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Runtime error
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import numpy as np
def vec3(x, y, z):
return np.array([x, y, z], dtype=np.float32)
def radians(v):
return np.radians(v)
def identity():
return np.identity(4, dtype=np.float32)
def empty():
return np.zeros([4, 4], dtype=np.float32)
def magnitude(v):
return np.linalg.norm(v)
def normalize(v):
m = magnitude(v)
return v if m == 0 else v / m
def dot(u, v):
return np.sum(u * v)
def cross(u, v):
res = vec3(0, 0, 0)
res[0] = u[1] * v[2] - u[2] * v[1]
res[1] = u[2] * v[0] - u[0] * v[2]
res[2] = u[0] * v[1] - u[1] * v[0]
return res
# below functions can be optimized
def translate(m, v):
res = np.copy(m)
res[:, 3] = m[:, 0] * v[0] + m[:, 1] * v[1] + m[:, 2] * v[2] + m[:, 3]
return res
def rotate(m, angle, v):
a = angle
c = np.cos(a)
s = np.sin(a)
axis = normalize(v)
temp = (1 - c) * axis
rot = empty()
rot[0][0] = c + temp[0] * axis[0]
rot[0][1] = temp[0] * axis[1] + s * axis[2]
rot[0][2] = temp[0] * axis[2] - s * axis[1]
rot[1][0] = temp[1] * axis[0] - s * axis[2]
rot[1][1] = c + temp[1] * axis[1]
rot[1][2] = temp[1] * axis[2] + s * axis[0]
rot[2][0] = temp[2] * axis[0] + s * axis[1]
rot[2][1] = temp[2] * axis[1] - s * axis[0]
rot[2][2] = c + temp[2] * axis[2]
res = empty()
res[:, 0] = m[:, 0] * rot[0][0] + m[:, 1] * rot[0][1] + m[:, 2] * rot[0][2]
res[:, 1] = m[:, 0] * rot[1][0] + m[:, 1] * rot[1][1] + m[:, 2] * rot[1][2]
res[:, 2] = m[:, 0] * rot[2][0] + m[:, 1] * rot[2][1] + m[:, 2] * rot[2][2]
res[:, 3] = m[:, 3]
return res
def perspective(fovy, aspect, zNear, zFar):
tanHalfFovy = np.tan(fovy / 2)
res = empty()
res[0][0] = 1 / (aspect * tanHalfFovy)
res[1][1] = 1 / (tanHalfFovy)
res[2][3] = -1
res[2][2] = - (zFar + zNear) / (zFar - zNear)
res[3][2] = -(2 * zFar * zNear) / (zFar - zNear)
return res.T
def ortho(left, right, bottom, top, zNear, zFar):
# res = np.ones([4, 4], dtype=np.float32)
res = identity()
res[0][0] = 2 / (right - left)
res[1][1] = 2 / (top - bottom)
res[2][2] = - 2 / (zFar - zNear)
res[3][0] = - (right + left) / (right - left)
res[3][1] = - (top + bottom) / (top - bottom)
res[3][2] = - (zFar + zNear) / (zFar - zNear)
return res.T
def lookat(eye, center, up):
f = normalize(center - eye)
s = normalize(cross(f, up))
u = cross(s, f)
res = identity()
res[0][0] = s[0]
res[1][0] = s[1]
res[2][0] = s[2]
res[0][1] = u[0]
res[1][1] = u[1]
res[2][1] = u[2]
res[0][2] = -f[0]
res[1][2] = -f[1]
res[2][2] = -f[2]
res[3][0] = -dot(s, eye)
res[3][1] = -dot(u, eye)
res[3][2] = -dot(f, eye)
return res.T
def transform(d, m):
return np.dot(m, d.T).T
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