sphere: more intersection computation

lib/shapes/sphere.cpp

@@ -20,15 +20,49 @@ auto hrt::shapes::sphere::intersect(const hrt::core::ray *r, float *t_hit,
     hrt::core::point phi_t;
 
     /* Transform the ray to object space */
+    core::ray ro;
+    (*world_to_object)(*r, &ro);
+
     /* Compute the quadractic sphere coefficients */
+    float A = ro.direction.x*ro.direction.x +
+        ro.direction.y*ro.direction.y + ro.direction.z*ro.direction.z;
+    float B = 2 * (ro.direction.x*ro.origin.x +
+                   ro.direction.y*ro.origin.y + ro.direction.z*ro.origin.z);
+    float C = ro.origin.x*ro.origin.x + ro.origin.y*ro.origin.y +
+        ro.origin.z*ro.origin.z - radius*radius;
+
     /* Solve the quadratic equation for t values */
+    float discriminant = B*B - 4*A*C;
+    if (discriminant < 0) { return false; }
+    float t0 = (-B + std::sqrt(discriminant)) / (2.0f * A);
+    float t1 = (-B - std::sqrt(discriminant)) / (2.0f * A);
+    if (t0 > t1) {
+        float ttmp = t1;
+        t1 = t0;
+        t0 = ttmp;
+    }
+
+    /* Compute intersection distance along ray */
+    if (t0 > ro.maxt || t1 < ro.mint) { return false; }
+    *t_hit = t0;
+    if (t0 < ro.mint) {
+        *t_hit = t1;
+        if (*t_hit > ro.maxt) { return false; }
+    }
+
+    /* Compute sphere hit position and \phi */
+    core::point p_hit = ro(*t_hit);
+    phi = atan2f(phi_t.y, phi_t.x);
+    if (phi < 0.f) phi += 2.f*M_PI;
+
     /* Test sphere intersection against clipping parameters */
     /* Find a parametric representatino of a sphere hit */
     /* Initialize the DifferentialGeometry from the parametric information */
     /* Update t_hit for quadractic intersection */
     /* compute ray_epsilon for quadratic intersection */
 
     /* TODO: REMOVE */
+    (void) p_hit;
     (void) r;
     (void) t_hit;
     (void) ray_epsilon;