1 2/*- 3 * morph3d.c - Shows 3D morphing objects 4 * 5 * Converted to GLUT by brianp on 1/1/98 6 * 7 * This program was inspired on a WindowsNT(R)'s screen saver. It was written 8 * from scratch and it was not based on any other source code. 9 * 10 * Porting it to xlock (the final objective of this code since the moment I 11 * decided to create it) was possible by comparing the original Mesa's gear 12 * demo with it's ported version, so thanks for Danny Sung for his indirect 13 * help (look at gear.c in xlock source tree). NOTE: At the moment this code 14 * was sent to Brian Paul for package inclusion, the XLock Version was not 15 * available. In fact, I'll wait it to appear on the next Mesa release (If you 16 * are reading this, it means THIS release) to send it for xlock package 17 * inclusion). It will probably there be a GLUT version too. 18 * 19 * Thanks goes also to Brian Paul for making it possible and inexpensive 20 * to use OpenGL at home. 21 * 22 * Since I'm not a native english speaker, my apologies for any gramatical 23 * mistake. 24 * 25 * My e-mail addresses are 26 * 27 * vianna@cat.cbpf.br 28 * and 29 * marcelo@venus.rdc.puc-rio.br 30 * 31 * Marcelo F. Vianna (Feb-13-1997) 32 */ 33 34/* 35This document is VERY incomplete, but tries to describe the mathematics used 36in the program. At this moment it just describes how the polyhedra are 37generated. On futhurer versions, this document will be probabbly improved. 38 39Since I'm not a native english speaker, my apologies for any gramatical 40mistake. 41 42Marcelo Fernandes Vianna 43- Undergraduate in Computer Engeneering at Catholic Pontifical University 44- of Rio de Janeiro (PUC-Rio) Brasil. 45- e-mail: vianna@cat.cbpf.br or marcelo@venus.rdc.puc-rio.br 46- Feb-13-1997 47 48POLYHEDRA GENERATION 49 50For the purpose of this program it's not sufficient to know the polyhedra 51vertexes coordinates. Since the morphing algorithm applies a nonlinear 52transformation over the surfaces (faces) of the polyhedron, each face has 53to be divided into smaller ones. The morphing algorithm needs to transform 54each vertex of these smaller faces individually. It's a very time consoming 55task. 56 57In order to reduce calculation overload, and since all the macro faces of 58the polyhedron are transformed by the same way, the generation is made by 59creating only one face of the polyhedron, morphing it and then rotating it 60around the polyhedron center. 61 62What we need to know is the face radius of the polyhedron (the radius of 63the inscribed sphere) and the angle between the center of two adjacent 64faces using the center of the sphere as the angle's vertex. 65 66The face radius of the regular polyhedra are known values which I decided 67to not waste my time calculating. Following is a table of face radius for 68the regular polyhedra with edge length = 1: 69 70 TETRAHEDRON : 1/(2*sqrt(2))/sqrt(3) 71 CUBE : 1/2 72 OCTAHEDRON : 1/sqrt(6) 73 DODECAHEDRON : T^2 * sqrt((T+2)/5) / 2 -> where T=(sqrt(5)+1)/2 74 ICOSAHEDRON : (3*sqrt(3)+sqrt(15))/12 75 76I've not found any reference about the mentioned angles, so I needed to 77calculate them, not a trivial task until I figured out how :) 78Curiously these angles are the same for the tetrahedron and octahedron. 79A way to obtain this value is inscribing the tetrahedron inside the cube 80by matching their vertexes. So you'll notice that the remaining unmatched 81vertexes are in the same straight line starting in the cube/tetrahedron 82center and crossing the center of each tetrahedron's face. At this point 83it's easy to obtain the bigger angle of the isosceles triangle formed by 84the center of the cube and two opposite vertexes on the same cube face. 85The edges of this triangle have the following lenghts: sqrt(2) for the base 86and sqrt(3)/2 for the other two other edges. So the angle we want is: 87 +-----------------------------------------------------------+ 88 | 2*ARCSIN(sqrt(2)/sqrt(3)) = 109.47122063449069174 degrees | 89 +-----------------------------------------------------------+ 90For the cube this angle is obvious, but just for formality it can be 91easily obtained because we also know it's isosceles edge lenghts: 92sqrt(2)/2 for the base and 1/2 for the other two edges. So the angle we 93want is: 94 +-----------------------------------------------------------+ 95 | 2*ARCSIN((sqrt(2)/2)/1) = 90.000000000000000000 degrees | 96 +-----------------------------------------------------------+ 97For the octahedron we use the same idea used for the tetrahedron, but now 98we inscribe the cube inside the octahedron so that all cubes's vertexes 99matches excatly the center of each octahedron's face. It's now clear that 100this angle is the same of the thetrahedron one: 101 +-----------------------------------------------------------+ 102 | 2*ARCSIN(sqrt(2)/sqrt(3)) = 109.47122063449069174 degrees | 103 +-----------------------------------------------------------+ 104For the dodecahedron it's a little bit harder because it's only relationship 105with the cube is useless to us. So we need to solve the problem by another 106way. The concept of Face radius also exists on 2D polygons with the name 107Edge radius: 108 Edge Radius For Pentagon (ERp) 109 ERp = (1/2)/TAN(36 degrees) * VRp = 0.6881909602355867905 110 (VRp is the pentagon's vertex radio). 111 Face Radius For Dodecahedron 112 FRd = T^2 * sqrt((T+2)/5) / 2 = 1.1135163644116068404 113Why we need ERp? Well, ERp and FRd segments forms a 90 degrees angle, 114completing this triangle, the lesser angle is a half of the angle we are 115looking for, so this angle is: 116 +-----------------------------------------------------------+ 117 | 2*ARCTAN(ERp/FRd) = 63.434948822922009981 degrees | 118 +-----------------------------------------------------------+ 119For the icosahedron we can use the same method used for dodecahedron (well 120the method used for dodecahedron may be used for all regular polyhedra) 121 Edge Radius For Triangle (this one is well known: 1/3 of the triangle height) 122 ERt = sin(60)/3 = sqrt(3)/6 = 0.2886751345948128655 123 Face Radius For Icosahedron 124 FRi= (3*sqrt(3)+sqrt(15))/12 = 0.7557613140761707538 125So the angle is: 126 +-----------------------------------------------------------+ 127 | 2*ARCTAN(ERt/FRi) = 41.810314895778596167 degrees | 128 +-----------------------------------------------------------+ 129 130*/ 131 132 133#include <stdio.h> 134#include <stdlib.h> 135#ifndef _WIN32 136#include <unistd.h> 137#endif 138#include "glut_wrap.h" 139#include <math.h> 140 141#define Scale 0.3 142 143#define VectMul(X1,Y1,Z1,X2,Y2,Z2) (Y1)*(Z2)-(Z1)*(Y2),(Z1)*(X2)-(X1)*(Z2),(X1)*(Y2)-(Y1)*(X2) 144#define sqr(A) ((A)*(A)) 145 146/* Increasing this values produces better image quality, the price is speed. */ 147/* Very low values produces erroneous/incorrect plotting */ 148#define tetradivisions 23 149#define cubedivisions 20 150#define octadivisions 21 151#define dodecadivisions 10 152#define icodivisions 15 153 154#define tetraangle 109.47122063449069174 155#define cubeangle 90.000000000000000000 156#define octaangle 109.47122063449069174 157#define dodecaangle 63.434948822922009981 158#define icoangle 41.810314895778596167 159 160#ifndef Pi 161#define Pi 3.1415926535897932385 162#endif 163#define SQRT2 1.4142135623730951455 164#define SQRT3 1.7320508075688771932 165#define SQRT5 2.2360679774997898051 166#define SQRT6 2.4494897427831778813 167#define SQRT15 3.8729833462074170214 168#define cossec36_2 0.8506508083520399322 169#define cos72 0.3090169943749474241 170#define sin72 0.9510565162951535721 171#define cos36 0.8090169943749474241 172#define sin36 0.5877852522924731292 173 174/*************************************************************************/ 175 176static int mono=0; 177static int smooth=1; 178static int anim=1; 179static GLint WindH, WindW; 180static GLfloat step=0; 181static GLfloat seno; 182static int object; 183static int edgedivisions; 184static void (*draw_object)( void ); 185static float Magnitude; 186static float *MaterialColor[20]; 187 188static float front_shininess[] = {60.0}; 189static float front_specular[] = { 0.7, 0.7, 0.7, 1.0 }; 190static float ambient[] = { 0.0, 0.0, 0.0, 1.0 }; 191static float diffuse[] = { 1.0, 1.0, 1.0, 1.0 }; 192static float position0[] = { 1.0, 1.0, 1.0, 0.0 }; 193static float position1[] = {-1.0,-1.0, 1.0, 0.0 }; 194static float lmodel_ambient[] = { 0.5, 0.5, 0.5, 1.0 }; 195static float lmodel_twoside[] = {GL_TRUE}; 196 197static float MaterialRed[] = { 0.7, 0.0, 0.0, 1.0 }; 198static float MaterialGreen[] = { 0.1, 0.5, 0.2, 1.0 }; 199static float MaterialBlue[] = { 0.0, 0.0, 0.7, 1.0 }; 200static float MaterialCyan[] = { 0.2, 0.5, 0.7, 1.0 }; 201static float MaterialYellow[] = { 0.7, 0.7, 0.0, 1.0 }; 202static float MaterialMagenta[] = { 0.6, 0.2, 0.5, 1.0 }; 203static float MaterialWhite[] = { 0.7, 0.7, 0.7, 1.0 }; 204static float MaterialGray[] = { 0.2, 0.2, 0.2, 1.0 }; 205 206#define TRIANGLE(Edge, Amp, Divisions, Z) \ 207{ \ 208 GLfloat Xf,Yf,Xa,Yb,Xf2,Yf2; \ 209 GLfloat Factor,Factor1,Factor2; \ 210 GLfloat VertX,VertY,VertZ,NeiAX,NeiAY,NeiAZ,NeiBX,NeiBY,NeiBZ; \ 211 GLfloat Ax,Ay,Bx; \ 212 int Ri,Ti; \ 213 GLfloat Vr=(Edge)*SQRT3/3; \ 214 GLfloat AmpVr2=(Amp)/sqr(Vr); \ 215 GLfloat Zf=(Edge)*(Z); \ 216 \ 217 Ax=(Edge)*(+0.5/(Divisions)), Ay=(Edge)*(-SQRT3/(2*Divisions)); \ 218 Bx=(Edge)*(-0.5/(Divisions)); \ 219 \ 220 for (Ri=1; Ri<=(Divisions); Ri++) { \ 221 glBegin(GL_TRIANGLE_STRIP); \ 222 for (Ti=0; Ti<Ri; Ti++) { \ 223 Xf=(float)(Ri-Ti)*Ax + (float)Ti*Bx; \ 224 Yf=Vr+(float)(Ri-Ti)*Ay + (float)Ti*Ay; \ 225 Xa=Xf+0.001; Yb=Yf+0.001; \ 226 Factor=1-(((Xf2=sqr(Xf))+(Yf2=sqr(Yf)))*AmpVr2); \ 227 Factor1=1-((sqr(Xa)+Yf2)*AmpVr2); \ 228 Factor2=1-((Xf2+sqr(Yb))*AmpVr2); \ 229 VertX=Factor*Xf; VertY=Factor*Yf; VertZ=Factor*Zf; \ 230 NeiAX=Factor1*Xa-VertX; NeiAY=Factor1*Yf-VertY; NeiAZ=Factor1*Zf-VertZ; \ 231 NeiBX=Factor2*Xf-VertX; NeiBY=Factor2*Yb-VertY; NeiBZ=Factor2*Zf-VertZ; \ 232 glNormal3f(VectMul(NeiAX, NeiAY, NeiAZ, NeiBX, NeiBY, NeiBZ)); \ 233 glVertex3f(VertX, VertY, VertZ); \ 234 \ 235 Xf=(float)(Ri-Ti-1)*Ax + (float)Ti*Bx; \ 236 Yf=Vr+(float)(Ri-Ti-1)*Ay + (float)Ti*Ay; \ 237 Xa=Xf+0.001; Yb=Yf+0.001; \ 238 Factor=1-(((Xf2=sqr(Xf))+(Yf2=sqr(Yf)))*AmpVr2); \ 239 Factor1=1-((sqr(Xa)+Yf2)*AmpVr2); \ 240 Factor2=1-((Xf2+sqr(Yb))*AmpVr2); \ 241 VertX=Factor*Xf; VertY=Factor*Yf; VertZ=Factor*Zf; \ 242 NeiAX=Factor1*Xa-VertX; NeiAY=Factor1*Yf-VertY; NeiAZ=Factor1*Zf-VertZ; \ 243 NeiBX=Factor2*Xf-VertX; NeiBY=Factor2*Yb-VertY; NeiBZ=Factor2*Zf-VertZ; \ 244 glNormal3f(VectMul(NeiAX, NeiAY, NeiAZ, NeiBX, NeiBY, NeiBZ)); \ 245 glVertex3f(VertX, VertY, VertZ); \ 246 \ 247 } \ 248 Xf=(float)Ri*Bx; \ 249 Yf=Vr+(float)Ri*Ay; \ 250 Xa=Xf+0.001; Yb=Yf+0.001; \ 251 Factor=1-(((Xf2=sqr(Xf))+(Yf2=sqr(Yf)))*AmpVr2); \ 252 Factor1=1-((sqr(Xa)+Yf2)*AmpVr2); \ 253 Factor2=1-((Xf2+sqr(Yb))*AmpVr2); \ 254 VertX=Factor*Xf; VertY=Factor*Yf; VertZ=Factor*Zf; \ 255 NeiAX=Factor1*Xa-VertX; NeiAY=Factor1*Yf-VertY; NeiAZ=Factor1*Zf-VertZ; \ 256 NeiBX=Factor2*Xf-VertX; NeiBY=Factor2*Yb-VertY; NeiBZ=Factor2*Zf-VertZ; \ 257 glNormal3f(VectMul(NeiAX, NeiAY, NeiAZ, NeiBX, NeiBY, NeiBZ)); \ 258 glVertex3f(VertX, VertY, VertZ); \ 259 glEnd(); \ 260 } \ 261} 262 263#define SQUARE(Edge, Amp, Divisions, Z) \ 264{ \ 265 int Xi,Yi; \ 266 GLfloat Xf,Yf,Y,Xf2,Yf2,Y2,Xa,Yb; \ 267 GLfloat Factor,Factor1,Factor2; \ 268 GLfloat VertX,VertY,VertZ,NeiAX,NeiAY,NeiAZ,NeiBX,NeiBY,NeiBZ; \ 269 GLfloat Zf=(Edge)*(Z); \ 270 GLfloat AmpVr2=(Amp)/sqr((Edge)*SQRT2/2); \ 271 \ 272 for (Yi=0; Yi<(Divisions); Yi++) { \ 273 Yf=-((Edge)/2.0) + ((float)Yi)/(Divisions)*(Edge); \ 274 Yf2=sqr(Yf); \ 275 Y=Yf+1.0/(Divisions)*(Edge); \ 276 Y2=sqr(Y); \ 277 glBegin(GL_QUAD_STRIP); \ 278 for (Xi=0; Xi<=(Divisions); Xi++) { \ 279 Xf=-((Edge)/2.0) + ((float)Xi)/(Divisions)*(Edge); \ 280 Xf2=sqr(Xf); \ 281 \ 282 Xa=Xf+0.001; Yb=Y+0.001; \ 283 Factor=1-((Xf2+Y2)*AmpVr2); \ 284 Factor1=1-((sqr(Xa)+Y2)*AmpVr2); \ 285 Factor2=1-((Xf2+sqr(Yb))*AmpVr2); \ 286 VertX=Factor*Xf; VertY=Factor*Y; VertZ=Factor*Zf; \ 287 NeiAX=Factor1*Xa-VertX; NeiAY=Factor1*Y-VertY; NeiAZ=Factor1*Zf-VertZ; \ 288 NeiBX=Factor2*Xf-VertX; NeiBY=Factor2*Yb-VertY; NeiBZ=Factor2*Zf-VertZ; \ 289 glNormal3f(VectMul(NeiAX, NeiAY, NeiAZ, NeiBX, NeiBY, NeiBZ)); \ 290 glVertex3f(VertX, VertY, VertZ); \ 291 \ 292 Xa=Xf+0.001; Yb=Yf+0.001; \ 293 Factor=1-((Xf2+Yf2)*AmpVr2); \ 294 Factor1=1-((sqr(Xa)+Yf2)*AmpVr2); \ 295 Factor2=1-((Xf2+sqr(Yb))*AmpVr2); \ 296 VertX=Factor*Xf; VertY=Factor*Yf; VertZ=Factor*Zf; \ 297 NeiAX=Factor1*Xa-VertX; NeiAY=Factor1*Yf-VertY; NeiAZ=Factor1*Zf-VertZ; \ 298 NeiBX=Factor2*Xf-VertX; NeiBY=Factor2*Yb-VertY; NeiBZ=Factor2*Zf-VertZ; \ 299 glNormal3f(VectMul(NeiAX, NeiAY, NeiAZ, NeiBX, NeiBY, NeiBZ)); \ 300 glVertex3f(VertX, VertY, VertZ); \ 301 } \ 302 glEnd(); \ 303 } \ 304} 305 306#define PENTAGON(Edge, Amp, Divisions, Z) \ 307{ \ 308 int Ri,Ti,Fi; \ 309 GLfloat Xf,Yf,Xa,Yb,Xf2,Yf2; \ 310 GLfloat x[6],y[6]; \ 311 GLfloat Factor,Factor1,Factor2; \ 312 GLfloat VertX,VertY,VertZ,NeiAX,NeiAY,NeiAZ,NeiBX,NeiBY,NeiBZ; \ 313 GLfloat Zf=(Edge)*(Z); \ 314 GLfloat AmpVr2=(Amp)/sqr((Edge)*cossec36_2); \ 315 \ 316 for(Fi=0;Fi<6;Fi++) { \ 317 x[Fi]=-cos( Fi*2*Pi/5 + Pi/10 )/(Divisions)*cossec36_2*(Edge); \ 318 y[Fi]=sin( Fi*2*Pi/5 + Pi/10 )/(Divisions)*cossec36_2*(Edge); \ 319 } \ 320 \ 321 for (Ri=1; Ri<=(Divisions); Ri++) { \ 322 for (Fi=0; Fi<5; Fi++) { \ 323 glBegin(GL_TRIANGLE_STRIP); \ 324 for (Ti=0; Ti<Ri; Ti++) { \ 325 Xf=(float)(Ri-Ti)*x[Fi] + (float)Ti*x[Fi+1]; \ 326 Yf=(float)(Ri-Ti)*y[Fi] + (float)Ti*y[Fi+1]; \ 327 Xa=Xf+0.001; Yb=Yf+0.001; \ 328 Factor=1-(((Xf2=sqr(Xf))+(Yf2=sqr(Yf)))*AmpVr2); \ 329 Factor1=1-((sqr(Xa)+Yf2)*AmpVr2); \ 330 Factor2=1-((Xf2+sqr(Yb))*AmpVr2); \ 331 VertX=Factor*Xf; VertY=Factor*Yf; VertZ=Factor*Zf; \ 332 NeiAX=Factor1*Xa-VertX; NeiAY=Factor1*Yf-VertY; NeiAZ=Factor1*Zf-VertZ; \ 333 NeiBX=Factor2*Xf-VertX; NeiBY=Factor2*Yb-VertY; NeiBZ=Factor2*Zf-VertZ; \ 334 glNormal3f(VectMul(NeiAX, NeiAY, NeiAZ, NeiBX, NeiBY, NeiBZ)); \ 335 glVertex3f(VertX, VertY, VertZ); \ 336 \ 337 Xf=(float)(Ri-Ti-1)*x[Fi] + (float)Ti*x[Fi+1]; \ 338 Yf=(float)(Ri-Ti-1)*y[Fi] + (float)Ti*y[Fi+1]; \ 339 Xa=Xf+0.001; Yb=Yf+0.001; \ 340 Factor=1-(((Xf2=sqr(Xf))+(Yf2=sqr(Yf)))*AmpVr2); \ 341 Factor1=1-((sqr(Xa)+Yf2)*AmpVr2); \ 342 Factor2=1-((Xf2+sqr(Yb))*AmpVr2); \ 343 VertX=Factor*Xf; VertY=Factor*Yf; VertZ=Factor*Zf; \ 344 NeiAX=Factor1*Xa-VertX; NeiAY=Factor1*Yf-VertY; NeiAZ=Factor1*Zf-VertZ; \ 345 NeiBX=Factor2*Xf-VertX; NeiBY=Factor2*Yb-VertY; NeiBZ=Factor2*Zf-VertZ; \ 346 glNormal3f(VectMul(NeiAX, NeiAY, NeiAZ, NeiBX, NeiBY, NeiBZ)); \ 347 glVertex3f(VertX, VertY, VertZ); \ 348 \ 349 } \ 350 Xf=(float)Ri*x[Fi+1]; \ 351 Yf=(float)Ri*y[Fi+1]; \ 352 Xa=Xf+0.001; Yb=Yf+0.001; \ 353 Factor=1-(((Xf2=sqr(Xf))+(Yf2=sqr(Yf)))*AmpVr2); \ 354 Factor1=1-((sqr(Xa)+Yf2)*AmpVr2); \ 355 Factor2=1-((Xf2+sqr(Yb))*AmpVr2); \ 356 VertX=Factor*Xf; VertY=Factor*Yf; VertZ=Factor*Zf; \ 357 NeiAX=Factor1*Xa-VertX; NeiAY=Factor1*Yf-VertY; NeiAZ=Factor1*Zf-VertZ; \ 358 NeiBX=Factor2*Xf-VertX; NeiBY=Factor2*Yb-VertY; NeiBZ=Factor2*Zf-VertZ; \ 359 glNormal3f(VectMul(NeiAX, NeiAY, NeiAZ, NeiBX, NeiBY, NeiBZ)); \ 360 glVertex3f(VertX, VertY, VertZ); \ 361 glEnd(); \ 362 } \ 363 } \ 364} 365 366static void draw_tetra( void ) 367{ 368 GLuint list; 369 370 list = glGenLists( 1 ); 371 glNewList( list, GL_COMPILE ); 372 TRIANGLE(2,seno,edgedivisions,0.5/SQRT6); 373 glEndList(); 374 375 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[0]); 376 glCallList(list); 377 glPushMatrix(); 378 glRotatef(180,0,0,1); 379 glRotatef(-tetraangle,1,0,0); 380 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[1]); 381 glCallList(list); 382 glPopMatrix(); 383 glPushMatrix(); 384 glRotatef(180,0,1,0); 385 glRotatef(-180+tetraangle,0.5,SQRT3/2,0); 386 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[2]); 387 glCallList(list); 388 glPopMatrix(); 389 glRotatef(180,0,1,0); 390 glRotatef(-180+tetraangle,0.5,-SQRT3/2,0); 391 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[3]); 392 glCallList(list); 393 394 glDeleteLists(list,1); 395} 396 397static void draw_cube( void ) 398{ 399 GLuint list; 400 401 list = glGenLists( 1 ); 402 glNewList( list, GL_COMPILE ); 403 SQUARE(2, seno, edgedivisions, 0.5) 404 glEndList(); 405 406 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[0]); 407 glCallList(list); 408 glRotatef(cubeangle,1,0,0); 409 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[1]); 410 glCallList(list); 411 glRotatef(cubeangle,1,0,0); 412 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[2]); 413 glCallList(list); 414 glRotatef(cubeangle,1,0,0); 415 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[3]); 416 glCallList(list); 417 glRotatef(cubeangle,0,1,0); 418 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[4]); 419 glCallList(list); 420 glRotatef(2*cubeangle,0,1,0); 421 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[5]); 422 glCallList(list); 423 424 glDeleteLists(list,1); 425} 426 427static void draw_octa( void ) 428{ 429 GLuint list; 430 431 list = glGenLists( 1 ); 432 glNewList( list, GL_COMPILE ); 433 TRIANGLE(2,seno,edgedivisions,1/SQRT6); 434 glEndList(); 435 436 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[0]); 437 glCallList(list); 438 glPushMatrix(); 439 glRotatef(180,0,0,1); 440 glRotatef(-180+octaangle,1,0,0); 441 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[1]); 442 glCallList(list); 443 glPopMatrix(); 444 glPushMatrix(); 445 glRotatef(180,0,1,0); 446 glRotatef(-octaangle,0.5,SQRT3/2,0); 447 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[2]); 448 glCallList(list); 449 glPopMatrix(); 450 glPushMatrix(); 451 glRotatef(180,0,1,0); 452 glRotatef(-octaangle,0.5,-SQRT3/2,0); 453 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[3]); 454 glCallList(list); 455 glPopMatrix(); 456 glRotatef(180,1,0,0); 457 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[4]); 458 glCallList(list); 459 glPushMatrix(); 460 glRotatef(180,0,0,1); 461 glRotatef(-180+octaangle,1,0,0); 462 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[5]); 463 glCallList(list); 464 glPopMatrix(); 465 glPushMatrix(); 466 glRotatef(180,0,1,0); 467 glRotatef(-octaangle,0.5,SQRT3/2,0); 468 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[6]); 469 glCallList(list); 470 glPopMatrix(); 471 glRotatef(180,0,1,0); 472 glRotatef(-octaangle,0.5,-SQRT3/2,0); 473 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[7]); 474 glCallList(list); 475 476 glDeleteLists(list,1); 477} 478 479static void draw_dodeca( void ) 480{ 481 GLuint list; 482 483#define TAU ((SQRT5+1)/2) 484 485 list = glGenLists( 1 ); 486 glNewList( list, GL_COMPILE ); 487 PENTAGON(1,seno,edgedivisions,sqr(TAU) * sqrt((TAU+2)/5) / 2); 488 glEndList(); 489 490 glPushMatrix(); 491 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[0]); 492 glCallList(list); 493 glRotatef(180,0,0,1); 494 glPushMatrix(); 495 glRotatef(-dodecaangle,1,0,0); 496 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[1]); 497 glCallList(list); 498 glPopMatrix(); 499 glPushMatrix(); 500 glRotatef(-dodecaangle,cos72,sin72,0); 501 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[2]); 502 glCallList(list); 503 glPopMatrix(); 504 glPushMatrix(); 505 glRotatef(-dodecaangle,cos72,-sin72,0); 506 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[3]); 507 glCallList(list); 508 glPopMatrix(); 509 glPushMatrix(); 510 glRotatef(dodecaangle,cos36,-sin36,0); 511 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[4]); 512 glCallList(list); 513 glPopMatrix(); 514 glRotatef(dodecaangle,cos36,sin36,0); 515 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[5]); 516 glCallList(list); 517 glPopMatrix(); 518 glRotatef(180,1,0,0); 519 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[6]); 520 glCallList(list); 521 glRotatef(180,0,0,1); 522 glPushMatrix(); 523 glRotatef(-dodecaangle,1,0,0); 524 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[7]); 525 glCallList(list); 526 glPopMatrix(); 527 glPushMatrix(); 528 glRotatef(-dodecaangle,cos72,sin72,0); 529 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[8]); 530 glCallList(list); 531 glPopMatrix(); 532 glPushMatrix(); 533 glRotatef(-dodecaangle,cos72,-sin72,0); 534 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[9]); 535 glCallList(list); 536 glPopMatrix(); 537 glPushMatrix(); 538 glRotatef(dodecaangle,cos36,-sin36,0); 539 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[10]); 540 glCallList(list); 541 glPopMatrix(); 542 glRotatef(dodecaangle,cos36,sin36,0); 543 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[11]); 544 glCallList(list); 545 546 glDeleteLists(list,1); 547} 548 549static void draw_ico( void ) 550{ 551 GLuint list; 552 553 list = glGenLists( 1 ); 554 glNewList( list, GL_COMPILE ); 555 TRIANGLE(1.5,seno,edgedivisions,(3*SQRT3+SQRT15)/12); 556 glEndList(); 557 558 glPushMatrix(); 559 560 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[0]); 561 glCallList(list); 562 glPushMatrix(); 563 glRotatef(180,0,0,1); 564 glRotatef(-icoangle,1,0,0); 565 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[1]); 566 glCallList(list); 567 glPushMatrix(); 568 glRotatef(180,0,1,0); 569 glRotatef(-180+icoangle,0.5,SQRT3/2,0); 570 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[2]); 571 glCallList(list); 572 glPopMatrix(); 573 glRotatef(180,0,1,0); 574 glRotatef(-180+icoangle,0.5,-SQRT3/2,0); 575 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[3]); 576 glCallList(list); 577 glPopMatrix(); 578 glPushMatrix(); 579 glRotatef(180,0,1,0); 580 glRotatef(-180+icoangle,0.5,SQRT3/2,0); 581 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[4]); 582 glCallList(list); 583 glPushMatrix(); 584 glRotatef(180,0,1,0); 585 glRotatef(-180+icoangle,0.5,SQRT3/2,0); 586 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[5]); 587 glCallList(list); 588 glPopMatrix(); 589 glRotatef(180,0,0,1); 590 glRotatef(-icoangle,1,0,0); 591 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[6]); 592 glCallList(list); 593 glPopMatrix(); 594 glRotatef(180,0,1,0); 595 glRotatef(-180+icoangle,0.5,-SQRT3/2,0); 596 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[7]); 597 glCallList(list); 598 glPushMatrix(); 599 glRotatef(180,0,1,0); 600 glRotatef(-180+icoangle,0.5,-SQRT3/2,0); 601 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[8]); 602 glCallList(list); 603 glPopMatrix(); 604 glRotatef(180,0,0,1); 605 glRotatef(-icoangle,1,0,0); 606 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[9]); 607 glCallList(list); 608 glPopMatrix(); 609 glRotatef(180,1,0,0); 610 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[10]); 611 glCallList(list); 612 glPushMatrix(); 613 glRotatef(180,0,0,1); 614 glRotatef(-icoangle,1,0,0); 615 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[11]); 616 glCallList(list); 617 glPushMatrix(); 618 glRotatef(180,0,1,0); 619 glRotatef(-180+icoangle,0.5,SQRT3/2,0); 620 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[12]); 621 glCallList(list); 622 glPopMatrix(); 623 glRotatef(180,0,1,0); 624 glRotatef(-180+icoangle,0.5,-SQRT3/2,0); 625 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[13]); 626 glCallList(list); 627 glPopMatrix(); 628 glPushMatrix(); 629 glRotatef(180,0,1,0); 630 glRotatef(-180+icoangle,0.5,SQRT3/2,0); 631 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[14]); 632 glCallList(list); 633 glPushMatrix(); 634 glRotatef(180,0,1,0); 635 glRotatef(-180+icoangle,0.5,SQRT3/2,0); 636 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[15]); 637 glCallList(list); 638 glPopMatrix(); 639 glRotatef(180,0,0,1); 640 glRotatef(-icoangle,1,0,0); 641 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[16]); 642 glCallList(list); 643 glPopMatrix(); 644 glRotatef(180,0,1,0); 645 glRotatef(-180+icoangle,0.5,-SQRT3/2,0); 646 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[17]); 647 glCallList(list); 648 glPushMatrix(); 649 glRotatef(180,0,1,0); 650 glRotatef(-180+icoangle,0.5,-SQRT3/2,0); 651 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[18]); 652 glCallList(list); 653 glPopMatrix(); 654 glRotatef(180,0,0,1); 655 glRotatef(-icoangle,1,0,0); 656 glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[19]); 657 glCallList(list); 658 659 glDeleteLists(list,1); 660} 661 662static void draw ( void ) { 663 glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT ); 664 665 glPushMatrix(); 666 667 glTranslatef( 0.0, 0.0, -10.0 ); 668 glScalef( Scale*WindH/WindW, Scale, Scale ); 669 glTranslatef(2.5*WindW/WindH*sin(step*1.11),2.5*cos(step*1.25*1.11),0); 670 glRotatef(step*100,1,0,0); 671 glRotatef(step*95,0,1,0); 672 glRotatef(step*90,0,0,1); 673 674 seno=(sin(step)+1.0/3.0)*(4.0/5.0)*Magnitude; 675 676 draw_object(); 677 678 glPopMatrix(); 679 680 glFlush(); 681 682 glutSwapBuffers(); 683 684} 685 686static void idle_( void ) 687{ 688 static double t0 = -1.; 689 double dt, t = glutGet(GLUT_ELAPSED_TIME) / 1000.0; 690 if (t0 < 0.0) 691 t0 = t; 692 dt = t - t0; 693 t0 = t; 694 695 step += dt; 696 697 glutPostRedisplay(); 698} 699 700static void reshape( int width, int height ) 701{ 702 glViewport(0, 0, WindW=(GLint)width, WindH=(GLint)height); 703 glMatrixMode(GL_PROJECTION); 704 glLoadIdentity(); 705 glFrustum( -1.0, 1.0, -1.0, 1.0, 5.0, 15.0 ); 706 glMatrixMode(GL_MODELVIEW); 707} 708 709static void pinit(void); 710 711static void key( unsigned char k, int x, int y ) 712{ 713 (void) x; 714 (void) y; 715 switch (k) { 716 case '1': object=1; break; 717 case '2': object=2; break; 718 case '3': object=3; break; 719 case '4': object=4; break; 720 case '5': object=5; break; 721 case ' ': mono^=1; break; 722 case 's': smooth^=1; break; 723 case 'a': 724 anim^=1; 725 if (anim) 726 glutIdleFunc( idle_ ); 727 else 728 glutIdleFunc(NULL); 729 break; 730 case 27: 731 exit(0); 732 } 733 pinit(); 734 glutPostRedisplay(); 735} 736 737static void pinit(void) 738{ 739 switch(object) { 740 case 1: 741 draw_object=draw_tetra; 742 MaterialColor[0]=MaterialRed; 743 MaterialColor[1]=MaterialGreen; 744 MaterialColor[2]=MaterialBlue; 745 MaterialColor[3]=MaterialWhite; 746 edgedivisions=tetradivisions; 747 Magnitude=2.5; 748 break; 749 case 2: 750 draw_object=draw_cube; 751 MaterialColor[0]=MaterialRed; 752 MaterialColor[1]=MaterialGreen; 753 MaterialColor[2]=MaterialCyan; 754 MaterialColor[3]=MaterialMagenta; 755 MaterialColor[4]=MaterialYellow; 756 MaterialColor[5]=MaterialBlue; 757 edgedivisions=cubedivisions; 758 Magnitude=2.0; 759 break; 760 case 3: 761 draw_object=draw_octa; 762 MaterialColor[0]=MaterialRed; 763 MaterialColor[1]=MaterialGreen; 764 MaterialColor[2]=MaterialBlue; 765 MaterialColor[3]=MaterialWhite; 766 MaterialColor[4]=MaterialCyan; 767 MaterialColor[5]=MaterialMagenta; 768 MaterialColor[6]=MaterialGray; 769 MaterialColor[7]=MaterialYellow; 770 edgedivisions=octadivisions; 771 Magnitude=2.5; 772 break; 773 case 4: 774 draw_object=draw_dodeca; 775 MaterialColor[ 0]=MaterialRed; 776 MaterialColor[ 1]=MaterialGreen; 777 MaterialColor[ 2]=MaterialCyan; 778 MaterialColor[ 3]=MaterialBlue; 779 MaterialColor[ 4]=MaterialMagenta; 780 MaterialColor[ 5]=MaterialYellow; 781 MaterialColor[ 6]=MaterialGreen; 782 MaterialColor[ 7]=MaterialCyan; 783 MaterialColor[ 8]=MaterialRed; 784 MaterialColor[ 9]=MaterialMagenta; 785 MaterialColor[10]=MaterialBlue; 786 MaterialColor[11]=MaterialYellow; 787 edgedivisions=dodecadivisions; 788 Magnitude=2.0; 789 break; 790 case 5: 791 draw_object=draw_ico; 792 MaterialColor[ 0]=MaterialRed; 793 MaterialColor[ 1]=MaterialGreen; 794 MaterialColor[ 2]=MaterialBlue; 795 MaterialColor[ 3]=MaterialCyan; 796 MaterialColor[ 4]=MaterialYellow; 797 MaterialColor[ 5]=MaterialMagenta; 798 MaterialColor[ 6]=MaterialRed; 799 MaterialColor[ 7]=MaterialGreen; 800 MaterialColor[ 8]=MaterialBlue; 801 MaterialColor[ 9]=MaterialWhite; 802 MaterialColor[10]=MaterialCyan; 803 MaterialColor[11]=MaterialYellow; 804 MaterialColor[12]=MaterialMagenta; 805 MaterialColor[13]=MaterialRed; 806 MaterialColor[14]=MaterialGreen; 807 MaterialColor[15]=MaterialBlue; 808 MaterialColor[16]=MaterialCyan; 809 MaterialColor[17]=MaterialYellow; 810 MaterialColor[18]=MaterialMagenta; 811 MaterialColor[19]=MaterialGray; 812 edgedivisions=icodivisions; 813 Magnitude=2.5; 814 break; 815 } 816 if (mono) { 817 int loop; 818 for (loop=0; loop<20; loop++) MaterialColor[loop]=MaterialGray; 819 } 820 if (smooth) { 821 glShadeModel( GL_SMOOTH ); 822 } else { 823 glShadeModel( GL_FLAT ); 824 } 825 826} 827 828int main(int argc, char **argv) 829{ 830 printf("Morph 3D - Shows morphing platonic polyhedra\n"); 831 printf("Author: Marcelo Fernandes Vianna (vianna@cat.cbpf.br)\n\n"); 832 printf(" [1] - Tetrahedron\n"); 833 printf(" [2] - Hexahedron (Cube)\n"); 834 printf(" [3] - Octahedron\n"); 835 printf(" [4] - Dodecahedron\n"); 836 printf(" [5] - Icosahedron\n"); 837 printf("[SPACE] - Toggle colored faces\n"); 838 printf("[RETURN] - Toggle smooth/flat shading\n"); 839 printf(" [ESC] - Quit\n"); 840 841 object=1; 842 843 glutInitWindowSize(640,480); 844 glutInit(&argc, argv); 845 846 glutInitDisplayMode( GLUT_DEPTH | GLUT_DOUBLE | GLUT_RGB ); 847 848 if (glutCreateWindow("Morph 3D - Shows morphing platonic polyhedra") <= 0) { 849 exit(0); 850 } 851 852 glClearDepth(1.0); 853 glClearColor( 0.0, 0.0, 0.0, 1.0 ); 854 glColor3f( 1.0, 1.0, 1.0 ); 855 856 glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT ); 857 glFlush(); 858 glutSwapBuffers(); 859 860 glLightfv(GL_LIGHT0, GL_AMBIENT, ambient); 861 glLightfv(GL_LIGHT0, GL_DIFFUSE, diffuse); 862 glLightfv(GL_LIGHT0, GL_POSITION, position0); 863 glLightfv(GL_LIGHT1, GL_AMBIENT, ambient); 864 glLightfv(GL_LIGHT1, GL_DIFFUSE, diffuse); 865 glLightfv(GL_LIGHT1, GL_POSITION, position1); 866 glLightModelfv(GL_LIGHT_MODEL_AMBIENT, lmodel_ambient); 867 glLightModelfv(GL_LIGHT_MODEL_TWO_SIDE, lmodel_twoside); 868 glEnable(GL_LIGHTING); 869 glEnable(GL_LIGHT0); 870 glEnable(GL_LIGHT1); 871 glEnable(GL_DEPTH_TEST); 872 glEnable(GL_NORMALIZE); 873 874 glMaterialfv(GL_FRONT_AND_BACK, GL_SHININESS, front_shininess); 875 glMaterialfv(GL_FRONT_AND_BACK, GL_SPECULAR, front_specular); 876 877 glHint(GL_FOG_HINT, GL_FASTEST); 878 glHint(GL_PERSPECTIVE_CORRECTION_HINT, GL_FASTEST); 879 glHint(GL_POLYGON_SMOOTH_HINT, GL_FASTEST); 880 881 pinit(); 882 883 glutReshapeFunc( reshape ); 884 glutKeyboardFunc( key ); 885 glutIdleFunc( idle_ ); 886 glutDisplayFunc( draw ); 887 glutMainLoop(); 888 889 return 0; 890} 891