Dear All:
Given my recent work on this bug:
http://bugs.winehq.org/show_bug.cgi?id=22918
and on D3DXCreateSphere, with the latest iteration being:
http://www.winehq.org/pipermail/wine-patches/2010-July/091176.html
I have been giving quite a bit of thought to d3dx9 and to mesh creation
functions in particular.
I have realized there is no "perfect" sphere creation function. Rather,
there are functions that may be optimized for different purposes.
Thus, I thought I'd pose the question - as to d3dx9, is our goal:
a) speed
b) code "prettiness"
c) something else?
I am tempted to think it is (a), but wanted to double check.
For example, I have taken a look, per Henri's suggestion (wrt teapot),
at freeglut 2.6.0 sources. For your reference:
> freeglut is released under the X-Consortium license.
Per http://www.winehq.org/pipermail/wine-devel/2010-July/085266.html, I
believe it is okay to look at this code. In fact, the license looks
strikingly like the one in:
http://source.winehq.org/git/wine.git/?a=blob;f=dlls/gdi32/region.c#l26
with X Consortium changed to Pawel W. Olstza (?)
In any case, I have taken the liberty of copying and pasting
glutSolidSphere to the top of the attached file. As you can see, it is
implemented in terms of triangle fans and quad strips. (You will notice,
btw, the use of lookup tables - fghCircleTable - for cos and sin, which
reinforces my belief that speed is our top interest in terms of a
graphics library).
Now you will note, my current D3DXCreateSphere patch:
http://www.winehq.org/pipermail/wine-patches/2010-July/091176.html
creates unique vertices and indices (creating indices on a per-vertex
basis per Henri's suggestion). I admit, this may not "look" as pretty as
having triangle fans and quad strips.
In fact, of course on possibility is to:
a) create helper functions that make triangle fans and quad strips -
because we are dealing with (unique) vertex buffers and index buffers
for our (triangular) faces, we will need additional floating point
comparison calls in each function to make sure that our vertices are
unique
b) use code a la freeglut to generate our vertex and index buffers
Now this code might be a little "prettier" to look at, but I see some
serious problems with this approach and would appreciate your
comments/feedback.
Here are some issues:
i) KISS (keep it simple .. umm .. silly) - although not a computer
scientist by formal training, I know well enough that in any system, the
more complex the system, the more opportunities for random behavior. In
other words, bugs. Clearly, this is why we have conformance tests. But
it seems like it would be overkill to have conformance tests for helper
functions, especially helper functions used in a test.
ii) Most importantly - this would add at least three floating point
comparisons per vertex that we add. This may not seem like a lot - until
you start thinking of a sphere with, say, 1000 vertices (not too much
for a spherical-looking sphere), and, say, for a game that generates 100
spheres. This means 100 x 1000 x 3 = 30000 extra floating point
comparisons (which would involve a subtraction and comparison because we
would be comparing to a predefined epsilon - not to mention the eternal
question - which epsilon do we use?)
Now this link is quite old:
http://www.phoronix.com/scan.php?page=article&item=wine_feb08_tests&num=1
but surely Wine is constantly being benchmarked as far as graphics
performance, since I believe one of the big uses of Wine currently is
for games.
Thus, it is reasonable that we do not want to take such a performance
hit.
In any case, this is my thought as to why
http://www.winehq.org/pipermail/wine-patches/2010-July/091176.html
is a good implementation for a sphere, rather than doing something more
high level.
And, in general, why we probably want to keep doing the vertex
buffer/index buffer approach, and forgo an approach where we:
(a) create non-unique vertices uses nice geometrical structures on the
fly (triangle fans, quad strips)
(b) generate vertex and index buffers from these on the fly.
However, as always, feedback appreciated.
Thank you and have a nice Saturday!
Misha
/*
* Draws a solid sphere
*/
void FGAPIENTRY glutSolidSphere(GLdouble radius, GLint slices, GLint stacks)
{
int i,j;
/* Adjust z and radius as stacks are drawn. */
double z0,z1;
double r0,r1;
/* Pre-computed circle */
double *sint1,*cost1;
double *sint2,*cost2;
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutSolidSphere" );
fghCircleTable(&sint1,&cost1,-slices);
fghCircleTable(&sint2,&cost2,stacks*2);
/* The top stack is covered with a triangle fan */
z0 = 1.0;
z1 = cost2[(stacks>0)?1:0];
r0 = 0.0;
r1 = sint2[(stacks>0)?1:0];
glBegin(GL_TRIANGLE_FAN);
glNormal3d(0,0,1);
glVertex3d(0,0,radius);
for (j=slices; j>=0; j--)
{
glNormal3d(cost1[j]*r1, sint1[j]*r1, z1 );
glVertex3d(cost1[j]*r1*radius, sint1[j]*r1*radius, z1*radius);
}
glEnd();
/* Cover each stack with a quad strip, except the top and bottom stacks */
for( i=1; i<stacks-1; i++ )
{
z0 = z1; z1 = cost2[i+1];
r0 = r1; r1 = sint2[i+1];
glBegin(GL_QUAD_STRIP);
for(j=0; j<=slices; j++)
{
glNormal3d(cost1[j]*r1, sint1[j]*r1, z1 );
glVertex3d(cost1[j]*r1*radius, sint1[j]*r1*radius, z1*radius);
glNormal3d(cost1[j]*r0, sint1[j]*r0, z0 );
glVertex3d(cost1[j]*r0*radius, sint1[j]*r0*radius, z0*radius);
}
glEnd();
}
/* The bottom stack is covered with a triangle fan */
z0 = z1;
r0 = r1;
glBegin(GL_TRIANGLE_FAN);
glNormal3d(0,0,-1);
glVertex3d(0,0,-radius);
for (j=0; j<=slices; j++)
{
glNormal3d(cost1[j]*r0, sint1[j]*r0, z0 );
glVertex3d(cost1[j]*r0*radius, sint1[j]*r0*radius, z0*radius);
}
glEnd();
/* Release sin and cos tables */
free(sint1);
free(cost1);
free(sint2);
free(cost2);
}
/*
* freeglut_geometry.c
*
* Freeglut geometry rendering methods.
*
* Copyright (c) 1999-2000 Pawel W. Olszta. All Rights Reserved.
* Written by Pawel W. Olszta, <ols...@sourceforge.net>
* Creation date: Fri Dec 3 1999
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the "Software"),
* to deal in the Software without restriction, including without limitation
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
* and/or sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included
* in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
* PAWEL W. OLSZTA BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
* IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
#include <GL/freeglut.h>
#include "freeglut_internal.h"
/*
* TODO BEFORE THE STABLE RELEASE:
*
* Following functions have been contributed by Andreas Umbach.
*
* glutWireCube() -- looks OK
* glutSolidCube() -- OK
*
* Those functions have been implemented by John Fay.
*
* glutWireTorus() -- looks OK
* glutSolidTorus() -- looks OK
* glutWireDodecahedron() -- looks OK
* glutSolidDodecahedron() -- looks OK
* glutWireOctahedron() -- looks OK
* glutSolidOctahedron() -- looks OK
* glutWireTetrahedron() -- looks OK
* glutSolidTetrahedron() -- looks OK
* glutWireIcosahedron() -- looks OK
* glutSolidIcosahedron() -- looks OK
*
* The Following functions have been updated by Nigel Stewart, based
* on FreeGLUT 2.0.0 implementations:
*
* glutWireSphere() -- looks OK
* glutSolidSphere() -- looks OK
* glutWireCone() -- looks OK
* glutSolidCone() -- looks OK
*/
/* -- INTERFACE FUNCTIONS -------------------------------------------------- */
/*
* Draws a wireframed cube. Code contributed by Andreas Umbach <mar...@dataway.ch>
*/
void FGAPIENTRY glutWireCube( GLdouble dSize )
{
double size = dSize * 0.5;
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutWireCube" );
# define V(a,b,c) glVertex3d( a size, b size, c size );
# define N(a,b,c) glNormal3d( a, b, c );
/* PWO: I dared to convert the code to use macros... */
glBegin( GL_LINE_LOOP ); N( 1.0, 0.0, 0.0); V(+,-,+); V(+,-,-); V(+,+,-); V(+,+,+); glEnd();
glBegin( GL_LINE_LOOP ); N( 0.0, 1.0, 0.0); V(+,+,+); V(+,+,-); V(-,+,-); V(-,+,+); glEnd();
glBegin( GL_LINE_LOOP ); N( 0.0, 0.0, 1.0); V(+,+,+); V(-,+,+); V(-,-,+); V(+,-,+); glEnd();
glBegin( GL_LINE_LOOP ); N(-1.0, 0.0, 0.0); V(-,-,+); V(-,+,+); V(-,+,-); V(-,-,-); glEnd();
glBegin( GL_LINE_LOOP ); N( 0.0,-1.0, 0.0); V(-,-,+); V(-,-,-); V(+,-,-); V(+,-,+); glEnd();
glBegin( GL_LINE_LOOP ); N( 0.0, 0.0,-1.0); V(-,-,-); V(-,+,-); V(+,+,-); V(+,-,-); glEnd();
# undef V
# undef N
}
/*
* Draws a solid cube. Code contributed by Andreas Umbach <mar...@dataway.ch>
*/
void FGAPIENTRY glutSolidCube( GLdouble dSize )
{
double size = dSize * 0.5;
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutSolidCube" );
# define V(a,b,c) glVertex3d( a size, b size, c size );
# define N(a,b,c) glNormal3d( a, b, c );
/* PWO: Again, I dared to convert the code to use macros... */
glBegin( GL_QUADS );
N( 1.0, 0.0, 0.0); V(+,-,+); V(+,-,-); V(+,+,-); V(+,+,+);
N( 0.0, 1.0, 0.0); V(+,+,+); V(+,+,-); V(-,+,-); V(-,+,+);
N( 0.0, 0.0, 1.0); V(+,+,+); V(-,+,+); V(-,-,+); V(+,-,+);
N(-1.0, 0.0, 0.0); V(-,-,+); V(-,+,+); V(-,+,-); V(-,-,-);
N( 0.0,-1.0, 0.0); V(-,-,+); V(-,-,-); V(+,-,-); V(+,-,+);
N( 0.0, 0.0,-1.0); V(-,-,-); V(-,+,-); V(+,+,-); V(+,-,-);
glEnd();
# undef V
# undef N
}
/*
* Compute lookup table of cos and sin values forming a cirle
*
* Notes:
* It is the responsibility of the caller to free these tables
* The size of the table is (n+1) to form a connected loop
* The last entry is exactly the same as the first
* The sign of n can be flipped to get the reverse loop
*/
static void fghCircleTable(double **sint,double **cost,const int n)
{
int i;
/* Table size, the sign of n flips the circle direction */
const int size = abs(n);
/* Determine the angle between samples */
const double angle = 2*M_PI/(double)( ( n == 0 ) ? 1 : n );
/* Allocate memory for n samples, plus duplicate of first entry at the end */
*sint = (double *) calloc(sizeof(double), size+1);
*cost = (double *) calloc(sizeof(double), size+1);
/* Bail out if memory allocation fails, fgError never returns */
if (!(*sint) || !(*cost))
{
free(*sint);
free(*cost);
fgError("Failed to allocate memory in fghCircleTable");
}
/* Compute cos and sin around the circle */
(*sint)[0] = 0.0;
(*cost)[0] = 1.0;
for (i=1; i<size; i++)
{
(*sint)[i] = sin(angle*i);
(*cost)[i] = cos(angle*i);
}
/* Last sample is duplicate of the first */
(*sint)[size] = (*sint)[0];
(*cost)[size] = (*cost)[0];
}
/*
* Draws a solid sphere
*/
void FGAPIENTRY glutSolidSphere(GLdouble radius, GLint slices, GLint stacks)
{
int i,j;
/* Adjust z and radius as stacks are drawn. */
double z0,z1;
double r0,r1;
/* Pre-computed circle */
double *sint1,*cost1;
double *sint2,*cost2;
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutSolidSphere" );
fghCircleTable(&sint1,&cost1,-slices);
fghCircleTable(&sint2,&cost2,stacks*2);
/* The top stack is covered with a triangle fan */
z0 = 1.0;
z1 = cost2[(stacks>0)?1:0];
r0 = 0.0;
r1 = sint2[(stacks>0)?1:0];
glBegin(GL_TRIANGLE_FAN);
glNormal3d(0,0,1);
glVertex3d(0,0,radius);
for (j=slices; j>=0; j--)
{
glNormal3d(cost1[j]*r1, sint1[j]*r1, z1 );
glVertex3d(cost1[j]*r1*radius, sint1[j]*r1*radius, z1*radius);
}
glEnd();
/* Cover each stack with a quad strip, except the top and bottom stacks */
for( i=1; i<stacks-1; i++ )
{
z0 = z1; z1 = cost2[i+1];
r0 = r1; r1 = sint2[i+1];
glBegin(GL_QUAD_STRIP);
for(j=0; j<=slices; j++)
{
glNormal3d(cost1[j]*r1, sint1[j]*r1, z1 );
glVertex3d(cost1[j]*r1*radius, sint1[j]*r1*radius, z1*radius);
glNormal3d(cost1[j]*r0, sint1[j]*r0, z0 );
glVertex3d(cost1[j]*r0*radius, sint1[j]*r0*radius, z0*radius);
}
glEnd();
}
/* The bottom stack is covered with a triangle fan */
z0 = z1;
r0 = r1;
glBegin(GL_TRIANGLE_FAN);
glNormal3d(0,0,-1);
glVertex3d(0,0,-radius);
for (j=0; j<=slices; j++)
{
glNormal3d(cost1[j]*r0, sint1[j]*r0, z0 );
glVertex3d(cost1[j]*r0*radius, sint1[j]*r0*radius, z0*radius);
}
glEnd();
/* Release sin and cos tables */
free(sint1);
free(cost1);
free(sint2);
free(cost2);
}
/*
* Draws a wire sphere
*/
void FGAPIENTRY glutWireSphere(GLdouble radius, GLint slices, GLint stacks)
{
int i,j;
/* Adjust z and radius as stacks and slices are drawn. */
double r;
double x,y,z;
/* Pre-computed circle */
double *sint1,*cost1;
double *sint2,*cost2;
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutWireSphere" );
fghCircleTable(&sint1,&cost1,-slices );
fghCircleTable(&sint2,&cost2, stacks*2);
/* Draw a line loop for each stack */
for (i=1; i<stacks; i++)
{
z = cost2[i];
r = sint2[i];
glBegin(GL_LINE_LOOP);
for(j=0; j<=slices; j++)
{
x = cost1[j];
y = sint1[j];
glNormal3d(x,y,z);
glVertex3d(x*r*radius,y*r*radius,z*radius);
}
glEnd();
}
/* Draw a line loop for each slice */
for (i=0; i<slices; i++)
{
glBegin(GL_LINE_STRIP);
for(j=0; j<=stacks; j++)
{
x = cost1[i]*sint2[j];
y = sint1[i]*sint2[j];
z = cost2[j];
glNormal3d(x,y,z);
glVertex3d(x*radius,y*radius,z*radius);
}
glEnd();
}
/* Release sin and cos tables */
free(sint1);
free(cost1);
free(sint2);
free(cost2);
}
/*
* Draws a solid cone
*/
void FGAPIENTRY glutSolidCone( GLdouble base, GLdouble height, GLint slices, GLint stacks )
{
int i,j;
/* Step in z and radius as stacks are drawn. */
double z0,z1;
double r0,r1;
const double zStep = height / ( ( stacks > 0 ) ? stacks : 1 );
const double rStep = base / ( ( stacks > 0 ) ? stacks : 1 );
/* Scaling factors for vertex normals */
const double cosn = ( height / sqrt ( height * height + base * base ));
const double sinn = ( base / sqrt ( height * height + base * base ));
/* Pre-computed circle */
double *sint,*cost;
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutSolidCone" );
fghCircleTable(&sint,&cost,-slices);
/* Cover the circular base with a triangle fan... */
z0 = 0.0;
z1 = zStep;
r0 = base;
r1 = r0 - rStep;
glBegin(GL_TRIANGLE_FAN);
glNormal3d(0.0,0.0,-1.0);
glVertex3d(0.0,0.0, z0 );
for (j=0; j<=slices; j++)
glVertex3d(cost[j]*r0, sint[j]*r0, z0);
glEnd();
/* Cover each stack with a quad strip, except the top stack */
for( i=0; i<stacks-1; i++ )
{
glBegin(GL_QUAD_STRIP);
for(j=0; j<=slices; j++)
{
glNormal3d(cost[j]*sinn, sint[j]*sinn, cosn);
glVertex3d(cost[j]*r0, sint[j]*r0, z0 );
glVertex3d(cost[j]*r1, sint[j]*r1, z1 );
}
z0 = z1; z1 += zStep;
r0 = r1; r1 -= rStep;
glEnd();
}
/* The top stack is covered with individual triangles */
glBegin(GL_TRIANGLES);
glNormal3d(cost[0]*sinn, sint[0]*sinn, cosn);
for (j=0; j<slices; j++)
{
glVertex3d(cost[j+0]*r0, sint[j+0]*r0, z0 );
glVertex3d(0, 0, height);
glNormal3d(cost[j+1]*sinn, sint[j+1]*sinn, cosn );
glVertex3d(cost[j+1]*r0, sint[j+1]*r0, z0 );
}
glEnd();
/* Release sin and cos tables */
free(sint);
free(cost);
}
/*
* Draws a wire cone
*/
void FGAPIENTRY glutWireCone( GLdouble base, GLdouble height, GLint slices, GLint stacks)
{
int i,j;
/* Step in z and radius as stacks are drawn. */
double z = 0.0;
double r = base;
const double zStep = height / ( ( stacks > 0 ) ? stacks : 1 );
const double rStep = base / ( ( stacks > 0 ) ? stacks : 1 );
/* Scaling factors for vertex normals */
const double cosn = ( height / sqrt ( height * height + base * base ));
const double sinn = ( base / sqrt ( height * height + base * base ));
/* Pre-computed circle */
double *sint,*cost;
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutWireCone" );
fghCircleTable(&sint,&cost,-slices);
/* Draw the stacks... */
for (i=0; i<stacks; i++)
{
glBegin(GL_LINE_LOOP);
for( j=0; j<slices; j++ )
{
glNormal3d(cost[j]*sinn, sint[j]*sinn, cosn);
glVertex3d(cost[j]*r, sint[j]*r, z );
}
glEnd();
z += zStep;
r -= rStep;
}
/* Draw the slices */
r = base;
glBegin(GL_LINES);
for (j=0; j<slices; j++)
{
glNormal3d(cost[j]*sinn, sint[j]*sinn, cosn );
glVertex3d(cost[j]*r, sint[j]*r, 0.0 );
glVertex3d(0.0, 0.0, height);
}
glEnd();
/* Release sin and cos tables */
free(sint);
free(cost);
}
/*
* Draws a solid cylinder
*/
void FGAPIENTRY glutSolidCylinder(GLdouble radius, GLdouble height, GLint slices, GLint stacks)
{
int i,j;
/* Step in z and radius as stacks are drawn. */
double z0,z1;
const double zStep = height / ( ( stacks > 0 ) ? stacks : 1 );
/* Pre-computed circle */
double *sint,*cost;
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutSolidCylinder" );
fghCircleTable(&sint,&cost,-slices);
/* Cover the base and top */
glBegin(GL_TRIANGLE_FAN);
glNormal3d(0.0, 0.0, -1.0 );
glVertex3d(0.0, 0.0, 0.0 );
for (j=0; j<=slices; j++)
glVertex3d(cost[j]*radius, sint[j]*radius, 0.0);
glEnd();
glBegin(GL_TRIANGLE_FAN);
glNormal3d(0.0, 0.0, 1.0 );
glVertex3d(0.0, 0.0, height);
for (j=slices; j>=0; j--)
glVertex3d(cost[j]*radius, sint[j]*radius, height);
glEnd();
/* Do the stacks */
z0 = 0.0;
z1 = zStep;
for (i=1; i<=stacks; i++)
{
if (i==stacks)
z1 = height;
glBegin(GL_QUAD_STRIP);
for (j=0; j<=slices; j++ )
{
glNormal3d(cost[j], sint[j], 0.0 );
glVertex3d(cost[j]*radius, sint[j]*radius, z0 );
glVertex3d(cost[j]*radius, sint[j]*radius, z1 );
}
glEnd();
z0 = z1; z1 += zStep;
}
/* Release sin and cos tables */
free(sint);
free(cost);
}
/*
* Draws a wire cylinder
*/
void FGAPIENTRY glutWireCylinder(GLdouble radius, GLdouble height, GLint slices, GLint stacks)
{
int i,j;
/* Step in z and radius as stacks are drawn. */
double z = 0.0;
const double zStep = height / ( ( stacks > 0 ) ? stacks : 1 );
/* Pre-computed circle */
double *sint,*cost;
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutWireCylinder" );
fghCircleTable(&sint,&cost,-slices);
/* Draw the stacks... */
for (i=0; i<=stacks; i++)
{
if (i==stacks)
z = height;
glBegin(GL_LINE_LOOP);
for( j=0; j<slices; j++ )
{
glNormal3d(cost[j], sint[j], 0.0);
glVertex3d(cost[j]*radius, sint[j]*radius, z );
}
glEnd();
z += zStep;
}
/* Draw the slices */
glBegin(GL_LINES);
for (j=0; j<slices; j++)
{
glNormal3d(cost[j], sint[j], 0.0 );
glVertex3d(cost[j]*radius, sint[j]*radius, 0.0 );
glVertex3d(cost[j]*radius, sint[j]*radius, height);
}
glEnd();
/* Release sin and cos tables */
free(sint);
free(cost);
}
/*
* Draws a wire torus
*/
void FGAPIENTRY glutWireTorus( GLdouble dInnerRadius, GLdouble dOuterRadius, GLint nSides, GLint nRings )
{
double iradius = dInnerRadius, oradius = dOuterRadius, phi, psi, dpsi, dphi;
double *vertex, *normal;
int i, j;
double spsi, cpsi, sphi, cphi ;
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutWireTorus" );
if ( nSides < 1 ) nSides = 1;
if ( nRings < 1 ) nRings = 1;
/* Allocate the vertices array */
vertex = (double *)calloc( sizeof(double), 3 * nSides * nRings );
normal = (double *)calloc( sizeof(double), 3 * nSides * nRings );
glPushMatrix();
dpsi = 2.0 * M_PI / (double)nRings ;
dphi = -2.0 * M_PI / (double)nSides ;
psi = 0.0;
for( j=0; j<nRings; j++ )
{
cpsi = cos ( psi ) ;
spsi = sin ( psi ) ;
phi = 0.0;
for( i=0; i<nSides; i++ )
{
int offset = 3 * ( j * nSides + i ) ;
cphi = cos ( phi ) ;
sphi = sin ( phi ) ;
*(vertex + offset + 0) = cpsi * ( oradius + cphi * iradius ) ;
*(vertex + offset + 1) = spsi * ( oradius + cphi * iradius ) ;
*(vertex + offset + 2) = sphi * iradius ;
*(normal + offset + 0) = cpsi * cphi ;
*(normal + offset + 1) = spsi * cphi ;
*(normal + offset + 2) = sphi ;
phi += dphi;
}
psi += dpsi;
}
for( i=0; i<nSides; i++ )
{
glBegin( GL_LINE_LOOP );
for( j=0; j<nRings; j++ )
{
int offset = 3 * ( j * nSides + i ) ;
glNormal3dv( normal + offset );
glVertex3dv( vertex + offset );
}
glEnd();
}
for( j=0; j<nRings; j++ )
{
glBegin(GL_LINE_LOOP);
for( i=0; i<nSides; i++ )
{
int offset = 3 * ( j * nSides + i ) ;
glNormal3dv( normal + offset );
glVertex3dv( vertex + offset );
}
glEnd();
}
free ( vertex ) ;
free ( normal ) ;
glPopMatrix();
}
/*
* Draws a solid torus
*/
void FGAPIENTRY glutSolidTorus( GLdouble dInnerRadius, GLdouble dOuterRadius, GLint nSides, GLint nRings )
{
double iradius = dInnerRadius, oradius = dOuterRadius, phi, psi, dpsi, dphi;
double *vertex, *normal;
int i, j;
double spsi, cpsi, sphi, cphi ;
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutSolidTorus" );
if ( nSides < 1 ) nSides = 1;
if ( nRings < 1 ) nRings = 1;
/* Increment the number of sides and rings to allow for one more point than surface */
nSides ++ ;
nRings ++ ;
/* Allocate the vertices array */
vertex = (double *)calloc( sizeof(double), 3 * nSides * nRings );
normal = (double *)calloc( sizeof(double), 3 * nSides * nRings );
glPushMatrix();
dpsi = 2.0 * M_PI / (double)(nRings - 1) ;
dphi = -2.0 * M_PI / (double)(nSides - 1) ;
psi = 0.0;
for( j=0; j<nRings; j++ )
{
cpsi = cos ( psi ) ;
spsi = sin ( psi ) ;
phi = 0.0;
for( i=0; i<nSides; i++ )
{
int offset = 3 * ( j * nSides + i ) ;
cphi = cos ( phi ) ;
sphi = sin ( phi ) ;
*(vertex + offset + 0) = cpsi * ( oradius + cphi * iradius ) ;
*(vertex + offset + 1) = spsi * ( oradius + cphi * iradius ) ;
*(vertex + offset + 2) = sphi * iradius ;
*(normal + offset + 0) = cpsi * cphi ;
*(normal + offset + 1) = spsi * cphi ;
*(normal + offset + 2) = sphi ;
phi += dphi;
}
psi += dpsi;
}
glBegin( GL_QUADS );
for( i=0; i<nSides-1; i++ )
{
for( j=0; j<nRings-1; j++ )
{
int offset = 3 * ( j * nSides + i ) ;
glNormal3dv( normal + offset );
glVertex3dv( vertex + offset );
glNormal3dv( normal + offset + 3 );
glVertex3dv( vertex + offset + 3 );
glNormal3dv( normal + offset + 3 * nSides + 3 );
glVertex3dv( vertex + offset + 3 * nSides + 3 );
glNormal3dv( normal + offset + 3 * nSides );
glVertex3dv( vertex + offset + 3 * nSides );
}
}
glEnd();
free ( vertex ) ;
free ( normal ) ;
glPopMatrix();
}
/*
*
*/
void FGAPIENTRY glutWireDodecahedron( void )
{
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutWireDodecahedron" );
/* Magic Numbers: It is possible to create a dodecahedron by attaching two pentagons to each face of
* of a cube. The coordinates of the points are:
* (+-x,0, z); (+-1, 1, 1); (0, z, x )
* where x = (-1 + sqrt(5))/2, z = (1 + sqrt(5))/2 or
* x = 0.61803398875 and z = 1.61803398875.
*/
glBegin ( GL_LINE_LOOP ) ;
glNormal3d ( 0.0, 0.525731112119, 0.850650808354 ) ; glVertex3d ( 0.0, 1.61803398875, 0.61803398875 ) ; glVertex3d ( -1.0, 1.0, 1.0 ) ; glVertex3d ( -0.61803398875, 0.0, 1.61803398875 ) ; glVertex3d ( 0.61803398875, 0.0, 1.61803398875 ) ; glVertex3d ( 1.0, 1.0, 1.0 ) ;
glEnd () ;
glBegin ( GL_LINE_LOOP ) ;
glNormal3d ( 0.0, 0.525731112119, -0.850650808354 ) ; glVertex3d ( 0.0, 1.61803398875, -0.61803398875 ) ; glVertex3d ( 1.0, 1.0, -1.0 ) ; glVertex3d ( 0.61803398875, 0.0, -1.61803398875 ) ; glVertex3d ( -0.61803398875, 0.0, -1.61803398875 ) ; glVertex3d ( -1.0, 1.0, -1.0 ) ;
glEnd () ;
glBegin ( GL_LINE_LOOP ) ;
glNormal3d ( 0.0, -0.525731112119, 0.850650808354 ) ; glVertex3d ( 0.0, -1.61803398875, 0.61803398875 ) ; glVertex3d ( 1.0, -1.0, 1.0 ) ; glVertex3d ( 0.61803398875, 0.0, 1.61803398875 ) ; glVertex3d ( -0.61803398875, 0.0, 1.61803398875 ) ; glVertex3d ( -1.0, -1.0, 1.0 ) ;
glEnd () ;
glBegin ( GL_LINE_LOOP ) ;
glNormal3d ( 0.0, -0.525731112119, -0.850650808354 ) ; glVertex3d ( 0.0, -1.61803398875, -0.61803398875 ) ; glVertex3d ( -1.0, -1.0, -1.0 ) ; glVertex3d ( -0.61803398875, 0.0, -1.61803398875 ) ; glVertex3d ( 0.61803398875, 0.0, -1.61803398875 ) ; glVertex3d ( 1.0, -1.0, -1.0 ) ;
glEnd () ;
glBegin ( GL_LINE_LOOP ) ;
glNormal3d ( 0.850650808354, 0.0, 0.525731112119 ) ; glVertex3d ( 0.61803398875, 0.0, 1.61803398875 ) ; glVertex3d ( 1.0, -1.0, 1.0 ) ; glVertex3d ( 1.61803398875, -0.61803398875, 0.0 ) ; glVertex3d ( 1.61803398875, 0.61803398875, 0.0 ) ; glVertex3d ( 1.0, 1.0, 1.0 ) ;
glEnd () ;
glBegin ( GL_LINE_LOOP ) ;
glNormal3d ( -0.850650808354, 0.0, 0.525731112119 ) ; glVertex3d ( -0.61803398875, 0.0, 1.61803398875 ) ; glVertex3d ( -1.0, 1.0, 1.0 ) ; glVertex3d ( -1.61803398875, 0.61803398875, 0.0 ) ; glVertex3d ( -1.61803398875, -0.61803398875, 0.0 ) ; glVertex3d ( -1.0, -1.0, 1.0 ) ;
glEnd () ;
glBegin ( GL_LINE_LOOP ) ;
glNormal3d ( 0.850650808354, 0.0, -0.525731112119 ) ; glVertex3d ( 0.61803398875, 0.0, -1.61803398875 ) ; glVertex3d ( 1.0, 1.0, -1.0 ) ; glVertex3d ( 1.61803398875, 0.61803398875, 0.0 ) ; glVertex3d ( 1.61803398875, -0.61803398875, 0.0 ) ; glVertex3d ( 1.0, -1.0, -1.0 ) ;
glEnd () ;
glBegin ( GL_LINE_LOOP ) ;
glNormal3d ( -0.850650808354, 0.0, -0.525731112119 ) ; glVertex3d ( -0.61803398875, 0.0, -1.61803398875 ) ; glVertex3d ( -1.0, -1.0, -1.0 ) ; glVertex3d ( -1.61803398875, -0.61803398875, 0.0 ) ; glVertex3d ( -1.61803398875, 0.61803398875, 0.0 ) ; glVertex3d ( -1.0, 1.0, -1.0 ) ;
glEnd () ;
glBegin ( GL_LINE_LOOP ) ;
glNormal3d ( 0.525731112119, 0.850650808354, 0.0 ) ; glVertex3d ( 1.61803398875, 0.61803398875, 0.0 ) ; glVertex3d ( 1.0, 1.0, -1.0 ) ; glVertex3d ( 0.0, 1.61803398875, -0.61803398875 ) ; glVertex3d ( 0.0, 1.61803398875, 0.61803398875 ) ; glVertex3d ( 1.0, 1.0, 1.0 ) ;
glEnd () ;
glBegin ( GL_LINE_LOOP ) ;
glNormal3d ( 0.525731112119, -0.850650808354, 0.0 ) ; glVertex3d ( 1.61803398875, -0.61803398875, 0.0 ) ; glVertex3d ( 1.0, -1.0, 1.0 ) ; glVertex3d ( 0.0, -1.61803398875, 0.61803398875 ) ; glVertex3d ( 0.0, -1.61803398875, -0.61803398875 ) ; glVertex3d ( 1.0, -1.0, -1.0 ) ;
glEnd () ;
glBegin ( GL_LINE_LOOP ) ;
glNormal3d ( -0.525731112119, 0.850650808354, 0.0 ) ; glVertex3d ( -1.61803398875, 0.61803398875, 0.0 ) ; glVertex3d ( -1.0, 1.0, 1.0 ) ; glVertex3d ( 0.0, 1.61803398875, 0.61803398875 ) ; glVertex3d ( 0.0, 1.61803398875, -0.61803398875 ) ; glVertex3d ( -1.0, 1.0, -1.0 ) ;
glEnd () ;
glBegin ( GL_LINE_LOOP ) ;
glNormal3d ( -0.525731112119, -0.850650808354, 0.0 ) ; glVertex3d ( -1.61803398875, -0.61803398875, 0.0 ) ; glVertex3d ( -1.0, -1.0, -1.0 ) ; glVertex3d ( 0.0, -1.61803398875, -0.61803398875 ) ; glVertex3d ( 0.0, -1.61803398875, 0.61803398875 ) ; glVertex3d ( -1.0, -1.0, 1.0 ) ;
glEnd () ;
}
/*
*
*/
void FGAPIENTRY glutSolidDodecahedron( void )
{
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutSolidDodecahedron" );
/* Magic Numbers: It is possible to create a dodecahedron by attaching two pentagons to each face of
* of a cube. The coordinates of the points are:
* (+-x,0, z); (+-1, 1, 1); (0, z, x )
* where x = (-1 + sqrt(5))/2, z = (1 + sqrt(5))/2 or
* x = 0.61803398875 and z = 1.61803398875.
*/
glBegin ( GL_POLYGON ) ;
glNormal3d ( 0.0, 0.525731112119, 0.850650808354 ) ; glVertex3d ( 0.0, 1.61803398875, 0.61803398875 ) ; glVertex3d ( -1.0, 1.0, 1.0 ) ; glVertex3d ( -0.61803398875, 0.0, 1.61803398875 ) ; glVertex3d ( 0.61803398875, 0.0, 1.61803398875 ) ; glVertex3d ( 1.0, 1.0, 1.0 ) ;
glEnd () ;
glBegin ( GL_POLYGON ) ;
glNormal3d ( 0.0, 0.525731112119, -0.850650808354 ) ; glVertex3d ( 0.0, 1.61803398875, -0.61803398875 ) ; glVertex3d ( 1.0, 1.0, -1.0 ) ; glVertex3d ( 0.61803398875, 0.0, -1.61803398875 ) ; glVertex3d ( -0.61803398875, 0.0, -1.61803398875 ) ; glVertex3d ( -1.0, 1.0, -1.0 ) ;
glEnd () ;
glBegin ( GL_POLYGON ) ;
glNormal3d ( 0.0, -0.525731112119, 0.850650808354 ) ; glVertex3d ( 0.0, -1.61803398875, 0.61803398875 ) ; glVertex3d ( 1.0, -1.0, 1.0 ) ; glVertex3d ( 0.61803398875, 0.0, 1.61803398875 ) ; glVertex3d ( -0.61803398875, 0.0, 1.61803398875 ) ; glVertex3d ( -1.0, -1.0, 1.0 ) ;
glEnd () ;
glBegin ( GL_POLYGON ) ;
glNormal3d ( 0.0, -0.525731112119, -0.850650808354 ) ; glVertex3d ( 0.0, -1.61803398875, -0.61803398875 ) ; glVertex3d ( -1.0, -1.0, -1.0 ) ; glVertex3d ( -0.61803398875, 0.0, -1.61803398875 ) ; glVertex3d ( 0.61803398875, 0.0, -1.61803398875 ) ; glVertex3d ( 1.0, -1.0, -1.0 ) ;
glEnd () ;
glBegin ( GL_POLYGON ) ;
glNormal3d ( 0.850650808354, 0.0, 0.525731112119 ) ; glVertex3d ( 0.61803398875, 0.0, 1.61803398875 ) ; glVertex3d ( 1.0, -1.0, 1.0 ) ; glVertex3d ( 1.61803398875, -0.61803398875, 0.0 ) ; glVertex3d ( 1.61803398875, 0.61803398875, 0.0 ) ; glVertex3d ( 1.0, 1.0, 1.0 ) ;
glEnd () ;
glBegin ( GL_POLYGON ) ;
glNormal3d ( -0.850650808354, 0.0, 0.525731112119 ) ; glVertex3d ( -0.61803398875, 0.0, 1.61803398875 ) ; glVertex3d ( -1.0, 1.0, 1.0 ) ; glVertex3d ( -1.61803398875, 0.61803398875, 0.0 ) ; glVertex3d ( -1.61803398875, -0.61803398875, 0.0 ) ; glVertex3d ( -1.0, -1.0, 1.0 ) ;
glEnd () ;
glBegin ( GL_POLYGON ) ;
glNormal3d ( 0.850650808354, 0.0, -0.525731112119 ) ; glVertex3d ( 0.61803398875, 0.0, -1.61803398875 ) ; glVertex3d ( 1.0, 1.0, -1.0 ) ; glVertex3d ( 1.61803398875, 0.61803398875, 0.0 ) ; glVertex3d ( 1.61803398875, -0.61803398875, 0.0 ) ; glVertex3d ( 1.0, -1.0, -1.0 ) ;
glEnd () ;
glBegin ( GL_POLYGON ) ;
glNormal3d ( -0.850650808354, 0.0, -0.525731112119 ) ; glVertex3d ( -0.61803398875, 0.0, -1.61803398875 ) ; glVertex3d ( -1.0, -1.0, -1.0 ) ; glVertex3d ( -1.61803398875, -0.61803398875, 0.0 ) ; glVertex3d ( -1.61803398875, 0.61803398875, 0.0 ) ; glVertex3d ( -1.0, 1.0, -1.0 ) ;
glEnd () ;
glBegin ( GL_POLYGON ) ;
glNormal3d ( 0.525731112119, 0.850650808354, 0.0 ) ; glVertex3d ( 1.61803398875, 0.61803398875, 0.0 ) ; glVertex3d ( 1.0, 1.0, -1.0 ) ; glVertex3d ( 0.0, 1.61803398875, -0.61803398875 ) ; glVertex3d ( 0.0, 1.61803398875, 0.61803398875 ) ; glVertex3d ( 1.0, 1.0, 1.0 ) ;
glEnd () ;
glBegin ( GL_POLYGON ) ;
glNormal3d ( 0.525731112119, -0.850650808354, 0.0 ) ; glVertex3d ( 1.61803398875, -0.61803398875, 0.0 ) ; glVertex3d ( 1.0, -1.0, 1.0 ) ; glVertex3d ( 0.0, -1.61803398875, 0.61803398875 ) ; glVertex3d ( 0.0, -1.61803398875, -0.61803398875 ) ; glVertex3d ( 1.0, -1.0, -1.0 ) ;
glEnd () ;
glBegin ( GL_POLYGON ) ;
glNormal3d ( -0.525731112119, 0.850650808354, 0.0 ) ; glVertex3d ( -1.61803398875, 0.61803398875, 0.0 ) ; glVertex3d ( -1.0, 1.0, 1.0 ) ; glVertex3d ( 0.0, 1.61803398875, 0.61803398875 ) ; glVertex3d ( 0.0, 1.61803398875, -0.61803398875 ) ; glVertex3d ( -1.0, 1.0, -1.0 ) ;
glEnd () ;
glBegin ( GL_POLYGON ) ;
glNormal3d ( -0.525731112119, -0.850650808354, 0.0 ) ; glVertex3d ( -1.61803398875, -0.61803398875, 0.0 ) ; glVertex3d ( -1.0, -1.0, -1.0 ) ; glVertex3d ( 0.0, -1.61803398875, -0.61803398875 ) ; glVertex3d ( 0.0, -1.61803398875, 0.61803398875 ) ; glVertex3d ( -1.0, -1.0, 1.0 ) ;
glEnd () ;
}
/*
*
*/
void FGAPIENTRY glutWireOctahedron( void )
{
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutWireOctahedron" );
#define RADIUS 1.0f
glBegin( GL_LINE_LOOP );
glNormal3d( 0.577350269189, 0.577350269189, 0.577350269189); glVertex3d( RADIUS, 0.0, 0.0 ); glVertex3d( 0.0, RADIUS, 0.0 ); glVertex3d( 0.0, 0.0, RADIUS );
glNormal3d( 0.577350269189, 0.577350269189,-0.577350269189); glVertex3d( RADIUS, 0.0, 0.0 ); glVertex3d( 0.0, 0.0,-RADIUS ); glVertex3d( 0.0, RADIUS, 0.0 );
glNormal3d( 0.577350269189,-0.577350269189, 0.577350269189); glVertex3d( RADIUS, 0.0, 0.0 ); glVertex3d( 0.0, 0.0, RADIUS ); glVertex3d( 0.0,-RADIUS, 0.0 );
glNormal3d( 0.577350269189,-0.577350269189,-0.577350269189); glVertex3d( RADIUS, 0.0, 0.0 ); glVertex3d( 0.0,-RADIUS, 0.0 ); glVertex3d( 0.0, 0.0,-RADIUS );
glNormal3d(-0.577350269189, 0.577350269189, 0.577350269189); glVertex3d(-RADIUS, 0.0, 0.0 ); glVertex3d( 0.0, 0.0, RADIUS ); glVertex3d( 0.0, RADIUS, 0.0 );
glNormal3d(-0.577350269189, 0.577350269189,-0.577350269189); glVertex3d(-RADIUS, 0.0, 0.0 ); glVertex3d( 0.0, RADIUS, 0.0 ); glVertex3d( 0.0, 0.0,-RADIUS );
glNormal3d(-0.577350269189,-0.577350269189, 0.577350269189); glVertex3d(-RADIUS, 0.0, 0.0 ); glVertex3d( 0.0,-RADIUS, 0.0 ); glVertex3d( 0.0, 0.0, RADIUS );
glNormal3d(-0.577350269189,-0.577350269189,-0.577350269189); glVertex3d(-RADIUS, 0.0, 0.0 ); glVertex3d( 0.0, 0.0,-RADIUS ); glVertex3d( 0.0,-RADIUS, 0.0 );
glEnd();
#undef RADIUS
}
/*
*
*/
void FGAPIENTRY glutSolidOctahedron( void )
{
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutSolidOctahedron" );
#define RADIUS 1.0f
glBegin( GL_TRIANGLES );
glNormal3d( 0.577350269189, 0.577350269189, 0.577350269189); glVertex3d( RADIUS, 0.0, 0.0 ); glVertex3d( 0.0, RADIUS, 0.0 ); glVertex3d( 0.0, 0.0, RADIUS );
glNormal3d( 0.577350269189, 0.577350269189,-0.577350269189); glVertex3d( RADIUS, 0.0, 0.0 ); glVertex3d( 0.0, 0.0,-RADIUS ); glVertex3d( 0.0, RADIUS, 0.0 );
glNormal3d( 0.577350269189,-0.577350269189, 0.577350269189); glVertex3d( RADIUS, 0.0, 0.0 ); glVertex3d( 0.0, 0.0, RADIUS ); glVertex3d( 0.0,-RADIUS, 0.0 );
glNormal3d( 0.577350269189,-0.577350269189,-0.577350269189); glVertex3d( RADIUS, 0.0, 0.0 ); glVertex3d( 0.0,-RADIUS, 0.0 ); glVertex3d( 0.0, 0.0,-RADIUS );
glNormal3d(-0.577350269189, 0.577350269189, 0.577350269189); glVertex3d(-RADIUS, 0.0, 0.0 ); glVertex3d( 0.0, 0.0, RADIUS ); glVertex3d( 0.0, RADIUS, 0.0 );
glNormal3d(-0.577350269189, 0.577350269189,-0.577350269189); glVertex3d(-RADIUS, 0.0, 0.0 ); glVertex3d( 0.0, RADIUS, 0.0 ); glVertex3d( 0.0, 0.0,-RADIUS );
glNormal3d(-0.577350269189,-0.577350269189, 0.577350269189); glVertex3d(-RADIUS, 0.0, 0.0 ); glVertex3d( 0.0,-RADIUS, 0.0 ); glVertex3d( 0.0, 0.0, RADIUS );
glNormal3d(-0.577350269189,-0.577350269189,-0.577350269189); glVertex3d(-RADIUS, 0.0, 0.0 ); glVertex3d( 0.0, 0.0,-RADIUS ); glVertex3d( 0.0,-RADIUS, 0.0 );
glEnd();
#undef RADIUS
}
/* Magic Numbers: r0 = ( 1, 0, 0 )
* r1 = ( -1/3, 2 sqrt(2) / 3, 0 )
* r2 = ( -1/3, -sqrt(2) / 3, sqrt(6) / 3 )
* r3 = ( -1/3, -sqrt(2) / 3, -sqrt(6) / 3 )
* |r0| = |r1| = |r2| = |r3| = 1
* Distance between any two points is 2 sqrt(6) / 3
*
* Normals: The unit normals are simply the negative of the coordinates of the point not on the surface.
*/
#define NUM_TETR_FACES 4
static GLdouble tet_r[4][3] = { { 1.0, 0.0, 0.0 },
{ -0.333333333333, 0.942809041582, 0.0 },
{ -0.333333333333, -0.471404520791, 0.816496580928 },
{ -0.333333333333, -0.471404520791, -0.816496580928 } } ;
static GLint tet_i[4][3] = /* Vertex indices */
{
{ 1, 3, 2 }, { 0, 2, 3 }, { 0, 3, 1 }, { 0, 1, 2 }
} ;
/*
*
*/
void FGAPIENTRY glutWireTetrahedron( void )
{
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutWireTetrahedron" );
glBegin( GL_LINE_LOOP ) ;
glNormal3d ( -tet_r[0][0], -tet_r[0][1], -tet_r[0][2] ) ; glVertex3dv ( tet_r[1] ) ; glVertex3dv ( tet_r[3] ) ; glVertex3dv ( tet_r[2] ) ;
glNormal3d ( -tet_r[1][0], -tet_r[1][1], -tet_r[1][2] ) ; glVertex3dv ( tet_r[0] ) ; glVertex3dv ( tet_r[2] ) ; glVertex3dv ( tet_r[3] ) ;
glNormal3d ( -tet_r[2][0], -tet_r[2][1], -tet_r[2][2] ) ; glVertex3dv ( tet_r[0] ) ; glVertex3dv ( tet_r[3] ) ; glVertex3dv ( tet_r[1] ) ;
glNormal3d ( -tet_r[3][0], -tet_r[3][1], -tet_r[3][2] ) ; glVertex3dv ( tet_r[0] ) ; glVertex3dv ( tet_r[1] ) ; glVertex3dv ( tet_r[2] ) ;
glEnd() ;
}
/*
*
*/
void FGAPIENTRY glutSolidTetrahedron( void )
{
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutSolidTetrahedron" );
glBegin( GL_TRIANGLES ) ;
glNormal3d ( -tet_r[0][0], -tet_r[0][1], -tet_r[0][2] ) ; glVertex3dv ( tet_r[1] ) ; glVertex3dv ( tet_r[3] ) ; glVertex3dv ( tet_r[2] ) ;
glNormal3d ( -tet_r[1][0], -tet_r[1][1], -tet_r[1][2] ) ; glVertex3dv ( tet_r[0] ) ; glVertex3dv ( tet_r[2] ) ; glVertex3dv ( tet_r[3] ) ;
glNormal3d ( -tet_r[2][0], -tet_r[2][1], -tet_r[2][2] ) ; glVertex3dv ( tet_r[0] ) ; glVertex3dv ( tet_r[3] ) ; glVertex3dv ( tet_r[1] ) ;
glNormal3d ( -tet_r[3][0], -tet_r[3][1], -tet_r[3][2] ) ; glVertex3dv ( tet_r[0] ) ; glVertex3dv ( tet_r[1] ) ; glVertex3dv ( tet_r[2] ) ;
glEnd() ;
}
/*
*
*/
static double icos_r[12][3] = {
{ 1.0, 0.0, 0.0 },
{ 0.447213595500, 0.894427191000, 0.0 },
{ 0.447213595500, 0.276393202252, 0.850650808354 },
{ 0.447213595500, -0.723606797748, 0.525731112119 },
{ 0.447213595500, -0.723606797748, -0.525731112119 },
{ 0.447213595500, 0.276393202252, -0.850650808354 },
{ -0.447213595500, -0.894427191000, 0.0 },
{ -0.447213595500, -0.276393202252, 0.850650808354 },
{ -0.447213595500, 0.723606797748, 0.525731112119 },
{ -0.447213595500, 0.723606797748, -0.525731112119 },
{ -0.447213595500, -0.276393202252, -0.850650808354 },
{ -1.0, 0.0, 0.0 }
};
static int icos_v [20][3] = {
{ 0, 1, 2 },
{ 0, 2, 3 },
{ 0, 3, 4 },
{ 0, 4, 5 },
{ 0, 5, 1 },
{ 1, 8, 2 },
{ 2, 7, 3 },
{ 3, 6, 4 },
{ 4, 10, 5 },
{ 5, 9, 1 },
{ 1, 9, 8 },
{ 2, 8, 7 },
{ 3, 7, 6 },
{ 4, 6, 10 },
{ 5, 10, 9 },
{ 11, 9, 10 },
{ 11, 8, 9 },
{ 11, 7, 8 },
{ 11, 6, 7 },
{ 11, 10, 6 }
};
void FGAPIENTRY glutWireIcosahedron( void )
{
int i ;
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutWireIcosahedron" );
for ( i = 0; i < 20; i++ )
{
double normal[3] ;
normal[0] = ( icos_r[icos_v[i][1]][1] - icos_r[icos_v[i][0]][1] ) * ( icos_r[icos_v[i][2]][2] - icos_r[icos_v[i][0]][2] ) - ( icos_r[icos_v[i][1]][2] - icos_r[icos_v[i][0]][2] ) * ( icos_r[icos_v[i][2]][1] - icos_r[icos_v[i][0]][1] ) ;
normal[1] = ( icos_r[icos_v[i][1]][2] - icos_r[icos_v[i][0]][2] ) * ( icos_r[icos_v[i][2]][0] - icos_r[icos_v[i][0]][0] ) - ( icos_r[icos_v[i][1]][0] - icos_r[icos_v[i][0]][0] ) * ( icos_r[icos_v[i][2]][2] - icos_r[icos_v[i][0]][2] ) ;
normal[2] = ( icos_r[icos_v[i][1]][0] - icos_r[icos_v[i][0]][0] ) * ( icos_r[icos_v[i][2]][1] - icos_r[icos_v[i][0]][1] ) - ( icos_r[icos_v[i][1]][1] - icos_r[icos_v[i][0]][1] ) * ( icos_r[icos_v[i][2]][0] - icos_r[icos_v[i][0]][0] ) ;
glBegin ( GL_LINE_LOOP ) ;
glNormal3dv ( normal ) ;
glVertex3dv ( icos_r[icos_v[i][0]] ) ;
glVertex3dv ( icos_r[icos_v[i][1]] ) ;
glVertex3dv ( icos_r[icos_v[i][2]] ) ;
glEnd () ;
}
}
/*
*
*/
void FGAPIENTRY glutSolidIcosahedron( void )
{
int i ;
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutSolidIcosahedron" );
glBegin ( GL_TRIANGLES ) ;
for ( i = 0; i < 20; i++ )
{
double normal[3] ;
normal[0] = ( icos_r[icos_v[i][1]][1] - icos_r[icos_v[i][0]][1] ) * ( icos_r[icos_v[i][2]][2] - icos_r[icos_v[i][0]][2] ) - ( icos_r[icos_v[i][1]][2] - icos_r[icos_v[i][0]][2] ) * ( icos_r[icos_v[i][2]][1] - icos_r[icos_v[i][0]][1] ) ;
normal[1] = ( icos_r[icos_v[i][1]][2] - icos_r[icos_v[i][0]][2] ) * ( icos_r[icos_v[i][2]][0] - icos_r[icos_v[i][0]][0] ) - ( icos_r[icos_v[i][1]][0] - icos_r[icos_v[i][0]][0] ) * ( icos_r[icos_v[i][2]][2] - icos_r[icos_v[i][0]][2] ) ;
normal[2] = ( icos_r[icos_v[i][1]][0] - icos_r[icos_v[i][0]][0] ) * ( icos_r[icos_v[i][2]][1] - icos_r[icos_v[i][0]][1] ) - ( icos_r[icos_v[i][1]][1] - icos_r[icos_v[i][0]][1] ) * ( icos_r[icos_v[i][2]][0] - icos_r[icos_v[i][0]][0] ) ;
glNormal3dv ( normal ) ;
glVertex3dv ( icos_r[icos_v[i][0]] ) ;
glVertex3dv ( icos_r[icos_v[i][1]] ) ;
glVertex3dv ( icos_r[icos_v[i][2]] ) ;
}
glEnd () ;
}
/*
*
*/
static double rdod_r[14][3] = {
{ 0.0, 0.0, 1.0 },
{ 0.707106781187, 0.000000000000, 0.5 },
{ 0.000000000000, 0.707106781187, 0.5 },
{ -0.707106781187, 0.000000000000, 0.5 },
{ 0.000000000000, -0.707106781187, 0.5 },
{ 0.707106781187, 0.707106781187, 0.0 },
{ -0.707106781187, 0.707106781187, 0.0 },
{ -0.707106781187, -0.707106781187, 0.0 },
{ 0.707106781187, -0.707106781187, 0.0 },
{ 0.707106781187, 0.000000000000, -0.5 },
{ 0.000000000000, 0.707106781187, -0.5 },
{ -0.707106781187, 0.000000000000, -0.5 },
{ 0.000000000000, -0.707106781187, -0.5 },
{ 0.0, 0.0, -1.0 }
} ;
static int rdod_v [12][4] = {
{ 0, 1, 5, 2 },
{ 0, 2, 6, 3 },
{ 0, 3, 7, 4 },
{ 0, 4, 8, 1 },
{ 5, 10, 6, 2 },
{ 6, 11, 7, 3 },
{ 7, 12, 8, 4 },
{ 8, 9, 5, 1 },
{ 5, 9, 13, 10 },
{ 6, 10, 13, 11 },
{ 7, 11, 13, 12 },
{ 8, 12, 13, 9 }
};
static double rdod_n[12][3] = {
{ 0.353553390594, 0.353553390594, 0.5 },
{ -0.353553390594, 0.353553390594, 0.5 },
{ -0.353553390594, -0.353553390594, 0.5 },
{ 0.353553390594, -0.353553390594, 0.5 },
{ 0.000000000000, 1.000000000000, 0.0 },
{ -1.000000000000, 0.000000000000, 0.0 },
{ 0.000000000000, -1.000000000000, 0.0 },
{ 1.000000000000, 0.000000000000, 0.0 },
{ 0.353553390594, 0.353553390594, -0.5 },
{ -0.353553390594, 0.353553390594, -0.5 },
{ -0.353553390594, -0.353553390594, -0.5 },
{ 0.353553390594, -0.353553390594, -0.5 }
};
void FGAPIENTRY glutWireRhombicDodecahedron( void )
{
int i ;
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutWireRhombicDodecahedron" );
for ( i = 0; i < 12; i++ )
{
glBegin ( GL_LINE_LOOP ) ;
glNormal3dv ( rdod_n[i] ) ;
glVertex3dv ( rdod_r[rdod_v[i][0]] ) ;
glVertex3dv ( rdod_r[rdod_v[i][1]] ) ;
glVertex3dv ( rdod_r[rdod_v[i][2]] ) ;
glVertex3dv ( rdod_r[rdod_v[i][3]] ) ;
glEnd () ;
}
}
/*
*
*/
void FGAPIENTRY glutSolidRhombicDodecahedron( void )
{
int i ;
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutSolidRhombicDodecahedron" );
glBegin ( GL_QUADS ) ;
for ( i = 0; i < 12; i++ )
{
glNormal3dv ( rdod_n[i] ) ;
glVertex3dv ( rdod_r[rdod_v[i][0]] ) ;
glVertex3dv ( rdod_r[rdod_v[i][1]] ) ;
glVertex3dv ( rdod_r[rdod_v[i][2]] ) ;
glVertex3dv ( rdod_r[rdod_v[i][3]] ) ;
}
glEnd () ;
}
void FGAPIENTRY glutWireSierpinskiSponge ( int num_levels, GLdouble offset[3], GLdouble scale )
{
int i, j ;
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutWireSierpinskiSponge" );
if ( num_levels == 0 )
{
for ( i = 0 ; i < NUM_TETR_FACES ; i++ )
{
glBegin ( GL_LINE_LOOP ) ;
glNormal3d ( -tet_r[i][0], -tet_r[i][1], -tet_r[i][2] ) ;
for ( j = 0; j < 3; j++ )
{
double x = offset[0] + scale * tet_r[tet_i[i][j]][0] ;
double y = offset[1] + scale * tet_r[tet_i[i][j]][1] ;
double z = offset[2] + scale * tet_r[tet_i[i][j]][2] ;
glVertex3d ( x, y, z ) ;
}
glEnd () ;
}
}
else if ( num_levels > 0 )
{
GLdouble local_offset[3] ; /* Use a local variable to avoid buildup of roundoff errors */
num_levels -- ;
scale /= 2.0 ;
for ( i = 0 ; i < NUM_TETR_FACES ; i++ )
{
local_offset[0] = offset[0] + scale * tet_r[i][0] ;
local_offset[1] = offset[1] + scale * tet_r[i][1] ;
local_offset[2] = offset[2] + scale * tet_r[i][2] ;
glutWireSierpinskiSponge ( num_levels, local_offset, scale ) ;
}
}
}
void FGAPIENTRY glutSolidSierpinskiSponge ( int num_levels, GLdouble offset[3], GLdouble scale )
{
int i, j ;
FREEGLUT_EXIT_IF_NOT_INITIALISED ( "glutSolidSierpinskiSponge" );
if ( num_levels == 0 )
{
glBegin ( GL_TRIANGLES ) ;
for ( i = 0 ; i < NUM_TETR_FACES ; i++ )
{
glNormal3d ( -tet_r[i][0], -tet_r[i][1], -tet_r[i][2] ) ;
for ( j = 0; j < 3; j++ )
{
double x = offset[0] + scale * tet_r[tet_i[i][j]][0] ;
double y = offset[1] + scale * tet_r[tet_i[i][j]][1] ;
double z = offset[2] + scale * tet_r[tet_i[i][j]][2] ;
glVertex3d ( x, y, z ) ;
}
}
glEnd () ;
}
else if ( num_levels > 0 )
{
GLdouble local_offset[3] ; /* Use a local variable to avoid buildup of roundoff errors */
num_levels -- ;
scale /= 2.0 ;
for ( i = 0 ; i < NUM_TETR_FACES ; i++ )
{
local_offset[0] = offset[0] + scale * tet_r[i][0] ;
local_offset[1] = offset[1] + scale * tet_r[i][1] ;
local_offset[2] = offset[2] + scale * tet_r[i][2] ;
glutSolidSierpinskiSponge ( num_levels, local_offset, scale ) ;
}
}
}
/*** END OF FILE ***/
