def intersect_caps(self, shape_ray: Ray, xs: GroupIntersections):
# caps only matter if the cylinder is closed, and might possibly be
# intersected by the ray.
if not self.closed or abs(shape_ray.direction.y) < EPSILON:
return
# check for an intersection with the lower end cap by intersecting
# the ray with the plane at y=cyl.minimum
t = (self.minimum - shape_ray.origin.y) / shape_ray.direction.y
if check_cap(shape_ray, t, self.minimum):
xs.add_intersection(Intersection(t, self))
# check for an intersection with the upper end by intersecting
# the ray with the plane at y=cyl.maximum
t = (self.maximum - shape_ray.origin.y) / shape_ray.direction.y
if check_cap(shape_ray, t, self.maximum):
xs.add_intersection(Intersection(t, self))
def local_intersect(self, shape_ray: Ray) -> GroupIntersections:
a = shape_ray.direction.x**2 + shape_ray.direction.z**2
# ray is parallel to the y axis
if a < EPSILON:
xs = GroupIntersections()
self.intersect_caps(shape_ray, xs)
return xs
b = 2 * shape_ray.origin.x * shape_ray.direction.x +\
2 * shape_ray.origin.z * shape_ray.direction.z
c = shape_ray.origin.x**2 + shape_ray.origin.z**2 - 1
discriminant = b**2 - 4 * a * c
# ray does not intersect the cylinder
if discriminant < 0:
return GroupIntersections()
t0 = (-b - math.sqrt(discriminant)) / (2 * a)
t1 = (-b + math.sqrt(discriminant)) / (2 * a)
if t0 > t1:
t0, t1 = t1, t0
xs = GroupIntersections()
y0 = shape_ray.origin.y + t0 * shape_ray.direction.y
if self.minimum < y0 < self.maximum:
xs.add_intersection(Intersection(t0, self))
y1 = shape_ray.origin.y + t1 * shape_ray.direction.y
if self.minimum < y1 < self.maximum:
xs.add_intersection(Intersection(t1, self))
self.intersect_caps(shape_ray, xs)
return xs
def local_intersect(self, shape_ray: Ray) -> GroupIntersections:
a = shape_ray.direction.x ** 2 - shape_ray.direction.y ** 2 + shape_ray.direction.z ** 2
b = 2 * shape_ray.origin.x * shape_ray.direction.x - \
2 * shape_ray.origin.y * shape_ray.direction.y + \
2 * shape_ray.origin.z * shape_ray.direction.z
xs = GroupIntersections()
# if a == 0 and b == 0:
if abs(a) < EPSILON and abs(b) < EPSILON:
self.intersect_caps(shape_ray, xs)
return xs
c = (shape_ray.origin.x ** 2) - (shape_ray.origin.y ** 2) + (shape_ray.origin.z ** 2)
if abs(a) < EPSILON:
t = -c / (2 * b)
xs.add_intersection(Intersection(t, self))
self.intersect_caps(shape_ray, xs)
return xs
discriminant = b ** 2 - 4 * a * c
# ray does not intersect the cylinder
if discriminant < 0:
return GroupIntersections()
t0 = (-b - math.sqrt(discriminant)) / (2 * a)
t1 = (-b + math.sqrt(discriminant)) / (2 * a)
if t0 > t1:
t0, t1 = t1, t0
y0 = shape_ray.origin.y + t0 * shape_ray.direction.y
if self.minimum < y0 < self.maximum:
xs.add_intersection(Intersection(t0, self))
y1 = shape_ray.origin.y + t1 * shape_ray.direction.y
if self.minimum < y1 < self.maximum:
xs.add_intersection(Intersection(t1, self))
self.intersect_caps(shape_ray, xs)
return xs
