def __init__(self, *args):
if len(args) == 2: # 点法式构造 A(x-x0)+B(y-y0)+C(z-z0)=0
xPoint, xVector = args
self.__point0 = deepcopy(xPoint)
if xVector.z == 0:
self.__point1 = deepcopy(self.__point0)
self.__point1.z += 1
self.__point2 = Point3D(0, 0, 0)
self.__point2.x = self.__point0.x - (self.__point1.z - self.__point0.z) * xVector.y
self.__point2.y = self.__point0.y + (self.__point1.z - self.__point0.z) * xVector.x
self.__point2.z = self.__point0.z + (self.__point1.x - self.__point0.x) * xVector.y \
- (self.__point1.y - self.__point0.y) * xVector.x
else:
temp = Operations.dotMultiply(xPoint, xVector)
self.__point1 = Point3D(xPoint.x, xPoint.y + 1, 0)
self.__point2 = Point3D(xPoint.x + 1, xPoint.y, 0)
self.__point1.z = (temp - xVector.x * self.__point1.x - xVector.y * self.__point1.y) / xVector.z
self.__point2.z = (temp - xVector.x * self.__point2.x - xVector.y * self.__point2.y) / xVector.z
elif len(args) == 3: # 三点式构造
self.__point0 = args[0]
self.__point1 = args[1]
self.__point2 = args[2]
else:
self.__point0 = None
self.__point1 = None
self.__point2 = None
def __init__(self,
xVertex1=Point3D(),
xVertex2=Point3D(),
xVertex3=Point3D()):
assert isinstance(xVertex1, Point3D) and isinstance(
xVertex2, Point3D) and isinstance(xVertex3, Point3D)
self.__vertex1 = deepcopy(xVertex1)
self.__vertex2 = deepcopy(xVertex2)
self.__vertex3 = deepcopy(xVertex3)
def __init__(self,
xMaxPoint=Point3D(1, 1, 1),
xMinPoint=Point3D(-1, -1, -1)):
"""
Box初始化，两个点构造一个与世界坐标系平行的Box
:param xMaxPoint:
:param xMinPoint:
"""
assert isinstance(xMaxPoint, Point3D) and isinstance(
xMinPoint, Point3D)
self.__maxPoint = deepcopy(xMaxPoint)
self.__minPoint = deepcopy(xMinPoint)
def conjugateQuaternion(self):
# 共轭四元数
tempS = self.__s
tempVx = -self.__v.x
tempVy = -self.__v.y
tempVz = -self.__v.z
return Quaternion(tempS, Point3D(tempVx, tempVy, tempVz))
def __mul__(self, other):
assert isinstance(other, Quaternion)
tempS = self.__s * other.__s - self.__v.x * other.__v.x - self.__v.y * other.__v.y - self.__v.z * other.__v.z
tempVx = self.__s * other.__v.x + self.__v.x * other.__s + self.__v.y * other.__v.z - self.__v.z * other.__v.y
tempVy = self.__s * other.__v.y - self.__v.x * other.__v.z + self.__v.y * other.__s + self.__v.z * other.__v.x
tempVz = self.__s * other.__v.z + self.__v.x + other.__v.y - self.__v.y * other.__v.x + self.__v.z * other.__s
return Quaternion(tempS, Point3D(tempVx, tempVy, tempVz))
def matrixToQuaternion(xMatrix):
# 由矩阵到四元数的转换
assert isinstance(xMatrix, Matrix3D)
tempQ0 = (xMatrix.trace() + 1)**0.5 / 2
tempQ1 = (xMatrix[1][2] - xMatrix[2][1]) / (4 * tempQ0)
tempQ2 = (xMatrix[2][0] - xMatrix[0][2]) / (4 * tempQ0)
tempQ3 = (xMatrix[0][1] - xMatrix[1][0]) / (4 * tempQ0)
return Quaternion(tempQ0, Point3D(tempQ1, tempQ2, tempQ3))
def crossMultiply(xPoint1, xPoint2):
if isinstance(xPoint1, Point3D) and isinstance(xPoint2, Point3D):
# 三维向量叉乘，求同时垂直于两个向量的向量
tempX = xPoint1.y * xPoint2.z - xPoint1.z * xPoint2.y
tempY = xPoint1.x * xPoint2.z - xPoint1.z * xPoint2.x
tempZ = xPoint1.x * xPoint2.y - xPoint1.y * xPoint2.x
return Point3D(tempX, tempY, tempZ)
else:
return None
def dotMul(xQuaternion: Quaternion, yQuaternion: Quaternion):
# 点乘
assert isinstance(xQuaternion, Quaternion) and isinstance(
yQuaternion, Quaternion)
tempS = xQuaternion.s * yQuaternion.s
tempVx = xQuaternion.v.x * yQuaternion.v.x
tempVy = xQuaternion.v.y * yQuaternion.v.y
tempVz = xQuaternion.v.z * yQuaternion.v.z
return Quaternion(tempS, Point3D(tempVx, tempVy, tempVz))
def __init__(self, xFacet=Point3D(), xVertex=Triangle()):
"""
三角面片初始化函数
:param xFacet: 法向量
:param xVertex: 顶点(3个)
"""
self.__facet = deepcopy(xFacet)
self.__vertex = deepcopy(xVertex)
def __init__(self, xOrigin=Point3D(), xDirection=Point3D(1, 1, 0)):
assert isinstance(xOrigin, Point3D) and isinstance(xDirection, Point3D)
self.__origin = deepcopy(xOrigin)
self.__direction = deepcopy(xDirection)
assert isinstance(xMatrix, Matrix3D)
tempQ0 = (xMatrix.trace() + 1)**0.5 / 2
tempQ1 = (xMatrix[1][2] - xMatrix[2][1]) / (4 * tempQ0)
tempQ2 = (xMatrix[2][0] - xMatrix[0][2]) / (4 * tempQ0)
tempQ3 = (xMatrix[0][1] - xMatrix[1][0]) / (4 * tempQ0)
return Quaternion(tempQ0, Point3D(tempQ1, tempQ2, tempQ3))
def quaternionToMatrix(xQuaternion):
# 由四元数到矩阵的转换
assert isinstance(xQuaternion, Quaternion)
tempQ0 = xQuaternion.s
tempQ1 = xQuaternion.v.x
tempQ2 = xQuaternion.v.y
tempQ3 = xQuaternion.v.z
R00 = 1 - 2 * tempQ2**2 - 2 * tempQ3**2
R01 = 2 * tempQ1 * tempQ2 + 2 * tempQ0 * tempQ3
R02 = 2 * tempQ1 * tempQ3 - 2 * tempQ0 * tempQ2
R10 = 2 * tempQ1 * tempQ2 - 2 * tempQ0 * tempQ3
R11 = 1 - 2 * tempQ1**2 - 2 * tempQ3**2
R12 = 2 * tempQ2 * tempQ3 + 2 * tempQ0 * tempQ1
R20 = 2 * tempQ1 * tempQ3 + 2 * tempQ0 * tempQ2
R21 = 2 * tempQ2 * tempQ3 - 2 * tempQ0 * tempQ1
R22 = 1 - 2 * tempQ1**2 - 2 * tempQ2**2
return Matrix3D([[R00, R01, R02], [R10, R11, R12], [R20, R21, R22]])
if __name__ == '__main__':
testQuaternion = Quaternion(1, Point3D(1, 2, 3))
print(testQuaternion)
@property
def vertex2(self):
return self.__vertex2
@property
def vertex3(self):
return self.__vertex3
@vertex1.setter
def vertex1(self, xVertex1):
self.__vertex1 = deepcopy(xVertex1)
@vertex2.setter
def vertex2(self, xVertex2):
self.__vertex2 = deepcopy(xVertex2)
@vertex3.setter
def vertex3(self, xVertex3):
self.__vertex3 = deepcopy(xVertex3)
def __str__(self):
return '[%s,%s,%s]' % (self.__vertex1, self.__vertex2, self.__vertex3)
if __name__ == '__main__':
testPoint1 = Point3D(0, 0, 0)
testPoint2 = Point3D(1, 0, 0)
testPoint3 = Point3D(0, 1, 0)
testTriangle = Triangle(testPoint1, testPoint2, testPoint3)
print(testTriangle)
@property
def point1(self):
return self.__point1
@property
def point2(self):
return self.__point2
@point0.setter
def point0(self, xPoint):
self.__point0 = xPoint
@point1.setter
def point1(self, xPoint):
self.__point1 = xPoint
@point2.setter
def point2(self, xPoint):
self.__point2 = xPoint
def __str__(self):
return '[%s,\n %s,\n %s]' % (self.__point0, self.__point1, self.__point2)
if __name__ == '__main__':
pt1 = Point3D(1, 1, 1)
pt2 = Point3D(1, 2, 2)
pt3 = Point3D(1, 2, 1)
ttt = Plane(pt1, pt2, pt3)
print(ttt.normVector())