def ray4(FOVh, FOVv):
'''
Parameters:
FOVh (float): Horizontal field of view in radians
FOVv (float): Vertical field of view in radians
Returns:
vector3d.vector.Vector: normalised vector
'''
ray = Vector(-math.tan(FOVv / 2), math.tan(FOVh / 2), -1)
return ray.normalize()
def rotateRays(ray1, ray2, ray3, ray4, roll, pitch, yaw):
"""Rotates the four ray-vectors around all 3 axes
Parameters:
ray1 (vector3d.vector.Vector): First ray-vector
ray2 (vector3d.vector.Vector): Second ray-vector
ray3 (vector3d.vector.Vector): Third ray-vector
ray4 (vector3d.vector.Vector): Fourth ray-vector
roll float: Roll rotation
pitch float: Pitch rotation
yaw float: Yaw rotation
Returns:
Returns new rotated ray-vectors
"""
sinAlpha = math.sin(yaw)
sinBeta = math.sin(pitch)
sinGamma = math.sin(roll)
cosAlpha = math.cos(yaw)
cosBeta = math.cos(pitch)
cosGamma = math.cos(roll)
m00 = cosAlpha * cosBeta
m01 = cosAlpha * sinBeta * sinGamma - sinAlpha * cosGamma
m02 = cosAlpha * sinBeta * cosGamma + sinAlpha * sinGamma
m10 = sinAlpha * cosBeta
m11 = sinAlpha * sinBeta * sinGamma + cosAlpha * cosGamma
m12 = sinAlpha * sinBeta * cosGamma - cosAlpha * sinGamma
m20 = -sinBeta
m21 = cosBeta * sinGamma
m22 = cosBeta * cosGamma
# Matrix rotationMatrix = new Matrix(new double[][]{{m00, m01, m02}, {m10, m11, m12}, {m20, m21, m22}})
rotationMatrix = np.array([[m00, m01, m02], [m10, m11, m12],
[m20, m21, m22]])
# Matrix ray1Matrix = new Matrix(new double[][]{{ray1.x}, {ray1.y}, {ray1.z}})
# Matrix ray2Matrix = new Matrix(new double[][]{{ray2.x}, {ray2.y}, {ray2.z}})
# Matrix ray3Matrix = new Matrix(new double[][]{{ray3.x}, {ray3.y}, {ray3.z}})
# Matrix ray4Matrix = new Matrix(new double[][]{{ray4.x}, {ray4.y}, {ray4.z}})
ray1Matrix = np.array([[ray1.x], [ray1.y], [ray1.z]])
ray2Matrix = np.array([[ray2.x], [ray2.y], [ray2.z]])
ray3Matrix = np.array([[ray3.x], [ray3.y], [ray3.z]])
ray4Matrix = np.array([[ray4.x], [ray4.y], [ray4.z]])
res1 = rotationMatrix.dot(ray1Matrix)
res2 = rotationMatrix.dot(ray2Matrix)
res3 = rotationMatrix.dot(ray3Matrix)
res4 = rotationMatrix.dot(ray4Matrix)
rotatedRay1 = Vector(res1[0, 0], res1[1, 0], res1[2, 0])
rotatedRay2 = Vector(res2[0, 0], res2[1, 0], res2[2, 0])
rotatedRay3 = Vector(res3[0, 0], res3[1, 0], res3[2, 0])
rotatedRay4 = Vector(res4[0, 0], res4[1, 0], res4[2, 0])
rayArray = [rotatedRay1, rotatedRay2, rotatedRay3, rotatedRay4]
return rayArray
def getBoundingPolygon(FOVh, FOVv, altitude, roll, pitch, heading):
'''Get corners of the polygon captured by the camera on the ground.
The calculations are performed in the axes origin (0, 0, altitude)
and the points are not yet translated to camera's X-Y coordinates.
Parameters:
FOVh (float): Horizontal field of view in radians
FOVv (float): Vertical field of view in radians
altitude (float): Altitude of the camera in meters
heading (float): Heading of the camera (z axis) in radians
roll (float): Roll of the camera (x axis) in radians
pitch (float): Pitch of the camera (y axis) in radians
Returns:
vector3d.vector.Vector: Array with 4 points defining a polygon
'''
# import ipdb; ipdb.set_trace()
ray11 = CameraCalculator.ray1(FOVh, FOVv)
ray22 = CameraCalculator.ray2(FOVh, FOVv)
ray33 = CameraCalculator.ray3(FOVh, FOVv)
ray44 = CameraCalculator.ray4(FOVh, FOVv)
rotatedVectors = CameraCalculator.rotateRays(ray11, ray22, ray33,
ray44, roll, pitch,
heading)
origin = Vector(0, 0, altitude)
intersections = CameraCalculator.getRayGroundIntersections(
rotatedVectors, origin)
return intersections
def render(screen: pygame.Surface, objects: Tuple[Geometry],
lights: Tuple[Light]):
screen.lock()
for j in range(-int(SCREEN[1] / 2), int(SCREEN[1] / 2)):
for i in range(-int(SCREEN[0] / 2), int(SCREEN[0] / 2)):
x = (2 * (i + 0.5)) / (SCREEN[0] - 1) * math.tan(FOV / 2.0) * int(
SCREEN[0]) / SCREEN[1]
y = -(2 * (j + 0.5)) / (SCREEN[1] - 1) * math.tan(FOV / 2.0)
direction = Vector(x, y, -1).normalize()
screen.set_at((i + int(SCREEN[0] / 2), j + int(SCREEN[1] / 2)),
cast_ray(Vector(0, 0, 0), direction, tuple(objects),
tuple(lights)))
pygame.display.flip()
screen.unlock()
def cast_ray(orig: Vector,
direction: Vector,
objects: Tuple[Geometry],
lights: Tuple[Light],
depth=0):
c = None
res, hit, N, obj_hit = scene_intersect(orig, direction, objects)
if depth > 4 or not res:
return (128, 200, 255)
refl_dir = reflect(direction, N).normalize()
refl_orig = hit - N * 0.001 if refl_dir * N < 0 else hit + N * 0.001
refl_color = cast_ray(refl_orig, refl_dir, objects, lights, depth + 1)
obj_to_render = obj_hit
if hit:
diffuse_light_intens = 0
specular_light_intens = 0
for light in lights:
light_dir = (light.pos - hit).normalize()
diffuse_light_intens += light.intensity * max(0.0, light_dir * N)
specular_light_intens += pow(
max(0.0, -reflect(-light_dir, N) * direction),
obj_to_render.specular()) * light.intensity
c = obj_to_render.diffuse_color(
) * diffuse_light_intens * obj_to_render.albedo().x + Vector(
1.0, 1.0,
1.0) * specular_light_intens * 255 * obj_to_render.albedo(
).y + Vector(*refl_color) * obj_to_render.albedo().z
if c.x > 255:
c.x = 255
if c.y > 255:
c.y = 255
if c.z > 255:
c.z = 255
return (int(c.x), int(c.y), int(c.z))
def findRayGroundIntersection(ray, origin):
"""
Finds a ray-vector's intersection with the ground approximated by a planeç
Parameters:
ray (vector3d.vector.Vector): Ray-vector
origin (vector3d.vector.Vector): Camera's position
Returns:
vector3d.vector.Vector
"""
# Parametric form of an equation
# P = origin + vector * t
x = Vector(origin.x, ray.x)
y = Vector(origin.y, ray.y)
z = Vector(origin.z, ray.z)
# Equation of the horizontal plane (ground)
# -z = 0
# Calculate t by substituting z
t = -(z.x / z.y)
# Substitute t in the original parametric equations to get points of intersection
return Vector(x.x + x.y * t, y.x + y.y * t, z.x + z.y * t)
def getBoundingPolygon(FOVh,
FOVv,
roll,
pitch,
yaw,
camera_pos=(0.0, 0.0, 100.0),
units="feet"):
'''Get corners of the polygon captured by the camera on the ground.
The calculations are performed in the axes origin (0, 0, altitude)
and the points are not yet translated to camera's X-Y coordinates.
Parameters:
FOVh (float): Horizontal field of view in degrees
FOVv (float): Vertical field of view in degrees
roll (float): Roll of the camera (x axis) in degrees
yaw (float): Heading of the camera (z axis) in degrees
pitch (float): Pitch of the camera (y axis) in degrees
camera_pos (float): Tuple. XYZ coordinate of camera
units (str): Units label
Returns:
vector3d.vector.Vector: Array with 4 points defining a polygon
'''
# import ipdb; ipdb.set_trace()
# Convert into radians
FOVh = np.radians(float(FOVh))
FOVv = np.radians(float(FOVv))
roll = np.radians(float(roll))
pitch = np.radians(float(pitch))
yaw = np.radians(float(yaw))
ray11 = CameraCalculator.ray1(FOVh, FOVv)
ray22 = CameraCalculator.ray2(FOVh, FOVv)
ray33 = CameraCalculator.ray3(FOVh, FOVv)
ray44 = CameraCalculator.ray4(FOVh, FOVv)
rotatedVectors = CameraCalculator.rotateRays(ray11, ray22, ray33,
ray44, roll, pitch, yaw)
origin = Vector(camera_pos[0], camera_pos[1], camera_pos[2])
intersections = CameraCalculator.getRayGroundIntersections(
rotatedVectors, origin)
return intersections
def main():
objects = [
Sphere(Vector(-3, 0, -16), 4,
Material(Vector(0.0, 0.4, 0.9), (Vector(255, 255, 255)), 50)),
Sphere(Vector(9, 1, -16), 7,
Material(Vector(0.9, 0.1, 0.2), Vector(255, 128, 255), 10)),
Sphere(Vector(-8, 5, -16), 2,
Material(Vector(0.4, 0.5, 0.4), Vector(0, 128, 0), 100))
]
lights = [
Light(Vector(-20, 20, 20), 1.5),
Light(Vector(30, 50, -25), 1.3),
Light(Vector(30, 20, 30), 0.7)
]
pygame.init()
pygame.display.set_caption("SW RT")
screen = pygame.display.set_mode((int(SCREEN[0]), int(SCREEN[1])))
while True:
st = time.time()
render(screen, objects, lights)
print(time.time() - st)
pygame.display.flip()
objects[0].pos.x += 1
for event in pygame.event.get():
if event.type == pygame.QUIT:
return
