diff options
| -rw-r--r-- | main_simple_scanner.cpp | 19 |
1 files changed, 12 insertions, 7 deletions
diff --git a/main_simple_scanner.cpp b/main_simple_scanner.cpp index e57ef03..c0760fa 100644 --- a/main_simple_scanner.cpp +++ b/main_simple_scanner.cpp @@ -52,18 +52,23 @@ public: // sphere hit formula: |Source + Direction * time - Center| = radius // |(Sx + Dx * t - Cx, Sy + Dy * t - Cy, Sz + Dz * t - Cz)| = radius + const auto c2s = r.source() - center; // center to source // A = D dot D const double a = dot(r.direction(), r.direction()); - // B = 2(S - C) dot D - const double b = 2 * dot(r.source() - center, r.direction()); - const auto rel_src = r.source() - center; // relative position of ray source + // H = (S - C) dot D + const auto h = dot(c2s, r.direction()); + // B = 2H ( not used in our optimized routine ) // C = (S - C) dot (S - C) - radius^2 - const double c = dot(rel_src, rel_src) - radius * radius; - const auto delta = b * b - 4 * a * c; - const auto hit = delta >= 0; + const double c = dot(c2s, c2s) - radius * radius; + // 4delta = H^2 - AC + // delta_q = H^2 - AC (quarter delta) + const double delta_q = h * h - a * c; + + const auto hit = delta_q >= 0; if (hit) { // the smaller root is the first point the ray hits, so return that one - t = (-b - sqrt(delta)) / (2.0 * a); + // t = ( -H +- sqrt{ delta_q } ) / A + t = (-h - sqrt(delta_q)) / a; } return hit; } |