3x3 Sobel normal gradient convolution for procedural coastlines

To highlight continental boundaries and island archipelagos without adding heavy vector geometry, TerraGemini applies a discrete $3 \times 3$ Sobel convolution filter across the 4K raster landmass mask $I(x, y)$:

$G_x = \begin{bmatrix} -1 & 0 & +1 \\ -2 & 0 & +2 \\ -1 & 0 & +1 \end{bmatrix} * I(x, y), \quad G_y = \begin{bmatrix} -1 & -2 & -1 \\ 0 & 0 & 0 \\ +1 & +2 & +1 \end{bmatrix} * I(x, y)$

The normalized edge magnitude is computed per vertex:

$S_{\text{edge}}(x, y) = \min\left(1.0, \frac{\sqrt{G_x(x, y)^2 + G_y(x, y)^2}}{4.0}\right)$

Dynamic Shader Coastline Modulation

In the vertex and fragment shaders, the uniform u_edge_sensitivity dynamically scales point size and brightness along coastlines:

float threshold = 1.0 - (u_edge_sensitivity * 0.85 + 0.08);
float edgeFactor = smoothstep(threshold, 1.0, a_edge_strength);
gl_PointSize = clamp(baseSize * fresnel * (1.0 + 1.6 * edgeFactor * u_edge_sensitivity), 1.0, 64.0);

This emphasizes continental boundaries while preserving smooth, anti-aliased transitions under high-speed globe rotation.