```/// LSU EE 4702-1 (Fall 2015), GPU Programming
//
/// Homework 3 -- SOLUTION
//

/// Instructions
//
//  Solution discussion: http://www.ece.lsu.edu/koppel/gpup/2015/hw03_sol.pdf

#if 0
/// SOLUTION OUTLINE

/// Parts of Solution
//
//  - Preparing a Texture
//  - Division of Platform into Overlays (Use many small textures.)
//  - Coordinate Spaces: Object (balls) to Overlays to Texture Pixels

/// Code Organization

/// Platform_Overlay
//
Platform_Overlay* platform_overlays;  // Array of overlays.
//
//  A data structure holding info about texture that covers part of platform.
//
//  Platform is covered by nx * ny (default 40*40) overlays ..
//  .. arranged in a grid.
//
//  Initialized in My_Piece_Of_The_World::init():

/// Overlay Rationale
//
//  We expect to update texture on CPU and send it back go GPU.
//
//  This may happen every frame.
//
//  Suppose minimum scuff size is 1/100 of a tile:
//    19 * 19 platform tiles  * 100 * 100  * 24 bytes / texel
//    = 86640000 B
//
//  Recall: PCIe x16:  15.8 GB/s
//  Suppose we want a frame rate of 60 f/s
//   15.8 10^9 / ( 60 * 86640000 ) = 3.04
//   About 1/3 of the capacity will be used for texture updates.

#endif
/// 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.)
//
//  'c'    Clean the platform.
//  '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;

class Platform_Overlay {
public:
Platform_Overlay():data(NULL){}

// Note: When using the array below as an argument to glTexImage2D
// use data format GL_RGBA and type GL_FLOAT.
//
pColor *data;
GLuint txid;

bool texture_modified;
bool texture_object_initialized;

pCoor vertices[4];

};

/// Homework 3 All Problems
//
//   Use this class to define variables and member functions.
//   Don't modify hw03-graphics.cc.
//
class My_Piece_Of_The_World {
public:
My_Piece_Of_The_World(World& wp):w(wp){};
World& w;
Platform_Overlay* platform_overlays;  // Array of overlays.
Platform_Overlay sample_overlay;
int nx, nz;          // Number of overlays along each dimension.
int num_overlays;
int twid_x, twid_z;  // Dimensions of each texture in texels.
int num_texels;
float wid_x, wid_z;  // Width of each overlay in object space units.
float wid_x_inv, wid_z_inv;  // Their inverses.

/// SOLUTION
float scale_x_obj_to_texel;
float scale_z_obj_to_texel;

// Minimum x- and z- object space coordinate for most recent overlay.
float overlay_xmin, overlay_zmin;

void init();
void sample_tex_make();

// Return the platform overlay that includes pos, or NULL if pos is
// not on platform.
//
Platform_Overlay* po_get(pCoor pos);

//
// Homework 3: These are suggested functions.
//

// Convert object space coordinate to texel coordinate relative
// to overlay po.
pCoor po_get_lcoor(Platform_Overlay *po, pCoor pos);

// Return the texel at lpos in po.
pColor* po_get_texel(Platform_Overlay *po, pCoor lpos);

/// SOLUTION -- Problem 1(a)
int po_get_tidx(pCoor lpos);

//
// Homework 3: These functions must be implemented.
//
void render();
void clean();
};

// 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;

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;
};

#include "hw03-graphics.cc"

void
My_Piece_Of_The_World::init()
{
// Number of overlays along each direction.
//
nx = 40; nz = 40;
num_overlays = nx * nz;

// Number of texels along each dimension of each overlay's texture.
//
twid_x = 256; twid_z = 256;
num_texels = twid_x * twid_z;

sample_tex_make();

platform_overlays = new Platform_Overlay[num_overlays];

// Dimensions of overlay in object-space coordinates.
//
wid_x = ( w.platform_xmax - w.platform_xmin ) / nx;
wid_z = ( w.platform_zmax - w.platform_zmin ) / nz;
wid_x_inv = 1.0 / wid_x;
wid_z_inv = 1.0 / wid_z;

/// SOLUTION -- Problem 1a
//
//  Compute variables that will come in handy when converting
//  from object space coordinates to texel coordinates (for our overlay).
//
scale_x_obj_to_texel = wid_x_inv * twid_x;
scale_z_obj_to_texel = wid_z_inv * twid_z;
}

void
My_Piece_Of_The_World::sample_tex_make()
{
/// Homework 3 -- Sample Code

// Code in this routine creates a texture with a big red X, and
// loads it into a texture object.  The texture object can
// be used as a substitute for the "scuffed" texture before
// the scuffed texture part of this assignment is finished.

Platform_Overlay* const po = &sample_overlay;

// Allocate storage for the array of texels.
//
if ( !po->data ) po->data = new pColor[ num_texels ];

// Initialize the texels to black and transparent. (Alpha = 0)
//
memset(po->data,0,num_texels*sizeof(po->data[0]));

// Thickness of the strokes making up the letter ex.
//
const int thickness = max(2, twid_x/10);

// Write the letter ex, a big one, in the texture.
//
for ( int tx=0; tx<twid_x-thickness; tx++ )
{
// Note: Compute tz without assuming twid_x == twid_z.
int tz_raw = float(tx)/twid_x * twid_z;
int tz = min(tz_raw,twid_z-1);

// Array index of texel at (tx,tz).
//
int idx  = tx              + tz * twid_x; // Lower left to upper right.
int idx2 = twid_x - 1 - tx + tz * twid_x; // Lower right to upper left.

// Write colors to texels.
//
for ( int i=0; i<thickness; i++ )
{
po->data[idx+i] = color_red;
po->data[idx+i].a = 1;
po->data[idx2-i] = color_red;
po->data[idx2-i].a = 1;
}
}

// Create a new texture object.
//
glGenTextures(1,&po->txid);

// Make our new texture object the current texture object.
//
glBindTexture(GL_TEXTURE_2D,po->txid);
//
// Subsequent OpenGL calls operating on GL_TEXTURE_2D ..
// .. will now operate on po->txid, our new texture object.

// Tell OpenGL to generate MIPMAP levels for us.
//
glTexParameteri(GL_TEXTURE_2D, GL_GENERATE_MIPMAP, 1);

// Load our texture into the texture object.
//
glTexImage2D
(GL_TEXTURE_2D,
0,                // Level of Detail (0 is base).
GL_RGBA,          // Internal format to be used for texture.
twid_x, twid_z,
0,                // Border
GL_RGBA,          // GL_BGRA: Format of data read by this call.
GL_FLOAT,         // Size of component.
(void*)po->data   // Pointer to the texture data.
);
}

/// SOLUTION -- Problem 1a
int
My_Piece_Of_The_World::po_get_tidx(pCoor lpos)
{
// Return an index for the texel array corresponding to texel coord lpos.
const int idx = int(lpos.x) + twid_x * int(lpos.z);
return idx;
}

pColor*
My_Piece_Of_The_World::po_get_texel(Platform_Overlay *po, pCoor lpos)
{
/// SOLUTION -- Problem 1a

// Use our function to get the array index corresponding to lpos.
const int idx = po_get_tidx(lpos);

// If it's out of range return null ..
if ( idx < 0 || idx >= num_texels ) return NULL;
// .. otherwise return the texel.
return &po->data[ idx ];
}

pCoor
My_Piece_Of_The_World::po_get_lcoor(Platform_Overlay *po, pCoor pos)
{
pCoor lc;
/// SOLUTION -- Problem 1a.

// Convert object space coordinates to texel coordinates.
// Variables overlay_xmin and overlay_zmin were set when the overlay
// was retrieved.
//
lc.x = ( pos.x - overlay_xmin ) * scale_x_obj_to_texel;
lc.z = ( pos.z - overlay_zmin ) * scale_z_obj_to_texel;
lc.y = 0;
lc.w = 0;
return lc;
}

Platform_Overlay*
My_Piece_Of_The_World::po_get(pCoor pos)
{
// Convert object-space coordinate, pos, into an overlay space, (x,z) ..
// .. in which (0,0) is the lower-left overlay, etc.

const int x = ( pos.x - w.platform_xmin ) * wid_x_inv;
if ( x < 0 || x >= nx ) return NULL;
const int z = ( pos.z - w.platform_zmin ) * wid_z_inv;
if ( z < 0 || z >= nz ) return NULL;
overlay_xmin = w.platform_xmin + x * wid_x;
overlay_zmin = w.platform_zmin + z * wid_z;

// Retrieve the overlay in which pos lies.
//
Platform_Overlay* const po = &platform_overlays[x + z * nz];

if ( !po->data )
{
/// SOLUTION -- Problem 1a
// This overlay has never been visited, initialize texel array.

// Allocate the color array.
po->data = new pColor[num_texels];

// Initialize it. Note that this makes the colors transparent.
memset(po->data,0,num_texels*sizeof(po->data[0]));

po->texture_object_initialized = false;

// Pre-compute the object-space coordinates of the corners of
// the overlay. These will be used when constructing the primitive
// on which the texture will be applied.
//
pCoor* const vertices = po->vertices;
vertices[0] =
pCoor( w.platform_xmin + x * wid_x, 0.01, w.platform_zmin + z * wid_z );
vertices[1] = vertices[0] + pVect(wid_x,0,0);
vertices[2] = vertices[1] + pVect(0,0,wid_z);
vertices[3] = vertices[0] + pVect(0,0,wid_z);
po->texture_modified = true;
}

return po;
}

void
My_Piece_Of_The_World::render()
{
/// Homework 3 -- Lots of stuff in this routine.

// [ ] Enable at least some of the following:
//     -- Texturing.
//     -- Texture application mode.
//     -- The Alpha Test
//     -- Blending.
//
// See demo-8-texture.cc for examples.

/// SOLUTION -- Problem 1b

// Turn on texturing.
glEnable(GL_TEXTURE_2D);

// Specify which texture unit to use.
glActiveTexture(GL_TEXTURE0);

// Specify how texel and the primitive's lighted color should be
// combined. Use modulation, so that scuffs are affected by
// lighting.
glTexEnvi(GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_MODULATE);

// Turn on the alpha test. This is not needed if blending is in use.
if ( w.opt_tryout1 ) glEnable(GL_ALPHA_TEST);

// Only write fragments corresponding to scuffed parts of the texture.
glAlphaFunc(GL_GREATER,0.4);

// Turn on blending so that scuffs are combined with what's already there.
glEnable(GL_BLEND);

// Set the blend equation to blend colors, but to write the alpha value
// carried by the fragment (from our texture).
glBlendFuncSeparate
(GL_SRC_ALPHA,GL_ONE_MINUS_SRC_ALPHA, GL_ZERO, GL_ONE);

for ( int i=0; i<num_overlays; i++ )
{
Platform_Overlay* const po = &platform_overlays[i];
if ( !po->data ) continue;

if ( !po->texture_object_initialized )
{
po->texture_object_initialized = true;

// [x] Do something here.
/// SOLUTION -- Problem 1b.

//  This is the first time we've used this particular overlay,
//  so we need to create a texture object for it and set its
//  parameters.
//
glGenTextures(1,&po->txid);
glBindTexture(GL_TEXTURE_2D,po->txid);
glTexParameteri(GL_TEXTURE_2D, GL_GENERATE_MIPMAP, 1);
glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_MIN_FILTER,
GL_LINEAR_MIPMAP_LINEAR);
glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_MAG_FILTER,GL_LINEAR);
}

glBindTexture(GL_TEXTURE_2D,po->txid);

if ( po->texture_modified )
{
/// SOLUTION -- Problem 1a.
// We've modified the texture since the last render, so
// we need to update OpenGL's copy.

po->texture_modified = false;

// [x] Send texel array (po->data) to OpenGL.

glTexImage2D
(GL_TEXTURE_2D,
0,                // Level of Detail (0 is base).
GL_RGBA,          // Internal format to be used for texture.
twid_x, twid_z,
0,                // Border
GL_RGBA,     // GL_BGRA: Format of data read by this call.
GL_FLOAT,    // Size of component.
(void*)po->data);
pError_Check();
}

/// SOLUTION -- 1a
//
//  If tryout2 is active (press 'Y' to toggle) show the red x texture
//
if ( w.opt_tryout2 ) glBindTexture(GL_TEXTURE_2D, sample_overlay.txid);

// [x] Render primitive(s) matching shape of overlay.

/// SOLUTION -- 1a
//
//  Apply the texture to a quad. Note that we are using
//  our pre-computed vertices.
//
glNormal3f(0,-1,0);
glColor3fv(color_white);
glTexCoord2f(0,0);
glVertex3fv(po->vertices[0]);
glTexCoord2f(1,0);
glVertex3fv(po->vertices[1]);
glTexCoord2f(1,1);
glVertex3fv(po->vertices[2]);
glTexCoord2f(0,1);
glVertex3fv(po->vertices[3]);
glEnd();
}

// [x] Disable anything turned on at the start.

glDisable(GL_ALPHA_TEST);
glDisable(GL_BLEND);
glDisable(GL_TEXTURE_2D);
}

void
My_Piece_Of_The_World::clean()
{
/// Homework 3:  [ ] Remove scuffs from dirty textures.

/// SOLUTION -- Problem 1.
//
//  Free any textures that are present.

for ( int i=0; i<num_overlays; i++ )
{
Platform_Overlay* const po = &platform_overlays[i];
if ( !po->data ) continue;

// Tell OpenGL to free the texture object, including the
// texture data that it has copied from us.
//
glDeleteTextures(1,&po->txid);

// Free our own texel array.
//
free( po->data );

// Update variables to reflect clean state.
//
po->data = NULL;
po->texture_modified = false;
po->texture_object_initialized = false;
}
}

void
World::init()
{
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_ride = false;

init_graphics();

mp.init();

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();
}

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

/// Initialize Simulation
//

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

pCoor first_pos(13.4,14,-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;
}

//
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;

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;

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->color = color_green;
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;

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;

{
// 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 =

// 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; )
{
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;

const float dist_above = ball->position.y - ball->radius;

const bool collision =
platform_collision_possible(ball->position) && dist_above < 0;

if ( collision )
{
const float spring_constant_plat =
ball->velocity.y < 0 ? 100000 : 50000;
const float fric_coefficient = 0.1;
const float force_up = -dist_above * spring_constant_plat;
const float delta_v_up = force_up / mass * delta_t;
const float fric_force_mag = fric_coefficient * force_up;
pNorm surface_v(ball->velocity.x,0,ball->velocity.z);
const float delta_v_surf = fric_force_mag / mass * delta_t;
if ( delta_v_surf > surface_v.magnitude )
{
// Ignoring other forces?
delta_v =
pVect(-ball->velocity.x,delta_v.y,-ball->velocity.z);
}
else
{
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.
//

/// SOLUTION -- Problem 1a
//
//  Remember previous ball position, used for scuff mark.
//
pCoor pos_prev = ball->position;

ball->position += ball->velocity * delta_t;

if ( !collision ) continue;

/// Homework 3
//
//  [x] Retrieve the correct overlay.
//  [ ] Determine area of platform that ball is touching.
//  [ ] Convert to texel coordinate units.
//  [ ] Modify texels in array.
//  [ ] Set po->texture_modified iff any texels change.

Platform_Overlay* const po = mp.po_get(ball->position);

if ( !po ) continue;

/// SOLUTION -- Problem 1a.
//
//  Find the location of all of the texels scuffed
//  by this ball during this timestep. The length
//  of the scuff mark is based on the old and new positions,
//  the width of the scuff mark is based on the intersection
//  of the ball with the platform.

// Current ball location in texel coordinates.
//
pCoor ball_lcor = mp.po_get_lcoor(po,ball->position);

// Previous location of ball in texel coordinates.
//
pCoor prev_lcor = mp.po_get_lcoor(po,pos_prev);

float width = mp.scale_x_obj_to_texel *

// Direction along scuff mark (based on sliding motion).
//
pNorm skid(prev_lcor,ball_lcor);

// Find direction along width of scuff mark.
//
pNorm nskid = cross( skid, pVect(0,1,0) );

// Iterate over texel locations scuffed by ball.
//
for ( float t = -width; t <= skid.magnitude+width; t++ )
for ( float u = -width; u < max(width,1.0f); u++ )
{
pCoor tex_pos = prev_lcor + t * skid + u * nskid;
pColor* const texel = mp.po_get_texel(po,tex_pos);

// If texel is not on overlay po then just skip it.
//
if ( !texel ) continue;

// Don't bother if already scuffed. If we wanted to be
// fancy we could add this balls color onto what is already
// there. But we don't want to be fancy.
//
if ( texel->a ) continue;

po->texture_modified = true;
*texel = ball->color;
texel->a = 0.8;
}

}
}

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() {mp.render();}

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);
}
```