From afb833d4e89c312460a4ab9ed6a7a8ca4ebbfe1c Mon Sep 17 00:00:00 2001 From: jtg Date: Thu, 19 Aug 1999 00:55:39 +0000 Subject: Initial revision --- progs/demos/morph3d.c | 892 ++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 892 insertions(+) create mode 100644 progs/demos/morph3d.c (limited to 'progs/demos/morph3d.c') diff --git a/progs/demos/morph3d.c b/progs/demos/morph3d.c new file mode 100644 index 00000000000..30ca9221448 --- /dev/null +++ b/progs/demos/morph3d.c @@ -0,0 +1,892 @@ +/* $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 +#include +#ifndef _WIN32 +#include +#endif +#include +#include +#include + +#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