/// LSU EE 4702-1 (Fall 2015), GPU Programming // /// Homework 3 -- SOLUTION // /// Your Name: SOLUTION /// Instructions // // Read the assignment: http://www.ece.lsu.edu/koppel/gpup/2015/hw03.pdf // Solution discussion: http://www.ece.lsu.edu/koppel/gpup/2015/hw03_sol.pdf #if 0 /// SOLUTION OUTLINE /// Parts of Solution // // - Preparing a Texture // - Division of Platform into Overlays (Use many small textures.) // - Coordinate Spaces: Object (balls) to Overlays to Texture Pixels /// Code Organization /// Platform_Overlay // Platform_Overlay* platform_overlays; // Array of overlays. // // A data structure holding info about texture that covers part of platform. // // Platform is covered by nx * ny (default 40*40) overlays .. // .. arranged in a grid. // // Initialized in My_Piece_Of_The_World::init(): /// Overlay Rationale // // We expect to update texture on CPU and send it back go GPU. // // This may happen every frame. // // Suppose minimum scuff size is 1/100 of a tile: // 19 * 19 platform tiles * 100 * 100 * 24 bytes / texel // = 86640000 B // // Recall: PCIe x16: 15.8 GB/s // Suppose we want a frame rate of 60 f/s // 15.8 10^9 / ( 60 * 86640000 ) = 3.04 // About 1/3 of the capacity will be used for texture updates. #endif /// 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.) // // 'c' Clean the platform. // '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; class Platform_Overlay { public: Platform_Overlay():data(NULL){} // Note: When using the array below as an argument to glTexImage2D // use data format GL_RGBA and type GL_FLOAT. // pColor *data; GLuint txid; bool texture_modified; bool texture_object_initialized; pCoor vertices[4]; }; /// Homework 3 All Problems // // Use this class to define variables and member functions. // Don't modify hw03-graphics.cc. // class My_Piece_Of_The_World { public: My_Piece_Of_The_World(World& wp):w(wp){}; World& w; Platform_Overlay* platform_overlays; // Array of overlays. Platform_Overlay sample_overlay; int nx, nz; // Number of overlays along each dimension. int num_overlays; int twid_x, twid_z; // Dimensions of each texture in texels. int num_texels; float wid_x, wid_z; // Width of each overlay in object space units. float wid_x_inv, wid_z_inv; // Their inverses. /// SOLUTION float scale_x_obj_to_texel; float scale_z_obj_to_texel; // Minimum x- and z- object space coordinate for most recent overlay. float overlay_xmin, overlay_zmin; void init(); void sample_tex_make(); // Return the platform overlay that includes pos, or NULL if pos is // not on platform. // Platform_Overlay* po_get(pCoor pos); // // Homework 3: These are suggested functions. // // Convert object space coordinate to texel coordinate relative // to overlay po. pCoor po_get_lcoor(Platform_Overlay *po, pCoor pos); // Return the texel at lpos in po. pColor* po_get_texel(Platform_Overlay *po, pCoor lpos); /// SOLUTION -- Problem 1(a) int po_get_tidx(pCoor lpos); // // Homework 3: These functions must be implemented. // void render(); void clean(); }; // 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; 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; }; #include "hw03-graphics.cc" void My_Piece_Of_The_World::init() { // Number of overlays along each direction. // nx = 40; nz = 40; num_overlays = nx * nz; // Number of texels along each dimension of each overlay's texture. // twid_x = 256; twid_z = 256; num_texels = twid_x * twid_z; sample_tex_make(); platform_overlays = new Platform_Overlay[num_overlays]; // Dimensions of overlay in object-space coordinates. // wid_x = ( w.platform_xmax - w.platform_xmin ) / nx; wid_z = ( w.platform_zmax - w.platform_zmin ) / nz; wid_x_inv = 1.0 / wid_x; wid_z_inv = 1.0 / wid_z; /// SOLUTION -- Problem 1a // // Compute variables that will come in handy when converting // from object space coordinates to texel coordinates (for our overlay). // scale_x_obj_to_texel = wid_x_inv * twid_x; scale_z_obj_to_texel = wid_z_inv * twid_z; } void My_Piece_Of_The_World::sample_tex_make() { /// Homework 3 -- Sample Code // Code in this routine creates a texture with a big red X, and // loads it into a texture object. The texture object can // be used as a substitute for the "scuffed" texture before // the scuffed texture part of this assignment is finished. Platform_Overlay* const po = &sample_overlay; // Allocate storage for the array of texels. // if ( !po->data ) po->data = new pColor[ num_texels ]; // Initialize the texels to black and transparent. (Alpha = 0) // memset(po->data,0,num_texels*sizeof(po->data[0])); // Thickness of the strokes making up the letter ex. // const int thickness = max(2, twid_x/10); // Write the letter ex, a big one, in the texture. // for ( int tx=0; tx<twid_x-thickness; tx++ ) { // Note: Compute tz without assuming twid_x == twid_z. int tz_raw = float(tx)/twid_x * twid_z; int tz = min(tz_raw,twid_z-1); // Array index of texel at (tx,tz). // int idx = tx + tz * twid_x; // Lower left to upper right. int idx2 = twid_x - 1 - tx + tz * twid_x; // Lower right to upper left. // Write colors to texels. // for ( int i=0; i<thickness; i++ ) { po->data[idx+i] = color_red; po->data[idx+i].a = 1; po->data[idx2-i] = color_red; po->data[idx2-i].a = 1; } } // Create a new texture object. // glGenTextures(1,&po->txid); // Make our new texture object the current texture object. // glBindTexture(GL_TEXTURE_2D,po->txid); // // Subsequent OpenGL calls operating on GL_TEXTURE_2D .. // .. will now operate on po->txid, our new texture object. // Tell OpenGL to generate MIPMAP levels for us. // glTexParameteri(GL_TEXTURE_2D, GL_GENERATE_MIPMAP, 1); // Load our texture into the texture object. // glTexImage2D (GL_TEXTURE_2D, 0, // Level of Detail (0 is base). GL_RGBA, // Internal format to be used for texture. twid_x, twid_z, 0, // Border GL_RGBA, // GL_BGRA: Format of data read by this call. GL_FLOAT, // Size of component. (void*)po->data // Pointer to the texture data. ); } /// SOLUTION -- Problem 1a int My_Piece_Of_The_World::po_get_tidx(pCoor lpos) { // Return an index for the texel array corresponding to texel coord lpos. const int idx = int(lpos.x) + twid_x * int(lpos.z); return idx; } pColor* My_Piece_Of_The_World::po_get_texel(Platform_Overlay *po, pCoor lpos) { /// SOLUTION -- Problem 1a // Use our function to get the array index corresponding to lpos. const int idx = po_get_tidx(lpos); // If it's out of range return null .. if ( idx < 0 || idx >= num_texels ) return NULL; // .. otherwise return the texel. return &po->data[ idx ]; } pCoor My_Piece_Of_The_World::po_get_lcoor(Platform_Overlay *po, pCoor pos) { pCoor lc; /// SOLUTION -- Problem 1a. // Convert object space coordinates to texel coordinates. // Variables overlay_xmin and overlay_zmin were set when the overlay // was retrieved. // lc.x = ( pos.x - overlay_xmin ) * scale_x_obj_to_texel; lc.z = ( pos.z - overlay_zmin ) * scale_z_obj_to_texel; lc.y = 0; lc.w = 0; return lc; } Platform_Overlay* My_Piece_Of_The_World::po_get(pCoor pos) { // Convert object-space coordinate, pos, into an overlay space, (x,z) .. // .. in which (0,0) is the lower-left overlay, etc. const int x = ( pos.x - w.platform_xmin ) * wid_x_inv; if ( x < 0 || x >= nx ) return NULL; const int z = ( pos.z - w.platform_zmin ) * wid_z_inv; if ( z < 0 || z >= nz ) return NULL; overlay_xmin = w.platform_xmin + x * wid_x; overlay_zmin = w.platform_zmin + z * wid_z; // Retrieve the overlay in which pos lies. // Platform_Overlay* const po = &platform_overlays[x + z * nz]; if ( !po->data ) { /// SOLUTION -- Problem 1a // This overlay has never been visited, initialize texel array. // Allocate the color array. po->data = new pColor[num_texels]; // Initialize it. Note that this makes the colors transparent. memset(po->data,0,num_texels*sizeof(po->data[0])); po->texture_object_initialized = false; // Pre-compute the object-space coordinates of the corners of // the overlay. These will be used when constructing the primitive // on which the texture will be applied. // pCoor* const vertices = po->vertices; vertices[0] = pCoor( w.platform_xmin + x * wid_x, 0.01, w.platform_zmin + z * wid_z ); vertices[1] = vertices[0] + pVect(wid_x,0,0); vertices[2] = vertices[1] + pVect(0,0,wid_z); vertices[3] = vertices[0] + pVect(0,0,wid_z); po->texture_modified = true; } return po; } void My_Piece_Of_The_World::render() { /// Homework 3 -- Lots of stuff in this routine. // [ ] Enable at least some of the following: // -- Texturing. // -- Texture application mode. // -- The Alpha Test // -- Blending. // // See demo-8-texture.cc for examples. /// SOLUTION -- Problem 1b // Turn on texturing. glEnable(GL_TEXTURE_2D); // Specify which texture unit to use. glActiveTexture(GL_TEXTURE0); // Specify how texel and the primitive's lighted color should be // combined. Use modulation, so that scuffs are affected by // lighting. glTexEnvi(GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_MODULATE); // Turn on the alpha test. This is not needed if blending is in use. if ( w.opt_tryout1 ) glEnable(GL_ALPHA_TEST); // Only write fragments corresponding to scuffed parts of the texture. glAlphaFunc(GL_GREATER,0.4); // Turn on blending so that scuffs are combined with what's already there. glEnable(GL_BLEND); // Set the blend equation to blend colors, but to write the alpha value // carried by the fragment (from our texture). glBlendFuncSeparate (GL_SRC_ALPHA,GL_ONE_MINUS_SRC_ALPHA, GL_ZERO, GL_ONE); for ( int i=0; i<num_overlays; i++ ) { Platform_Overlay* const po = &platform_overlays[i]; if ( !po->data ) continue; if ( !po->texture_object_initialized ) { po->texture_object_initialized = true; // [x] Do something here. /// SOLUTION -- Problem 1b. // This is the first time we've used this particular overlay, // so we need to create a texture object for it and set its // parameters. // glGenTextures(1,&po->txid); glBindTexture(GL_TEXTURE_2D,po->txid); glTexParameteri(GL_TEXTURE_2D, GL_GENERATE_MIPMAP, 1); glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_MIN_FILTER, GL_LINEAR_MIPMAP_LINEAR); glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_MAG_FILTER,GL_LINEAR); } glBindTexture(GL_TEXTURE_2D,po->txid); if ( po->texture_modified ) { /// SOLUTION -- Problem 1a. // We've modified the texture since the last render, so // we need to update OpenGL's copy. po->texture_modified = false; // [x] Send texel array (po->data) to OpenGL. glTexImage2D (GL_TEXTURE_2D, 0, // Level of Detail (0 is base). GL_RGBA, // Internal format to be used for texture. twid_x, twid_z, 0, // Border GL_RGBA, // GL_BGRA: Format of data read by this call. GL_FLOAT, // Size of component. (void*)po->data); pError_Check(); } /// SOLUTION -- 1a // // If tryout2 is active (press 'Y' to toggle) show the red x texture // instead of our own. // if ( w.opt_tryout2 ) glBindTexture(GL_TEXTURE_2D, sample_overlay.txid); // [x] Render primitive(s) matching shape of overlay. /// SOLUTION -- 1a // // Apply the texture to a quad. Note that we are using // our pre-computed vertices. // glBegin(GL_QUADS); glNormal3f(0,-1,0); glColor3fv(color_white); glTexCoord2f(0,0); glVertex3fv(po->vertices[0]); glTexCoord2f(1,0); glVertex3fv(po->vertices[1]); glTexCoord2f(1,1); glVertex3fv(po->vertices[2]); glTexCoord2f(0,1); glVertex3fv(po->vertices[3]); glEnd(); } // [x] Disable anything turned on at the start. glDisable(GL_ALPHA_TEST); glDisable(GL_BLEND); glDisable(GL_TEXTURE_2D); } void My_Piece_Of_The_World::clean() { /// Homework 3: [ ] Remove scuffs from dirty textures. /// SOLUTION -- Problem 1. // // Free any textures that are present. for ( int i=0; i<num_overlays; i++ ) { Platform_Overlay* const po = &platform_overlays[i]; if ( !po->data ) continue; // Tell OpenGL to free the texture object, including the // texture data that it has copied from us. // glDeleteTextures(1,&po->txid); // Free our own texel array. // free( po->data ); // Update variables to reflect clean state. // po->data = NULL; po->texture_modified = false; po->texture_object_initialized = false; } } 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"); ball_eye = NULL; opt_ride = false; init_graphics(); mp.init(); 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(); } /// /// Physical Simulation Code /// /// Initialize Simulation // void World::ball_setup_1() { // Arrange and size balls to form a pendulum. pCoor first_pos(13.4,14,-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; } // 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; 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; 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->color = color_green; 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->color = color_green; 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; 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; ) { // 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. // const float mass = max( ball->mass, ball->mass_min ); pVect delta_v = ( ball->force / mass ) * delta_t; const float dist_above = ball->position.y - ball->radius; const bool collision = platform_collision_possible(ball->position) && dist_above < 0; if ( collision ) { const float spring_constant_plat = ball->velocity.y < 0 ? 100000 : 50000; const float fric_coefficient = 0.1; const float force_up = -dist_above * spring_constant_plat; const float delta_v_up = force_up / mass * delta_t; const float fric_force_mag = fric_coefficient * force_up; pNorm surface_v(ball->velocity.x,0,ball->velocity.z); const float delta_v_surf = fric_force_mag / mass * delta_t; if ( delta_v_surf > surface_v.magnitude ) { // Ignoring other forces? delta_v = pVect(-ball->velocity.x,delta_v.y,-ball->velocity.z); } else { 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. // /// SOLUTION -- Problem 1a // // Remember previous ball position, used for scuff mark. // pCoor pos_prev = ball->position; ball->position += ball->velocity * delta_t; if ( !collision ) continue; /// Homework 3 // // [x] Retrieve the correct overlay. // [ ] Determine area of platform that ball is touching. // [ ] Convert to texel coordinate units. // [ ] Modify texels in array. // [ ] Set po->texture_modified iff any texels change. Platform_Overlay* const po = mp.po_get(ball->position); if ( !po ) continue; /// SOLUTION -- Problem 1a. // // Find the location of all of the texels scuffed // by this ball during this timestep. The length // of the scuff mark is based on the old and new positions, // the width of the scuff mark is based on the intersection // of the ball with the platform. // Current ball location in texel coordinates. // pCoor ball_lcor = mp.po_get_lcoor(po,ball->position); // Previous location of ball in texel coordinates. // pCoor prev_lcor = mp.po_get_lcoor(po,pos_prev); float width = mp.scale_x_obj_to_texel * sqrt( ball->radius * ball->radius - pos_prev.y * pos_prev.y ); // Direction along scuff mark (based on sliding motion). // pNorm skid(prev_lcor,ball_lcor); // Find direction along width of scuff mark. // pNorm nskid = cross( skid, pVect(0,1,0) ); // Iterate over texel locations scuffed by ball. // for ( float t = -width; t <= skid.magnitude+width; t++ ) for ( float u = -width; u < max(width,1.0f); u++ ) { pCoor tex_pos = prev_lcor + t * skid + u * nskid; pColor* const texel = mp.po_get_texel(po,tex_pos); // If texel is not on overlay po then just skip it. // if ( !texel ) continue; // Don't bother if already scuffed. If we wanted to be // fancy we could add this balls color onto what is already // there. But we don't want to be fancy. // if ( texel->a ) continue; po->texture_modified = true; *texel = ball->color; texel->a = 0.8; } } } 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() {mp.render();} 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); }