# T4 Adding Quadrilaterals (MS4)

### Revise aabb to avoid zero thickness 

add a private method pad\_to\_minimums() in aabb.h

```cpp
class aabb {
  public:
    interval x, y, z;

    aabb() {} // The default AABB is empty, since intervals are empty by default.

    aabb(const interval& x, const interval& y, const interval& z)
      : x(x), y(y), z(z) {
        pad_to_minimums(); // <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
      }

    aabb(const point3& a, const point3& b) {
        // Treat the two points a and b as extrema for the bounding box, so we don't require a
        // particular minimum/maximum coordinate order.

        x = (a[0] <= b[0]) ? interval(a[0], b[0]) : interval(b[0], a[0]);
        y = (a[1] <= b[1]) ? interval(a[1], b[1]) : interval(b[1], a[1]);
        z = (a[2] <= b[2]) ? interval(a[2], b[2]) : interval(b[2], a[2]);

        pad_to_minimums(); // <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
    }
    
    // ...
        // >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
private:

    void pad_to_minimums() {
        // Adjust the AABB so that no side is narrower than some delta, padding if necessary.

        double delta = 0.0001;
        if (x.size() < delta) x = x.expand(delta);
        if (y.size() < delta) y = y.expand(delta);
        if (z.size() < delta) z = z.expand(delta);
    }
     // <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
};

```

### Add a quad class

create quad.h, add a class quad, implementing the abstract class hittable.

The hit method calcuates the intersection point of a ray and a plane using the following formula:

<figure><img src="https://3464970502-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3JUKGJZ67JX02QZdPhsy%2Fuploads%2FRlNd0QnIqka6F79YXPTT%2Fimage.png?alt=media&#x26;token=00890bea-d28d-4c5c-afb0-7ab04ee73d24" alt="" width="375"><figcaption></figcaption></figure>

is\_interior() checks if the intersection point is within the quadrilateral.

```cpp
#ifndef QUAD_H
#define QUAD_H

#include "hittable.h"

class quad : public hittable {
  public:
    quad(const point3& Q, const vec3& u, const vec3& v, shared_ptr<material> mat)
      : Q(Q), u(u), v(v), mat(mat)
    {
        auto n = cross(u, v);
        normal = unit_vector(n);
        D = dot(normal, Q);
        w = n / dot(n,n);

        set_bounding_box();
    }
 
    virtual void set_bounding_box() {
        // Compute the bounding box of all four vertices.
        auto bbox_diagonal1 = aabb(Q, Q + u + v);
        auto bbox_diagonal2 = aabb(Q + u, Q + v);
        bbox = aabb(bbox_diagonal1, bbox_diagonal2);
    }

    aabb bounding_box() const override { return bbox; }

    bool hit(const ray& r, interval ray_t, hit_record& rec) const override {
                auto denom = dot(normal, r.direction());

        // No hit if the ray is parallel to the plane.
        if (std::fabs(denom) < 1e-8)
            return false;

        // Return false if the hit point parameter t is outside the ray interval.
        auto t = (D - dot(normal, r.origin())) / denom;
        if (!ray_t.contains(t))
            return false;

        // Determine if the hit point lies within the planar shape using its plane coordinates.
        auto intersection = r.at(t);
        vec3 planar_hitpt_vector = intersection - Q;
        auto alpha = dot(w, cross(planar_hitpt_vector, v));
        auto beta = dot(w, cross(u, planar_hitpt_vector));

        if (!is_interior(alpha, beta, rec))
            return false;

        rec.t = t;
        rec.p = intersection;
        rec.mat = mat;
        rec.set_face_normal(r, normal);

        return true;
    }

    virtual bool is_interior(double a, double b, hit_record& rec) const {
        interval unit_interval = interval(0, 1);
        // Given the hit point in plane coordinates, return false if it is outside the
        // primitive, otherwise set the hit record UV coordinates and return true.

        if (!unit_interval.contains(a) || !unit_interval.contains(b))
            return false;

        rec.u = a;
        rec.v = b;
        return true;
    }

  private:
    point3 Q;
    vec3 u, v;
    vec3 w; // normalised normal direction
    shared_ptr<material> mat;

    aabb bbox;
    vec3 normal;
    double D;
};

#endif
```

### Add a quad scene in main.cpp

include quad.h in main.cpp and&#x20;

create an open box scene using quadss as follows:

```cpp
#include "rtweekend.h"

#include "bvh.h"  
#include "camera.h"
#include "hittable.h"
#include "hittable_list.h"
#include "material.h" 
#include "sphere.h"
#include "texture.h" 
#include "quad.h"  // <<<<<<<<<<<<<<<<<<<<<<<<

// >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
void quads() {
    hittable_list world;

    // Materials
    auto left_red     = make_shared<lambertian>(color(1.0, 0.2, 0.2));
    auto back_green   = make_shared<lambertian>(color(0.2, 1.0, 0.2));
    auto right_blue   = make_shared<lambertian>(color(0.2, 0.2, 1.0));
    auto upper_orange = make_shared<lambertian>(color(1.0, 0.5, 0.0));
    auto lower_teal   = make_shared<lambertian>(color(0.2, 0.8, 0.8));

    // Quads
    world.add(make_shared<quad>(point3(-3,-2, 5), vec3(0, 0,-4), vec3(0, 4, 0), left_red));
    world.add(make_shared<quad>(point3(-2,-2, 0), vec3(4, 0, 0), vec3(0, 4, 0), back_green));
    world.add(make_shared<quad>(point3( 3,-2, 1), vec3(0, 0, 4), vec3(0, 4, 0), right_blue));
    world.add(make_shared<quad>(point3(-2, 3, 1), vec3(4, 0, 0), vec3(0, 0, 4), upper_orange));
    world.add(make_shared<quad>(point3(-2,-3, 5), vec3(4, 0, 0), vec3(0, 0,-4), lower_teal));

    camera cam;

    cam.aspect_ratio      = 1.0;
    cam.image_width       = 400;
    cam.samples_per_pixel = 100;
    cam.max_depth         = 50;

    cam.vfov     = 80;
    cam.lookfrom = point3(0,0,9);
    cam.lookat   = point3(0,0,0);
    cam.vup      = vec3(0,1,0);

    cam.defocus_angle = 0;

    cam.render(world);
}
// <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

// ...

int main() {
    quads();
}
```

### Build and Run

Build you programme, if successful, run your program. I am using the following:

```
Measure-Command { ./ray01.exe > image27.ppm}
```

Your output image should be similar to the following:

<figure><img src="https://3464970502-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3JUKGJZ67JX02QZdPhsy%2Fuploads%2FXDzi5W92AHq8mUZykWup%2F60437656-a76e-4e60-a6a1-30107698e918.png?alt=media&#x26;token=b2b928f9-69ac-44e1-91be-f765b0e3ad75" alt="" width="475"><figcaption></figcaption></figure>