ray: add ray-sphere intersection test

ray.cpp

@@ -71,6 +71,31 @@ util::ray<S,T>::intersect (AABB<S,T> r) const
 }
 
 
+///----------------------------------------------------------------------------
+/// returns the smallest distance from ray origin to a sphere intersection
+///
+/// returns NaN on miss
+template <size_t S, typename T>
+T
+util::ray<S,T>::intersect (sphere<S,T> s) const
+{
+    T b = dot (d, p - s.c);
+    T c = dot (p - s.c, p - s.c) - s.r * s.r;
+
+    T D = b * b - c;
+    if (D < 0)
+        return std::numeric_limits<T>::quiet_NaN ();
+
+    auto t_ = std::sqrt (D);
+    auto t0 = -b + t_;
+    auto t1 = -b - t_;
+
+    return t1 >= 0 ? t1 :
+           t0 >= 0 ? t0 :
+           std::numeric_limits<T>::quiet_NaN ();
+}
+
+
 ///----------------------------------------------------------------------------
 /// returns the closest parameter along the ray to a given point
 template <size_t S, typename T>

ray.hpp

@@ -18,9 +18,11 @@
 #define __UTIL_RAY_HPP
 
 #include "point.hpp"
-#include "vector.hpp"
+
-#include "plane.hpp"
 #include "aabb.hpp"
+#include "plane.hpp"
+#include "sphere.hpp"
+#include "vector.hpp"
 
 namespace util {
     template <size_t S, typename T>
@@ -30,6 +32,7 @@ namespace util {
 
         T intersect (plane<S,T>) const;
         T intersect (AABB<S,T>) const;
+        T intersect (sphere<S,T>) const;
 
         T closest (point<S,T>) const;
 

test/ray.cpp

@@ -40,7 +40,16 @@ test_intersect_aabb (util::TAP::logger &tap)
 void
 test_intersect_sphere (util::TAP::logger &tap)
 {
-    ;
+    const util::sphere3f s = {{0.f, 0.f, 0.f}, 1.f};
+
+    const util::ray3f r0 {{0.f, 2.f, 0.f}, {0.f, -1.f, 0.f}};
+    tap.expect_eq (r0.intersect (s), 1.f, "ray-sphere simple");
+
+    const util::ray3f r1 {{0.f, 1.f, 0.f}, {0.f, 1.f, 0.f}};
+    tap.expect_eq (r1.intersect (s), 0.f, "ray-sphere adjacent");
+
+    const util::ray3f r2 {{0.f, 2.f, 0.f}, {0.f, 1.f, 0.f}};
+    tap.expect_nan (r2.intersect (s), "ray-sphere no-intersect");
 }