```/// LSU EE 7700-1 (Sp 2009), Graphics Processors
//
/// Homework 1 and 2 SOLUTION

// This file contains the solution to Homework 1 and the programming
// part of the solution to Homework 2.

/// Instructions

// Follow the class account setup instructions linked to the
// class procedures page, http://www.ece.lsu.edu/koppel/gp/proc.html

// For instructions on how to check out edit, compile, and debug, see
// the "Programming Homework Work Flow" entry on the procedures page,
// http://www.ece.lsu.edu/koppel/gp/proc.html.
//
// For those instructions you need to know that:
//
//  This assignment is at SVN URI https://svn.ece.lsu.edu/svn/gp/hw/2009/hw1
//  (That is .../2009/hw1, there is no separate hw2 directory.)
//  Do "svn update" to get the hw2.cc file.
//
//  After all Homework 1 solutions have been submitted this file
//  will be updated with eye motion changes.
//
//  The assignment instructions are in:
//  http://www.ece.lsu.edu/koppel/gp/2009/hw02.pdf

// For the solutions to the coding problems below edit this file.

// The main code is in routine render_light.
// The routine sample_code provides examples of the geometry objects.

/// Keyboard Commands

/// Eye and Light Location
//   Arrows, Page Up, Page Down
//   Move either the light or, after Homework 1 solved, the eye.
//   After pressing 'l' the keys move the light, after pressing 'e'
//   they move the eye (viewer location). The eye and light location
//   coordinates are displayed in the upper left. The eye
//   location coordinates show what *should* be displayed,
//   until Homework 1 is solved that is not what is actually
//   displayed (except for the initial view).

/// Eye Direction
//   Home, End, Delete, Insert
//   Turn the eye direction (after Problem 1 solved).
//   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,
//   until Homework 1 is solved the vector won't match the image.

/// Lighting Options
//   d, a, n, +, -
//   d: Toggle use of distance in computing vertex lighting.
//   a: Toggle use of normal in computing vertex lighting.
//   n: Switch between using triangle normal and tube normal.
//   +,-: Change intensity of light.

/// Screenshot
//   F12
//   Pressing F12 will write a png image. The file name base will
//   match the executable name, for example, "hw1.png".

/// Problem 1, 2, 3

// See http://www.ece.lsu.edu/koppel/gp/2009/hw02.pdf

#include <stdio.h>
#include <strings.h>
#include <stdlib.h>
#include <deque>

#include "frame_buffer.h"
#include "coord.h"

/// Vertex Object
//
// Holds coordinates, color, and normal.
//

class pVertex : public pCoor {
public:
pVertex(float xp, float yp, float zp):pCoor(xp,yp,zp){};
pVertex(float xp, float yp, float zp, uint32_t color):
pCoor(xp,yp,zp){set_color(color);};
pVertex(pCoor c, pVect n, uint32_t color)
:pCoor(c),normal(n){set_color(color);}
pVertex():pCoor(){};
pVertex(pVertex *v){ *this = *v; }
void set_color(uint32_t colorp)
{
color = colorp;
red = float( 0xff & ( color >> 16 ) );
green = float( 0xff & ( color >> 8 ) );
blue = float( 0xff & color );
}
float red, green, blue;
uint32_t color;
pVect normal;
};

void
sample_code()
{
// This routine contains examples of how to use the geometric
// classes such as coordinate, vertex, and matrix.  It is not
// supposed to do anything useful.

// For more details on these classes read the code in coord.h.

/// Coordinate Construction
//
pCoor c1(11,22,33);  // w is 1 by default.
pCoor c2(1,2,3,0.5); // w is 0.5
pCoor c2b(&c2);   // Copy of c2.
pCoor c3(5,1,8);
printf("x component of c1 is %.1f\n",c1.x);

/// Vertex Construction
//
// A vertex is a coordinate that can hold a color and normal.
// Operations on coordinates also work on vertices.
//
pVertex v1(11,22,33);   // Vertex at same coordinates as c1.
pVertex v2(2,4,6);      // Vertex at same coordinates as c2.
pVertex v3(5,1,8,0xff); // Fourth arg is color, not w.

/// Vector Construction
//
pVect vec(1,2,3);       // Construct using x, y, and z components.
pVect vec_12(c1,c2);    // Const. using two coords, result is c2 - c1.
pVect vec_21(c2,c1);
pVect vec_23(v2,v3);    // Const. using two vertices, result is v3 - v2.
pVect vec_xa(vec_21,vec_23);  // Cross product: (c1-c2) x (c3-c2).
pVect vec_xb(c1,c2,c3);       // Cross product: (c1-c2) x (c3-c2).

/// Matrix Construction
//
pMatrix m1; m1.a[0][0] = 1; m1.a[0][1] = 0;   // Set each element by hand.
pMatrix_Translate trans1(1,2,3);    // Translate +1 x, +2 y, +3 z.
pMatrix_Rotation rot1(vec, 1.2);    // Rotate around axis VEC by 1.2 radians.
pMatrix_Rotation rot2(vec_12, vec_23);  // Rotate vec_12 to vec_23.

/// Coordinate and Vector Operators
//
pVect vec_12b = c2 - c1;   // Subtraction of coords yields vector.
pVect vec_12c = v2 - v1;   // Coordinate operators work on vertices too.
pCoor c2c = c1 + vec_12b;  // Coord + vec yields a coordinate.
pVect vscaled = 5 * vec_12b;  // Multiply each element.

/// Matrix Multiplication Operator
//
pCoor cx1 = trans1 * c1;   // Use trans1 (above) to transform c1.
pCoor cx2 = trans1 * rot1 * rot2 * c1;  // Three matrices and a coord.
pMatrix m = trans1 * rot1 * rot2;
pCoor vx3 = m * c1;

/// Coordinate Member Functions
//
cx1.homogenize();         // Divide all elements by w
cx1.homogenize_keep_w();  // Divide x, y, and z by w. (Be careful.)

/// Vector Member Functions
//
float length_12b = vec_12b.magnitude();  // Length of vector.
float length_12c = vec_12c.normalize();  // Return length, then normalize.

/// Matrix Member Functions.
//
pMatrix m2;  // Member functions set matrix to indicated transformation.
m2.set_zero(); m2.set_identity(); m2.set_scale(0.5); m2.set_translate(1,2,3);
m2.set_frustum(1,2,3,4);
m2.transpose();
m2.invert3x3();  // Note: Only inverts 3x3 submatrix.

/// Miscellaneous Functions
//
float d1223a = dot(vec_21,vec_23);    // Dot product of vectors.
float d1223b = dot(c1,c2,c3);         // Dot product (c1-c2) x (c3-c2).
pVect c1223a = cross(vec_21,vec_23);  // Cross product of vectors.
pVect c1223b = cross(c1,c2,c3);       // Cross product (c1-c2) x (c3-c2).

float a1223a = pangle(vec_21,vec_23); // Angle between vectors, in [0,pi].
float a1223b = pangle(c1,c2,c3);      // Angle between c1 c2 c3, in [0,pi].

pMatrix minv = invert3x3(m);   // Invert 3x3 submatrix.

if ( length_12b + length_12c + d1223a + d1223b + a1223a + a1223b == 1111 )
printf("Pacify compiler.\n");

}

/// Vertex List
//
// Declare vertex list types so that many vertices can easily be
// operated on.
//
typedef std::deque<pVertex*> pVertex_List;
typedef pVertex_List::iterator pVertex_Iterator;

/// Vertex Sort
//
// Sort three vertices at vertex list iterator position.
//
class pSortVertices {
public:
pSortVertices(pVertex_Iterator& ci)
{
rv_idx = 0;
for ( int i=0; i<3; i++ ) v[i] = ci[i];
swap(0,1); swap(0,2); swap(1,2);
}
operator pVertex& () { return *v[rv_idx++]; }
private:
void swap(int a, int b)
{
if ( v[a]->y <= v[b]->y ) return;
pVertex* const t = v[a];  v[a] = v[b];  v[b] = t;
}
pVertex* v[3];
int rv_idx;
};

int clampi(float valp, int min, int max)
{
const int val = (int) valp;
if ( val < min ) return min;
if ( val > max ) return max;
return val;
}

/// Interpolation Object
//
// Return x and y values on line connecting two points. Skips
// out-of-range values.
//
// Can be instantiated to advance in +x direction or +y direction.
//
class pInterpolate {
public:

pInterpolate(pVertex& v0, pVertex& v1, int ymin, int ymax)
{ set(v0, v1, ymin, ymax); }

void set(pVertex& v0, pVertex& v1, int ymin, int ymax)
{
const float y_range_inv = 1.0 / ( v1.y - v0.y );
yi_last = ymax < int(v1.y) ? ymax : int(v1.y);
const float pre_y = float(ymin) - v0.y;
const bool scissor = pre_y > 0.0;
yi = scissor ? ymin : int(v0.y);
const float y_range_part_inv = 1.0 / ( v1.y - yi );
#define DELTA(item) \
const float dtrue_##item = (v1.item - v0.item) * y_range_inv; \
item = v0.item + ( scissor ? pre_y * dtrue_##item : 0.0 ); \
d_##item = (v1.item - item) * y_range_part_inv;
DELTA(red); DELTA(green); DELTA(blue); DELTA(x); DELTA(z);
#undef DELTA
}

pInterpolate(pInterpolate& v0, pInterpolate& v1, int xmin, int xmax)
{
pInterpolate& vmin = v0.x < v1.x ? v0 : v1;
pInterpolate& vmax = v0.x < v1.x ? v1 : v0;
const float x_range_inv = 1.0 / ( vmax.x - vmin.x );
xi_last = xmax < int(vmax.x) ? xmax : int(vmax.x);
const float pre_x = float(xmin) - vmin.x;
const bool scissor = pre_x > 0.0;
xi = scissor ? xmin : int(vmin.x);
const float x_range_part_inv = 1.0 / ( vmax.x - xi );
#define DELTA(item) \
const float dtrue_##item = (vmax.item - vmin.item) * x_range_inv; \
item = vmin.item + ( scissor ? pre_x * dtrue_##item : 0.0 ); \
d_##item = (vmax.item - item) * x_range_part_inv;
DELTA(red); DELTA(green); DELTA(blue); DELTA(z);
#undef DELTA
}

bool keep_going_y() { return yi <= yi_last; }
bool keep_going_x() { return xi <= xi_last; }

void advance_y() { advance_common();  x += d_x;  yi++; }
void advance_x() { advance_common();  xi++; }

void advance_common()
{
red += d_red;  green += d_green;  blue += d_blue;  z += d_z;
}

uint32_t color()
{
return ( ( clampi(red,0,255) << 0 )
| ( clampi(green,0,255) << 8 )
| ( clampi(blue,0,255) << 16 ) );
}
float d_red, d_green, d_blue, d_x, d_z, red, green, blue, x, z;
int xi, xi_last, yi, yi_last;
};

// Add an unlighted tetrahedron to VTX_LIST at LOC of size SIZE.
//
void
insert_tetrahedron(pVertex_List& vtx_list, pCoor& loc, float size)
{
pCoor v0(loc.x,loc.y,loc.z);
pCoor v1(loc.x,loc.y-size,loc.z+size);
pCoor v2(loc.x-.866*size,loc.y-size,loc.z-0.5*size);
pCoor v3(loc.x+.866*size,loc.y-size,loc.z-0.5*size);
const int32_t c1 = 0x1ffffff, c2 = 0x100ff00;
pVect n;
# define TRI(va,vb,vc) \
n = cross(va,vb,vc); \
vtx_list.push_back( new pVertex(va,n,c1) ); \
vtx_list.push_back( new pVertex(vb,n,c2) ); \
vtx_list.push_back( new pVertex(vc,n,c2) );
TRI(v0,v1,v2); TRI(v0,v2,v3); TRI(v0,v3,v1);
# undef TRI
}

void
render_light(pFrame_Buffer &frame_buffer)
{
// This routine will be called automatically each time the frame
// buffer needs to be painted.

///
/// User and Light Locations
///

static pCoor eye_location(1,0.5,3);
static pVect eye_direction(0,0,-1);
static pCoor light_location(1.4, 0, -2.5 );
static bool opt_move_light = true;

///
/// Light Location and Lighting Options
///

static bool opt_attenuation = true;
static bool opt_v_to_light = true;
static bool opt_triangle_normal = false;
static float opt_light_intensity = 2;
static bool opt_split_triangles = false;  // Part of homework 2.

///
/// Adjust options based on user input.
///

pVect adjustment(0,0,0);
pVect user_rot_axis(0,0,0);

switch ( frame_buffer.keyboard_key ) {
case FB_KEY_LEFT: adjustment.x = -0.1; break;
case FB_KEY_RIGHT: adjustment.x = 0.1; break;
case FB_KEY_UP: adjustment.y = 0.1; break;
case FB_KEY_DOWN: adjustment.y = -0.1; break;
case FB_KEY_PAGE_DOWN: adjustment.z = 0.1; break;
case FB_KEY_PAGE_UP: adjustment.z = -0.1; break;
case FB_KEY_DELETE: user_rot_axis.y = 1; break;
case FB_KEY_INSERT: user_rot_axis.y =  -1; break;
case FB_KEY_HOME: user_rot_axis.x = 1; break;
case FB_KEY_END: user_rot_axis.x = -1; break;
case '-':case '_': opt_light_intensity *= 0.9; break;
case '+':case '=': opt_light_intensity *= 1.1; break;
case 'd': case 'D': opt_attenuation = !opt_attenuation; break;
case 'a': case 'A': opt_v_to_light = !opt_v_to_light; break;
case 'l': case 'L': opt_move_light = true; break;
case 'n': case 'N': opt_triangle_normal = !opt_triangle_normal; break;
case 'e': case 'E': opt_move_light = false; break;
case 's': case 'S': opt_split_triangles = !opt_split_triangles; break;
default: break;
}

// Update eye_direction based on keyboard command.
//
if ( user_rot_axis.x || user_rot_axis.y )
eye_direction *= pMatrix_Rotation(user_rot_axis, M_PI * 0.03);

/// HOMEWORK 1 PROBLEM 1 SOLUTION
//
pMatrix_Rotation rotall(eye_direction,pVect(0,0,-1));

// Update eye_location based on keyboard command.
//
if ( adjustment.x || adjustment.y || adjustment.z )
{

/// HOMEWORK 1 PROBLEM 2 SOLUTION
//
adjustment *= invert3x3(rotall);

if ( opt_move_light ) light_location += adjustment;
else                  eye_location += adjustment;
}

//
// User Messages  (Magically inserted into frame buffer.)
//

frame_buffer.fbprintf
("Lighting : distance - %s,  angle - %s,  normals - %s  "
"('d', 'a', 'n', '+', '-' to change)\n",
opt_attenuation ? "ON" : "OFF", opt_v_to_light ? "ON" : "OFF",
opt_triangle_normal ? "TRIANGLE" : "VERTEX");

frame_buffer.fbprintf
("Eye location: [%.1f, %.1f, %.1f]  "
"(%suse arrow and page keys to move).\n",
eye_location.x, eye_location.y, eye_location.z,
opt_move_light ? "press 'e' then " : "" );

frame_buffer.fbprintf
("Light location: [%.1f, %.1f, %.1f]  "
"(%suse arrow and page keys to move).\n",
light_location.x, light_location.y, light_location.z,
opt_move_light ? "" : "press 'l' then ");

frame_buffer.fbprintf
("Eye direction: [%.2f, %.2f, %.2f]  "
"(use 'Home', 'End', 'Del', 'Insert' keys to turn).\n",
eye_direction.x, eye_direction.y, eye_direction.z);

frame_buffer.fbprintf
("Split triangles %s ('s' to change).\n",
opt_split_triangles ? "ON" : "OFF");

// Instantiate list of vertices.
//
pVertex_List vtx_list;

const uint32_t color_gold = 0xf9b237;    // LSU Spirit Gold
const uint32_t color_purple = 0x580da6;  // LSU Spirit Purple

// Insert big purple triangle into the vertex list.
//
{
pVertex* const v0 = new pVertex( 1.5, 0, -3.2, color_purple );
pVertex* const v1 = new pVertex( 0, 5, -5, color_purple );
pVertex* const v2 = new pVertex( 9, 6, -9, color_purple );
v0->normal = v1->normal = v2->normal = cross(*v0,*v1,*v2);
vtx_list.push_back( v0 );
vtx_list.push_back( v1 );
vtx_list.push_back( v2 );
}

//
// Insert a tessellated tube into the vertex list.
//

const float r = 2;                  // Tube radius.
const float x_shift = 0.4;          // Tube x offset.
const int pattern_levels = 50;      // Tube depth (z direction.)
const float pattern_width = 20;     // Triangle size (circumferential).
const float pattern_pitch_z = 0.25; // Triangle size (z axis).

float z = -1;

// Outer Loop: z axis (down axis of tube).
//
for ( int i = 0; i < pattern_levels; i++ )
{
const float next_z = z - pattern_pitch_z;
const float last_z = z + pattern_pitch_z;
const float delta_theta = M_PI / pattern_width;
float theta = i & 1 ? delta_theta : 0;
const uint32_t marker_color[] =
{0xaa, 0xaa0000, 0x111111, 0xaa00,};
// -x        +y        -y        +x
// Left      Up        Down      Right
// Red       Blue      Gray      Green
float marker_target = i & 1 ? M_PI_2 - delta_theta - 0.00001 : 10000;
int marker_idx = 0;

// Inner Loop: around circumference of tube.
//
while ( theta < 4 * M_PI )
{
const float z1 = theta < 2 * M_PI ? next_z : last_z;

uint32_t color = color_gold;
if ( theta >= marker_target && marker_idx < 4 )
{
color = marker_color[marker_idx++];
marker_target += M_PI_2;
}

pVertex* const v0 =
new pVertex( x_shift + r * cos(theta), r * sin(theta), z, color );
if ( !opt_triangle_normal )
v0->normal = pVect(-cos(theta),-sin(theta),0);

theta += delta_theta;
pVertex* const v1 =
new pVertex( x_shift + r * cos(theta), r * sin(theta), z1, color);
if ( !opt_triangle_normal )
v1->normal = pVect(-cos(theta),-sin(theta),0);

theta += delta_theta;
pVertex* const v2 =
new pVertex( x_shift + r * cos(theta), r * sin(theta), z, color );
if ( !opt_triangle_normal )
v2->normal = pVect(-cos(theta),-sin(theta),0);

if ( opt_triangle_normal )
v0->normal = v1->normal = v2->normal = cross(*v0,*v1,*v2);

vtx_list.push_back( v0 );
vtx_list.push_back( v1 );
vtx_list.push_back( v2 );
}
z = next_z;
}

// Insert light position marker (green tetrahedron) into vertex list.
//
insert_tetrahedron(vtx_list,light_location,0.05);

///
/// Rendering Pipeline Starts Here
///

// Indicate to frame buffer simulator that for purposes of showing
// timing, code above is part of application (included in frame time
// but not render time) and that code below is part of rendering
// pipeline.
//
frame_buffer.render_timing_start();

const int win_width = frame_buffer.get_width();
const int win_height = frame_buffer.get_height();
const int fb_size = win_width * win_height;
int32_t* const f_buffer = frame_buffer.get_buffer();

// Allocate and initialize a z buffer.
// (Note: Allocation only needs be performed when size changes.)
//
float* const z_buffer = (float*) malloc( fb_size * sizeof(*z_buffer) );
for ( int i=0; i<fb_size; i++ ) z_buffer[i] = 1;

///
/// Compute Coordinate Transformations
///

// Compute transformation from object space to eye space.
//
pMatrix_Translate center_eye(-1,-0.5,-3);

/// HOMEWORK 1 PROBLEM 1 SOLUTION
//
pMatrix_Translate ctr(-eye_location.x,-eye_location.y,-eye_location.z);
pMatrix object_to_eye = rotall * ctr;

// Compute transformation from eye space to window space.
//
const float aspect = float(win_width) / win_height;
pMatrix_Frustum frustum(1.6,1.6/aspect,1,5000);
pMatrix_Translate center_window(1,1,0);
pMatrix_Scale scale(win_width/2,win_height/2);
pMatrix eye_to_window = scale * center_window * frustum;

// Compute matrix needed to transform normals.
//
pMatrix normal_to_eye(object_to_eye);
normal_to_eye.transpose(); normal_to_eye.invert3x3();

///
/// Transform Coordinates and Normals from Object Space to Eye Space
///
for ( pVertex_Iterator ci = vtx_list.begin(); ci < vtx_list.end(); ci++ )
{
pVertex& v = **ci;
v *= object_to_eye;
v.normal *= normal_to_eye;
v.normal.normalize();
v.homogenize();
}

// Convert light location to eye space.
//
pCoor light_location_e = object_to_eye * light_location;

/// HOMEWORK 2 SOLUTION STARTS
//
pVertex_List vtx_list_split;

///
/// Split triangles.
///
for ( pVertex_Iterator ci = vtx_list.begin(); ci < vtx_list.end(); )
{
pVertex& v1 = **ci++;
pVertex& v2 = **ci++;
pVertex& v3 = **ci++;

pVect tnormal(v1,v2,v3); tnormal.normalize();

pVect l_to_v1(light_location_e,v1);
const float l_to_plane_dist = dot(l_to_v1,tnormal);
pCoor closest = light_location_e + l_to_plane_dist * tnormal;

const pVect n1(v1,closest,v2);
const pVect n2(v2,closest,v3);
const pVect n3(v3,closest,v1);
const double dn12 = dot(n1,n2);
const double dn23 = dot(n2,n3);

#define TRI(s,newV)                                                       \
vtx_list_split.push_back(new pVertex(s & 1 ? newV : v1 ) );             \
vtx_list_split.push_back(new pVertex(s & 2 ? newV : v2 ) );             \
vtx_list_split.push_back(new pVertex(s & 4 ? newV : v3 ) );

if ( !opt_split_triangles
|| v1.color & 0x1000000 || dn12 <= 0 || dn23 <= 0 )
{
TRI(0,v1);
}
else
{
pVect new_norm = v1.normal + v2.normal + v3.normal;
new_norm.normalize();
pVertex newV
(closest,new_norm, opt_triangle_normal ? 0xaa0505 : v1.color);

TRI(1,newV); TRI(2,newV); TRI(4,newV);

}
#undef TRI
delete &v1;
delete &v2;
delete &v3;
}

vtx_list = vtx_list_split;
//
/// HOMEWORK 2 SOLUTION ENDS

///
/// Apply Lighting to Vertices
///
for ( pVertex_Iterator ci = vtx_list.begin(); ci < vtx_list.end(); ci++ )
{
pVertex& v = **ci;
const bool vertex_no_lighting = v.color & 0x1000000;
if ( vertex_no_lighting ) continue;

// Compute vectors from vertex to light and to viewer.
//
pVect v_to_light(v,light_location_e);
pVect v_to_viewer(v,pCoor(0,0,0));

// Distance from vertex to light.
//
const float length = v_to_light.normalize();

// Lighting coefficients and attenuation with distance.
//
const float k0 = 0.9;
const float k1 = 0.0;
const float k2 = 0.3;
const float attenuation =
!opt_attenuation ? 1.0
: 1.0 / ( k0 + k1 * length + k2 * length * length );

// Projections:
//   1: vertex (normal) is facing light (or viewer).
//   0: vertex (normal) is orthogonal (90 degrees) from light.
//  -1: vertex (normal) is facing opposite direction of light.
//
const float dot_v_to_light = dot(v.normal,v_to_light);
const float dot_v_to_viewer = dot(v.normal,v_to_viewer);

// Assume back side (-normal direction) is same color as front.
//
const float v_to_light_scale =
dot_v_to_viewer < 0 ? -dot_v_to_light : dot_v_to_light;

// Combine effect of distance (attenuation) and surface normal
// (v_to_light_scale).
//
const float scale = opt_light_intensity * attenuation
* ( !opt_v_to_light ? 1.0 : v_to_light_scale );

// Convert material property color to lighted color.
//
v.red *= scale;  v.green *= scale;  v.blue *= scale;
}

///
/// Transform Coordinates from Eye Space to Window Space
///
for ( pVertex_Iterator ci = vtx_list.begin(); ci < vtx_list.end(); ci++ )
{
pVertex& v = **ci;
v *= eye_to_window;
v.homogenize_keep_w();
}

///
/// Rasterize Primitives
///
for ( pVertex_Iterator ci = vtx_list.begin(); ci < vtx_list.end(); ci += 3 )
{
pSortVertices sort(ci); // Sort next 3 items in list.
pVertex& c0w = sort;    // Coordinate with smallest y.
pVertex& c1w = sort;
pVertex& c2w = sort;    // Coordinate with largest y.

// Reject primitive if at least one vertex behind eye.
// (It would have been better to clip them earlier.)
//
if ( c0w.w <= 0 || c1w.w <= 0 || c2w.w <= 0 ) continue;

// Instantiate interpolation objects.
//
// Each object instantiated with two vertices and a valid
// range of y values.  The object will compute x and y along the
// line connecting the vertices, skipping y values < 0 or
// >= win_width.
//
// Interpolation objects also interpolate z and color components.
//
pInterpolate interp_02(c0w,c2w,0,win_height-1);
pInterpolate interp_012(c0w,c1w,0,win_height-1);

// Compute position (index) in frame buffer of first row to be written.
//
int fb_line_idx = interp_02.yi * win_width;

// Outer Loop: Iterate from smallest y to largest y.
//
while ( interp_02.keep_going_y() )
{

// If point c1w reached then switch interp_012 to line
// connecting c1w and c2w.
//
if ( ! interp_012.keep_going_y() )
interp_012.set(c1w,c2w,0,win_height-1);

// Instantiate x-axis interpolation object using the two
// y-axis interpolation objects, interp_02 and interp_012.
// The new object will compute points on the line connecting
// the current position of interp_02 and interp_012.
//
pInterpolate interp_line(interp_02,interp_012,0,win_width-1);

// Inner Loop: Iterate along x axis.
//
while ( interp_line.keep_going_x() )
{
const int fb_idx = fb_line_idx + interp_line.xi;

// If z value to be written is smaller (in front of) z value
// already there then go ahead and write frame buffer.
//
if ( interp_line.z < z_buffer[ fb_idx ] )
{
f_buffer[ fb_idx ] = interp_line.color();
z_buffer[ fb_idx ] = interp_line.z;
}

// Tell interpolation object to advance in x direction.
//
interp_line.advance_x();
}

// Tell interpolation objects to advance in y direction.
//
interp_02.advance_y();  interp_012.advance_y();

// Advance the frame buffer index.
//
fb_line_idx += win_width;
}
}

// A paint routine is no place for a memory leak!
// (And excessive dynamic memory allocation, but this is only a demo.)
//
for ( pVertex_Iterator ci = vtx_list.begin(); ci < vtx_list.end(); ci++ )
delete *ci;
free(z_buffer);
}

int
main(int argc, char **argv)
{
pFrame_Buffer frame_buffer(argc,argv);

// Frame buffer object will call render_light routine, where
// most of our work is done, whenever the window needs to be updated,
// including after keyboard key presses.
//
frame_buffer.show(render_light);
return 0;
}
```