mollweide-points.yaml

# contributors: @patriciogv @meetar
import: mercator-functions.yaml
styles:
    projection_points:
        mix: mollweide-points
    mollweide-points:
        mix: mercator-functions
        shaders:
            defines:
                EARTH_RADIUS: 6378137.0
                PI: 3.14159265358979323846
                HALF_PI: 1.570796327
                QUARTER_PI: .785398163
                deg2rad(d): (d)*PI/180.0
                rad2deg(d): (d)*180.0/PI
                SQRT2: sqrt(2.0)

                # MAX_ITER: 10
                TOLERANCE: .0000001

            blocks:
                global: |
                    // http://wiki.openstreetmap.org/wiki/Mercator
                    float y2lat_d (float y) { return rad2deg( atan(exp( deg2rad(y) )) * 2.0 - HALF_PI ); }
                    float x2lon_d (float x) { return x; }

                    float lat2y_d(float lat) { return rad2deg( log(tan( deg2rad(lat) / 2.0 +  PI/4.0 )) ); }
                    float lon2x_d(float lon) { return lon; }

                    float sp = sin(HALF_PI);
                    float r = sqrt(PI * 2.0 * sp / PI);
                    float cx = SQRT2 / HALF_PI;
                    float cy = SQRT2;

                    // convert from lat/lon to mollweide -- Adapted from https://github.com/d3/d3-geo-projection/blob/master/src/mollweide.js
                    float mollweideBromleyTheta(float phi) {
                        float cpsinPhi = PI * sin(phi);
                        for ( int i = 4; i != 0; i--) {
                          float delta = (phi + sin(phi) - cpsinPhi) / (1. + cos(phi));
                          phi -= delta;
                        }
                        return phi / 2.;
                    }

                    // x,y = lambda, phi
                    vec2 mollweide(float lambda, float phi) {
                        phi = mollweideBromleyTheta(phi);
                        return vec2(cx * lambda * cos(phi), cy * sin(phi));
                    }
                position: |
                    // mercator position of the current vertex, u_map_position = center of screen,
                    // position.xy = vertex screen position in meters from the center of the screen
                    vec2 mercator = u_map_position.xy + position.xy;
                    float lat = y2lat_m(position.y);
                    float lon = x2lon_m(position.x);
                    if (abs(lon) > 180.) {
                        // clip the point
                        position.xy = vec2(3.402823466e+38);
                    } else {
                        // bend map into mollweide
                        lon = max(-180., lon);
                        lon = min(180., lon);
                        vec2 new = mollweide(deg2rad(lon), deg2rad(lat));
                        // TODO: factor out this magic number – possibly something related to the difference in coordinate systems?
                        float magic_number = 100.;
                        new = vec2(lon2x_m(new.x)*magic_number, lat2y_m(new.y)*magic_number);
                        position.xy = new;
                    }