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<pre class="sourcecodebox">//---------------------------------------------------------------------------
//
// File: KleinSurface.mm
//
// Abstract: Klein surface geometry class
// Based on the work by Philip Rideout ((C) 2002-2006 3Dlabs Inc.)
//
// Disclaimer: IMPORTANT: This Apple software is supplied to you by
// Inc. ("Apple") in consideration of your agreement to the following terms,
// and your use, installation, modification or redistribution of this Apple
// software constitutes acceptance of these terms. If you do not agree with
// these terms, please do not use, install, modify or redistribute this
// Apple software.
//
// In consideration of your agreement to abide by the following terms, and
// subject to these terms, Apple grants you a personal, non-exclusive
// license, under Apple's copyrights in this original Apple software (the
// "Apple Software"), to use, reproduce, modify and redistribute the Apple
// Software, with or without modifications, in source and/or binary forms;
// provided that if you redistribute the Apple Software in its entirety and
// without modifications, you must retain this notice and the following
// text and disclaimers in all such redistributions of the Apple Software.
// Neither the name, trademarks, service marks or logos of Apple Inc. may
// be used to endorse or promote products derived from the Apple Software
// without specific prior written permission from Apple. Except as
// expressly stated in this notice, no other rights or licenses, express
// or implied, are granted by Apple herein, including but not limited to
// any patent rights that may be infringed by your derivative works or by
// other works in which the Apple Software may be incorporated.
//
// The Apple Software is provided by Apple on an "AS IS" basis. APPLE
// MAKES NO WARRANTIES, EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION
// THE IMPLIED WARRANTIES OF NON-INFRINGEMENT, MERCHANTABILITY AND FITNESS
// FOR A PARTICULAR PURPOSE, REGARDING THE APPLE SOFTWARE OR ITS USE AND
// OPERATION ALONE OR IN COMBINATION WITH YOUR PRODUCTS.
//
// IN NO EVENT SHALL APPLE BE LIABLE FOR ANY SPECIAL, INDIRECT, INCIDENTAL
// OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) ARISING IN ANY WAY OUT OF THE USE, REPRODUCTION,
// MODIFICATION AND/OR DISTRIBUTION OF THE APPLE SOFTWARE, HOWEVER CAUSED
// AND WHETHER UNDER THEORY OF CONTRACT, TORT (INCLUDING NEGLIGENCE),
// STRICT LIABILITY OR OTHERWISE, EVEN IF APPLE HAS BEEN ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
// Copyright (c) 2004-2007 Apple Inc., All rights reserved.
//
//---------------------------------------------------------------------------
//------------------------------------------------------------------------
//------------------------------------------------------------------------
#include <cmath>
//------------------------------------------------------------------------
#include "GeometryConstants.h"
//------------------------------------------------------------------------
#include "Vector3.hpp"
//------------------------------------------------------------------------
#import "KleinSurface.h"
//------------------------------------------------------------------------
//------------------------------------------------------------------------
static const GLfloat kEpsilon = 0.00001f;
//------------------------------------------------------------------------
//------------------------------------------------------------------------
typedef struct
{
FVector3 p[4];
FVector3 normal;
} Vertex;
//------------------------------------------------------------------------
//-------------------------------------------------------------------------
static void KleinSurfaceCompute( FVector2& domain, FVector3& range )
{
GLfloat u = (1 - domain.u) * kTwoPi;
GLfloat v = domain.v * kTwoPi;
GLfloat x0 = 3 * cosf(u) * (1 + sinf(u)) + (2 * (1 - cosf(u) / 2)) * cosf(u) * cosf(v);
GLfloat y0 = 8 * sinf(u) + (2 * (1 - cosf(u) / 2)) * sinf(u) * cosf(v);
GLfloat x1 = 3 * cosf(u) * (1 + sinf(u)) + (2 * (1 - cosf(u) / 2)) * cosf(v + kPi);
GLfloat y1 = 8 * sinf(u);
range.x = u < kPi ? x0 : x1;
range.y = u < kPi ? y0 : y1;
range.z = (2 * (1 - cosf(u) / 2)) * sinf(v);
range = range / 10;
range.y = -range.y;
// Tweak the texture coordinates.
domain.u *= 4;
} // KleinSurfaceCompute
//-------------------------------------------------------------------------
//
// Flip the normals along a segment of the Klein bottle so that we don't
// need two-sided lighting.
//
//-------------------------------------------------------------------------
static inline bool KleinSurfaceFlipNormals(const GLfloat u)
{
return (u < .125);
} // KleinSurfaceFlipNormals
//-------------------------------------------------------------------------
static void GetKleinSurfaceVertex(const bool flippedKleinSurface, GLfloat du, GLfloat dv, FVector2& domain, Vertex& vKlein)
{
GLfloat u = domain.u;
GLfloat v = domain.v;
KleinSurfaceCompute(domain, vKlein.p[0]);
FVector2 z1(u + du/2, v);
KleinSurfaceCompute(z1, vKlein.p[1]);
FVector2 z2(u + du/2 + du, v);
KleinSurfaceCompute(z2, vKlein.p[3]);
if (flippedKleinSurface)
{
FVector2 z3(u + du/2, v - dv);
KleinSurfaceCompute(z3, vKlein.p[2]);
} // if
else
{
FVector2 z4(u + du/2, v + dv);
KleinSurfaceCompute(z4, vKlein.p[2]);
} // else
} // GetKleinSurfaceVertex
//-------------------------------------------------------------------------
static void SetKleinSurfaceVertexAttributes(Vertex& vKlein)
{
GLint tangentLoc = -1;
GLint binormalLoc = -1;
FVector3 tangent = vKlein.p[3] - vKlein.p[1];
FVector3 binormal = vKlein.p[2] - vKlein.p[1];
vKlein.normal = tangent ^ binormal; // Exterior cross product
if (vKlein.normal.magnitude() < kEpsilon)
{
vKlein.normal = vKlein.p[0];
} // if
vKlein.normal.normalize();
if (tangent.magnitude() < kEpsilon)
{
tangent = binormal ^ vKlein.normal; // Exterior cross product
} // if
tangent.normalize();
glVertexAttrib3fv(tangentLoc, tangent.getVector().V);
binormal.normalize();
binormal = -binormal;
glVertexAttrib3fv( binormalLoc, binormal.getVector().V);
} // SetKleinSurfaceVertexAttributes
//-------------------------------------------------------------------------
static void NewKleinSurfaceVertex(FVector2& domain, Vertex& vKlein)
{
FPosition2 w = domain.getVector();
glNormal3fv( vKlein.normal.getVector().V );
glTexCoord2f( w.s, w.t );
glVertex3fv( vKlein.p[0].getVector().V );
} // NewKleinSurfaceVertex
//-------------------------------------------------------------------------
//
// Send out a normal, texture coordinate, vertex coordinate, and an
// optional custom attribute.
//
//-------------------------------------------------------------------------
static void KleinSurfaceGetVertex(const bool flippedKleinSurface, GLfloat du, GLfloat dv, FVector2& domain)
{
Vertex vKlein;
GetKleinSurfaceVertex(flippedKleinSurface, du, dv, domain, vKlein);
SetKleinSurfaceVertexAttributes(vKlein);
NewKleinSurfaceVertex(domain, vKlein);
} // KleinSurfaceGetVertex
//-------------------------------------------------------------------------
static GLuint KleinSurfaceNewDisplayList(GLint tessellationFactor)
{
GLuint displayList;
GLint stacks = tessellationFactor / 2;
GLfloat u;
GLfloat v;
GLfloat du = 1.0f / (GLfloat) tessellationFactor;
GLfloat dv = 1.0f / (GLfloat) stacks;
bool flippedKleinSurface;
displayList = glGenLists(1);
glNewList(displayList, GL_COMPILE);
for (u = 0; u < 1 - du / 2; u += du)
{
glBegin(GL_QUAD_STRIP);
flippedKleinSurface = KleinSurfaceFlipNormals(u);
if ( flippedKleinSurface )
{
for (v = 0; v < 1 + dv / 2; v += dv)
{
FVector2 domain1(u + du, v);
FVector2 domain2(u, v);
KleinSurfaceGetVertex(flippedKleinSurface, du, dv, domain1);
KleinSurfaceGetVertex(flippedKleinSurface, du, dv, domain2);
} // for
} // if
else
{
for (v = 0; v < 1 + dv / 2; v += dv)
{
FVector2 domain1(u, v);
FVector2 domain2(u + du, v);
KleinSurfaceGetVertex(flippedKleinSurface, du, dv, domain1);
KleinSurfaceGetVertex(flippedKleinSurface, du, dv, domain2);
} // for
} // else
glEnd();
} // for
glEndList();
return displayList;
} // KleinSurfaceNewDisplayList
//-------------------------------------------------------------------------
//------------------------------------------------------------------------
static void GetKleinSurfaceDisplayList(const GLint tessellationFactor, GLuint *displayList)
{
// Delete existing list
if(*displayList)
{
glDeleteLists(*displayList, 1);
*displayList = 0;
} // if
// Now get the display list
*displayList = KleinSurfaceNewDisplayList(tessellationFactor);
} // GetSurfaceGeometryDisplayList
//------------------------------------------------------------------------
//------------------------------------------------------------------------
@implementation KleinSurface
//------------------------------------------------------------------------
-(id) init
{
tessellationFactor = 35;
displayList = 0;
return self;
} // init
//------------------------------------------------------------------------
- (void) setTessellationFactor:(GLint)theTessellationFactor
{
tessellationFactor = theTessellationFactor;
} // setTessellationFactor
//------------------------------------------------------------------------
- (GLuint) getDisplayList
{
GetKleinSurfaceDisplayList(tessellationFactor, &displayList);
return displayList;
} // getDisplayList
//------------------------------------------------------------------------
- (void) dealloc
{
// delete the last used display list
if(displayList)
{
glDeleteLists(displayList, 1);
} // if
displayList = 0;
[super dealloc];
} // dealloc
//------------------------------------------------------------------------
@end
//------------------------------------------------------------------------
//------------------------------------------------------------------------
</pre>
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