/// 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; }