Sources/Classes/Application/Model/OpenGL/Surfaces/Exotic Surfaces/OpenGLExoticSurface.mm
//--------------------------------------------------------------------------- |
// |
// File: OpenGLExoticSurface.mm |
// |
// Abstract: Exotic surface geometry class |
// |
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//--------------------------------------------------------------------------- |
// |
// Uses techniques described by Paul Bourke 1999 - 2002 |
// Tranguloid Trefoil and other example surfaces by Roger Bagula |
// see <http://astronomy.swin.edu.au/~pbourke/surfaces/> |
// |
//--------------------------------------------------------------------------- |
//------------------------------------------------------------------------ |
//------------------------------------------------------------------------ |
#import <cmath> |
#import <vector> |
//------------------------------------------------------------------------ |
#import "Vector3.h" |
//------------------------------------------------------------------------ |
#import "GeometryConstants.h" |
#import "OpenGLExoticSurface.h" |
//------------------------------------------------------------------------ |
//------------------------------------------------------------------------ |
typedef void (*OpenGLExoticSurfaceComputeFuncPtr)(GLdouble u, GLdouble v, Math::Vector3<GLdouble> &p); |
//------------------------------------------------------------------------ |
//------------------------------------------------------------------------ |
struct OpenGLExoticSurfaceVertex |
{ |
Math::Vector3<GLdouble> positions; |
Math::Vector3<GLdouble> normals; |
Math::Vector3<GLdouble> texCoords; |
}; |
typedef struct OpenGLExoticSurfaceVertex OpenGLExoticSurfaceVertex; |
//------------------------------------------------------------------------ |
typedef std::vector<OpenGLExoticSurfaceVertex> OpenGLExoticSurfaceVertices; |
//------------------------------------------------------------------------ |
struct OpenGLExoticSurfaceGeometry |
{ |
GLint mnRows; |
GLint mnColumns; |
OpenGLExoticSurfaceVertices m_Vertices; |
}; |
typedef struct OpenGLExoticSurfaceGeometry OpenGLExoticSurfaceGeometry; |
//------------------------------------------------------------------------ |
//------------------------------------------------------------------------ |
// |
// Note that -Pi <= u <= Pi and -Pi <= v <= Pi |
// |
//------------------------------------------------------------------------ |
static void OpenGLExoticSurfaceTranguloidTrefoil(GLdouble u, |
GLdouble v, |
Math::Vector3<GLdouble> &p) |
{ |
GLdouble t = v + kTwoPiThird; |
GLdouble w = 2.0 * u; |
GLdouble A = 2.0 + cos(t); |
GLdouble B = 2.0 + cos(v); |
p.x = 2.0 * sin(3.0 * u) / B; |
p.y = 2.0 * (sin(u) + 2.0 * sin(w)) / A; |
p.z = 0.25 * (cos(u) - 2.0 * cos(w)) * A * B; |
} // OpenGLExoticSurfaceTranguloidTrefoil |
//------------------------------------------------------------------------ |
static void OpenGLExoticSurfaceTriaxialTritorus(GLdouble u, |
GLdouble v, |
Math::Vector3<GLdouble> &p) |
{ |
p.x = 2.0 * sin(u) * (1.0 + cos(v)); |
p.y = 2.0 * sin(u + kTwoPiThird) * (1.0 + cos(v + kTwoPiThird)); |
p.z = 2.0 * sin(u + kFourPiThird) * (1.0 + cos(v + kFourPiThird)); |
} // OpenGLExoticSurfaceTriaxialTritorus |
//------------------------------------------------------------------------ |
static void OpenGLExoticSurfaceStiletto(GLdouble u, |
GLdouble v, |
Math::Vector3<GLdouble> &p) |
{ |
// reverse u and v for better distribution or points |
GLdouble s = u; |
GLdouble t = 0.0; |
GLdouble w = 0.0; |
u = v + kPi; |
v = 0.5 * (s + kPi); // convert to: 0 <= u <= 2 kPi, 0 <= v <= 2 kPi |
w = v + kTwoPiThird; |
t = pow(sin(w),2.0) * pow(cos(w),2.0); |
p.x = 4.0 * (2.0 + cos(u)) * pow(cos(v), 3.0) * sin(v); |
p.y = 4.0 * (2.0 + cos(u + kTwoPiThird)) * t; |
p.z = -4.0 * (2.0 + cos(u - kTwoPiThird)) * t; |
} // OpenGLExoticSurfaceStiletto |
//------------------------------------------------------------------------ |
static void OpenGLExoticSurfaceSlippers(GLdouble u, |
GLdouble v, |
Math::Vector3<GLdouble> &p) |
{ |
GLdouble w = u; |
GLdouble s = 0.0; |
GLdouble t = 0.0; |
u = v + kTwoPi; |
v = w + kPi; // convert to: 0 <= u <= 4 kPi, 0 <= v <= 2 kPi |
s = kTwoPiThird + v; |
t = kTwoPiThird - v; |
p.x = 4.0 * (2.0 + cos(u)) * pow(cos(v), 3.0) * sin(v); |
p.y = 4.0 * (2.0 + cos(u + kTwoPiThird)) * pow(cos(s), 2.0) * pow(sin(s), 2.0); |
p.z = -4.0 * (2.0 + cos(u - kTwoPiThird)) * pow(cos(t), 2.0) * pow(sin(t), 3.0); |
} // OpenGLExoticSurfaceSlippers |
//------------------------------------------------------------------------ |
static void OpenGLExoticSurfaceMaedersOwl(GLdouble u, |
GLdouble v, |
Math::Vector3<GLdouble> &p) |
{ |
GLdouble t = 0.0; |
GLdouble r = 0.0; |
GLdouble s = 0.0; |
u = 2.0 * (u + kPi); |
v = kTwoPiInv * (v + kPi); // convert to: 0 <= u <= 4 kPi, 0 <= v <= 1 |
t = 2.0 * u; |
r = 0.5 * v * v; |
s = 3.0 * v; |
p.x = s * cos(u) - r * cos(t); |
p.y = -s * sin(u) - r * sin(t); |
p.z = 4.0 * pow(v,1.5) * cos(1.5*u); |
} // OpenGLExoticSurfaceMaedersOwl |
//------------------------------------------------------------------------ |
static void OpenGLExoticSurfaceDefault(GLdouble u, |
GLdouble v, |
Math::Vector3<GLdouble> &p) |
{ |
p.x = 0.0; |
p.y = 0.0; |
p.z = 0.0; |
} // OpenGLExoticSurfaceDefault |
//------------------------------------------------------------------------ |
// |
// From a surface type, get a function pointer for computing parametric |
// values for a specific surface. |
// |
//------------------------------------------------------------------------ |
static OpenGLExoticSurfaceComputeFuncPtr OpenGLExoticSurfaceGetComputeFuncPtr(const OpenGLExoticSurfaceType surfaceType) |
{ |
OpenGLExoticSurfaceComputeFuncPtr glExoticSurfaceCompute = NULL; |
switch( surfaceType ) |
{ |
case kTranguloidTrefoil: |
glExoticSurfaceCompute = &OpenGLExoticSurfaceTranguloidTrefoil; |
break; |
case kTriaxialTritorus: |
glExoticSurfaceCompute = &OpenGLExoticSurfaceTriaxialTritorus; |
break; |
case kStilettoSurface: |
glExoticSurfaceCompute = &OpenGLExoticSurfaceStiletto; |
break; |
case kSlipperSurface: |
glExoticSurfaceCompute = &OpenGLExoticSurfaceSlippers; |
break; |
case kMaedersOwlSurface: |
glExoticSurfaceCompute = &OpenGLExoticSurfaceMaedersOwl; |
break; |
case kDefaultSurface: |
default: |
glExoticSurfaceCompute = &OpenGLExoticSurfaceDefault; |
break; |
} // switch |
return glExoticSurfaceCompute; |
} // OpenGLExoticSurfaceGetComputeFuncPtr |
//------------------------------------------------------------------------ |
static void OpenGLExoticSurfaceCreateWithType(const OpenGLExoticSurfaceType surfaceType, |
OpenGLExoticSurfaceGeometry *geometry) |
{ |
GLint i; |
GLint j; |
GLint maxI = geometry->mnRows; |
GLint maxJ = geometry->mnColumns; |
GLdouble invMaxI = 1.0 / (GLdouble)maxI; |
GLdouble invMaxJ = 1.0 / (GLdouble)maxJ; |
GLdouble u[2] = { 0.0, 0.0 }; |
GLdouble delta = 0.0005; |
Math::Vector3<GLdouble> position[2]; |
OpenGLExoticSurfaceVertex vertex; |
OpenGLExoticSurfaceComputeFuncPtr glExoticSurfaceCompute = OpenGLExoticSurfaceGetComputeFuncPtr( surfaceType ); |
for( i = 0; i < maxI; i++ ) |
{ |
for( j = 0; j < maxJ; j++ ) |
{ |
u[0] = kTwoPi * (i % maxI) * invMaxI - kPi; |
u[1] = kTwoPi * (j % maxJ) * invMaxJ - kPi ; |
glExoticSurfaceCompute(u[0], u[1], vertex.positions); |
glExoticSurfaceCompute(u[0] + delta, u[1], position[0]); |
glExoticSurfaceCompute(u[0], u[1] + delta, position[1]); |
vertex.normals = normalv(vertex.positions, position[0], position[1]); |
vertex.texCoords.s = (GLdouble)i * invMaxI * 5.0; |
vertex.texCoords.t = (GLdouble)j * invMaxJ; |
geometry->m_Vertices.push_back(vertex); |
} // for |
} // for |
} // OpenGLExoticSurfaceCreateWithType |
//------------------------------------------------------------------------ |
static void OpenGLExoticSurfaceCreateVertex(const GLint index, |
OpenGLExoticSurfaceGeometry *geometry) |
{ |
glNormal3dv(geometry->m_Vertices[index].normals.array); |
glTexCoord2dv(geometry->m_Vertices[index].texCoords.array); |
glVertex3dv(geometry->m_Vertices[index].positions.array); |
} // OpenGLExoticSurfaceCreateVertex |
//------------------------------------------------------------------------ |
static GLuint OpenGLExoticSurfaceCreateDisplayList(OpenGLExoticSurfaceGeometry *geometry) |
{ |
GLuint displayList = 0; |
GLint maxI = geometry->mnRows; |
GLint maxJ = geometry->mnColumns; |
if( (maxI > 0) && (maxJ > 0) ) |
{ |
displayList = glGenLists(1); |
glNewList(displayList, GL_COMPILE); |
{ |
GLint i; |
GLint j; |
GLint k; |
GLint l; |
GLint m; |
for( i = 0; i < maxI; i++ ) |
{ |
glBegin(GL_TRIANGLE_STRIP); |
for( j = 0; j <= maxJ; j++ ) |
{ |
m = j % maxJ; |
k = (i % maxI) * maxJ + m; |
OpenGLExoticSurfaceCreateVertex(k, geometry); |
l = ((i + 1) % maxI) * maxJ + m; |
OpenGLExoticSurfaceCreateVertex(l, geometry); |
} // for |
glEnd(); |
} // for |
} |
glEndList(); |
} // if |
return displayList; |
} // OpenGLExoticSurfaceCreateDisplayList |
//------------------------------------------------------------------------ |
static GLuint OpenGLExoticSurfaceCreateWithProperties(const OpenGLExoticSurfaceType surfaceType, |
const GLuint subdivisions, |
const GLuint xyRatio) |
{ |
OpenGLExoticSurfaceGeometry geometry; |
geometry.mnRows = subdivisions * xyRatio; |
geometry.mnColumns = subdivisions; |
// Build surface |
OpenGLExoticSurfaceCreateWithType(surfaceType, &geometry); |
// Now get the display list |
GLuint displayList = OpenGLExoticSurfaceCreateDisplayList(&geometry); |
return displayList; |
} // OpenGLExoticSurfaceCreateWithProperties |
//------------------------------------------------------------------------ |
//------------------------------------------------------------------------ |
@implementation OpenGLExoticSurface |
//------------------------------------------------------------------------ |
//------------------------------------------------------------------------ |
- (id) initExoticSurfaceWithType:(const OpenGLExoticSurfaceType)theSurfaceType |
subdivisions:(const GLuint)theSubdivisions |
ratio:(const GLuint)theRatio |
{ |
self = [super init]; |
if( self ) |
{ |
mnDisplayList = OpenGLExoticSurfaceCreateWithProperties(theSurfaceType, |
theSubdivisions, |
theRatio); |
} // if |
return self; |
} // initExoticSurfaceWithType |
//------------------------------------------------------------------------ |
- (void) dealloc |
{ |
// delete the last used display list |
if( mnDisplayList ) |
{ |
glDeleteLists(mnDisplayList, 1); |
} // if |
[super dealloc]; |
} // dealloc |
//------------------------------------------------------------------------ |
- (GLuint) displayList |
{ |
return mnDisplayList; |
} // displayList |
//------------------------------------------------------------------------ |
- (void) callList |
{ |
glCallList( mnDisplayList ); |
} // callList |
//------------------------------------------------------------------------ |
@end |
//------------------------------------------------------------------------ |
//------------------------------------------------------------------------ |
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