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shadercoder/ConeTraceAnalytic.txt

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Created August 29, 2018 07:03
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  1. @sebbbi sebbbi created this gist Aug 27, 2018.
    23 changes: 23 additions & 0 deletions ConeTraceAnalytic.txt
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    Spherical cap cone analytic solution is a 1d problem, since the cone cap sphere slides along the ray. The intersection point to empty space sphere is always on the ray.

    S : radius of cone cap sphere at t=1
    r(d) : cone cap sphere radius at distance d

    r(d) = d*S

    p = distance of current SDF sample
    SDF(p) = sdf function result at location p
    x = distance after conservative step

    The equation:
    p + SDF(p) = x + r(x)

    Simplify:
    p + SDF(p) = x + x*S ; substitute r(d) = d*S
    x(1+S) = p + SDF(p)
    x = (p + SDF(p)) / (1+S)

    Substitute: C = 1 / (1+S)
    x = (p + SDF(p)) * C ; <--- this is the code executed in shader

    C is stored to constant buffer and precalculated on CPU.