Chapter 13 - Cone not rendering bottom cap properly

Hello,

I am trying to render a capped cone with min and max of -1 and 1 respectively. However, as seen from the attached image, something goes slightly wrong when rendering the bottom of the cone - the cap seems to cut off a part of the cone. Below is my Cone.h - any help is appreciated!



class Cone : public Geometry

{

public:

Cone()

: Geometry(), ymin(-1), ymax(1), closed(true) {}

Cone(float min, float max, bool c = true)

: Geometry(), ymin(min), ymax(max), closed(c) {}

Cone(const Matrix& _transform, const Material& mat)

: Geometry(_transform, mat), ymin(-1), ymax(1), closed(true) {}

Cone(const Matrix& _transform, const Material& mat, float min, float max, bool c = true)

: Geometry(_transform, mat), ymin(min), ymax(max), closed(c) {}



Tuple normalAt(const Tuple& point) const

{

Tuple ObjectNormal = point * inverseTransform;

float dist = ObjectNormal.x * ObjectNormal.x + ObjectNormal.z * ObjectNormal.z;

Tuple t;

if (dist < 1.0f && ObjectNormal.y > ymax)

t = Tuple(0, 1, 0, 0);

else if (dist < 1.0f && ObjectNormal.y < ymin)

t = Tuple(0, -1, 0, 0);



float y = sqrtf(ObjectNormal.x * ObjectNormal.x + ObjectNormal.z * ObjectNormal.z);

if (ObjectNormal.y > 0.0f)

y = -y;

t = Tuple(ObjectNormal.x, y, ObjectNormal.z, 0);



t *= inverseTransform.transposed();

t.w = 0;

return t;

}



std::vector<Intersection> intersects(Ray& r)

{

Ray ray = r.transformed(inverseTransform);



float a = ray.direction.x * ray.direction.x - ray.direction.y * ray.direction.y + ray.direction.z * ray.direction.z;

float b = 2.0f * ray.origin.x * ray.direction.x - 2.0f * ray.origin.y * ray.direction.y + 2.0f * ray.origin.z * ray.direction.z;

float c = ray.origin.x * ray.origin.x - ray.origin.y * ray.origin.y + ray.origin.z * ray.origin.z;



std::vector<Intersection> intersects;

if (fabsf(a) < 0.005f && fabsf(b) >= 0.005f)

intersects.push_back({ -c / 2 * b, this });



if (fabsf(a) >= 0.005f)

{

float disc = b * b - 4 * a * c;

if (disc >= 0.0f)

{

float t0 = (-b - sqrtf(disc)) / (2 * a);

float t1 = (-b + sqrtf(disc)) / (2 * a);

if (t0 > t1)

std::swap(t0, t1);



Tuple nearHit = ray.position(t0);

if (nearHit.y > ymin && nearHit.y < ymax)

intersects.push_back({ t0, this });

Tuple farHit = ray.position(t1);

if (farHit.y > ymin && farHit.y < ymax)

intersects.push_back({ t1, this });

}

}

capIntersects(ray, intersects);



return intersects;

}



float ymin;

float ymax;

bool closed;



private:

bool checkCap(Ray& r, float dist, float y)

{

Tuple t = r.position(dist);

return (t.x * t.x + t.z * t.z) <= (y * y);

}



void capIntersects(Ray& r, std::vector<Intersection>& intersects)

{

if (closed == false || fabsf(r.direction.y) <= 0.005f)

return;



float t0 = (ymin - r.origin.y) / r.direction.y;

if (checkCap(r, t0, ymin))

intersects.push_back({ t0, this });

float t1 = (ymax - r.origin.y) / r.direction.y;

if (checkCap(r, t1, ymax))

intersects.push_back({ t1, this });

}

};