#version 310 es

layout(local_size_x = 8, local_size_y = 8) in;

layout(binding = 0) uniform sampler2D uHeight;
layout(binding = 1) uniform sampler2D uDisplacement;
layout(rgba16f, binding = 2) uniform writeonly mediump image2D iHeightDisplacement;
layout(rgba16f, binding = 3) uniform writeonly mediump image2D iGradJacobian;

layout(binding = 4) uniform UBO
{
    vec4 uInvSize;
    vec4 uScale;
};

mediump float jacobian(mediump vec2 dDdx, mediump vec2 dDdy)
{
    return (1.0 + dDdx.x) * (1.0 + dDdy.y) - dDdx.y * dDdy.x;
}
#define LAMBDA 1.2

void main()
{
    vec4 uv = (vec2(gl_GlobalInvocationID.xy) * uInvSize.xy).xyxy + 0.5 * uInvSize;

    float h = textureLod(uHeight, uv.xy, 0.0).x;

    // Compute the heightmap gradient by simple differentiation.
    float x0 = textureLodOffset(uHeight, uv.xy, 0.0, ivec2(-1, 0)).x;
    float x1 = textureLodOffset(uHeight, uv.xy, 0.0, ivec2(+1, 0)).x;
    float y0 = textureLodOffset(uHeight, uv.xy, 0.0, ivec2(0, -1)).x;
    float y1 = textureLodOffset(uHeight, uv.xy, 0.0, ivec2(0, +1)).x;
    vec2 grad = uScale.xy * 0.5 * vec2(x1 - x0, y1 - y0);

    // Displacement map must be sampled with a different offset since it's a smaller texture.
    vec2 displacement = LAMBDA * textureLod(uDisplacement, uv.zw, 0.0).xy;

    // Compute jacobian.
    vec2 dDdx = 0.5 * LAMBDA * (
        textureLodOffset(uDisplacement, uv.zw, 0.0, ivec2(+1, 0)).xy -
        textureLodOffset(uDisplacement, uv.zw, 0.0, ivec2(-1, 0)).xy);
    vec2 dDdy = 0.5 * LAMBDA * (
        textureLodOffset(uDisplacement, uv.zw, 0.0, ivec2(0, +1)).xy -
        textureLodOffset(uDisplacement, uv.zw, 0.0, ivec2(0, -1)).xy);
    float j = jacobian(dDdx * uScale.z, dDdy * uScale.z);

    displacement = vec2(0.0);

    // Read by vertex shader/tess shader.
    imageStore(iHeightDisplacement, ivec2(gl_GlobalInvocationID.xy), vec4(h, displacement, 0.0));

    // Read by fragment shader.
    imageStore(iGradJacobian, ivec2(gl_GlobalInvocationID.xy), vec4(grad, j, 0.0));
}