/// LSU EE 4702-1 (Fall 2016), GPU Programming // /// Homework 1 --- SOLUTION // /// /// Instructions // // Read the assignment: http://www.ece.lsu.edu/koppel/gpup/2016/hw01.pdf // // Edit this file only. Contact the instructor if you believe that // code in other files, such as hw01-graphics.cc needs to be edited. // // Answers to questions that don't require writing code (for // example, a question like "Explain why...") can be put in this // file as comments or can be submitted separately (on paper or view // E-mail). // // Only add comments where necessary, for example, to explain code // that's not obvious or to describe what the code is based on (if // it's not yours). // // There is no need to use comments to mark your code. // // Try to clean up your code by removing any commented-out // variations. /// Purpose // // Demonstrate simulation of string modeled as point masses and springs /// What Code Does // Simulates a string of beads over a platform. The string is modeled // as point masses connected by springs with a long relaxed // length. 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.) // // '1' Set up scene 1. // '2' Set up scene 2. // '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. // '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 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 <math.h> #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 "shapes.h" /// /// Main Data Structures /// // // class World: All data about scene. class World; // Object Holding Ball State // class Ball { public: pCoor position; pVect velocity; float mass; float radius; bool contact; // Can be used for special effects. void push(pVect amt); void translate(pVect amt); void stop(); void freeze(); }; #include "hw01-graphics.cc" void World::init() { chain_length = 20; balls = new Ball[chain_length]; opt_globe = true; globe.radius = 0.5; globe.position = pCoor(15.2,12,-18.5); opt_globe_charge = 250; variable_control.insert(opt_globe_charge,"Globe's Electric Charge"); distance_relaxed = 15.0 / chain_length; opt_spring_constant = 1000; 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_time_step_easy = false; opt_air_resistance = 0.001; 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(); ball_setup_2(); } /// /// Physical Simulation Code /// /// Initialize Simulation // void World::ball_setup_1() { /// Arrange balls horizontally // Desired position of top ball. // pCoor top_pos(15.2, distance_relaxed * ( chain_length + 1 ), -18.5); // Desired distance between adjacent balls. // pVect ball_separation(distance_relaxed, 0, 0); for ( int i=0; i<chain_length; i++ ) { Ball* const ball = &balls[i]; ball->position = top_pos - i * ball_separation; ball->velocity = pVect(0,0,0); ball->radius = 0.3 * distance_relaxed; ball->mass = 4/3.0 * M_PI * pow(ball->radius,3); ball->contact = false; } opt_head_lock = true; } void World::ball_setup_2() { /// Arrange balls in direction dir. /// HOMEWORK 1: Solutions to Problems 1 and 2 here. // Desired position of top ball. // pCoor top_pos(15.2, distance_relaxed * ( chain_length + 1 ), -18.5); // Randomly chosen normal vector. // pNorm dir( drand48() - 0.5, -drand48() * 0.5, drand48() - 0.5 ); /// SOLUTION --- PROBLEM 1 // // Use unit vector dir and distance_relaxed to compute a vector // giving the desired ball-to-ball spacing. // pVect ball_to_ball = distance_relaxed * dir; for ( int i=0; i<chain_length; i++ ) { Ball* const ball = &balls[i]; /// SOLUTION --- PROBLEM 1, continued. // // Use ball_to_ball to find difference between top ball and // desired position of i'th ball. // pVect top_to_ball = i * ball_to_ball; // // And use this to find the position of the i'th ball. // ball->position = top_pos + top_to_ball; /// SOLUTION --- PROBLEM 2 // // To obtain smooth rotation, the velocity direction must be // orthogonal to the axis of rotation (the y axis in this case) // and orthogonal to a vector connecting the ball to the axis // of rotation. // pVect rot_axis(0,-1,0); // From problem description. // // So that all the balls rotate smoothly, the magnitude of the // velocity must be proportional to the distance between the // ball and the closest point on the axis. The distance from // the axis is dist = i * distance_relaxed * cos(theta), where // theta is the smallest angle between dir and rot_axis. // Fortunately, the magnitude of cross( rot_axis, top_to_ball ) // is dist, so the cross product provides both the correct // direction and the correct magnitude. // ball->velocity = 0.8 * cross( rot_axis, top_to_ball ); ball->radius = 0.3 * distance_relaxed; ball->mass = 4/3.0 * M_PI * pow(ball->radius,3); ball->contact = false; } opt_head_lock = true; } void World::ball_setup_3() { float delta_theta = 2 * M_PI / chain_length; const float circum = chain_length * distance_relaxed; const float circ_radius = circum / ( 2 * M_PI ); // Given: pNorm n(0,1,1); pCoor C(15.2,17.8,-18.5); pCoor P(C.x + circ_radius,17.8,C.z); // Compute: pNorm ax(C,P); // ax is a normal vector from C to P. pNorm ay = cross(ax,n); float r = ax.magnitude; // Construct points on circle: // for ( float theta = 0; theta < 2 * M_PI; theta += delta_theta ) for ( int i=0; i<chain_length; i++ ) { const float theta = i * delta_theta; pCoor pos = C + r * cos(theta) * ax + r * sin(theta) * ay; // Do something with pos.. Ball* const ball = &balls[i]; ball->position = pos; ball->velocity = pVect(0,0,0); ball->radius = ( i == chain_length - 1 ? 0.6 : 0.3 ) * distance_relaxed; ball->mass = 4/3.0 * M_PI * pow(ball->radius,3); ball->contact = false; } opt_head_lock = true; } void World::ball_setup_4() { } void World::ball_setup_5() { } /// Advance Simulation State by delta_t Seconds // void World::time_step_cpu_full(double delta_t) { time_step_count++; /// HOMEWORK 1: Solution to Problem 3 in this routine. // /// Compute force and update velocity of each ball. // for ( int i=0; i<chain_length; i++ ) { Ball* const ball = &balls[i]; // Skip locked balls. // if ( opt_head_lock && i == 0 || opt_tail_lock && i == chain_length - 1 ) { ball->velocity = pVect(0,0,0); continue; } pVect force(0,0,0); // Gravitational Force // force += ball->mass * gravity_accel; /// SOLUTION --- PROBLEM 3 // // Find the direction between the globe and the ball. The // repulsion force will be in this direction. // pNorm gdist(globe.position,ball->position); // // Compute the magnitude of the repulsion force. Note that // the pNorm::mag_sq member is being used to avoid re-computing // the square of the distance (magnitude). // const float eforce = opt_globe_charge * ball->mass / gdist.mag_sq; // // Apply the force. // if ( opt_globe ) force += eforce * gdist; // Spring Force from Neighbor Balls // for ( int n_idx: { i-1, i+1 } ) { if ( n_idx < 0 ) continue; if ( n_idx == chain_length ) break; Ball* const neighbor_ball = &balls[n_idx]; // Construct a normalized (Unit) Vector from ball to neighbor. // pNorm ball_to_neighbor( ball->position, neighbor_ball->position ); // Get distance between balls using pNorm member magnitude. // const float distance_between_balls = ball_to_neighbor.magnitude; // Compute by how much the spring is stretched (positive value) // or compressed (negative value). // const float spring_stretch = distance_between_balls - distance_relaxed; // Compute the speed of ball towards neighbor_ball. // pVect delta_v = neighbor_ball->velocity - ball->velocity; float delta_s = dot( delta_v, ball_to_neighbor ); // 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; force += spring_constant * spring_stretch * ball_to_neighbor; } // 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. // ball->velocity += ( force / ball->mass ) * delta_t; // Air Resistance // const double fs = pow(1+opt_air_resistance,-delta_t); ball->velocity *= fs; } /// /// Update Position of Each Ball /// for ( int i=0; i<chain_length; i++ ) { Ball* const ball = &balls[i]; // 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){balls[b].translate(amt);} void World::balls_push(pVect amt,int b){balls[b].push(amt);} void World::balls_translate(pVect amt) { for(int i=0;i<chain_length;i++)balls[i].translate(amt);} void World::balls_push(pVect amt) { for(int i=0;i<chain_length;i++)balls[i].push(amt);} void World::balls_stop() { for(int i=0;i<chain_length;i++)balls[i].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; const double time_step_duration = 0.0001; // Compute amount by which to advance simulation state for this frame. // const double duration = opt_single_time_step ? 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_full(time_step_duration); world_time += 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); }