def find_intersection(self, ray):
result = [0, False]
#Ray to sphere direction
oc = self.center - ray.origin
#Ray to sphere length squared
oc2 = dot_product(oc, oc)
#Distance to the sphere along the ray
#In other words, the point on the ray closest to the center
tca = float(dot_product(oc, ray.direction))
#Is the ray origin outside the sphere?
outside = oc2 > (self.radius ** 2)
if tca < 0.0 and outside:
return result
d2 = oc2 - tca * tca
thc = (self.radius * self.radius) - d2
if thc < 0.0:
return result
else:
if outside:
temp = tca - sqrt(thc)
else:
temp = tca + sqrt(thc)
if temp < 0.0:
return result
result[1] = True
result[0] = temp
return result
def phong_light(point, normal, eye, material):
#A variable to store the final color
point_color = [0, 0, 0]
#The ambient, diffuse and specular color of the material
a_color = material.diffuse_color
color = material.diffuse_color
s_color = material.specular_color
#Ensure that the normal is normalised
normal.normalise()
#The ambient coefficient ka
ambient_coefficient = 0.2
#Diffuse coefficient Kd
k_d = 1
#Specular coefficient Ks
k_s = 1
#Perform ambient lighting
i =0
while i < 3:
point_color[i] = ambient_coefficient * a_color[i]
i += 1
#For each light, compute the contribution to color
for light in lights:
#Calculate the light vector
light_vector = light.position - point
#Calculate the distance to the light
dist = light_vector.magnitude
#Then normalise it
light_vector.normalise()
#Calculate the view vector
view_vector = eye - point
view_vector.normalise()
#Compute the shadow ray
shadow_ray = Ray(point + light_vector * 0.001, light_vector)
#Check if there is an object in the way of the shadow ray
obj = get_first_intersection(shadow_ray, dist)
#If there is an object, this lights contribution isn't added
if obj[0] is not None:
continue;
#Else, light it up!
#Calculate the diffuse lighting
diffuse = max(dot_product(normal, light_vector), 0.0)
#Calculate the reflected ray
reflect= normal * 2.0 * diffuse - light_vector
reflect.normalise()
#Calculate the specular lighting
dp = max(dot_product(view_vector, light_vector), 0.0)
specular = pow(dp, material.specular_power)
#Add this lights contribution to each component of the color
i = 0
while i < 3:
point_color[i] += k_d * color[i] * diffuse\
+ k_s * s_color[i] * specular
i += 1
return point_color
def update(self, delta_time):
"""Animates the missile."""
# Moves missile based on its direction (the forward vector)
velocity = self.forward() * self.missile_speed
self.position += velocity * delta_time
# Rotate missile towards the player - Figure out where it is pointing and
# where do we want to point it
current_dir = self.forward()
desired_dir = (Vector3(0, 0, 0) - self.position).normalized()
# Find the angle between these two directions
dp = max(-1, min(1, dot_product(current_dir, desired_dir)))
angle = math.acos(dp)
# If the angle is larger than the ammount we can rotate a single frame,
# given by the time elapsed and the missile rotation speed, we need to
# clamp the value of the angle
if abs(angle) > self.missile_rotation_speed * delta_time:
angle = self.missile_rotation_speed * delta_time * math.copysign(
1, angle)
# Figure out the rotation axis to point the missile towards the desired direction
axis = cross_product(current_dir, desired_dir)
axis.normalize()
if (angle > 0.01):
# Rotate the missile towards the player
q = Quaternion.AngleAxis(axis, angle)
self.rotation = q * self.rotation
def find_intersection(self, ray):
result = [0.0, False]
rayD = dot_product(self.normal, ray.direction)
#Check if the ray is parallel to the plane
if fabs(rayD) < 0.0001:
return result
originD = -(dot_product(self.normal, ray.origin) + self.distance)
intersectDist = originD / rayD
#Check if the intersection is in front of the camera
if intersectDist < 0.0001:
return result
result[1] = True
result[0] = intersectDist
return result
def get_reflected_ray(original_ray, point, normal):
#Calculate the reflected ray
normal.normalise()
reflect_direction = original_ray.direction - normal * 2.0 * \
dot_product(original_ray.direction, normal)
reflect_direction.normalise()
reflected_ray = Ray(point + reflect_direction * 0.0001, reflect_direction)
return reflected_ray
def get_refracted_ray(ray, point, normal, obj):
#Refractive indices :: Hard coded for now
nc = 1.0
nt = 1.5
#Name changes - to keep track of things...
in_dir = ray.direction
#temp is used to decide if the ray is entering or exiting the medium
temp = dot_product(in_dir, normal)
if temp < 0.0:
into = True
nl = normal
else:
into = False
nl = - normal
#into tells you if the ray is entering or exiting!
#Determine n1 / n2
if into:
nnt = nc / nt
else:
nnt = nt / nc
#Next compute cos theta
ddn = dot_product(in_dir, nl)
#Now compute the other cosine
cos2t = 1 - (nnt * nnt) * (1 - ddn * ddn)
#Deal with total internal reflection
if cos2t < 0.0:
print "error"
refract_direction = None
else:
if into:
temp2 = normal * (ddn * nnt + sqrt(cos2t))
temp2.normalise()
refract_direction = in_dir * nnt - temp2
else:
temp2 = normal * (ddn * nnt + sqrt(cos2t))
temp2.normalise()
refract_direction = in_dir * nnt + temp2
refracted_ray = Ray(point + refract_direction * 0.001, refract_direction)
return refracted_ray
def lambert_light(point, normal, material):
diffuse_coefficient = 1
point_color = [0, 0, 0]
color = material.diffuse_color
normal.normalise()
for light in lights:
light_vector = light.position - point
light_vector.normalise()
shade = dot_product(light_vector, normal)
if shade < 0:
shade = 0
for i in range(len(point_color)):
point_color[i] += light.color[i] * color[i] * diffuse_coefficient *\
shade
return point_color
def create_terrain():
"""Creates a terrain, composed of different meshes (one per each type of material)
It support snow, water, grassland and cliffsize, based on hard-coded parameters"""
# Size of the terrain
size_x = 4
size_z = 4
# Number of divisions of the terrain. Vertex count scales with the square of this
div = 40
# Paramters for water and snow height/depth
water_depth = -0.1
snow_height = 0.15
px = size_x / div
pz = size_z / div
# For centering the terrain on the object center
origin = Vector3(-size_x * 0.5, 0, -size_z * 0.5)
# Create the meshes for each type of terrain
grass_mesh = Mesh("Terrain_Grass")
snow_mesh = Mesh("Terrain_Snow")
cliff_mesh = Mesh("Terrain_Cliff")
water_mesh = Mesh("Terrain_Water")
for dz in range(0, div):
for dx in range(0, div):
p1 = Vector3(dx * px, 0, dz * pz) + origin
p2 = Vector3((dx + 1) * px, 0, dz * pz) + origin
p3 = Vector3((dx + 1) * px, 0, (dz + 1) * pz) + origin
p4 = Vector3(dx * px, 0, (dz + 1) * pz) + origin
p1.y = sample_height(p1.x, p1.z)
p2.y = sample_height(p2.x, p2.z)
p3.y = sample_height(p3.x, p3.z)
p4.y = sample_height(p4.x, p4.z)
# Check if any of the points is underwater
water = clamp_to_water(p1, water_depth)
water |= clamp_to_water(p2, water_depth)
water |= clamp_to_water(p3, water_depth)
water |= clamp_to_water(p4, water_depth)
# Create the polygons
poly = []
poly.append(p1)
poly.append(p2)
poly.append(p3)
poly.append(p4)
if water:
# Polygon was under water, add it to that mesh
water_mesh.polygons.append(poly)
else:
# Check for snow height
avg_y = (p1.y + p2.y + p3.y + p4.y) * 0.25
if avg_y > snow_height:
# The polygon was above a certain point
snow_mesh.polygons.append(poly)
else:
# Check for cliff face, check the normal
normal = cross_product((p3 - p1).normalized(),
(p2 - p1).normalized())
if dot_product(normal, Vector3(0, 1, 0)) < 0.5:
cliff_mesh.polygons.append(poly)
else:
grass_mesh.polygons.append(poly)
# Create materials for the terrain
grass_material = Material(Color(0.1, 0.6, 0.1, 1), "GrassMaterial")
snow_material = Material(Color(0.8, 0.8, 0.8, 1), "SnowMaterial")
cliff_material = Material(Color(0.4, 0.4, 0.4, 1), "CliffMaterial")
water_material = Material(Color(0, 0.5, 0.7, 1), "WaterMaterial")
# Return meshes and materials
meshes = [grass_mesh, snow_mesh, cliff_mesh, water_mesh]
materials = [grass_material, snow_material, cliff_material, water_material]
return meshes, materials