def __init__(self, Pos, W, H, Fov=1, Samples=256):
"""
Initialises a Camera class.
Parameters:
Pos: Vec3. The position of the camera
W: Float. The camera width
H: Float. The camera height
Optional Parameters:
Fov: Float. The field of view constant of the camera. Default 1.
Samples: Int. The rendering sample rate. Deafault 256
"""
# Init variables
self.fov = Fov
self.w = W # Width
self.h = H # Height
self.pos = Pos # Camera position
self.samples = Samples # Sample Rate
self.normal = Vec3(0, 0, -1) # Normal (used for rotation)
self.bgColor = Vec3(1, 1, 1) # background colour
self.target = Vec3(0, 0, 0) # Camera target, used for rotation
self.barWidth = 50 # progress bar width
# Array for image data
self.image_array = [[0] * (self.w * 3) for i in range(self.h)]
# set rotation matrix
self.ca = self.setCamera()
def loadModel(self, path, mtl):
"""
Loads a model from a obj and mtl file.
Parmeters:
path: String. The path to the obj file
mtl: String. The path to the mtl file
"""
mat = None
if mtl is not None:
for line in open(mtl):
if "newmtl" in line:
# update current material
mat = line[7:].strip()
elif line[0:2] == "Kd":
# add material colour
self.materials[mat] = (
Vec3(*(map(float, line[3:].strip().split()))))
verts = []
for line in open(path):
# If line is a vertex
if line[0] == "v":
# Add vertex
verts.append(
Vec3(*(map(float, line[1:].strip().split(" ")))))
# If line is a face
if line[0] == "f":
# add face
a = line[1:].strip().split(" ")
self.addPrimitive(
Triangle(*[Copy(verts[int(i) - 1]) for i in a], mat))
# if line is a material declaration
if "usemtl" in line:
mat = line[7:].strip() # Update material
def __init__(self, orig=Vec3(0, 0, 0), dir=Vec3(0, 0, 0)):
"""
Initializes the ray.
Optional parameters:
orig: Vec3. The origin of the ray.
dir: Vec3. The direction of the ray.
"""
self.o = orig
self.d = Normalize(dir)
def midDay(scene):
sun = Sun(pos=Vec3(40, 100, 30))
# orient sun
sun.lookAt(Vec3(0, 0, 0))
# Add sun to scene
scene.addLight(sun)
# Create sky
sky = Sky()
# Add sky to scene
scene.addLight(sky)
def dusk(scene):
sun = Sun(pos=Vec3(40, 20, 0), colour=Vec3(0.4, 0.2, 0.4))
# orient sun
sun.lookAt(Vec3(0, 0, 0))
# Add sun to scene
scene.addLight(sun)
# Create sky
sky = Sky()
# Add sky to scene
scene.addLight(sky)
def __init__(self, b=AABB(Vec3(0, 0, 0), Vec3(0, 0, 0))):
"""
Initializes a Braunch Class
"""
self.leaves = []
self.braunches = []
self.materials = {}
self.bounds = b
self.lights = []
self.average = 0
self.time = 0
def __init__(self, size=2, normal=Vec3(0, 0, 1), pos=Vec3(1, 0, 0), colour=Vec3(0.77, 0.77, 0.72)):
"""
Initializes a sun class
Optional Parmeters:
size: Float. The size of the sun. Default 2
normal: Vec3. The direction the sun's facing. Default Vec3(0, 0, 1)
pos: Vec3. The position of the sun. Default Vec3(1, 0, 0)
colour: Vec3. The colour of the sun.
Default colour=Vec3(0.97, 0.97, 0.72)
"""
self.size = size
self.normal = normal
self.pos = pos
self.colour = colour
def intersectLeaves(self, leaves, ray):
close = (False, float("inf"), Vec3(0, 0, 0))
indie = None
self.average += len(leaves)
for i in leaves:
intersection = i.intersect(ray)
if intersection[0] and 0 < intersection[1] < close[1]:
close = intersection
indie = i
return close, indie
def diskPoint(normal):
"""
Returns a random point on a disk with a radius of 1
normal: Vec3. The normal of the disk to be used
return: Vec3. The random point
"""
theta = random() * 2 * pi # theta in radians (0-2)
mag = sqrt(random()) # sqrt makes the distribution uniform
y = sin(theta) * mag # Generate x and y coords with some trig
x = cos(theta) * mag
return orthonormal(Vec3(x, y, 0), normal) # rotate to match normal
def getDir(self, x, y):
"""
Get direction from pixel coordinates
Parameters:
x: The pixel's x coordinates
y: The pixel's y coordinates
"""
# calculate direction
d = Vec3(x / self.w * 2 - 1, y / self.h * 2 - 1, self.fov)
d = Normalize(d)
# Rotate to match camera rotation
return self.multMat(self.ca, d)
def fromScene(self, scene):
"""
Constructs an octree from a scene
Parameters:
Scene: Scene. The scene to construct an octree from.
"""
# Calculate the bounding box of the scene
minx = miny = minz = +10000
maxx = maxy = maxz = -10000
for i in scene.primitives:
minx = min(min(i.v0.x, i.v1.x, i.v2.x), minx)
miny = min(min(i.v0.y, i.v1.y, i.v2.y), miny)
minz = min(min(i.v0.z, i.v1.z, i.v2.z), minz)
maxx = max(max(i.v0.x, i.v1.x, i.v2.x), maxx)
maxy = max(max(i.v0.y, i.v1.y, i.v2.y), maxy)
maxz = max(max(i.v0.z, i.v1.z, i.v2.z), maxz)
self.bounds = AABB(Vec3(minx, miny, minz), Vec3(maxx, maxy, maxz))
for t in scene.primitives:
self.grow((t))
self.addMaterials(scene.materials)
self.addLights(scene.lights)
def setCamera(self):
"""
Updates the camera's rotation matrix
"""
ro = self.pos # ray origin
ta = self.target # ray target
cr = 0 # Angular rotation (should always be 0)
# Construct the matix using some fancy linear algebra
cw = Normalize(ta - ro)
cp = Vec3(sin(cr), cos(cr), 0.0)
cu = Normalize(Cross(cw, cp))
cv = Normalize(Cross(cu, cw))
return [cu, cv, cw]
def rendererCalcColor(self, ray, numBounce, tracer):
"""
Calculates a pixel colour given a starting ray using Monte Carlo magik!
Parameters:
ray: Ray. The ray to be traced
numBounce: Int. The number of bounces the ray is allowed to do
tracer: Scene. The scene
"""
# Variables for colour accumulation
tCol = Vec3(0, 0, 0)
gCol = Vec3(1, 1, 1)
for i in range(numBounce):
# intersect with seen
isec = tracer.worldIntersect(ray)
# intersection information
sec = isec["t"]
# if no intersection
if not sec[0]:
# stop the accumulation process or return the sky
if i == 0:
return self.bgColor
else:
break
# Calculate intersection position
pos = ray.o + (ray.d ^ sec[1])
# load material
material = isec["index"].mat
# Load surface colour and compute direct lighting
sCol = tracer.materials[material]
dCol = self.applyDirectLighting(pos, sec[2], tracer)
# Create new ray
ray = Ray(orig=pos + (sec[2] ^ 0.1),
dir=OrientedHemiDir(sec[2]))
# accumulate colours
gCol = sCol * gCol
tCol += gCol * dCol
# return the total colour
return tCol
def applyDirectLighting(self, pos, nor, scene):
"""
Applies Direct lighting
Parameters:
pos: Vec3. The point to apply the direct lighting
nor: Vec3. The surface normal.
scene: Scene. The scene.
"""
# start the accumulation
dCol = Vec3(0, 0, 0)
# iterate over lights and accumulate colors
for i in scene.lights:
dCol += i.calcDirect(pos, nor, scene)
return dCol
def multMat(self, mat, vec):
"""
Multiplies a Vec3 by a matrix.
Parameters:
mat: List<Vec3>. The matrix to be multiplied
vec: Vec3. The vector to be multiplied
"""
# Initialise the output vector
out = Vec3(0, 0, 0)
# iterate through the dimensions
dimensions = ["x", "y", "z"]
for i in range(3):
out = out + (mat[i] ^ getattr(vec, dimensions[i]))
return out
def intersect(self, ray):
"""Intersects a ray with a Triangle
ray: Ray the ray to be intersected
return: Tuple (Bool hit, Float distance, Vec3 normal)
"""
# Miss tuple
miss = (False, 0, Vec3(0, 0, 0))
normal = Vec3(0, 0, 0)
v0 = self.v0
v1 = self.v1
v2 = self.v2
# edges of the triangle
v0v1 = v1 - v0
v0v2 = v2 - v0
# Determinant of a 3*3 matrix using triple scaler product
pvec = Cross(ray.d, v0v2)
det = Dot(v0v1, pvec)
if det < 0.000001:
return miss
invDet = 1.0 / det
tvec = ray.o - v0
u = Dot(tvec, pvec) * invDet
# make sure the barycentric coordinates are in the triangle
if u < 0 or u > 1:
return miss
qvec = Cross(tvec, v0v1)
v = Dot(ray.d, qvec) * invDet
# make sure the barycentric coordinates are in the triangle
if v < 0 or u + v > 1:
return miss
return (True, Dot(v0v2, qvec) * invDet, self.normal)
def orthonormal(p, normal):
"""
Translates a normalized vector to have its z axis aligned along
a specific normal.
p: Vec3 the vector to be translated
normal: the normal for the vector to be translated around
"""
# create orthonormal basis around normal
w = normal
v = Cross(Vec3(0.00319, 0.0078, 1.0), w) # jittered up
v = Normalize(v) # normalize
u = Cross(v, w)
hemi_dir = (u ^ p.x) + (v ^ p.y) + (w ^ p.z) # linear projection
return Normalize(hemi_dir) # make direction
def sampleHemisphere(u1, u2):
"""Return a point on the hemisphere from polar coordinates
u1: Float. the radius of the polar coordinats
u2: Float. theta
return: Vec3. point on hemisphere
"""
# make r uniform over the sphere using the inverse itegral
# of the distribution density
r = sqrt(u1)
# scale theta to radians
theta = 2 * pi * u2
# calculate x and y
x = r * cos(theta)
y = r * sin(theta)
return Vec3(x, y, sqrt(max(0, 1 - u1)))
def worldIntersect(self, ray):
"""
intersects the ray with the octree.
Parameters:
r: Ray. The ray to intersect
return: Tuple (Bool hit, Float distance, Vec3 normal)
"""
# the closest intersection so far
close = (False, float("inf"), Vec3(0, 0, 0))
index = -1
for i in range(len(self.primitives)):
intersection = self.primitives[i].intersect(ray)
self.average += 1
# if there's a new closest intersection update index and close
if intersection[0] and 0 < intersection[1] < close[1]:
close = intersection
index = i
return {"t": close, "index": self.primitives[index]}
def initRay(self, x):
for y in range(0, self.h):
col = Vec3(0, 0, 0)
# Aspect correction in the case the output image is not square
# This took me super long to figure out
mx = ((x + (self.h - self.w) / 2) * self.w/self.h)
# average the samples
for i in range(self.samples):
# calculate direction
# Adds the random to get anti-aliasing
a = self.getDir(mx + random(), y + random())
# create ray for rendering
ray = Ray(orig=self.pos, dir=a)
# render!
col = col + self.rendererCalcColor(ray, 4, self.tracer)
col = col ^ (1 / self.samples) # average the samples
self.savePixel(col, x, y) # save pixel
return "complete"
def worldIntersect(self, r):
"""
intersects the ray with the octree.
Parameters:
r: Ray. The ray to intersect
return: Tuple (Bool hit, Float distance, Vec3 normal)
"""
miss = (False, float("inf"), Vec3(0, 0, 0))
# Breadth first search
queue = [self]
index = None
for i in queue:
if i.bounds.intersect(r) < 1000:
# Check leaves
intersect, indet = self.intersectLeaves(i.leaves, r)
if intersect[0] and 0 < intersect[1] < miss[1]:
miss = intersect
index = indet
# Check braunches
queue += i.braunches
# print(total)
return {"t": miss, "index": index}
def render(self, tracer, imgOut):
"""
Renders a scene to an image
Parameters:
tracer: Scene. The scene to be rendered.
imgOut: String. The name of the output file
"""
# loop through all the pixels in the image
for x in range(self.w):
for y in range(self.h):
col = Vec3(0, 0, 0)
# Aspect correction in the case the output image is not square
# This took me super long to figure out
mx = ((x + (self.h - self.w) / 2) * self.w / self.h)
# average the samples
for i in range(self.samples):
# calculate direction
# Adds the random to get anti-aliasing
a = self.getDir(mx + random(), y + random())
# create ray for rendering
ray = Ray(orig=self.pos, dir=a)
# render!
col = col + self.rendererCalcColor(ray, 4, tracer)
col = col ^ (1 / self.samples) # average the samples
self.savePixel(col, x, y) # save pixel
# ===Update progress bar===
# Clear terminal
os.system('cls' if os.name == 'nt' else 'clear')
# Calculate progress
prog = int(round((x) / self.w * self.barWidth))
# Print progress bar
print("[" + "=" * prog + ">" + " " * (self.barWidth - prog) +
"] " + str(round(prog *
(100 / self.barWidth))) + "% completed")
# ===Save Image===
self.saveImage(imgOut) # save image
def subDivide(self):
"""
Subdivides into 8 smaller AABB's
returns: List. 8 smaller AABB's
"""
# A-H represent the 8 corners of the box
# M is the midpoint of the box
a = self.info[0]
g = self.info[1]
b = Vec3(g.x, a.y, a.z)
c = Vec3(g.x, a.y, g.z)
d = Vec3(a.x, a.y, g.z)
e = Vec3(a.x, g.y, a.z)
f = Vec3(b.x, g.y, b.z)
h = Vec3(d.x, g.y, g.z)
# Calculate midpoint
m = self.info[0] + ((self.info[1] - self.info[0]) ^ 0.5)
boxes = []
# Construct all 8 boxes
for i in [a, b, c, d, e, f, g, h]:
boxes.append(AABB(i, m))
return boxes
from Vector3 import Vec3, Cross, Normalize
from random import random
from math import pi, sin, cos
normal = Normalize(Vec3(1, 0, 0))
f = open("data.dat", "w")
def diskPoint():
theta = random() * pi * 2
mag = random()
x = cos(theta) * mag
y = sin(theta) * mag
return Vec3(x, y, 0)
for i in range(1000):
p = diskPoint()
f.write("{0} {1}\n".format(p.x, p.y))
w = normal
v = Cross(Vec3(0.00319, 0.0078, 1.0), w) # jittered up
v = Normalize(v) # normalize
u = Cross(v, w)
hemi_dir = (u ^ p.x) + (v ^ p.y) + (w ^ p.z)
hemi_dir = Normalize(hemi_dir)
# f.write("{0} {1} {2}\n".format(hemi_dir.x, hemi_dir.y, hemi_dir.z))
print(Normalize(hemi_dir))
def __init__(self, colour=Vec3(0.6, 0.6, 0.55)):
"""initializes a sky class
Optional parameters:
colour: Vec3. The colour of the sun. Default Vec3(0.4, 0.4, 0.45)
"""
self.colour = colour
from Vector3 import Vec3
from Camera import Camera
from Scene import Scene
from Sun import Sun
from Sky import Sky
from timeit import default_timer as timer
from Octree import Braunch
# turn on tree
useTree = False
# Create new scene
scene = Scene()
# Load Model and materials
scene.loadModel("models/pyramid.obj", "models/pyramid.mtl")
# Create Sun
sun = Sun(pos=Vec3(80, 50, 50))
sun.lookAt(Vec3(0, 0, 0))
scene.addLight(sun)
# Create sky
sky = Sky()
scene.addLight(sky)
# Create Camera
cam = Camera(Vec3(8, 4, 8), int(200), int(200), Fov=1.4, Samples=2)
cam.lookAt(Vec3(0, 3, 0))
# Render scene
ts = timer()
if useTree:
tree = Braunch()
tree.fromScene(scene)
cam.render(tree, "pyramid.png")
else:
message="File does not exist")
material = validInput("Material File (.obj): ",
path.isfile,
message="File does not exist")
width = inputInt("Output Width: ")
height = inputInt("Output Height: ")
while True:
proto = input("lighting (" + str([i for i in lighting.presets]) + "): ")
if proto in lighting.presets:
break
preset = proto
output = input("output image name: ")
# add the extension png if necessary
output += "" if output[-4:] == ".png" else ".png"
# Create new scene
scene = Scene()
# Load Model and materials
scene.loadModel(model, material)
# Add lighting
lighting.presets[preset](scene)
# Create Camera
cam = Camera(Vec3(-8, 5, 8), width, height, Fov=1.4, Samples=samples)
cam.lookAt(Vec3(0, 3, 0))
# Render scene
ts = timer()
cam.render(scene, output)
print("Render time: {}".format(timer() - ts))
print("Intersections: ", scene.average)
tmin, tmax = tmax, tmin
for a in ["y", "z"]:
b = getattr(ray.d, a)
if b == 0:
b += 0.000001
tymin = (getattr(self.min, a) - getattr(ray.o, a)) / \
b
tymax = (getattr(self.max, a) - getattr(ray.o, a)) / \
b
# Swap if necessary
if tymin > tymax:
tymin, tymax = tymax, tymin
# Check collision
if (tmin > tymax) or (tymin > tmax):
return False
# Update tmin and tmax
tmin = min(tmin, tymin)
tmax = max(tmax, tymax)
t = tmin
if (t < 0):
t = tmax
if t < 0:
return False
return True
aabb = AABB(Vec3(-1, -1, -1), Vec3(1, 1, 1))
ray = Ray(orig=Vec3(0, 0, -3), dir=Vec3(0, 0, -2))
z = aabb.intersect(ray)
print(z)
from Octree import Braunch
from Scene import Scene
from Vector3 import Vec3
from timeit import default_timer as timer
from Sun import Sun
from Sky import Sky
from Camera import Camera
# Create new scene
scene = Scene()
# Load Model and materials
scene.loadModel("untitled.obj", "untitled.mtl")
sun = Sun(pos=Vec3(-20, 30, 30))
sun.lookAt(Vec3(0, 0, 0))
scene.addLight(sun)
sun.size = 3
# Create sky
sky = Sky(colour=Vec3(0.3, 0.2, 0.3))
scene.addLight(sky)
# Create Camera
cam = Camera(Vec3(-4, 3, -5), 256, 256, Fov=1, Samples=7)
cam.lookAt(Vec3(0, 0, 0))
tree = Braunch()
tree.fromScene(scene)
tree.display()
# Render scene
ts = timer()
cam.render(tree)
treeTime = timer() - ts
# print("Render time: {}".format(timer()-ts))
def diskPoint():
theta = random() * pi * 2
mag = random()
x = cos(theta) * mag
y = sin(theta) * mag
return Vec3(x, y, 0)
