_to_tail / len;

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

Balls persist = move(balls);
pCoor marker_pos = first_pos + head_to_tail + pVect(0,1,0);
for ( Ball *marker : persist )
{ marker->position = marker_pos; marker_pos.y += 2 * marker_red->radius; }

auto new_ball = [&](pCoor pos)
{
// 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 = pos;
ball->locked = false;
ball->velocity = pVect(0,0,0);
ball->radius = 0.3;
ball->mass = 4/3.0 * M_PI * pow(ball->radius,3);
ball->contact = false;
return ball;
};

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

// 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.
//
head_ball = balls[0];
tail_ball = balls[balls-1];

const int obj_idx = max(1,len - 1 - len / 5);
Ball* const b0 = balls[obj_idx];
Ball* const b1 = balls[obj_idx+1];
pCoor pc = b1->position - 0.2 * delta_pos;
thing_1_apex = b0;
thing_1_base = b1;
thing_1_base->color = color_black;
pVect ayraw(0,1,0);
pNorm ax = delta_pos;
pNorm az = cross(ax,ayraw);
pNorm ay = cross(az,ax);
const double rrad = 4;
const int n = 3;
Balls ring;
for ( int i=0; i<n; i++ )
{
const double theta = i * 2 * M_PI / n;
Ball* const ball =
new_ball( pc + rrad * cos(theta) * ay + rrad * sin(theta) * az );
ball->color = color_lime_green;
ring += ball;
links += new Link( b0, ball );
links += new Link( b1, ball );
}
thing_1_ring = ring;
for ( int i=0; i<n; i++ )
links += new Link( ring[i], ring[(i+1)%n] );

opt_head_lock = true;    // Head ball will be frozen in space.
opt_tail_lock = true;    // Tail ball too.

balls += persist;
}

void
World::ball_setup_2()
{
// Arrange and size balls to form a pendulum.

pCoor first_pos(5.1,17.8,-13.1);
pNorm delta_dir = pVect(1,-1,0);
pVect delta_pos = distance_relaxed * delta_dir;

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

int i;
for ( i=0; i<chain_length/2; 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;

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

int sides = 4;
pNorm hx = delta_pos.x
? pVect(-delta_pos.y,delta_pos.x,0) : pVect(0, -delta_pos.z,delta_pos.y);
pNorm hy = cross(delta_pos,hx);
Ball* const l1 = balls.back();
for ( int i=0; i<sides; i++ )
{
const double angle = i * 2 * M_PI / sides;
Ball* const ball = balls += new Ball;
chain_starts += ball;
ball->position =
l1->position + delta_pos
+ 2 * distance_relaxed * cos(angle) * hx
+ 2 * distance_relaxed * sin(angle) * hy;
links += new Link( ball, l1 );
if ( i > 0 )
links += new Link( ball, chain_starts[i-1] );
if ( i > 1 && i == sides - 1 )
links += new Link( ball, chain_starts[0] );
if ( sides > 3 && i > sides/2 )
links += new Link( ball, chain_starts[i-sides/2] );
}

for ( int i=1; i<chain_length/2; i++ )
for ( int j=0; j<sides; j++ )
{
// 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 = chain_starts[j]->position + i * delta_pos;

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

for ( Ball* ball : balls )
{
ball->locked = false;
ball->velocity = pVect(0,0,0);
ball->radius = 0.3;
ball->mass = 4/3.0 * M_PI * pow(ball->radius,3);
ball->contact = false;
}

// 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.
//
head_ball = balls[0];
tail_ball = balls[balls-1];

opt_head_lock = true;    // Head ball will be frozen in space.
opt_tail_lock = false;   // Tail ball can move freely.

balls += persist;

}

void
World::ball_setup_3()
{
}

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++;

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

for ( Link *link: links )
{
// Spring Force from Neighbor Balls
//
Ball* const ball1 = link->ball1;
Ball* const ball2 = link->ball2;

// 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 =
distance_between_balls - link->distance_relaxed;

// 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 ( Ball *ball: balls )
{
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.
//
float mass = std::max(ball->mass, ball->mass_min );
ball->velocity += ( ball->force / mass ) * delta_t;

// 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;

// 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){head_ball->translate(amt);}
void World::balls_push(pVect amt,int b){head_ball->push(amt);}
void World::balls_translate(pVect amt)
{ for ( Ball *ball: balls ) ball->translate(amt); }
void World::balls_push(pVect amt)
{ for ( Ball *ball: balls ) ball->push(amt); }
void World::balls_stop()
{ for ( Ball *ball: balls ) ball->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 )
{
/// Advance simulation state.

// 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;
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);
}
```