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/usr/share/celestia/shaders/ringshadow.vp is in celestia-common 1.6.1+dfsg-3.

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!!VP1.0

# Vertex program used for applying ring shadow textures.  Ray cast from a
# point on the object in the direction of the sun (assumed to be an
# infinitely distant light source here.)  Compute the intersection of
# the ray with the ring plane.  Then use the distance of the intersection
# point from the planet's center to compute a texture coordinate.  Vertex
# programs are cool!
#
# c[0]..c[3] contains the concatenation of the modelview and projection
# matrices.
# c[16] contains the light direction in object space
# c[20] contains the color
# c[41] is [ inner ring radius, 1/ring width, 0, 0.5 ]
# c[42] is 1 / sunDir.y
# c[43] contains scaling vector [1 1-oblateness 1 0]

# Transform the vertex by the modelview matrix
DP4   o[HPOS].x, c[0], v[OPOS];
DP4   o[HPOS].y, c[1], v[OPOS];
DP4   o[HPOS].z, c[2], v[OPOS];
DP4   o[HPOS].w, c[3], v[OPOS];

# Scale by oblateness . . . off for now because it makes Saturn look
# weird, even though I think it's more realistic.
# MUL   R2, v[OPOS], c[43];
MOV   R2, v[OPOS];

MUL   R1.x, R2.y, -c[42].x;
MAX   R1.x, R1.x, c[42].w;  # Clamp to zero--don't trace both directions
MAD   R0, R1.x, c[16], R2;

# Compute the distance from the center.  The s coordinate is the distance
# from the center, modified by the ring width and inner radius
DP3   R0.x, R0, R0;
RSQ   R0.x, R0.x;
RCP   R0.x, R0.x;

# Scale and bias by ring width and radius
ADD   R0.x, R0.x, -c[41].x;
MUL   R0.x, R0.x, c[41].y;
# Now we have our s coordinate . . .
MOV   o[TEX0].x, R0.x;
# The t coordinate is always 0.5
MOV   o[TEX0].y, c[41].w;

MOV   o[COL0], c[20];

END