def norm(v0):
"""
Input: 1 size 3 vector
Output: Size 3 vector with the normal of the vector
"""
v0length = length(v0)
if not v0length:
return V3(0, 0, 0)
return V3(v0.x / v0length, v0.y / v0length, v0.z / v0length)
def cross(v0, v1):
"""
Input: 2 size 3 vectors
Output: Size 3 vector with the cross product
"""
return V3(
v0.y * v1.z - v0.z * v1.y,
v0.z * v1.x - v0.x * v1.z,
v0.x * v1.y - v0.y * v1.x,
)
def barycentric(A, B, C, P):
"""
Input: 3 size 2 vectors and a point
Output: 3 barycentric coordinates of the point in relation to the triangle formed
* returns -1, -1, -1 for degenerate triangles
"""
cx, cy, cz = cross(V3(B.x - A.x, C.x - A.x, A.x - P.x),
V3(B.y - A.y, C.y - A.y, A.y - P.y))
if abs(cz) < 1:
return -1, -1, -1 # this triangle is degenerate, return anything outside
# [cx cy cz] = [u v 1]
u = cx / cz
v = cy / cz
w = 1 - (u + v)
return w, v, u
def load(self, filename, translate, scale):
model = Obj(filename)
light = V3(0, 0, 1)
for face in model.faces:
vcount = len(face)
if vcount == 3:
f1 = face[0][0] - 1
f2 = face[1][0] - 1
f3 = face[2][0] - 1
a = self.transform(model.vertices[f1], translate, scale)
b = self.transform(model.vertices[f2], translate, scale)
c = self.transform(model.vertices[f3], translate, scale)
normal = norm(cross(sub(b, a), sub(c, a)))
intensity = dot(normal, light)
grey = round(255 * intensity)
if grey < 0:
continue
self.triangle(a, b, c, intensity)
else:
# assuming 4
f1 = face[0][0] - 1
f2 = face[1][0] - 1
f3 = face[2][0] - 1
f4 = face[3][0] - 1
vertices = [
self.transform(model.vertices[f1], translate, scale),
self.transform(model.vertices[f2], translate, scale),
self.transform(model.vertices[f3], translate, scale),
self.transform(model.vertices[f4], translate, scale)
]
normal = norm(
cross(sub(vertices[0], vertices[1]),
sub(vertices[1],
vertices[2]))) # no necesitamos dos normales!!
intensity = dot(normal, light)
grey = round(255 * intensity)
if grey < 0:
continue # dont paint this face
# vertices are ordered, no need to sort!
# vertices.sort(key=lambda v: v.x + v.y)
A, B, C, D = vertices
self.triangle(A, B, C, intensity)
self.triangle(A, C, D, intensity)
def mul(v0, k):
"""
Input: 2 size 3 vectors
Output: Size 3 vector with the per element multiplication
"""
return V3(v0.x * k, v0.y * k, v0.z * k)
def sub(v0, v1):
"""
Input: 2 size 3 vectors
Output: Size 3 vector with the per element substraction
"""
return V3(v0.x - v1.x, v0.y - v1.y, v0.z - v1.z)
def transform(self, vertex, translate=(0, 0, 0), scale=(1, 1, 1)):
# returns a vertex 3, translated and transformed
return V3(round((vertex[0] + translate[0]) * scale[0]),
round((vertex[1] + translate[1]) * scale[1]),
round((vertex[2] + translate[2]) * scale[2]))
def sum(v0, v1):
"""
Input: 2 size 3 vectors
Output: Size 3 vector with the per element sum
"""
return V3(v0.x + v1.x, v0.y + v1.y, v0.z + v1.z)
def __init__(self):
self.paintColor = WHITE
self.bufferColor = BLACK
self.light = V3(0, 0, 1)
