//=========================================================================== /*virtual*/ double CylindricalInversion::EvaluatePartialZ( const c3ga::vectorE3GA& point ) const { double x = point.get_e1(); double y = point.get_e2(); double z = point.get_e3(); return 4.0*z*z*z + 2.0*A*x*z + 2.0*B*z + 4.0*x*x*z; }
//=========================================================================== /*virtual*/ double CylindricalInversion::EvaluatePartialX( const c3ga::vectorE3GA& point ) const { double x = point.get_e1(); double y = point.get_e2(); double z = point.get_e3(); double x2 = x * x; double y2 = y * y; double z2 = z * z; return 4.0*x2*x + 3.0*A*x2 + A*y2 + A*z2 + 2.0*B*x + 4.0*x*( y2 + z2 ); }
//================================================================================= /*static*/ bool Node::WriteVectorE3GA( lua_State* L, Context& context, const std::string& name, const c3ga::vectorE3GA& vector ) { lua_newtable( L ); WriteNumber( L, context, "x", vector.get_e1() ); WriteNumber( L, context, "y", vector.get_e2() ); WriteNumber( L, context, "z", vector.get_e3() ); lua_setfield( L, -2, name.c_str() ); return true; }
//=========================================================================== /*virtual*/ double DoubleTorus::EvaluatePartialY( const c3ga::vectorE3GA& point ) const { double x = point.get_e1(); double y = point.get_e2(); double z = point.get_e3(); double x2 = x * x; double y2 = y * y; double z2 = z * z; // f_y(x,y,z) = 16x^2y + 16x^4y + 4y^3 return 16.0*x2*y + 10.0*x2*x2*y + 4.0*y2*y; }
//=========================================================================== /*virtual*/ double DoubleTorus::EvaluatePartialX( const c3ga::vectorE3GA& point ) const { double x = point.get_e1(); double y = point.get_e2(); double z = point.get_e3(); double x2 = x * x; double y2 = y * y; double z2 = z * z; double x4 = x2 * x2; // f_x(x,y,z) = 64x^3 - 192x^5 - 16xy^2 + 128x^7 + 32x^3y^2 return 64.0*x2*x - 192.0*x4*x - 16.0*x*y2 + 128.0*x4*x2*x + 3.0*x2*x*y2; }
//=========================================================================== /*virtual*/ double DoubleTorus::Evaluate( const c3ga::vectorE3GA& point ) const { double x = point.get_e1(); double y = point.get_e2(); double z = point.get_e3(); double x2 = x * x; double y2 = y * y; double z2 = z * z; double x4 = x2 * x2; // f(x,y,z) = 16x^4 - 32x^6 - 8x^2y^2 + 16x^8 + 8x^4y^2 + y^4 + z^2 + 0.25 return 16.0*x4 - 32.0*x4*x2 - 8.0*x2*y2 + 16.0*x4*x4 + 8.0*x4*y2 + y2*y2 + z2 + 0.25; }
//=========================================================================== /*virtual*/ double CylindricalInversion::Evaluate( const c3ga::vectorE3GA& point ) const { double x = point.get_e1(); double y = point.get_e2(); double z = point.get_e3(); double x2 = x * x; double y2 = y * y; double z2 = z * z; double x4 = x2 * x2; double y4 = y2 * y2; double z4 = z2 * z2; return x4 + y4 + z4 + A*x*( x2 + y2 + z2 ) + B*( x2 + z2 ) + 2.0*x2*( y2 + z2 ); }
//=========================================================================== // A coordinate system is layed out on the plane and the texture is // scaled into the first quadrant of that system. UV coordintes // will go outside of the range [0,1]x[0,1] if the given surface point // is not in the square of this first quadrant. /*virtual*/ bool Plane::CalculateTextureCoordinates( const c3ga::vectorE3GA& point, c3ga::vectorE3GA& textureCoordinates ) const { c3ga::bivectorE3GA plane = c3ga::gp( normal, c3ga::I3 ); c3ga::vectorE3GA uAxis, vAxis; uAxis.set( c3ga::vectorE3GA::coord_e1_e2_e3, 1.0, 0.0, 0.0 ); uAxis = c3ga::lc( c3ga::lc( uAxis, plane ), c3ga::reverse( plane ) ); if( c3ga::norm( uAxis ) == 0.0 ) { uAxis.set( c3ga::vectorE3GA::coord_e1_e2_e3, 0.0, 1.0, 0.0 ); uAxis = c3ga::lc( c3ga::lc( uAxis, plane ), c3ga::reverse( plane ) ); if( c3ga::norm( uAxis ) == 0.0 ) { uAxis.set( c3ga::vectorE3GA::coord_e1_e2_e3, 0.0, 0.0, 1.0 ); uAxis = c3ga::lc( c3ga::lc( uAxis, plane ), c3ga::reverse( plane ) ); if( c3ga::norm( uAxis ) == 0.0 ) return false; } } uAxis = c3ga::unit( uAxis ); vAxis = c3ga::gp( c3ga::op( normal, uAxis ), c3ga::I3 ); c3ga::vectorE3GA vector = point - center; // This works, because the UV axes are orthonormal. double u = c3ga::lc( vector, uAxis ) / textureScale; double v = c3ga::lc( vector, vAxis ) / textureScale; textureCoordinates.set( c3ga::vectorE3GA::coord_e1_e2_e3, u, v, 0.0 ); return true; }
//=========================================================================== /*virtual*/ double DoubleTorus::EvaluatePartialZ( const c3ga::vectorE3GA& point ) const { double z = point.get_e3(); // f_z(x,y,z) = 2z return 2.0*z; }
//================================================================================= /*static*/ bool Node::ReadVectorE3GA( lua_State* L, Context& context, const std::string& name, c3ga::vectorE3GA& vector, const c3ga::vectorE3GA* defaultValue /*= 0*/ ) { bool success = false; int top = lua_gettop( L ); try { if( defaultValue ) vector = *defaultValue; else vector.set( c3ga::vectorE3GA::coord_e1_e2_e3, 0.0, 0.0, 0.0 ); lua_getfield( L, -1, name.c_str() ); if( lua_isnil( L, -1 ) || !lua_istable( L, -1 ) ) { if( context.GetNodeReadingDisposition() == Context::NONEXISTENCE_OF_FIELD_IS_FATAL_ERROR ) throw new Error( "ReadVectorE3GA failed to read \"%s\" as a table.", name.c_str() ); } else { if( !ReadNumber( L, context, "x", vector.m_e1, 0.0 ) ) throw new Error( "ReadVectorE3GA failed to read \"x\" from \"%s\".", name.c_str() ); if( !ReadNumber( L, context, "y", vector.m_e2, 0.0 ) ) throw new Error( "ReadVectorE3GA failed to read \"y\" from \"%s\".", name.c_str() ); if( !ReadNumber( L, context, "z", vector.m_e3, 0.0 ) ) throw new Error( "ReadVectorE3GA failed to read \"z\" from \"%s\".", name.c_str() ); } // Pop the vector table. lua_pop( L, 1 ); success = true; } catch( Error* error ) { context.IssueError( error ); } lua_settop( L, top ); return success; }
//===================================================================================== /*static*/ void Sphere::RenderSphereTriangle( const c3ga::vectorE3GA& point0, const c3ga::vectorE3GA& point1, const c3ga::vectorE3GA& point2, const c3ga::evenVersor& evenVersor, int subDivisionCount ) { if( subDivisionCount == 0 ) { c3ga::vectorE3GA normal0, normal1, normal2; normal0 = point0; normal1 = point1; normal2 = point2; c3ga::normalizedPoint cp0 = c3ga::normalizedPoint( c3ga::normalizedPoint::coord_e1_e2_e3_ni, point0.get_e1(), point0.get_e2(), point0.get_e3(), c3ga::norm2( point0 ) ); c3ga::normalizedPoint cp1 = c3ga::normalizedPoint( c3ga::normalizedPoint::coord_e1_e2_e3_ni, point1.get_e1(), point1.get_e2(), point1.get_e3(), c3ga::norm2( point1 ) ); c3ga::normalizedPoint cp2 = c3ga::normalizedPoint( c3ga::normalizedPoint::coord_e1_e2_e3_ni, point2.get_e1(), point2.get_e2(), point2.get_e3(), c3ga::norm2( point2 ) ); // Each of these dual spheres has a radius of zero, so they're really points in space. // Notice that while the given versor is NOT a unit-versor, I am applying it here as // such, because doing so gives us the normalized dual sphere in the end. c3ga::dualSphere ds0 = c3ga::applyUnitVersor( evenVersor, cp0 ); c3ga::dualSphere ds1 = c3ga::applyUnitVersor( evenVersor, cp1 ); c3ga::dualSphere ds2 = c3ga::applyUnitVersor( evenVersor, cp2 ); glNormal3d( normal0.get_e1(), normal0.get_e2(), normal0.get_e3() ); glVertex3d( ds0.get_e1(), ds0.get_e2(), ds0.get_e3() ); glNormal3d( normal1.get_e1(), normal1.get_e2(), normal1.get_e3() ); glVertex3d( ds1.get_e1(), ds1.get_e2(), ds1.get_e3() ); glNormal3d( normal2.get_e1(), normal2.get_e2(), normal2.get_e3() ); glVertex3d( ds2.get_e1(), ds2.get_e2(), ds2.get_e3() ); } else { c3ga::vectorE3GA point01, point12, point20; point01 = c3ga::unit( c3ga::add( c3ga::gp( point0, 0.5 ), c3ga::gp( point1, 0.5 ) ) ); point12 = c3ga::unit( c3ga::add( c3ga::gp( point1, 0.5 ), c3ga::gp( point2, 0.5 ) ) ); point20 = c3ga::unit( c3ga::add( c3ga::gp( point2, 0.5 ), c3ga::gp( point0, 0.5 ) ) ); subDivisionCount--; RenderSphereTriangle( point0, point01, point20, evenVersor, subDivisionCount ); RenderSphereTriangle( point1, point12, point01, evenVersor, subDivisionCount ); RenderSphereTriangle( point2, point20, point12, evenVersor, subDivisionCount ); RenderSphereTriangle( point01, point12, point20, evenVersor, subDivisionCount ); } }