 Solution

For single-shot ray tracing, construct one primary ray per pixel, normally through its centre on the image plane, with the camera centre as origin for perspective projection. Transform the ray into the scene's coordinates, or consistently transform all the scene geometry into camera coordinates.

Intersect that primary ray with the scene's triangles, using part (c), and retain the accepted hit with the smallest nonnegative parameter $\lambda$. This nearest-hit selection supplies visibility: farther surfaces cannot show through the first opaque surface. If there is no hit, write the background colour. At a hit $p$, obtain its material colour and front unit normal vector and set $\hat{V}$ toward the camera.

For each point light at ${\ell }_j$, form ${\hat{L}}_j=({\ell }_j-p)/\Vert {\ell }_j-p\Vert$, calculate the specular reflection direction, and evaluate its diffuse and specular contributions using the Phong reflection model. Sum the contributions and add ambient illumination once:The coloured surface can supply colour-dependent diffuse weights, and each source can have its own colour. Convert the result into the output image's colour encoding and range. Single-shot here means direct local shading after one primary visibility ray; no reflected or transmitted secondary viewing rays are followed. Part (e) adds secondary visibility queries for the lights.