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Math3D.py
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import math
class Vec3:
def __init__(self, x, y, z):
self.x = x
self.y = y
self.z = z
def __str__(self) -> str:
return str(self.x) + '\n' + str(self.y) + '\n' + str(self.z) + '\n'
class Vec4:
def __init__(self, x, y, z, w=1):
self.x = x
self.y = y
self.z = z
self.w = w
def __str__(self) -> str:
return str(self.x) + '\n' + str(self.y) + '\n' + str(self.z) + '\n' + str(self.w) + '\n'
class Mat4:
def __init__(self):
# identity matrix
self.matrix = [[0 for x in range(4)] for y in range(4)]
for i in range(4):
self.matrix[i][i] = 1
def __str__(self) -> str:
string = ""
for i in range(4):
for j in range(4):
string += str(self.matrix[i][j]) + " "
string += '\n'
return string
def __mul__(self, other):
if type(other) is Vec4:
x = self.matrix[0][0] * other.x + self.matrix[0][1] * other.y + self.matrix[0][2] * other.z + self.matrix[0][3] * other.w
y = self.matrix[1][0] * other.x + self.matrix[1][1] * other.y + self.matrix[1][2] * other.z + self.matrix[1][3] * other.w
z = self.matrix[2][0] * other.x + self.matrix[2][1] * other.y + self.matrix[2][2] * other.z + self.matrix[2][3] * other.w
w = self.matrix[3][0] * other.x + self.matrix[3][1] * other.y + self.matrix[3][2] * other.z + self.matrix[3][3] * other.w
return Vec4(x, y, z, w)
if type(other) is Mat4:
new_mat = Mat4()
new_mat.matrix = [[0 for x in range(4)] for y in range(4)]
a = self.matrix
b = other.matrix
new_mat.matrix[0][0] = a[0][0] * b[0][0] + a[0][1] * b[1][0] + a[0][2] * b[2][0] + a[0][3] * b[3][0]
new_mat.matrix[0][1] = a[0][0] * b[0][1] + a[0][1] * b[1][1] + a[0][2] * b[2][1] + a[0][3] * b[3][1]
new_mat.matrix[0][2] = a[0][0] * b[0][2] + a[0][1] * b[1][2] + a[0][2] * b[2][2] + a[0][3] * b[3][2]
new_mat.matrix[0][3] = a[0][0] * b[0][3] + a[0][1] * b[1][3] + a[0][2] * b[2][3] + a[0][3] * b[3][3]
new_mat.matrix[1][0] = a[1][0] * b[0][0] + a[1][1] * b[1][0] + a[1][2] * b[2][0] + a[1][3] * b[3][0]
new_mat.matrix[1][1] = a[1][0] * b[0][1] + a[1][1] * b[1][1] + a[1][2] * b[2][1] + a[1][3] * b[3][1]
new_mat.matrix[1][2] = a[1][0] * b[0][2] + a[1][1] * b[1][2] + a[1][2] * b[2][2] + a[1][3] * b[3][2]
new_mat.matrix[1][3] = a[1][0] * b[0][3] + a[1][1] * b[1][3] + a[1][2] * b[2][3] + a[1][3] * b[3][3]
new_mat.matrix[2][0] = a[2][0] * b[0][0] + a[2][1] * b[1][0] + a[2][2] * b[2][0] + a[2][3] * b[3][0]
new_mat.matrix[2][1] = a[2][0] * b[0][1] + a[2][1] * b[1][1] + a[2][2] * b[2][1] + a[2][3] * b[3][1]
new_mat.matrix[2][2] = a[2][0] * b[0][2] + a[2][1] * b[1][2] + a[2][2] * b[2][2] + a[2][3] * b[3][2]
new_mat.matrix[2][3] = a[2][0] * b[0][3] + a[2][1] * b[1][3] + a[2][2] * b[2][3] + a[2][3] * b[3][3]
new_mat.matrix[3][0] = a[3][0] * b[0][0] + a[3][1] * b[1][0] + a[3][2] * b[2][0] + a[3][3] * b[3][0]
new_mat.matrix[3][1] = a[3][0] * b[0][1] + a[3][1] * b[1][1] + a[3][2] * b[2][1] + a[3][3] * b[3][1]
new_mat.matrix[3][2] = a[3][0] * b[0][2] + a[3][1] * b[1][2] + a[3][2] * b[2][2] + a[3][3] * b[3][2]
new_mat.matrix[3][3] = a[3][0] * b[0][3] + a[3][1] * b[1][3] + a[3][2] * b[2][3] + a[3][3] * b[3][3]
return new_mat
def __rmul__(self, other):
if type(other) is Vec4:
x = self.matrix[0][0] * other.x + self.matrix[0][1] * other.y + self.matrix[0][2] * other.z + self.matrix[0][3] * other.w
y = self.matrix[1][0] * other.x + self.matrix[1][1] * other.y + self.matrix[1][2] * other.z + self.matrix[1][3] * other.w
z = self.matrix[2][0] * other.x + self.matrix[2][1] * other.y + self.matrix[2][2] * other.z + self.matrix[2][3] * other.w
w = self.matrix[3][0] * other.x + self.matrix[3][1] * other.y + self.matrix[3][2] * other.z + self.matrix[3][3] * other.w
return Vec4(x, y, z, w)
if type(other) is Mat4:
new_mat = Mat4()
new_mat.matrix = [[0 for x in range(4)] for y in range(4)]
a = self.matrix
b = other.matrix
new_mat.matrix[0][0] = a[0][0] * b[0][0] + a[0][1] * b[1][0] + a[0][2] * b[2][0] + a[0][3] * b[3][0]
new_mat.matrix[0][1] = a[0][0] * b[0][1] + a[0][1] * b[1][1] + a[0][2] * b[2][1] + a[0][3] * b[3][1]
new_mat.matrix[0][2] = a[0][0] * b[0][2] + a[0][1] * b[1][2] + a[0][2] * b[2][2] + a[0][3] * b[3][2]
new_mat.matrix[0][3] = a[0][0] * b[0][3] + a[0][1] * b[1][3] + a[0][2] * b[2][3] + a[0][3] * b[3][3]
new_mat.matrix[1][0] = a[1][0] * b[0][0] + a[1][1] * b[1][0] + a[1][2] * b[2][0] + a[1][3] * b[3][0]
new_mat.matrix[1][1] = a[1][0] * b[0][1] + a[1][1] * b[1][1] + a[1][2] * b[2][1] + a[1][3] * b[3][1]
new_mat.matrix[1][2] = a[1][0] * b[0][2] + a[1][1] * b[1][2] + a[1][2] * b[2][2] + a[1][3] * b[3][2]
new_mat.matrix[1][3] = a[1][0] * b[0][3] + a[1][1] * b[1][3] + a[1][2] * b[2][3] + a[1][3] * b[3][3]
new_mat.matrix[2][0] = a[2][0] * b[0][0] + a[2][1] * b[1][0] + a[2][2] * b[2][0] + a[2][3] * b[3][0]
new_mat.matrix[2][1] = a[2][0] * b[0][1] + a[2][1] * b[1][1] + a[2][2] * b[2][1] + a[2][3] * b[3][1]
new_mat.matrix[2][2] = a[2][0] * b[0][2] + a[2][1] * b[1][2] + a[2][2] * b[2][2] + a[2][3] * b[3][2]
new_mat.matrix[2][3] = a[2][0] * b[0][3] + a[2][1] * b[1][3] + a[2][2] * b[2][3] + a[2][3] * b[3][3]
new_mat.matrix[3][0] = a[3][0] * b[0][0] + a[3][1] * b[1][0] + a[3][2] * b[2][0] + a[3][3] * b[3][0]
new_mat.matrix[3][1] = a[3][0] * b[0][1] + a[3][1] * b[1][1] + a[3][2] * b[2][1] + a[3][3] * b[3][1]
new_mat.matrix[3][2] = a[3][0] * b[0][2] + a[3][1] * b[1][2] + a[3][2] * b[2][2] + a[3][3] * b[3][2]
new_mat.matrix[3][3] = a[3][0] * b[0][3] + a[3][1] * b[1][3] + a[3][2] * b[2][3] + a[3][3] * b[3][3]
return new_mat
def translate(mat, vec3):
mat.matrix[0][3] = vec3.x
mat.matrix[1][3] = vec3.y
mat.matrix[2][3] = vec3.z
def rotate(mat, angle, vec3):
angle_x = vec3.x * angle
angle_y = vec3.y * angle
angle_z = vec3.z * angle
matB = Mat4()
matA = mat
#x rotation
matB.matrix[1][1] = math.cos(angle_x)
matB.matrix[1][2] = -math.sin(angle_x)
matB.matrix[2][1] = math.sin(angle_x)
matB.matrix[2][2] = math.cos(angle_x)
matA *= matB
#y rotation
matB = Mat4()
matB.matrix[0][0] = math.cos(angle_y)
matB.matrix[0][2] = math.sin(angle_y)
matB.matrix[2][0] = -math.sin(angle_y)
matB.matrix[2][2] = math.cos(angle_y)
matA *= matB
#z rotation
matB = Mat4()
matB.matrix[0][0] = math.cos(angle_z)
matB.matrix[0][1] = -math.sin(angle_z)
matB.matrix[1][0] = math.sin(angle_z)
matB.matrix[1][1] = math.cos(angle_z)
matA *= matB
mat.matrix = matA.matrix