Now that your ray tracer generates camera rays, we need to be able to answer the core query in ray tracing: “does this ray hit this object?” Here, you will start by implementing ray-object intersection routines against the two types of objects in the starter code: triangles and spheres.

First, take a look at rays/object.h for the interface of the Object class. An Object can be either a Tri_Mesh, a Shape, a BVH(which you will implement in Task $$3$$), or a list of Objects. Right now, we are only dealing with Tri_Mesh’s case and Shape’s case, and their interfaces are in rays/tri_mesh.h and rays/shapes.h, respectively. Tri_Mesh contains a BVH of Triangle, and in this task you will be working with the Triangle class. For Shape, you are going to work with a Sphere, which is the major type of Shape in Scotty 3D.

Now, you need to implement the hit routine for both Triangle and Sphere. hit takes in a ray, and returns a Trace structure, which contains the following information:

• hit: a boolean representing if there is a hit or not.
• distance: the distance from the origin of the ray to the hit point.
• position: the position of the hit point. This can be computed from ray.at(distance) since the ray’s direction is normalized.
• normal: the shading normal of the surface at the hit point. The shading normal for a triangle is computed by linear interpolation from per-vertex normals using the barycentric coordinates of the hit point as their weights. The shading normal for a sphere is the same as its geometric normal.
• origin: the origin of the query ray (ignore).
• material: the material ID of the hit object (ignore).

In order to correctly implement hit, you will also need to understand some of the fields in the Ray structure defined in lib/ray.h.

• point: the 3D point of origin of the ray
• dir: the 3D direction of the ray (always normalized)
• dist_bounds: the minimum and maximum distance along the ray. Primitive intersections that lie outside the [ray.dist_bounds.x, ray.dist_bounds.y] range should be disregarded.
• depth: the recursive depth of the ray (Used in task $$4$$).
• throughput: the fraction of incoming light along this ray that will contribute to the final image (Optionally used in task $$4$$).

One important detail of the ray structure is that dist_bounds is a mutable field. This means that it can be modified even in const rays, for example within Triangle::hit. When finding the first intersection of a ray and the scene, you will want to update the ray’s dist_bounds value after finding each hit with scene geometry. By bounding the ray as tightly as possible, your ray tracer will be able to avoid unnecessary tests with scene geometry that is known to not be able to result in a closest hit, resulting in higher performance.

## Reference Results

You should now be able to render all of the example scenes colored based on surface normals. Note that scenes with high geometric complexity will be extremely slow until you implement task 3. Here is dodecahedron.dae, cbox.dae, and cow.dae: