feat(examples): add the scene representation, camera and intersection

Sphere and plane records, camera ray generation from field of view and aspect
ratio, and the nearest-hit search across the scene.

examples/raytracer/src/scene/camera.c

@@ -0,0 +1,27 @@
+#include "rt_scene.h"
+#include <math.h>
+
+camera camera_make(vec3 look_from, vec3 look_at, vec3 up, double fov_deg, double aspect) {
+    double theta = fov_deg * 3.14159265358979323846 / 180.0;
+    double half_height = tan(theta / 2.0);
+    double half_width = aspect * half_height;
+
+    vec3 w = v3norm(v3sub(look_from, look_at));
+    vec3 u = v3norm(v3cross(up, w));
+    vec3 v = v3cross(w, u);
+
+    camera c;
+    c.origin = look_from;
+    c.horizontal = v3scale(u, 2.0 * half_width);
+    c.vertical = v3scale(v, 2.0 * half_height);
+    c.lower_left = v3sub(v3sub(v3sub(look_from, v3scale(u, half_width)), v3scale(v, half_height)), w);
+    return c;
+}
+
+ray camera_ray(const camera *c, double u, double v) {
+    vec3 target = v3add(v3add(c->lower_left, v3scale(c->horizontal, u)), v3scale(c->vertical, v));
+    ray r;
+    r.origin = c->origin;
+    r.dir = v3norm(v3sub(target, c->origin));
+    return r;
+}

examples/raytracer/src/scene/hit.c

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+#include "rt_scene.h"
+#include <math.h>
+
+static int sphere_hit(const sphere *s, ray r, double tmin, double tmax, hit *out) {
+    vec3 oc = v3sub(r.origin, s->center);
+    double a = v3len2(r.dir);
+    double half_b = v3dot(oc, r.dir);
+    double c = v3len2(oc) - s->radius * s->radius;
+    double disc = half_b * half_b - a * c;
+    if (disc < 0.0) return 0;
+
+    double root = sqrt(disc);
+    double t = (-half_b - root) / a;
+    if (t < tmin || t > tmax) {
+        t = (-half_b + root) / a;
+        if (t < tmin || t > tmax) return 0;
+    }
+
+    out->t = t;
+    out->point = v3add(r.origin, v3scale(r.dir, t));
+    vec3 outward = v3scale(v3sub(out->point, s->center), 1.0 / s->radius);
+    out->front = v3dot(r.dir, outward) < 0.0;
+    out->normal = out->front ? outward : v3neg(outward);
+    out->mat = s->mat;
+    return 1;
+}
+
+int scene_hit(const scene *s, ray r, double tmin, double tmax, hit *out) {
+    hit best;
+    int found = 0;
+    double closest = tmax;
+
+    for (int i = 0; i < s->count; i++) {
+        hit h;
+        if (sphere_hit(&s->spheres[i], r, tmin, closest, &h)) {
+            found = 1;
+            closest = h.t;
+            best = h;
+        }
+    }
+    if (found) *out = best;
+    return found;
+}