Skip to content

CwPlane3d

src.cwmath.cwplane3d

CwPlane3d

Plane class for 3D planes.

Source code in src/cwmath/cwplane3d.py 
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
class CwPlane3d:
    """Plane class for 3D planes. """

    def __init__(self, point_3d, normal_vector):
        self._coefficient_a = normal_vector.x
        self._coefficient_b = normal_vector.y
        self._coefficient_c = normal_vector.z
        self._constant_d = -(self._coefficient_a * point_3d.x + self._coefficient_b * point_3d.y + self._coefficient_c * point_3d.z)   

    @property
    def coefficient_a(self) -> float:
        return self._coefficient_a

    @coefficient_a.setter
    def coefficient_a(self, value: float) -> None:
        self._coefficient_a = value

    @property
    def coefficient_b(self) -> float:
        return self._coefficient_b

    @coefficient_b.setter
    def coefficient_b(self, value: float) -> None:
        self._coefficient_b = value

    @property
    def coefficient_c(self) -> float:
        return self._coefficient_c

    @coefficient_c.setter
    def coefficient_c(self, value: float) -> None:
        self._coefficient_c = value

    @property
    def constant_d(self) -> float:
        return self._constant_d

    @constant_d.setter
    def constant_d(self, value: float) -> None:
        self._constant_d = value

    def __call__(self, x: float, y: float, z: float) -> float:
        """ Calculate the value of the plane at a given point.

        Args:
            x: x-coordinate of the point
            y: y-coordinate of the point
            z: z-coordinate of the point


        Returns:
            float: value of the plane at the given point
        """
        return self._coefficient_a * x + self._coefficient_b * y + self._coefficient_c * z + self._constant_d

    def __str__(self) -> str:
        return f'{self._coefficient_a}x + {self._coefficient_b}y + {self._coefficient_c}z + {self._constant_d} = 0'

    def __repr__(self) -> str:
        return f'CwPlane3d({self._coefficient_a}, {self._coefficient_b}, {self._coefficient_c}, {self._constant_d})'

    def __eq__(self, other: 'CwPlane3d') -> bool:
        return abs(self._coefficient_a - other._coefficient_a) < 1e-6 and abs(
            self._coefficient_b - other._coefficient_b) < 1e-6 and abs(
            self._coefficient_c - other._coefficient_c) < 1e-6 and abs(
            self._constant_d - other._constant_d) < 1e-6

    def __ne__(self, other: 'CwPlane3d') -> bool:
        return not self.__eq__(other)

    def __iter__(self):
        yield self._coefficient_a
        yield self._coefficient_b
        yield self._coefficient_c
        yield self._constant_d

    def __getitem__(self, index: int) -> float:
        return (self._coefficient_a, self._coefficient_b, self._coefficient_c, self._constant_d)[index]

    def __setitem__(self, index: int, value: float) -> None:
        if index == 0:
            self._coefficient_a = value
        elif index == 1:
            self._coefficient_b = value
        elif index == 2:
            self._coefficient_c = value
        elif index == 3:
            self._constant_d = value

    def is_parallel(self, other: 'CwPlane3d') -> bool:
        """ Checks if two planes are parallel.

        Args:
            other: 3d plane

        Returns:
            if the planes are parallel
        """
        return abs(self._coefficient_a * other._coefficient_b - self._coefficient_b * other._coefficient_a) < 1e-6 and abs(
            self._coefficient_a * other._coefficient_c - self._coefficient_c * other._coefficient_a) < 1e-6 and abs(
            self._coefficient_b * other._coefficient_c - self._coefficient_c * other._coefficient_b) < 1e-6

    def is_perpendicular(self, other: 'CwPlane3d') -> bool:
        """ Checks if two planes are perpendicular.

        Args:
            other: 3d plane

        Returns:
            if the planes are perpendicular
        """
        return abs(
            self._coefficient_a * other._coefficient_a + self._coefficient_b * other._coefficient_b + self._coefficient_c * other._coefficient_c) < 1e-6

    def is_coplanar(self, other: 'CwPlane3d') -> bool:
        """ Checks if two planes are coplanar.

        Args:
            other: 3d plane

        Returns:
            if the planes are coplanar
        """
        if other._coefficient_a == 0:
            return self._coefficient_a == 0
        if other._coefficient_b == 0:
            return self._coefficient_b == 0
        if other._coefficient_c == 0:
            return self._coefficient_c == 0

        return self._coefficient_a / other._coefficient_a \
                == self._coefficient_b / other._coefficient_b \
                == self._coefficient_c / other._coefficient_c

    def is_point_on_plane(self, point: 'cwvector3d.CwVector3d') -> bool:
        """ Checks if a point is on the plane.

        Args:
            point: point

        Returns:
            if the point is on the plane
        """
        return abs(
            self._coefficient_a * point.x + self._coefficient_b * point.y + self._coefficient_c * point.z + self._constant_d) < 1e-6

    def distance_to_point(self, point: 'cwvector3d.CwVector3d') -> float:
        """ Calculates the distance from a point to the plane.
        The distance from a point to a plane is given by the formula:
        |ax + by + cz + d| / sqrt(a^2 + b^2 + c^2)
        where (a, b, c) is the normal vector of the plane,
        (x, y, z) are the coordinates of the point, and
        d is the constant term in the plane equation.

        Args:
            point: point

        Returns:
            distance from the point to the plane
        """
        numerator = abs(self._coefficient_a * point.x + self._coefficient_b * point.y + self._coefficient_c * point.z + self._constant_d)
        denominator = sqrt(self._coefficient_a**2 + self._coefficient_b**2 + self._coefficient_c**2)
        return numerator / denominator

    def distance_to_plane(self, other: 'CwPlane3d') -> float:
        """ Calculates the distance from a plane to another plane.

        Args:
            other: 3d plane

        Returns:
            distance to plane
        """
        return abs(self._constant_d - other._constant_d) / sqrt(
            self._coefficient_a ** 2 + self._coefficient_b ** 2 + self._coefficient_c ** 2)

__call__(x, y, z)

Calculate the value of the plane at a given point.

Parameters:

Name Type Description Default
x float

x-coordinate of the point

 required
y float

y-coordinate of the point

 required
z float

z-coordinate of the point

 required

Returns:

Name Type Description
float float

value of the plane at the given point
Source code in src/cwmath/cwplane3d.py 
49
50
51
52
53
54
55
56
57
58
59
60
61
def __call__(self, x: float, y: float, z: float) -> float:
    """ Calculate the value of the plane at a given point.

    Args:
        x: x-coordinate of the point
        y: y-coordinate of the point
        z: z-coordinate of the point


    Returns:
        float: value of the plane at the given point
    """
    return self._coefficient_a * x + self._coefficient_b * y + self._coefficient_c * z + self._constant_d

distance_to_plane(other)

Calculates the distance from a plane to another plane.

Parameters:

Name Type Description Default
other CwPlane3d

3d plane

 required

Returns:

Type Description
float

distance to plane
Source code in src/cwmath/cwplane3d.py 
172
173
174
175
176
177
178
179
180
181
182
def distance_to_plane(self, other: 'CwPlane3d') -> float:
    """ Calculates the distance from a plane to another plane.

    Args:
        other: 3d plane

    Returns:
        distance to plane
    """
    return abs(self._constant_d - other._constant_d) / sqrt(
        self._coefficient_a ** 2 + self._coefficient_b ** 2 + self._coefficient_c ** 2)

distance_to_point(point)

Calculates the distance from a point to the plane. The distance from a point to a plane is given by the formula: |ax + by + cz + d| / sqrt(a^2 + b^2 + c^2) where (a, b, c) is the normal vector of the plane, (x, y, z) are the coordinates of the point, and d is the constant term in the plane equation.

Parameters:

Name Type Description Default
point CwVector3d

point

 required

Returns:

Type Description
float

distance from the point to the plane
Source code in src/cwmath/cwplane3d.py 
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
def distance_to_point(self, point: 'cwvector3d.CwVector3d') -> float:
    """ Calculates the distance from a point to the plane.
    The distance from a point to a plane is given by the formula:
    |ax + by + cz + d| / sqrt(a^2 + b^2 + c^2)
    where (a, b, c) is the normal vector of the plane,
    (x, y, z) are the coordinates of the point, and
    d is the constant term in the plane equation.

    Args:
        point: point

    Returns:
        distance from the point to the plane
    """
    numerator = abs(self._coefficient_a * point.x + self._coefficient_b * point.y + self._coefficient_c * point.z + self._constant_d)
    denominator = sqrt(self._coefficient_a**2 + self._coefficient_b**2 + self._coefficient_c**2)
    return numerator / denominator

is_coplanar(other)

Checks if two planes are coplanar.

Parameters:

Name Type Description Default
other CwPlane3d

3d plane

 required

Returns:

Type Description
bool

if the planes are coplanar
Source code in src/cwmath/cwplane3d.py 
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
def is_coplanar(self, other: 'CwPlane3d') -> bool:
    """ Checks if two planes are coplanar.

    Args:
        other: 3d plane

    Returns:
        if the planes are coplanar
    """
    if other._coefficient_a == 0:
        return self._coefficient_a == 0
    if other._coefficient_b == 0:
        return self._coefficient_b == 0
    if other._coefficient_c == 0:
        return self._coefficient_c == 0

    return self._coefficient_a / other._coefficient_a \
            == self._coefficient_b / other._coefficient_b \
            == self._coefficient_c / other._coefficient_c

is_parallel(other)

Checks if two planes are parallel.

Parameters:

Name Type Description Default
other CwPlane3d

3d plane

 required

Returns:

Type Description
bool

if the planes are parallel
Source code in src/cwmath/cwplane3d.py 
 97
 98
 99
100
101
102
103
104
105
106
107
108
def is_parallel(self, other: 'CwPlane3d') -> bool:
    """ Checks if two planes are parallel.

    Args:
        other: 3d plane

    Returns:
        if the planes are parallel
    """
    return abs(self._coefficient_a * other._coefficient_b - self._coefficient_b * other._coefficient_a) < 1e-6 and abs(
        self._coefficient_a * other._coefficient_c - self._coefficient_c * other._coefficient_a) < 1e-6 and abs(
        self._coefficient_b * other._coefficient_c - self._coefficient_c * other._coefficient_b) < 1e-6

is_perpendicular(other)

Checks if two planes are perpendicular.

Parameters:

Name Type Description Default
other CwPlane3d

3d plane

 required

Returns:

Type Description
bool

if the planes are perpendicular
Source code in src/cwmath/cwplane3d.py 
110
111
112
113
114
115
116
117
118
119
120
def is_perpendicular(self, other: 'CwPlane3d') -> bool:
    """ Checks if two planes are perpendicular.

    Args:
        other: 3d plane

    Returns:
        if the planes are perpendicular
    """
    return abs(
        self._coefficient_a * other._coefficient_a + self._coefficient_b * other._coefficient_b + self._coefficient_c * other._coefficient_c) < 1e-6

is_point_on_plane(point)

Checks if a point is on the plane.

Parameters:

Name Type Description Default
point CwVector3d

point

 required

Returns:

Type Description
bool

if the point is on the plane
Source code in src/cwmath/cwplane3d.py 
142
143
144
145
146
147
148
149
150
151
152
def is_point_on_plane(self, point: 'cwvector3d.CwVector3d') -> bool:
    """ Checks if a point is on the plane.

    Args:
        point: point

    Returns:
        if the point is on the plane
    """
    return abs(
        self._coefficient_a * point.x + self._coefficient_b * point.y + self._coefficient_c * point.z + self._constant_d) < 1e-6