/// LSU EE 4702-1 (Fall 2016), GPU Programming // /// Homework 2 -- SOLUTION // /// Instructions // // Read the assignment: http://www.ece.lsu.edu/koppel/gpup/2016/hw02.pdf /// Purpose // // Demonstrate simulation of point masses connected by springs. /// What Code Does // Simulates balls connected by springs over a platform. Balls and // springs can be initialized in different arrangements (called // scenes). Currently scene 1 is a simple string of beads. The // platform consists of tiles, some are purple-tinted mirrors (showing // a reflection of the ball), the others show the course syllabus. /// Keyboard Commands // /// Object (Eye, Light, Ball) Location or Push // Arrows, Page Up, Page Down // Move object or push ball, depending on mode. // With shift key pressed, motion is 5x faster. // 'e': Move eye. // 'l': Move light. // 'b': Move head (first) ball. (Change position but not velocity.) // 'B': Push head ball. (Add velocity.) // /// Eye Direction // 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.) // // 'w' Twirl balls around axis formed by head and tail. (Prob 2 soln). // '1' Set up scene 1. // '2' Set up scene 2. // '3' Set up scene 3. // 'p' Pause simulation. (Press again to resume.) // ' ' (Space bar.) Advance simulation by 1/30 second. // 'S- ' (Shift-space bar.) Advance simulation by one time step. // 'h' Freeze position of first (head) ball. (Press again to release.) // 't' Freeze position of last (tail) ball. (Press again to release.) // 's' Stop balls. // 'g' Turn gravity on and off. // 'y' Toggle value of opt_tryout1. Intended for experiments and debugging. // 'Y' Toggle value of opt_tryout2. Intended for experiments and debugging. // '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)), color(color_lsu_spirit_purple){} Link(Ball *b1, Ball *b2, pColor colorp):ball1(b1),ball2(b2), distance_relaxed(pDistance(b1->position,b2->position)), color(colorp){} Ball* const ball1; Ball* const ball2; float distance_relaxed; pColor color; }; // Declare containers and iterators for Balls and Links. // (See util_container.h.) // typedef pVectorI<Link> Links; typedef pVectorI_Iter<Link> LIter; typedef pVectorI<Ball> Balls; typedef pVectorI_Iter<Ball> BIter; typedef pVector<pCoor> pCoors; typedef pVector<pVect> pVects; #include "hw02-graphics.cc" 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"); init_graphics(); pNorm dir_right = cross(pVect(0,-1,0),eye_direction); pCoor first_pos(13.4,15.8,-9.2); const float sample_size = 4; const float sample_thickness = sample_size / 10; pVect sample_x = sample_size * dir_right; pCoor sample_start = first_pos - 3.3 * 1.5 * sample_x; for ( int i=0; i<3; i++ ) { sample_a[i] = sample_start + sample_x * i * 1.5; sample_b[i] = sample_a[i] - pVect(0,sample_size,0); sample_c[i] = sample_a[i] + sample_thickness * dir_right; } auto tr = [&](pCoor *co) { co[0] = co[-3] + pVect(0,-first_pos.y/2,0); }; for ( int i=3; i<6; i++ ) { tr(sample_a+i);tr(sample_b+i);tr(sample_c+i);} ball_setup_2(); 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::render_it_demo(pCoor a, pCoor b, pCoor c, int version) { /// DO NOT put homework solution in this routine. // // This routine can be modified for experimentation, but don't // put solution here. The solution should go in to render_it. pNorm dir_z = cross(c,b,a); glColorMaterial(GL_FRONT,GL_AMBIENT_AND_DIFFUSE); glMaterialfv(GL_BACK,GL_AMBIENT_AND_DIFFUSE,color_gray); glBegin(GL_TRIANGLES); glColor3fv(color_red); glNormal3fv(dir_z); glVertex3fv(a); glVertex3fv(b); glVertex3fv(c); glEnd(); if ( version == 0 ) return; // Add coordinates to a container (something based on a standard C // library vector) so they can be easily iterated over. pCoors coords; coords += a; coords += b; coords += c; // Create a second set of coordinates by translating first set. pCoors more_coords; for ( pCoor co: coords ) more_coords += co + pVect(0.5,0,0); // Take the original coordinates and rotate them, and // put these new coordinates in more_coords. // pMatrix_Rotation rot(dir_z, M_PI/10); // Rotation transform around dir_z. pMatrix m = pMatrix_Translate(b) * rot * pMatrix_Translate(-b); if ( version == 2 ) for ( pCoor co: coords ) more_coords += m * co; // Render the transformed coordinates. glBegin(GL_TRIANGLES); glColor3fv(color_cyan); glNormal3fv(dir_z); for ( pCoor co: more_coords ) glVertex3fv( co ); glEnd(); } void World::render_it(pCoor a, pCoor b, pCoor c, int version) { pNorm dir_z = cross(c,b,a); pNorm dir_dn(a,b); pNorm dir_rt(a,c); // Right /// SOLUTION // /// Construct L shape. // float edge_len = dir_dn.magnitude; float width = dir_rt.magnitude; float hwidth = width / 2; // Naming scheme: // l0: Point on left edge, // l1: point a bit over to the right of l0,... // r0, t0, b0: point on right, top, bottom edge respectively. // pCoor p_l0t2 = a + width * dir_dn; pCoor p_l1t1 = a + hwidth * ( dir_rt + dir_dn ); pCoor p_l2t0 = a + width * dir_rt; pCoor p_l2t2 = p_l2t0 + width * dir_dn; pCoor p_l2b2 = c + (edge_len - width ) * dir_dn; pCoor p_r2b0 = b + (edge_len - width ) * dir_rt; pCoor p_r2b2 = p_r2b0 - width * dir_dn; pCoor p_r1b1 = p_r2b0 + hwidth * ( dir_rt - dir_dn ); pCoor p_r0b0 = b + edge_len * dir_rt; pCoors coords; coords += p_l2t0; coords += a; coords += p_l1t1; coords += p_l0t2; coords += p_l2t2; coords += b; coords += p_l2b2; coords += p_r2b0; coords += p_r2b2; coords += p_r1b1; glColorMaterial(GL_FRONT,GL_AMBIENT_AND_DIFFUSE); glMaterialfv(GL_BACK,GL_AMBIENT_AND_DIFFUSE,color_gray); // Find center of square to be formed using two L shapes. // pCoor p_ctr = a + 0.5 * pVect(a,p_r0b0); if ( version > 0 ) { // Construct transformation matrix that will rotate L shape into // position. pMatrix m = pMatrix_Translate(p_ctr) * pMatrix_Rotation(dir_z,M_PI) * pMatrix_Translate(-p_ctr); // Use transformation to add rotated points on to list. // for ( pCoor co: pCoors(coords) ) coords += m * co; } if ( version < 2 ) { // Render the L or the square. glBegin(GL_TRIANGLE_STRIP); glColor3fv(color_yellow); glNormal3fv(dir_z); for ( pCoor co: coords ) glVertex3fv( co ); glEnd(); return; } pCoor cube_ctr = p_ctr - 0.5 * edge_len * dir_z; // Rotate the square to form a cube. for ( int axis_num = 0; axis_num < 2; axis_num++ ) { pVect axis = axis_num == 0 ? dir_dn : dir_rt; for ( int face = 0; face < 4; face++ ) { if ( axis_num == 1 && ( ( face & 1 ) == 0 ) ) continue; const double angle = face * M_PI / 2; pMatrix_Rotation rot(axis,angle); pMatrix m = pMatrix_Translate(cube_ctr) * rot * pMatrix_Translate(-cube_ctr); glBegin(GL_TRIANGLE_STRIP); glColor3fv(color_yellow); // Use rot, not m, to rotate normal. (Vectors don't need to // be centered.) glNormal3fv(rot * dir_z); // Rotate coordinates. // for ( pCoor co: coords ) glVertex3fv( m * co ); glEnd(); } } } void World::objects_erase() { balls.erase(); links.erase(); chain_starts.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::ball_setup_2() { // Arrange and size balls to form a pendulum. pCoor first_pos(5.1,17.8,-13.1); pNorm delta_dir = pVect(1,-1,0); pVect delta_pos = distance_relaxed * delta_dir; // Remove objects from the simulated objects lists, balls and links. // The delete operator is used on objects in the lists. // objects_erase(); int i; for ( i=0; i<chain_length/2; i++ ) { // Construct a new ball and add it to the simulated objects list (balls). // Ball* const ball = balls += new Ball; // Initialize position and other information. // ball->position = first_pos + i * delta_pos; // If it's not the first ball link it to the previous ball. if ( i > 0 ) links += new Link( ball, balls[i-1] ); } int sides = 4; pNorm hx = delta_pos.x ? pVect(-delta_pos.y,delta_pos.x,0) : pVect(0, -delta_pos.z,delta_pos.y); pNorm hy = cross(delta_pos,hx); Ball* const l1 = balls.back(); for ( int i=0; i<sides; i++ ) { const double angle = i * 2 * M_PI / sides; Ball* const ball = balls += new Ball; chain_starts += ball; ball->position = l1->position + delta_pos + 2 * distance_relaxed * cos(angle) * hx + 2 * distance_relaxed * sin(angle) * hy; links += new Link( ball, l1 ); if ( i > 0 ) links += new Link( ball, chain_starts[i-1] ); if ( i > 1 && i == sides - 1 ) links += new Link( ball, chain_starts[0] ); if ( sides > 3 && i > sides/2 ) links += new Link( ball, chain_starts[i-sides/2] ); } for ( int i=1; i<chain_length/2; i++ ) for ( int j=0; j<sides; j++ ) { // Construct a new ball and add it to the simulated objects list (balls). // Ball* const ball = balls += new Ball; // Initialize position and other information. // ball->position = chain_starts[j]->position + i * delta_pos; // If it's not the first ball link it to the previous ball. links += new Link( ball, balls[balls-sides-1] ); } for ( Ball* ball : balls ) { ball->locked = false; ball->velocity = pVect(0,0,0); ball->radius = 0.3; ball->mass = 4/3.0 * M_PI * pow(ball->radius,3); ball->contact = false; } // The balls pointed to by head_ball and tail_ball can be manipulated // using the user interface (by pressing 'h' or 't', for example). // Set these variables. // head_ball = balls[0]; tail_ball = balls[balls-1]; opt_head_lock = true; // Head ball will be frozen in space. opt_tail_lock = false; // Tail ball can move freely. } void World::ball_setup_3() { } void World::ball_setup_4() { } void World::ball_setup_5() { } /// Advance Simulation State by delta_t Seconds // void World::time_step_cpu(double delta_t) { time_step_count++; for ( BIter ball(balls); ball; ) ball->force = ball->mass * gravity_accel; for ( LIter link(links); link; ) { // Spring Force from Neighbor Balls // Ball* const ball1 = link->ball1; Ball* const ball2 = link->ball2; // Construct a normalized (Unit) Vector from ball to neighbor. // pNorm ball_to_neighbor(ball1->position,ball2->position); const float distance_between_balls = ball_to_neighbor.magnitude; // Compute the speed of ball towards neighbor_ball. // pVect delta_v = ball2->velocity - ball1->velocity; float delta_s = dot( delta_v, ball_to_neighbor ); // Compute by how much the spring is stretched (positive value) // or compressed (negative value). // const float spring_stretch = distance_between_balls - link->distance_relaxed; // Determine whether spring is gaining energy (whether its length // is getting further from its relaxed length). // const bool gaining_e = ( delta_s > 0.0 ) == ( spring_stretch > 0 ); // Use a smaller spring constant when spring is loosing energy, // a quick and dirty way of simulating energy loss due to spring // friction. // const float spring_constant = gaining_e ? opt_spring_constant : opt_spring_constant * 0.7; ball1->force += spring_constant * spring_stretch * ball_to_neighbor; ball2->force -= spring_constant * spring_stretch * ball_to_neighbor; } /// /// Update Position of Each Ball /// for ( 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. // float mass = std::max(ball->mass, ball->mass_min ); ball->velocity += ( ball->force / mass ) * delta_t; // Air Resistance // const double fs = pow(1+opt_air_resistance,-delta_t); ball->velocity *= fs; // Update Position // // Assume that velocity is constant. // ball->position += ball->velocity * delta_t; // Possible Collision with Platform // // Skip if collision impossible. // if ( !platform_collision_possible(ball->position) ) continue; if ( ball->position.y >= 0 ) continue; // Snap ball position to surface. // ball->position.y = 0; // Reflect y (vertical) component of velocity, with a reduction // due to energy lost in the collision. // if ( ball->velocity.y < 0 ) ball->velocity.y = - 0.9 * ball->velocity.y; } } bool World::platform_collision_possible(pCoor pos) { // Assuming no motion in x or z axes. // return pos.x >= platform_xmin && pos.x <= platform_xmax && pos.z >= platform_zmin && pos.z <= platform_zmax; } /// External Modifications to State // // These allow the user to play with state while simulation // running. // Move the ball. // void Ball::translate(pVect amt) {position += amt;} // Add velocity to the ball. // void Ball::push(pVect amt) {velocity += amt;} // Set the velocity to zero. // void Ball::stop() {velocity = pVect(0,0,0); } // Set the velocity and rotation (not yet supported) to zero. // void Ball::freeze() {velocity = pVect(0,0,0); } void World::balls_translate(pVect amt,int b){head_ball->translate(amt);} void World::balls_push(pVect amt,int b){head_ball->push(amt);} void World::balls_translate(pVect amt) { for ( 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::frame_callback() { // This routine called whenever window needs to be updated. const double time_now = time_wall_fp(); if ( !opt_pause || opt_single_frame || opt_single_time_step ) { /// Advance simulation state. // Amount of time since the user saw the last frame. // const double wall_delta_t = time_now - last_frame_wall_time; // Compute amount by which to advance simulation state for this frame. // const double duration = opt_single_time_step ? opt_time_step_duration : opt_single_frame ? 1/30.0 : wall_delta_t; const double world_time_target = world_time + duration; while ( world_time < world_time_target ) { time_step_cpu(opt_time_step_duration); world_time += opt_time_step_duration; } // Reset these, just in case they were set. // opt_single_frame = opt_single_time_step = false; } last_frame_wall_time = time_now; render(); } int main(int argv, char **argc) { pOpenGL_Helper popengl_helper(argv,argc); World world(popengl_helper); popengl_helper.rate_set(30); popengl_helper.display_cb_set(world.frame_callback_w,&world); }