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Thread: OpenGL Texture Mapping [Equirectangular 2 Azimuthal Equidistant]

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    Help OpenGL Texture Mapping [Equirectangular 2 Azimuthal Equidistant]

    Hey, this is my first time here... was looking for some help from some cartography savy people

    I have created an almost spherical disk by joining lots of triangular/rectangular polygons together and have a equidistant image of the earth loaded as a texture map. What I am having trouble doing is converting/mapping the azimuthal equidistant points on the disk to a latitude and longitude so I can determing the texture coordinate. Here is a snippet of code where the disk is created:

    Code:
    void CreateDisk (double R, double x0, double y0, double z0)
    {
    	const double rad_inc = R/(disk_r_divs);
    	const double theta_inc = 2*PI/(disk_az_divs);
    	double theta, radius, b2[4], a2[4];
    	double latitude, longitude;
    	int n=0,i; // Current vertex
    
    	for(radius=0; radius < (R+rad_inc/2); radius+=rad_inc)
    	{
    		b2[0] = radius;
    		b2[1] = radius + rad_inc;
    		b2[2] = radius;
    		b2[3] = radius + rad_inc;
    
    		for(theta=0; theta <= PI2; theta+=theta_inc)
    		{
    			a2[0] = theta;
    			a2[1] = theta;
    			a2[2] = theta + theta_inc;
    			a2[3] = theta + theta_inc;
    
    			for (i=0; i<4; i++)
    			{
    				// disk coordinates
    				p_d[n].x = b2[i] * cos(a2[i]) + x0;
    				p_d[n].y = b2[i] * sin(a2[i]) + y0;
    				p_d[n].z = z0;
    
    				// TEXTURE COORDINATES CALCULATED HERE
    
    				n++;
    			}
    		}
    	}
    }
    The use of b2[] and a2[] are to calculate the other points of the rectangle. And are not really relavent to the problem I am havving (I think) so this code can be interpreted like this for simplicity:

    Code:
    void CreateDisk (double R, double x0, double y0, double z0)
    {
    	const double rad_inc = R/(disk_r_divs);
    	const double theta_inc = 2*PI/(disk_az_divs);
    	double theta, radius;
    	double latitude, longitude; //used to calculate texture coordinates
    	int n=0 // Current vertex
    
    	for(radius=0; radius < R; radius+=rad_inc)
    	{
    		for(theta=0; theta <= PI2; theta+=theta_inc)
    		{
    				// disk coordinates
    				p_d[n].x = b2[i] * cos(a2[i]) + x0;
    				p_d[n].y = b2[i] * sin(a2[i]) + y0;
    				p_d[n].z = z0;
    
    				// TEXTURE COORDINATES CALCULATED HERE
    
    				n++;
    		}
    	}
    }
    This code starts with a radius of 0 and then will sweep through theta (the azimuth of the map). Repeating with larger radii untill reaching R. Here is an example of the resulting disk:


    The problem I am havving is converting the cartesian (or polar if this is easier) coordinates to a latitude and longitude for the equirectangular map (This needs to be inserted where indicated in the code sample). I have managed managed a polar aspect by simply using a ratio of the radius and azimuth. (Note that the +0.5 and /PI2 and /R are to convert/normalise the latitude and longitude into a 0:1 range which is required by OpenGL.

    Code:
    		p_d[n].u = 0.5 + a2[i]/PI2; // + rotation
    		p_d[n].v = (b2[i])/R;
    This is the resulting image:


    For the oblique projection I am struggeling. The latest equations I have been trying to use where taken from Map Projections – A Working Manual (pg 196) http://books.google.com.au/books/rea...der&pg=GBS.PR1,
    the equations are reproduced here at Wolfram http://mathworld.wolfram.com/Azimuth...rojection.html.

    I implemented them in code as follows. b2[] can simply be considered a radius and a2[] an azimuth, p_d[n].y/x are the x/y coordinates:
    Code:
    				if (radius == 0)
    				{
    					latitude = lat0;
    					longitude = long0 + theta;
    				}
    				else
    				{
    					latitude = asin( cos(b2[i])*sin(lat0) + (p_d[n].y*sin(b2[i])*cos(lat0)/b2[i]) );
    
    					if (lat0 == PI_2)
    						longitude = long0 + atan( -p_d[n].x/p_d[n].y );
    					else if (lat0 == -PI_2)
    						longitude = long0 + atan( p_d[n].x/p_d[n].y );
    					else
    						longitude = long0 + atan( p_d[n].x*sin(b2[i])/( b2[i]*cos(lat0)*cos(b2[i])-p_d[n].y*sin(lat0)*sin(b2[i]) ) );
    				}
    
    				// convert lat/long to texture coordinates
    				p_d[n].u = longitude/PI2;
    				p_d[n].v = 0.5 + latitude/PI;
    The results seem somewhat correct but I don't even get the entire azimuthal projection (for example with australia at the centre you can't see much else). I have been trying to fix this for near a week and thought I should ask for help.

    Thanks.
    Last edited by felixrulz; 08-01-2012 at 12:17 AM. Reason: tried to mark thread as 'Solved'

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