1 uniform vec3 inv_matrix_m0;

     2 uniform vec3 inv_matrix_m1;

     3 uniform vec3 inv_matrix_m2;

     4 

     5 uniform vec2 ellipse_offset;

     6 

     7 // ellipse equation

     8 

     9 // s^2/a^2 + t^2/b^2 = 1

    10 //

    11 // implicit equation:

    12 // g(s,t) = 1 - s^2/r_s^2 - t^2/r_t^2

    13 

    14 // distance from ellipse:

    15 // grad = [dg/dx dg/dy]

    16 // d(s, t) ~= g(s, t) / |grad|

    17 

    18 // dg/dx = dg/ds * ds/dx + dg/dt * dt/dx

    19 // dg/dy = dg/ds * ds/dy + dg/dt * dt/dy

    20 

    21 float ellipse_aa()

    22 {

    23     mat3 mat;

    24 

    25     mat[0] = inv_matrix_m0;

    26     mat[1] = inv_matrix_m1;

    27     mat[2] = inv_matrix_m2;

    28 

    29     vec3 hcoords = mat * vec3(gl_FragCoord.xy + ellipse_offset, 1);

    30     float inv_w = 1.0 / hcoords.z;

    31     vec2 st = hcoords.xy * inv_w;

    32 

    33     vec4 xy = vec4(mat[0].xy, mat[1].xy);

    34     vec2 h = vec2(mat[0].z, mat[1].z);

    35 

    36     vec4 dstdxy = (xy.xzyw - h.xyxy * st.xxyy) * inv_w;

    37 

    38     //dstdxy.x = (mat[0].x - mat[0].z * st.x) * inv_w; // ds/dx

    39     //dstdxy.y = (mat[1].x - mat[1].z * st.x) * inv_w; // ds/dy

    40     //dstdxy.z = (mat[0].y - mat[0].z * st.y) * inv_w; // dt/dx

    41     //dstdxy.w = (mat[1].y - mat[1].z * st.y) * inv_w; // dt/dy

    42 

    43     vec2 inv_r = gl_TexCoord[0].xy;

    44     vec2 n = st * inv_r;

    45     float g = 1.0 - dot(n, n);

    46 

    47     vec2 dgdst = -2.0 * n * inv_r;

    48 

    49     vec2 grad = vec2(dot(dgdst, dstdxy.xz),

    50                      dot(dgdst, dstdxy.yw));

    51 

    52     return smoothstep(-0.5, 0.5, g * inversesqrt(dot(grad, grad)));

    53 }

    54 

    55 void main()

    56 {

    57     gl_FragColor = ellipse_aa().xxxx;

    58 }