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+/* $Id: morph3d.c,v 1.1 1999/08/19 00:55:40 jtg Exp $ */
+
+/*
+ * $Log: morph3d.c,v $
+ * Revision 1.1  1999/08/19 00:55:40  jtg
+ * Initial revision
+ *
+ * Revision 3.1  1998/06/29 02:37:30  brianp
+ * minor changes for Windows (Ted Jump)
+ *
+ * Revision 3.0  1998/02/14 18:42:29  brianp
+ * initial rev
+ *
+ */
+
+
+/*-
+ * morph3d.c - Shows 3D morphing objects
+ *
+ * Converted to GLUT by brianp on 1/1/98
+ *
+ * This program was inspired on a WindowsNT(R)'s screen saver. It was written 
+ * from scratch and it was not based on any other source code. 
+ * 
+ * Porting it to xlock (the final objective of this code since the moment I
+ * decided to create it) was possible by comparing the original Mesa's gear
+ * demo with it's ported version, so thanks for Danny Sung for his indirect
+ * help (look at gear.c in xlock source tree). NOTE: At the moment this code
+ * was sent to Brian Paul for package inclusion, the XLock Version was not
+ * available. In fact, I'll wait it to appear on the next Mesa release (If you
+ * are reading this, it means THIS release) to send it for xlock package 
+ * inclusion). It will probably there be a GLUT version too.
+ *
+ * Thanks goes also to Brian Paul for making it possible and inexpensive
+ * to use OpenGL at home.
+ *
+ * Since I'm not a native english speaker, my apologies for any gramatical
+ * mistake.
+ *
+ * My e-mail addresses are
+ *
+ * vianna@cat.cbpf.br 
+ *         and
+ * marcelo@venus.rdc.puc-rio.br
+ *
+ * Marcelo F. Vianna (Feb-13-1997)
+ */
+
+/*
+This document is VERY incomplete, but tries to describe the mathematics used
+in the program. At this moment it just describes how the polyhedra are 
+generated. On futhurer versions, this document will be probabbly improved.
+
+Since I'm not a native english speaker, my apologies for any gramatical
+mistake.
+
+Marcelo Fernandes Vianna 
+- Undergraduate in Computer Engeneering at Catholic Pontifical University
+- of Rio de Janeiro (PUC-Rio) Brasil.
+- e-mail: vianna@cat.cbpf.br or marcelo@venus.rdc.puc-rio.br
+- Feb-13-1997
+
+POLYHEDRA GENERATION
+
+For the purpose of this program it's not sufficient to know the polyhedra
+vertexes coordinates. Since the morphing algorithm applies a nonlinear 
+transformation over the surfaces (faces) of the polyhedron, each face has
+to be divided into smaller ones. The morphing algorithm needs to transform 
+each vertex of these smaller faces individually. It's a very time consoming
+task.
+
+In order to reduce calculation overload, and since all the macro faces of
+the polyhedron are transformed by the same way, the generation is made by 
+creating only one face of the polyhedron, morphing it and then rotating it
+around the polyhedron center. 
+
+What we need to know is the face radius of the polyhedron (the radius of 
+the inscribed sphere) and the angle between the center of two adjacent 
+faces using the center of the sphere as the angle's vertex.
+
+The face radius of the regular polyhedra are known values which I decided
+to not waste my time calculating. Following is a table of face radius for
+the regular polyhedra with edge length = 1:
+
+    TETRAHEDRON  : 1/(2*sqrt(2))/sqrt(3)
+    CUBE	 : 1/2
+    OCTAHEDRON   : 1/sqrt(6)
+    DODECAHEDRON : T^2 * sqrt((T+2)/5) / 2     -> where T=(sqrt(5)+1)/2
+    ICOSAHEDRON  : (3*sqrt(3)+sqrt(15))/12
+
+I've not found any reference about the mentioned angles, so I needed to
+calculate them, not a trivial task until I figured out how :)
+Curiously these angles are the same for the tetrahedron and octahedron.
+A way to obtain this value is inscribing the tetrahedron inside the cube
+by matching their vertexes. So you'll notice that the remaining unmatched
+vertexes are in the same straight line starting in the cube/tetrahedron
+center and crossing the center of each tetrahedron's face. At this point
+it's easy to obtain the bigger angle of the isosceles triangle formed by
+the center of the cube and two opposite vertexes on the same cube face.
+The edges of this triangle have the following lenghts: sqrt(2) for the base
+and sqrt(3)/2 for the other two other edges. So the angle we want is:
+     +-----------------------------------------------------------+
+     | 2*ARCSIN(sqrt(2)/sqrt(3)) = 109.47122063449069174 degrees |
+     +-----------------------------------------------------------+
+For the cube this angle is obvious, but just for formality it can be
+easily obtained because we also know it's isosceles edge lenghts:
+sqrt(2)/2 for the base and 1/2 for the other two edges. So the angle we 
+want is:
+     +-----------------------------------------------------------+
+     | 2*ARCSIN((sqrt(2)/2)/1)   = 90.000000000000000000 degrees |
+     +-----------------------------------------------------------+
+For the octahedron we use the same idea used for the tetrahedron, but now
+we inscribe the cube inside the octahedron so that all cubes's vertexes
+matches excatly the center of each octahedron's face. It's now clear that
+this angle is the same of the thetrahedron one:
+     +-----------------------------------------------------------+
+     | 2*ARCSIN(sqrt(2)/sqrt(3)) = 109.47122063449069174 degrees |
+     +-----------------------------------------------------------+
+For the dodecahedron it's a little bit harder because it's only relationship
+with the cube is useless to us. So we need to solve the problem by another
+way. The concept of Face radius also exists on 2D polygons with the name
+Edge radius:
+  Edge Radius For Pentagon (ERp)
+  ERp = (1/2)/TAN(36 degrees) * VRp = 0.6881909602355867905
+  (VRp is the pentagon's vertex radio).
+  Face Radius For Dodecahedron
+  FRd = T^2 * sqrt((T+2)/5) / 2 = 1.1135163644116068404
+Why we need ERp? Well, ERp and FRd segments forms a 90 degrees angle, 
+completing this triangle, the lesser angle is a half of the angle we are 
+looking for, so this angle is:
+     +-----------------------------------------------------------+
+     | 2*ARCTAN(ERp/FRd)	 = 63.434948822922009981 degrees |
+     +-----------------------------------------------------------+
+For the icosahedron we can use the same method used for dodecahedron (well
+the method used for dodecahedron may be used for all regular polyhedra)
+  Edge Radius For Triangle (this one is well known: 1/3 of the triangle height)
+  ERt = sin(60)/3 = sqrt(3)/6 = 0.2886751345948128655
+  Face Radius For Icosahedron
+  FRi= (3*sqrt(3)+sqrt(15))/12 = 0.7557613140761707538
+So the angle is:
+     +-----------------------------------------------------------+
+     | 2*ARCTAN(ERt/FRi)	 = 41.810314895778596167 degrees |
+     +-----------------------------------------------------------+
+
+*/
+
+
+#include <stdio.h>
+#include <stdlib.h>
+#ifndef _WIN32
+#include <unistd.h>
+#endif
+#include <GL/glut.h>
+#include <math.h>
+#include <string.h>
+
+#define Scale                      0.3
+
+#define VectMul(X1,Y1,Z1,X2,Y2,Z2) (Y1)*(Z2)-(Z1)*(Y2),(Z1)*(X2)-(X1)*(Z2),(X1)*(Y2)-(Y1)*(X2)
+#define sqr(A)                     ((A)*(A))
+
+/* Increasing this values produces better image quality, the price is speed. */
+/* Very low values produces erroneous/incorrect plotting */
+#define tetradivisions             23
+#define cubedivisions              20
+#define octadivisions              21
+#define dodecadivisions            10
+#define icodivisions               15
+
+#define tetraangle                 109.47122063449069174
+#define cubeangle                  90.000000000000000000
+#define octaangle                  109.47122063449069174
+#define dodecaangle                63.434948822922009981
+#define icoangle                   41.810314895778596167
+
+#ifndef Pi
+#define Pi                         3.1415926535897932385
+#endif
+#define SQRT2                      1.4142135623730951455
+#define SQRT3                      1.7320508075688771932
+#define SQRT5                      2.2360679774997898051
+#define SQRT6                      2.4494897427831778813
+#define SQRT15                     3.8729833462074170214
+#define cossec36_2                 0.8506508083520399322
+#define cos72                      0.3090169943749474241
+#define sin72                      0.9510565162951535721
+#define cos36                      0.8090169943749474241
+#define sin36                      0.5877852522924731292
+
+/*************************************************************************/
+
+static int       mono=0;
+static int       smooth=1;
+static GLint     WindH, WindW;
+static GLfloat   step=0;
+static GLfloat   seno;
+static int       object;
+static int       edgedivisions;
+static void      (*draw_object)( void );
+static float     Magnitude;
+static float     *MaterialColor[20];
+
+static float front_shininess[] =   {60.0};
+static float front_specular[]  =   { 0.7, 0.7, 0.7, 1.0 };
+static float ambient[]         =   { 0.0, 0.0, 0.0, 1.0 };
+static float diffuse[]         =   { 1.0, 1.0, 1.0, 1.0 };
+static float position0[]       =   { 1.0, 1.0, 1.0, 0.0 };
+static float position1[]       =   {-1.0,-1.0, 1.0, 0.0 };
+static float lmodel_ambient[]  =   { 0.5, 0.5, 0.5, 1.0 };
+static float lmodel_twoside[]  =   {GL_TRUE};
+
+static float MaterialRed[]     =   { 0.7, 0.0, 0.0, 1.0 };
+static float MaterialGreen[]   =   { 0.1, 0.5, 0.2, 1.0 };
+static float MaterialBlue[]    =   { 0.0, 0.0, 0.7, 1.0 };
+static float MaterialCyan[]    =   { 0.2, 0.5, 0.7, 1.0 };
+static float MaterialYellow[]  =   { 0.7, 0.7, 0.0, 1.0 };
+static float MaterialMagenta[] =   { 0.6, 0.2, 0.5, 1.0 };
+static float MaterialWhite[]   =   { 0.7, 0.7, 0.7, 1.0 };
+static float MaterialGray[]    =   { 0.2, 0.2, 0.2, 1.0 };
+
+#define TRIANGLE(Edge, Amp, Divisions, Z)                                                                        \
+{                                                                                                                \
+  GLfloat   Xf,Yf,Xa,Yb,Xf2,Yf2;                                                                                 \
+  GLfloat   Factor,Factor1,Factor2;                                                                              \
+  GLfloat   VertX,VertY,VertZ,NeiAX,NeiAY,NeiAZ,NeiBX,NeiBY,NeiBZ;                                               \
+  GLfloat   Ax,Ay,Bx;                                                                                            \
+  int       Ri,Ti;                                                                                               \
+  GLfloat   Vr=(Edge)*SQRT3/3;                                                                                   \
+  GLfloat   AmpVr2=(Amp)/sqr(Vr);                                                                                \
+  GLfloat   Zf=(Edge)*(Z);                                                                                       \
+                                                                                                                 \
+  Ax=(Edge)*(+0.5/(Divisions)), Ay=(Edge)*(-SQRT3/(2*Divisions));                                                \
+  Bx=(Edge)*(-0.5/(Divisions));                                                                                  \
+                                                                                                                 \
+  for (Ri=1; Ri<=(Divisions); Ri++) {                                                                            \
+    glBegin(GL_TRIANGLE_STRIP);                                                                                  \
+    for (Ti=0; Ti<Ri; Ti++) {                                                                                    \
+      Xf=(float)(Ri-Ti)*Ax + (float)Ti*Bx;                                                                       \
+      Yf=Vr+(float)(Ri-Ti)*Ay + (float)Ti*Ay;                                                                    \
+      Xa=Xf+0.001; Yb=Yf+0.001;                                                                                  \
+      Factor=1-(((Xf2=sqr(Xf))+(Yf2=sqr(Yf)))*AmpVr2);                                                           \
+      Factor1=1-((sqr(Xa)+Yf2)*AmpVr2);                                                                          \
+      Factor2=1-((Xf2+sqr(Yb))*AmpVr2);                                                                          \
+      VertX=Factor*Xf;        VertY=Factor*Yf;        VertZ=Factor*Zf;                                           \
+      NeiAX=Factor1*Xa-VertX; NeiAY=Factor1*Yf-VertY; NeiAZ=Factor1*Zf-VertZ;                                    \
+      NeiBX=Factor2*Xf-VertX; NeiBY=Factor2*Yb-VertY; NeiBZ=Factor2*Zf-VertZ;                                    \
+      glNormal3f(VectMul(NeiAX, NeiAY, NeiAZ, NeiBX, NeiBY, NeiBZ));                                             \
+      glVertex3f(VertX, VertY, VertZ);                                                                           \
+                                                                                                                 \
+      Xf=(float)(Ri-Ti-1)*Ax + (float)Ti*Bx;                                                                     \
+      Yf=Vr+(float)(Ri-Ti-1)*Ay + (float)Ti*Ay;                                                                  \
+      Xa=Xf+0.001; Yb=Yf+0.001;                                                                                  \
+      Factor=1-(((Xf2=sqr(Xf))+(Yf2=sqr(Yf)))*AmpVr2);                                                           \
+      Factor1=1-((sqr(Xa)+Yf2)*AmpVr2);                                                                          \
+      Factor2=1-((Xf2+sqr(Yb))*AmpVr2);                                                                          \
+      VertX=Factor*Xf;        VertY=Factor*Yf;        VertZ=Factor*Zf;                                           \
+      NeiAX=Factor1*Xa-VertX; NeiAY=Factor1*Yf-VertY; NeiAZ=Factor1*Zf-VertZ;                                    \
+      NeiBX=Factor2*Xf-VertX; NeiBY=Factor2*Yb-VertY; NeiBZ=Factor2*Zf-VertZ;                                    \
+      glNormal3f(VectMul(NeiAX, NeiAY, NeiAZ, NeiBX, NeiBY, NeiBZ));                                             \
+      glVertex3f(VertX, VertY, VertZ);                                                                           \
+                                                                                                                 \
+    }                                                                                                            \
+    Xf=(float)Ri*Bx;                                                                                             \
+    Yf=Vr+(float)Ri*Ay;                                                                                          \
+    Xa=Xf+0.001; Yb=Yf+0.001;                                                                                    \
+    Factor=1-(((Xf2=sqr(Xf))+(Yf2=sqr(Yf)))*AmpVr2);                                                             \
+    Factor1=1-((sqr(Xa)+Yf2)*AmpVr2);                                                                            \
+    Factor2=1-((Xf2+sqr(Yb))*AmpVr2);                                                                            \
+    VertX=Factor*Xf;        VertY=Factor*Yf;        VertZ=Factor*Zf;                                             \
+    NeiAX=Factor1*Xa-VertX; NeiAY=Factor1*Yf-VertY; NeiAZ=Factor1*Zf-VertZ;                                      \
+    NeiBX=Factor2*Xf-VertX; NeiBY=Factor2*Yb-VertY; NeiBZ=Factor2*Zf-VertZ;                                      \
+    glNormal3f(VectMul(NeiAX, NeiAY, NeiAZ, NeiBX, NeiBY, NeiBZ));                                               \
+    glVertex3f(VertX, VertY, VertZ);                                                                             \
+    glEnd();                                                                                                     \
+  }                                                                                                              \
+}
+
+#define SQUARE(Edge, Amp, Divisions, Z)                                                                          \
+{                                                                                                                \
+  int       Xi,Yi;                                                                                               \
+  GLfloat   Xf,Yf,Y,Xf2,Yf2,Y2,Xa,Yb;                                                                            \
+  GLfloat   Factor,Factor1,Factor2;                                                                              \
+  GLfloat   VertX,VertY,VertZ,NeiAX,NeiAY,NeiAZ,NeiBX,NeiBY,NeiBZ;                                               \
+  GLfloat   Zf=(Edge)*(Z);                                                                                       \
+  GLfloat   AmpVr2=(Amp)/sqr((Edge)*SQRT2/2);                                                                    \
+                                                                                                                 \
+  for (Yi=0; Yi<(Divisions); Yi++) {                                                                             \
+    Yf=-((Edge)/2.0) + ((float)Yi)/(Divisions)*(Edge);                                                           \
+    Yf2=sqr(Yf);                                                                                                 \
+    Y=Yf+1.0/(Divisions)*(Edge);                                                                                 \
+    Y2=sqr(Y);                                                                                                   \
+    glBegin(GL_QUAD_STRIP);                                                                                      \
+    for (Xi=0; Xi<=(Divisions); Xi++) {                                                                          \
+      Xf=-((Edge)/2.0) + ((float)Xi)/(Divisions)*(Edge);                                                         \
+      Xf2=sqr(Xf);                                                                                               \
+                                                                                                                 \
+      Xa=Xf+0.001; Yb=Y+0.001;                                                                                   \
+      Factor=1-((Xf2+Y2)*AmpVr2);                                                                                \
+      Factor1=1-((sqr(Xa)+Y2)*AmpVr2);                                                                           \
+      Factor2=1-((Xf2+sqr(Yb))*AmpVr2);                                                                          \
+      VertX=Factor*Xf;        VertY=Factor*Y;         VertZ=Factor*Zf;                                           \
+      NeiAX=Factor1*Xa-VertX; NeiAY=Factor1*Y-VertY;  NeiAZ=Factor1*Zf-VertZ;                                    \
+      NeiBX=Factor2*Xf-VertX; NeiBY=Factor2*Yb-VertY; NeiBZ=Factor2*Zf-VertZ;                                    \
+      glNormal3f(VectMul(NeiAX, NeiAY, NeiAZ, NeiBX, NeiBY, NeiBZ));                                             \
+      glVertex3f(VertX, VertY, VertZ);                                                                           \
+                                                                                                                 \
+      Xa=Xf+0.001; Yb=Yf+0.001;                                                                                  \
+      Factor=1-((Xf2+Yf2)*AmpVr2);                                                                               \
+      Factor1=1-((sqr(Xa)+Yf2)*AmpVr2);                                                                          \
+      Factor2=1-((Xf2+sqr(Yb))*AmpVr2);                                                                          \
+      VertX=Factor*Xf;        VertY=Factor*Yf;        VertZ=Factor*Zf;                                           \
+      NeiAX=Factor1*Xa-VertX; NeiAY=Factor1*Yf-VertY; NeiAZ=Factor1*Zf-VertZ;                                    \
+      NeiBX=Factor2*Xf-VertX; NeiBY=Factor2*Yb-VertY; NeiBZ=Factor2*Zf-VertZ;                                    \
+      glNormal3f(VectMul(NeiAX, NeiAY, NeiAZ, NeiBX, NeiBY, NeiBZ));                                             \
+      glVertex3f(VertX, VertY, VertZ);                                                                           \
+    }                                                                                                            \
+    glEnd();                                                                                                     \
+  }                                                                                                              \
+}
+
+#define PENTAGON(Edge, Amp, Divisions, Z)                                                                        \
+{                                                                                                                \
+  int       Ri,Ti,Fi;                                                                                            \
+  GLfloat   Xf,Yf,Xa,Yb,Xf2,Yf2;                                                                                 \
+  GLfloat   x[6],y[6];                                                                                           \
+  GLfloat   Factor,Factor1,Factor2;                                                                              \
+  GLfloat   VertX,VertY,VertZ,NeiAX,NeiAY,NeiAZ,NeiBX,NeiBY,NeiBZ;                                               \
+  GLfloat   Zf=(Edge)*(Z);                                                                                       \
+  GLfloat   AmpVr2=(Amp)/sqr((Edge)*cossec36_2);                                                                 \
+                                                                                                                 \
+  for(Fi=0;Fi<6;Fi++) {                                                                                          \
+    x[Fi]=-cos( Fi*2*Pi/5 + Pi/10 )/(Divisions)*cossec36_2*(Edge);                                                \
+    y[Fi]=sin( Fi*2*Pi/5 + Pi/10 )/(Divisions)*cossec36_2*(Edge);                                                \
+  }                                                                                                              \
+                                                                                                                 \
+  for (Ri=1; Ri<=(Divisions); Ri++) {                                                                            \
+    for (Fi=0; Fi<5; Fi++) {                                                                                     \
+      glBegin(GL_TRIANGLE_STRIP);                                                                                \
+      for (Ti=0; Ti<Ri; Ti++) {                                                                                  \
+        Xf=(float)(Ri-Ti)*x[Fi] + (float)Ti*x[Fi+1];                                                             \
+        Yf=(float)(Ri-Ti)*y[Fi] + (float)Ti*y[Fi+1];                                                             \
+        Xa=Xf+0.001; Yb=Yf+0.001;                                                                                \
+	Factor=1-(((Xf2=sqr(Xf))+(Yf2=sqr(Yf)))*AmpVr2);                                                         \
+	Factor1=1-((sqr(Xa)+Yf2)*AmpVr2);                                                                        \
+	Factor2=1-((Xf2+sqr(Yb))*AmpVr2);                                                                        \
+        VertX=Factor*Xf;        VertY=Factor*Yf;        VertZ=Factor*Zf;                                         \
+        NeiAX=Factor1*Xa-VertX; NeiAY=Factor1*Yf-VertY; NeiAZ=Factor1*Zf-VertZ;                                  \
+        NeiBX=Factor2*Xf-VertX; NeiBY=Factor2*Yb-VertY; NeiBZ=Factor2*Zf-VertZ;                                  \
+        glNormal3f(VectMul(NeiAX, NeiAY, NeiAZ, NeiBX, NeiBY, NeiBZ));                                           \
+	glVertex3f(VertX, VertY, VertZ);                                                                         \
+                                                                                                                 \
+        Xf=(float)(Ri-Ti-1)*x[Fi] + (float)Ti*x[Fi+1];                                                           \
+        Yf=(float)(Ri-Ti-1)*y[Fi] + (float)Ti*y[Fi+1];                                                           \
+        Xa=Xf+0.001; Yb=Yf+0.001;                                                                                \
+	Factor=1-(((Xf2=sqr(Xf))+(Yf2=sqr(Yf)))*AmpVr2);                                                         \
+	Factor1=1-((sqr(Xa)+Yf2)*AmpVr2);                                                                        \
+	Factor2=1-((Xf2+sqr(Yb))*AmpVr2);                                                                        \
+        VertX=Factor*Xf;        VertY=Factor*Yf;        VertZ=Factor*Zf;                                         \
+        NeiAX=Factor1*Xa-VertX; NeiAY=Factor1*Yf-VertY; NeiAZ=Factor1*Zf-VertZ;                                  \
+        NeiBX=Factor2*Xf-VertX; NeiBY=Factor2*Yb-VertY; NeiBZ=Factor2*Zf-VertZ;                                  \
+        glNormal3f(VectMul(NeiAX, NeiAY, NeiAZ, NeiBX, NeiBY, NeiBZ));                                           \
+	glVertex3f(VertX, VertY, VertZ);                                                                         \
+                                                                                                                 \
+      }                                                                                                          \
+      Xf=(float)Ri*x[Fi+1];                                                                                      \
+      Yf=(float)Ri*y[Fi+1];                                                                                      \
+      Xa=Xf+0.001; Yb=Yf+0.001;                                                                                  \
+      Factor=1-(((Xf2=sqr(Xf))+(Yf2=sqr(Yf)))*AmpVr2);                                                           \
+      Factor1=1-((sqr(Xa)+Yf2)*AmpVr2);                                                                          \
+      Factor2=1-((Xf2+sqr(Yb))*AmpVr2);                                                                          \
+      VertX=Factor*Xf;        VertY=Factor*Yf;        VertZ=Factor*Zf;                                           \
+      NeiAX=Factor1*Xa-VertX; NeiAY=Factor1*Yf-VertY; NeiAZ=Factor1*Zf-VertZ;                                    \
+      NeiBX=Factor2*Xf-VertX; NeiBY=Factor2*Yb-VertY; NeiBZ=Factor2*Zf-VertZ;                                    \
+      glNormal3f(VectMul(NeiAX, NeiAY, NeiAZ, NeiBX, NeiBY, NeiBZ));                                             \
+      glVertex3f(VertX, VertY, VertZ);                                                                           \
+      glEnd();                                                                                                   \
+    }                                                                                                            \
+  }                                                                                                              \
+}
+
+static void draw_tetra( void )
+{
+  GLuint list;
+
+  list = glGenLists( 1 );
+  glNewList( list, GL_COMPILE );
+  TRIANGLE(2,seno,edgedivisions,0.5/SQRT6);
+  glEndList();
+
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[0]);
+  glCallList(list);
+  glPushMatrix();
+  glRotatef(180,0,0,1);
+  glRotatef(-tetraangle,1,0,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[1]);
+  glCallList(list);
+  glPopMatrix();
+  glPushMatrix();
+  glRotatef(180,0,1,0);
+  glRotatef(-180+tetraangle,0.5,SQRT3/2,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[2]);
+  glCallList(list);
+  glPopMatrix();
+  glRotatef(180,0,1,0);
+  glRotatef(-180+tetraangle,0.5,-SQRT3/2,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[3]);
+  glCallList(list);
+
+  glDeleteLists(list,1);
+}
+
+static void draw_cube( void )
+{
+  GLuint list;
+
+  list = glGenLists( 1 );
+  glNewList( list, GL_COMPILE );
+  SQUARE(2, seno, edgedivisions, 0.5)
+  glEndList();
+
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[0]);
+  glCallList(list);
+  glRotatef(cubeangle,1,0,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[1]);
+  glCallList(list);
+  glRotatef(cubeangle,1,0,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[2]);
+  glCallList(list);
+  glRotatef(cubeangle,1,0,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[3]);
+  glCallList(list);
+  glRotatef(cubeangle,0,1,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[4]);
+  glCallList(list);
+  glRotatef(2*cubeangle,0,1,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[5]);
+  glCallList(list);
+
+  glDeleteLists(list,1);
+}
+
+static void draw_octa( void )
+{
+  GLuint list;
+
+  list = glGenLists( 1 );
+  glNewList( list, GL_COMPILE );
+  TRIANGLE(2,seno,edgedivisions,1/SQRT6);
+  glEndList();
+
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[0]);
+  glCallList(list);
+  glPushMatrix();
+  glRotatef(180,0,0,1);
+  glRotatef(-180+octaangle,1,0,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[1]);
+  glCallList(list);
+  glPopMatrix();
+  glPushMatrix();
+  glRotatef(180,0,1,0);
+  glRotatef(-octaangle,0.5,SQRT3/2,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[2]);
+  glCallList(list);
+  glPopMatrix();
+  glPushMatrix();
+  glRotatef(180,0,1,0);
+  glRotatef(-octaangle,0.5,-SQRT3/2,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[3]);
+  glCallList(list);
+  glPopMatrix();
+  glRotatef(180,1,0,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[4]);
+  glCallList(list);
+  glPushMatrix();
+  glRotatef(180,0,0,1);
+  glRotatef(-180+octaangle,1,0,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[5]);
+  glCallList(list);
+  glPopMatrix();
+  glPushMatrix();
+  glRotatef(180,0,1,0);
+  glRotatef(-octaangle,0.5,SQRT3/2,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[6]);
+  glCallList(list);
+  glPopMatrix();
+  glRotatef(180,0,1,0);
+  glRotatef(-octaangle,0.5,-SQRT3/2,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[7]);
+  glCallList(list);
+
+  glDeleteLists(list,1);
+}
+
+static void draw_dodeca( void )
+{
+  GLuint list;
+
+  #define TAU ((SQRT5+1)/2)
+
+  list = glGenLists( 1 );
+  glNewList( list, GL_COMPILE );
+  PENTAGON(1,seno,edgedivisions,sqr(TAU) * sqrt((TAU+2)/5) / 2);
+  glEndList();
+
+  glPushMatrix();
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[0]);
+  glCallList(list);
+  glRotatef(180,0,0,1);
+  glPushMatrix();
+  glRotatef(-dodecaangle,1,0,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[1]);
+  glCallList(list);
+  glPopMatrix();
+  glPushMatrix();
+  glRotatef(-dodecaangle,cos72,sin72,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[2]);
+  glCallList(list);
+  glPopMatrix();
+  glPushMatrix();
+  glRotatef(-dodecaangle,cos72,-sin72,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[3]);
+  glCallList(list);
+  glPopMatrix();
+  glPushMatrix();
+  glRotatef(dodecaangle,cos36,-sin36,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[4]);
+  glCallList(list);
+  glPopMatrix();
+  glRotatef(dodecaangle,cos36,sin36,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[5]);
+  glCallList(list);
+  glPopMatrix();
+  glRotatef(180,1,0,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[6]);
+  glCallList(list);
+  glRotatef(180,0,0,1);
+  glPushMatrix();
+  glRotatef(-dodecaangle,1,0,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[7]);
+  glCallList(list);
+  glPopMatrix();
+  glPushMatrix();
+  glRotatef(-dodecaangle,cos72,sin72,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[8]);
+  glCallList(list);
+  glPopMatrix();
+  glPushMatrix();
+  glRotatef(-dodecaangle,cos72,-sin72,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[9]);
+  glCallList(list);
+  glPopMatrix();
+  glPushMatrix();
+  glRotatef(dodecaangle,cos36,-sin36,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[10]);
+  glCallList(list);
+  glPopMatrix();
+  glRotatef(dodecaangle,cos36,sin36,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[11]);
+  glCallList(list);
+
+  glDeleteLists(list,1);
+}
+
+static void draw_ico( void )
+{
+  GLuint list;
+
+  list = glGenLists( 1 );
+  glNewList( list, GL_COMPILE );
+  TRIANGLE(1.5,seno,edgedivisions,(3*SQRT3+SQRT15)/12);
+  glEndList();
+
+  glPushMatrix();
+
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[0]);
+  glCallList(list);
+  glPushMatrix();
+  glRotatef(180,0,0,1);
+  glRotatef(-icoangle,1,0,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[1]);
+  glCallList(list);
+  glPushMatrix();
+  glRotatef(180,0,1,0);
+  glRotatef(-180+icoangle,0.5,SQRT3/2,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[2]);
+  glCallList(list);
+  glPopMatrix();
+  glRotatef(180,0,1,0);
+  glRotatef(-180+icoangle,0.5,-SQRT3/2,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[3]);
+  glCallList(list);
+  glPopMatrix();
+  glPushMatrix();
+  glRotatef(180,0,1,0);
+  glRotatef(-180+icoangle,0.5,SQRT3/2,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[4]);
+  glCallList(list);
+  glPushMatrix();
+  glRotatef(180,0,1,0);
+  glRotatef(-180+icoangle,0.5,SQRT3/2,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[5]);
+  glCallList(list);
+  glPopMatrix();
+  glRotatef(180,0,0,1);
+  glRotatef(-icoangle,1,0,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[6]);
+  glCallList(list);
+  glPopMatrix();
+  glRotatef(180,0,1,0);
+  glRotatef(-180+icoangle,0.5,-SQRT3/2,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[7]);
+  glCallList(list);
+  glPushMatrix();
+  glRotatef(180,0,1,0);
+  glRotatef(-180+icoangle,0.5,-SQRT3/2,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[8]);
+  glCallList(list);
+  glPopMatrix();
+  glRotatef(180,0,0,1);
+  glRotatef(-icoangle,1,0,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[9]);
+  glCallList(list);
+  glPopMatrix();
+  glRotatef(180,1,0,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[10]);
+  glCallList(list);
+  glPushMatrix();
+  glRotatef(180,0,0,1);
+  glRotatef(-icoangle,1,0,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[11]);
+  glCallList(list);
+  glPushMatrix();
+  glRotatef(180,0,1,0);
+  glRotatef(-180+icoangle,0.5,SQRT3/2,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[12]);
+  glCallList(list);
+  glPopMatrix();
+  glRotatef(180,0,1,0);
+  glRotatef(-180+icoangle,0.5,-SQRT3/2,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[13]);
+  glCallList(list);
+  glPopMatrix();
+  glPushMatrix();
+  glRotatef(180,0,1,0);
+  glRotatef(-180+icoangle,0.5,SQRT3/2,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[14]);
+  glCallList(list);
+  glPushMatrix();
+  glRotatef(180,0,1,0);
+  glRotatef(-180+icoangle,0.5,SQRT3/2,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[15]);
+  glCallList(list);
+  glPopMatrix();
+  glRotatef(180,0,0,1);
+  glRotatef(-icoangle,1,0,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[16]);
+  glCallList(list);
+  glPopMatrix();
+  glRotatef(180,0,1,0);
+  glRotatef(-180+icoangle,0.5,-SQRT3/2,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[17]);
+  glCallList(list);
+  glPushMatrix();
+  glRotatef(180,0,1,0);
+  glRotatef(-180+icoangle,0.5,-SQRT3/2,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[18]);
+  glCallList(list);
+  glPopMatrix();
+  glRotatef(180,0,0,1);
+  glRotatef(-icoangle,1,0,0);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, MaterialColor[19]);
+  glCallList(list);
+
+  glDeleteLists(list,1);
+}
+
+static void draw ( void ) {
+  glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT );
+
+  glPushMatrix();
+
+    glTranslatef( 0.0, 0.0, -10.0 );
+    glScalef( Scale*WindH/WindW, Scale, Scale );
+    glTranslatef(2.5*WindW/WindH*sin(step*1.11),2.5*cos(step*1.25*1.11),0);
+    glRotatef(step*100,1,0,0);
+    glRotatef(step*95,0,1,0);
+    glRotatef(step*90,0,0,1);
+
+  seno=(sin(step)+1.0/3.0)*(4.0/5.0)*Magnitude;
+
+  draw_object();
+
+  glPopMatrix();
+
+  glFlush();
+
+  glutSwapBuffers();
+
+  step+=0.05;
+}
+
+static void idle_( void )
+{
+   glutPostRedisplay();
+}
+
+static void reshape( int width, int height )
+{
+  glViewport(0, 0, WindW=(GLint)width, WindH=(GLint)height);
+  glMatrixMode(GL_PROJECTION);
+  glLoadIdentity();
+  glFrustum( -1.0, 1.0, -1.0, 1.0, 5.0, 15.0 );
+  glMatrixMode(GL_MODELVIEW);
+}
+
+static void pinit(void);
+
+static void key( unsigned char k, int x, int y )
+{
+  switch (k) {
+    case '1': object=1; break;
+    case '2': object=2; break;
+    case '3': object=3; break;
+    case '4': object=4; break;
+    case '5': object=5; break;
+    case ' ': mono^=1; break;
+    case 13: smooth^=1; break;
+    case 27:
+       exit(0);
+  }
+  pinit();
+}
+
+static void pinit(void)
+{
+  switch(object) {
+    case 1:
+      draw_object=draw_tetra;
+      MaterialColor[0]=MaterialRed;
+      MaterialColor[1]=MaterialGreen;
+      MaterialColor[2]=MaterialBlue;
+      MaterialColor[3]=MaterialWhite;
+      edgedivisions=tetradivisions;
+      Magnitude=2.5;
+      break;
+    case 2:
+      draw_object=draw_cube;
+      MaterialColor[0]=MaterialRed;
+      MaterialColor[1]=MaterialGreen;
+      MaterialColor[2]=MaterialCyan;
+      MaterialColor[3]=MaterialMagenta;
+      MaterialColor[4]=MaterialYellow;
+      MaterialColor[5]=MaterialBlue;
+      edgedivisions=cubedivisions;
+      Magnitude=2.0;
+      break;
+    case 3:
+      draw_object=draw_octa;
+      MaterialColor[0]=MaterialRed;
+      MaterialColor[1]=MaterialGreen;
+      MaterialColor[2]=MaterialBlue;
+      MaterialColor[3]=MaterialWhite;
+      MaterialColor[4]=MaterialCyan;
+      MaterialColor[5]=MaterialMagenta;
+      MaterialColor[6]=MaterialGray;
+      MaterialColor[7]=MaterialYellow;
+      edgedivisions=octadivisions;
+      Magnitude=2.5;
+      break;
+    case 4:
+      draw_object=draw_dodeca;
+      MaterialColor[ 0]=MaterialRed;
+      MaterialColor[ 1]=MaterialGreen;
+      MaterialColor[ 2]=MaterialCyan;
+      MaterialColor[ 3]=MaterialBlue;
+      MaterialColor[ 4]=MaterialMagenta;
+      MaterialColor[ 5]=MaterialYellow;
+      MaterialColor[ 6]=MaterialGreen;
+      MaterialColor[ 7]=MaterialCyan;
+      MaterialColor[ 8]=MaterialRed;
+      MaterialColor[ 9]=MaterialMagenta;
+      MaterialColor[10]=MaterialBlue;
+      MaterialColor[11]=MaterialYellow;
+      edgedivisions=dodecadivisions;
+      Magnitude=2.0;
+      break;
+    case 5:
+      draw_object=draw_ico;
+      MaterialColor[ 0]=MaterialRed;
+      MaterialColor[ 1]=MaterialGreen;
+      MaterialColor[ 2]=MaterialBlue;
+      MaterialColor[ 3]=MaterialCyan;
+      MaterialColor[ 4]=MaterialYellow;
+      MaterialColor[ 5]=MaterialMagenta;
+      MaterialColor[ 6]=MaterialRed;
+      MaterialColor[ 7]=MaterialGreen;
+      MaterialColor[ 8]=MaterialBlue;
+      MaterialColor[ 9]=MaterialWhite;
+      MaterialColor[10]=MaterialCyan;
+      MaterialColor[11]=MaterialYellow;
+      MaterialColor[12]=MaterialMagenta;
+      MaterialColor[13]=MaterialRed;
+      MaterialColor[14]=MaterialGreen;
+      MaterialColor[15]=MaterialBlue;
+      MaterialColor[16]=MaterialCyan;
+      MaterialColor[17]=MaterialYellow;
+      MaterialColor[18]=MaterialMagenta;
+      MaterialColor[19]=MaterialGray;
+      edgedivisions=icodivisions;
+      Magnitude=2.5;
+      break;
+  }
+  if (mono) {
+    int loop;
+    for (loop=0; loop<20; loop++) MaterialColor[loop]=MaterialGray;
+  }
+  if (smooth) {
+    glShadeModel( GL_SMOOTH );
+  } else {
+    glShadeModel( GL_FLAT );
+  }
+
+}
+
+void INIT(void)
+{
+  printf("Morph 3D - Shows morphing platonic polyhedra\n");
+  printf("Author: Marcelo Fernandes Vianna (vianna@cat.cbpf.br)\n\n");
+  printf("  [1]    - Tetrahedron\n");
+  printf("  [2]    - Hexahedron (Cube)\n");
+  printf("  [3]    - Octahedron\n");
+  printf("  [4]    - Dodecahedron\n");
+  printf("  [5]    - Icosahedron\n");
+  printf("[SPACE]  - Toggle colored faces\n");
+  printf("[RETURN] - Toggle smooth/flat shading\n");
+  printf(" [ESC]   - Quit\n");
+
+  object=1;
+
+  glutInitWindowPosition(0,0);
+  glutInitWindowSize(640,480);
+
+  glutInitDisplayMode( GLUT_DEPTH | GLUT_DOUBLE | GLUT_RGB );
+
+  if (glutCreateWindow("Morph 3D - Shows morphing platonic polyhedra") <= 0) {
+     exit(0);
+  }
+
+  glClearDepth(1.0);
+  glClearColor( 0.0, 0.0, 0.0, 1.0 );
+  glColor3f( 1.0, 1.0, 1.0 );
+
+  glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT );
+  glFlush();
+  glutSwapBuffers();
+
+  glLightfv(GL_LIGHT0, GL_AMBIENT, ambient);
+  glLightfv(GL_LIGHT0, GL_DIFFUSE, diffuse);
+  glLightfv(GL_LIGHT0, GL_POSITION, position0);
+  glLightfv(GL_LIGHT1, GL_AMBIENT, ambient);
+  glLightfv(GL_LIGHT1, GL_DIFFUSE, diffuse);
+  glLightfv(GL_LIGHT1, GL_POSITION, position1);
+  glLightModelfv(GL_LIGHT_MODEL_AMBIENT, lmodel_ambient);
+  glLightModelfv(GL_LIGHT_MODEL_TWO_SIDE, lmodel_twoside);
+  glEnable(GL_LIGHTING);
+  glEnable(GL_LIGHT0);
+  glEnable(GL_LIGHT1);
+  glEnable(GL_DEPTH_TEST);
+  glEnable(GL_NORMALIZE);
+
+  glMaterialfv(GL_FRONT_AND_BACK, GL_SHININESS, front_shininess);
+  glMaterialfv(GL_FRONT_AND_BACK, GL_SPECULAR, front_specular);
+
+  glHint(GL_FOG_HINT, GL_FASTEST);
+  glHint(GL_PERSPECTIVE_CORRECTION_HINT, GL_FASTEST);
+  glHint(GL_POLYGON_SMOOTH_HINT, GL_FASTEST);
+
+  pinit();
+
+  glutReshapeFunc( reshape );
+  glutKeyboardFunc( key );
+  glutIdleFunc( idle_ );
+  glutDisplayFunc( draw );
+  glutMainLoop();
+  
+}
+
+int main(int argc, char **argv)
+{
+  INIT();
+  return(0);
+}