/// LSU EE 4702-1 (Fall 2015), GPU Programming // /// Homework 2 -- SOLUTION // /// Instructions // // Assignment: http://www.ece.lsu.edu/koppel/gpup/2015/hw02.pdf // Solution: http://www.ece.lsu.edu/koppel/gpup/2015/hw02_sol.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, 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.) // 'B': Push head ball. (Add 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.) // // 'v' Cycle through display of links/balls (SKEL) and triangles (SKIN). // '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/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), 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; 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)), 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<Link> Links; typedef pVectorI_Iter<Link> LIter; typedef pVectorI<Ball> Balls; typedef pVectorI_Iter<Ball> BIter; /// SOLUTION -- Problem 2 struct Strip { Strip(Balls& b, pColor colour):balls(b),color(colour){} Strip(pColor colour):color(colour){} Balls balls; pColor color; }; typedef pVectorI<Strip> Strips; typedef pVectorI_Iter<Strip> SIter; /// Homework 2 All Problems // // Use this class to define variables and member functions. // Don't modify hw02-graphics.cc. // class My_Piece_Of_The_World { public: /// SOLUTION -- Problem 1 // float link_stressed_thd; // Amount of stretch to be considered stressed. float link_snap_thd; // Amount of stretch needed to snap link. pColor color_stressed; /// SOLUTION -- Problem 2 Strips strips; }; 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; Links links; /// SOLUTION -- Problem 2 // Strips strips; }; #include "hw02-graphics.cc" void World::init() { mp.color_stressed = pColor(1,0,0); // Red, what else? /// SOLUTION -- Problem 1 // // Define thresholds at which a link will be considered stressed and // will snap. mp.link_stressed_thd = 1.001; mp.link_snap_thd = 1.01; 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_view = 3; opt_ride = false; init_graphics(); 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; 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 ( BIter ball(balls); ball; ) ball->spring_constant_sum = 0; const double dtis = pow( opt_time_step_duration, 2 ); for ( LIter link(links); link; ) { 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 ( BIter ball(balls); ball; ) ball->mass_min = ball->spring_constant_sum * dtis; } void World::balls_twirl() { if ( !head_ball || !tail_ball ) return; pNorm axis(head_ball->position, tail_ball->position); for ( BIter ball(balls); ball; ) { pVect b_to_top(ball->position,head_ball->position); 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(); links.erase(); /// SOLUTION -- Problem 2 mp.strips.clear(); } /// /// Physical Simulation Code /// /// Initialize Simulation // void World::ball_setup_1() { // Arrange and size balls to form a pendulum. pCoor first_pos(13.4,17.8,-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->radius = 0.3; 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. // 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. } 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. // // truss_info->links // 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; Links& lprep = truss_info->links; // 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->radius = 0.15; ball->mass = 4/3.0 * M_PI * pow(ball->radius,3); ball->contact = false; } /// SOLUTION -- Problem 2 // // Prepare an array holding pointers to balls in the order needed // to construct a triangle strip. // for ( int j=0; j<num_sides; j++ ) { Strip* const strip = new Strip(color_chocolate); truss_info->strips += strip; for ( int i=0; i<num_units; i++ ) { const int idx = j + num_sides * i; // Compute the index of the ball at (i, (j-1) mod num_sides ). // const int pn_idx = idx + ( j == 0 ? num_sides - 1 : -1 ); // Add the ball corresponding to (i,j). // strip->balls += bprep[idx]; strip->balls += bprep[pn_idx]; } } // Create links. // 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++ ) lprep += new Link ( 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; head_ball->position = first_pos - delta_pos; for ( int j=0; j<sides; j++ ) links += new Link( head_ball, truss_info.balls[j], color_chocolate ); 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++ ) links += new Link( tail_ball, truss_info.balls[bsize-sides+j], color_chocolate ); for ( BIter ball(balls); ball; ) { ball->locked = false; ball->velocity = pVect(0,0,0); ball->radius = 0.15; ball->mass = 4/3.0 * M_PI * pow(ball->radius,3); ball->contact = false; } balls += truss_info.balls; links += truss_info.links; /// SOLUTION -- Problem 2 mp.strips += truss_info.strips; opt_tail_lock = false; opt_head_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; pNorm v_head = cross(b1->position,b2->position,b3->position); ti.unit_length = delta_dir.magnitude * v_head; make_truss(&ti); links += new Link(b0,ti.balls[0],color_red); links += new Link(b1,ti.balls[1],color_red); links += new Link(b2,ti.balls[2],color_red); links += new Link(b3,ti.balls[3],color_red); links += ti.links; balls += ti.balls; /// SOLUTION -- Problem 2 mp.strips += ti.strips; 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; head_ball->position = first_pos - delta_pos; for ( int j=0; j<sides; j++ ) links += new Link( head_ball, truss_info.balls[j], color_chocolate ); 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++ ) links += new Link( tail_ball, truss_info.balls[bsize-sides+j], color_chocolate ); for ( BIter ball(balls); ball; ) { ball->locked = false; ball->velocity = pVect(0,0,0); ball->radius = 0.15; ball->mass = 4/3.0 * M_PI * pow(ball->radius,3); ball->contact = false; } balls += truss_info.balls; links += truss_info.links; mp.strips += truss_info.strips; opt_tail_lock = false; opt_head_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. // if ( adj_t_stop ) { const double dt = min(world_time,adj_t_stop) - adj_t_prev; pVect adj = dt/adj_duration * adj_vector; balls_translate(adj,0); adj_t_prev = world_time; if ( world_time >= adj_t_stop ) adj_t_stop = 0; } for ( BIter ball(balls); ball; ) ball->force = ball->mass * gravity_accel; for ( LIter link(links); link; ) { /// Problem 1 and 3 solutions go here, and other places. /// SOLUTION -- Problem 1 // if ( link->snapped ) continue; // 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; /// SOLUTION -- Problem 1 // // First, check if link is at least stressed. // if ( link->distance_relaxed > 0.001 // Don't bother with very short links. && distance_between_balls > link->distance_relaxed * mp.link_stressed_thd ) { // Take appropriate action if snap threshold exceeded. // if ( distance_between_balls > link->distance_relaxed * mp.link_snap_thd ) link->snapped = true; // Find an amount by which to blend link's original color // and stressed color. // const float factor = ( distance_between_balls / link->distance_relaxed - mp.link_stressed_thd ) / ( mp.link_snap_thd - 1 ); link->color = max(0.0f,1-factor) * link->natural_color + factor * mp.color_stressed; } else { link->color = link->natural_color; } // 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; ) { /// Problem 3 solution goes here, and other places. 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; if ( platform_collision_possible(ball->position) && ball->position.y < 0 ) { // Use a high spring constant for the platform. To damp energy // use a smaller constant when ball is moving away from the // platform. // const float spring_constant_plat = ball->velocity.y < 0 ? 100000 : 50000; const float force_up = -ball->position.y * spring_constant_plat; const float delta_v_up = force_up / mass * delta_t; /// SOLUTION -- Problem 3 // // Use delta_v_op to compute a frictional force, and from // that a delta_v_surf. If delta_v_surf is so large that it // would reverse the direction of the ball then just stop // the ball. const float fric_coefficient = 0.1; // The amount of lateral frictional force is based on the // separation force (the force pushing the ball up). // const float fric_force_mag = fric_coefficient * force_up; // Compute the velocity of the ball along the surface. // pNorm surface_v(ball->velocity.x,0,ball->velocity.z); // Compute the change in velocity due to the frictional force. // const float delta_v_surf = fric_force_mag / mass * delta_t; // Check whether the change in velocity would reverse the direction. // if ( delta_v_surf > surface_v.magnitude ) { // Here the frictional change in velocity that was // computed would reverse the direction of the // ball. That really can't happen, the ball would just // stop (in the x and z directions). So set delta_v so // that it stops the ball. // delta_v = pVect(-ball->velocity.x,delta_v.y,-ball->velocity.z); } else { // The change in velocity will slow the ball down, so // apply it. // 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. // ball->position += ball->velocity * delta_t; } } 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 ( 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() { /// SOLUTION -- Problem 2. // Declare arrays used to hold vertex coordinates and normals. // pCoor *coord_buffer = NULL; pVect *norm_buffer = NULL; int buffer_elts = 0; // Number of elements in currently allocated array. // Iterate over each strip (truss side). // for ( SIter strip(mp.strips); strip; ) { const int elts = strip->balls; // If arrays are not large enough for this truss allocate more // storage. // if ( elts > buffer_elts ) { buffer_elts = elts; coord_buffer = (pCoor*) realloc(coord_buffer,elts*sizeof(coord_buffer[0])); norm_buffer = (pVect*) realloc(norm_buffer,elts*sizeof(norm_buffer[0])); } // Copy ball positions into vertex coordinate array. // for ( int i=0; i<elts; i++ ) coord_buffer[i] = strip->balls[i]->position; // Compute normals and copy them into normal array. // for ( int i=0; i<elts-2; i+=2 ) { // Consider coordinates i to i+3. For each one construct a // normal based on its two neighbors and add the normal to // norm_buffer. When the loop finishes an element of // norm_buffer will be the sum of two normals. // pVect vlateral0(coord_buffer[i],coord_buffer[i+1]); pVect vlateral1(coord_buffer[i+2],coord_buffer[i+3]); pVect vleft(coord_buffer[i],coord_buffer[i+2]); pVect vright(coord_buffer[i+1],coord_buffer[i+3]); pNorm nleft0(cross(vlateral0,vleft)); pNorm nright0(cross(vlateral0,vright)); pNorm nleft1(cross(vlateral1,vleft)); pNorm nright1(cross(vlateral1,vright)); if ( i == 0 ) { norm_buffer[0] = nleft0; norm_buffer[1] = nright0; } norm_buffer[i] += nleft0; norm_buffer[i+1] += nright0; norm_buffer[i+2] = nleft1; norm_buffer[i+3] = nright1; if ( i == elts - 3 ) { norm_buffer[i+2] += nleft1; norm_buffer[i+3] += nright1; } } // Render the strip. // glEnableClientState(GL_VERTEX_ARRAY); glVertexPointer(3, GL_FLOAT, sizeof(pCoor), coord_buffer); glEnableClientState(GL_NORMAL_ARRAY); glNormalPointer(GL_FLOAT, 0, norm_buffer); glColor3fv(strip->color); glDrawArrays(GL_TRIANGLE_STRIP, 0, elts); glDisableClientState(GL_NORMAL_ARRAY); glDisableClientState(GL_VERTEX_ARRAY); } free(coord_buffer); free(norm_buffer); } 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; 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); }