def local_intersect(self, shape_ray: Ray) -> GroupIntersections:
# TODO: Could avoid having to check all six faces?
xtmin, xtmax = check_axis(shape_ray.origin.x, shape_ray.direction.x)
ytmin, ytmax = check_axis(shape_ray.origin.y, shape_ray.direction.y)
ztmin, ztmax = check_axis(shape_ray.origin.z, shape_ray.direction.z)
tmin = max(xtmin, ytmin, ztmin)
tmax = min(xtmax, ytmax, ztmax)
if tmin > tmax:
return GroupIntersections()
return GroupIntersections(Intersection(tmin, self), Intersection(tmax, self))
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.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
def local_intersect(self, shape_ray: Ray) -> GroupIntersections:
# the vector from the sphere's center, to the ray origin
# remember: the sphere is centered at the world origin
sphere_to_ray = shape_ray.origin - point(0, 0, 0)
a = Vec3.dot(shape_ray.direction, shape_ray.direction)
b = 2 * Vec3.dot(shape_ray.direction, sphere_to_ray)
c = Vec3.dot(sphere_to_ray, sphere_to_ray) - 1
discriminant = (b**2) - (4 * a * c)
if discriminant < 0:
return GroupIntersections()
else:
t1 = Intersection((-b - math.sqrt(discriminant)) / (2 * a), self)
if discriminant == 0:
return GroupIntersections(t1, t1)
t2 = Intersection((-b + math.sqrt(discriminant)) / (2 * a), self)
return GroupIntersections(
t1, t2) if t1 < t2 else GroupIntersections(t2, t1)
def step_impl(context):
context.xs = GroupIntersections(Intersection(2.0, context.A),
Intersection(2.75, context.B),
Intersection(3.25, context.C),
Intersection(4.75, context.B),
Intersection(5.25, context.C),
Intersection(6.0, context.A))
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:
result = GroupIntersections()
dir_cross_e2 = Vec3.cross(shape_ray.direction, self.e2)
det = Vec3.dot(self.e1, dir_cross_e2)
if abs(det) < EPSILON:
return result
f = 1.0 / det
p1_to_origin = shape_ray.origin - self.p1
u = f * Vec3.dot(p1_to_origin, dir_cross_e2)
if u < 0 or u > 1:
return result
origin_cross_e1 = Vec3.cross(p1_to_origin, self.e1)
v = f * Vec3.dot(shape_ray.direction, origin_cross_e1)
if v < 0 or (u + v) > 1:
return result
t = f * Vec3.dot(self.e2, origin_cross_e1)
return GroupIntersections(Intersection(t, self))
def step_impl(context, t):
context.i2 = Intersection(t, context.s)
def step_impl(context, t, attribute):
instance = getattr(context, attribute)
context.i = Intersection(t, instance)
def step_impl(context):
context.xs = GroupIntersections(Intersection(1.8589, context.shape))
def step_impl(context):
context.xs = GroupIntersections(Intersection(-1, context.shape),
Intersection(1, context.shape))
def step_impl(context):
context.xs = GroupIntersections(
Intersection(-0.7071067811865476, context.shape),
Intersection(0.7071067811865476, context.shape))
def step_impl(context):
context.xs = GroupIntersections(
Intersection(1.4142135623730951, context.floor))
def step_impl(context):
context.xs = GroupIntersections(Intersection(-0.9899, context.A),
Intersection(-0.4899, context.B),
Intersection(0.4899, context.B),
Intersection(0.9899, context.A))