Introduction
Pyvect is a open source python module created for the purpose of simplifying the vector calculations such as finding the angle between vectors, projection of one vector over the other and much more…!
pyvect.dot()
About
Returns the dot product of the two given vectors.
Syntax
>>> dot(vector_1,vector_2)
vector_1 -First vector
vector_2 - Second vector
Return type
int
Example
>>> pyvect.dot([2,3,4],[1,5,3])
Output
29 |
pyvect.cross()
About
Returns the cross product (or) vector of the two given vectors.
Syntax
>>> cross(vector_1,vector_2)
vector_1 - First vector
vector_2 - Second vector
Return type
array
Example
>>> pyvect.cross([2,3,4],[1,5,3])
Output
array([-11,-2,7]) |
pyvect.angle()
About
Returns the angle formed by the two vectors in degrees.
Syntax
>>> angle(vector_1,vector_2)
vector_1 - First vector
vector_2 - Second vector
Return type
float
Example
>>> pyvect.angle([1,-1,0],[0,1,-1])
Output
2.0943951023931953 |
pyvect.projection()
About
Returns the projection formed by first vector to the second vector.
Syntax
>>> projection(vector_1,vector_2)
vector_1 - First vector
vector_2 - Second vector
Return type
float
Example
>>> pyvect.projection([1,2,3],[4,5,6])
Output
3.6467384467084143 |
pyvect.isperpendicular()
About
Returns True if two vectors are perpendicular to each other. (i.e) Dot product of the two vectors is zero.
Syntax
>>> isperpendicular(vector_1,vector_2)
vector_1 - First vector
vector_2 - Second vector
Return type
bool
Example
>>> pyvect.isperpendicular([-3,4,-7],[2,-51,-30])
Output
True |
pyvect.iscollinear()
About
Returns True if two vectors are collinear. (i.e) Cross product of the two vectors is zero.
Syntax
>>> iscollinear(vector_1,vector_2)
vector_1 - First vector
vector_2 - Second vector
Return type
bool
Example
>>> pyvect.iscollinear([1,2,3],[2,4,6])
Output
True |
pyvect.unit_vector()
About
Returns the unit vector of the given vector.
Syntax
>>> unit_vector(vector_1)
vector_1 - Vector provided to the function
Return type
array
Example
>>> pyvect.unit_vector([2,3,7])
Output
array([0.25400025, 0.38100038, 0.88900089]) |
pyvect.unit_normal()
About
Returns the unit normal vector of given two vectors
Syntax
>>> unit_normal(vector1,vector2)
vector_1 - First vector
vector_2 - Second vector
Return type
array
Example
>>> pyvect.unit_normal([2,1,1],[1,2,1])
Output
[array([-0.30151134, -0.30151134, 0.90453403]), array([ 0.30151134, 0.30151134, -0.90453403])] |
pyvect.bisector()
About
Returns a vector in the direction of the bisector of the angle between two vectors.
Syntax
>>> bisector(vector_1,vector_2)
vector_1 - First vector
vector_2 - Second vector
Return type
array
Example
>>> pyvect.bisector([1,4,3],[6,7,2])
Output
array([0.83211486, 1.52646306, 0.80034798]) |
pyvect.pos_vector()
About
Returns a position vector between any two given vectors.
Syntax
>>> pos_vector(vector_1,vector_2)
vector_1 - First vector
vector_2 - Second vector.
Return type
array
Example
>>> pyvect.pos_vector([1,3,4],[5,7,1])
Output
array([[3. , 5. , 2.5]]) |
pyvect.iscoplanar()
About
Returns the boolean value (True) if the given three vectors satisfy the condition.
Syntax
>>> iscoplanar(vector_1,vector_2,vector_3)
vector_1 - First vector
vector_2 - Second vector
vector_3 - Third vector.
Return type
bool
Example
>>> pyvect.iscoplanar([1,4,2],[5,3,8],[1,6,7])
Output
False |
pyvect.reciprocal()
About
Returns three reciprocal vector for the given three vectors.
Syntax
>>> reciprocal(vector_1,vector_2,vector_3)
vector_1 - First vector
vector_2 - Second vector
vector_3 - Third vector.
Return type
array
Example
>>> pyvect.reciprocal([1,4,2],[5,3,8],[1,6,7])
Output
|
pyvect.max_value()
About
Returns the maximum value between any two given vectors.
Syntax
>>> max_value(vector_1,vector_2)
vector_1 - First vector
vector_2 - Second vector.
Return type
float
Example
>>> pyvect.max_value([1,4,2],[5,3,8])
Output
45.36518488885502 |
pyvect.min_value()
About
Returns the minimum value between any two given vectors.
Syntax
>>> min_value(vector_1,vector_2)
vector_1 - First vector
vector_2 - Second vector.
Return type
float
Example
>>> pyvect.min_value([1,4,2],[5,3,8])
Output
-45.36518488885502 |
pyvect.area.triangle_adj()
About
Returns the area of a triangle where the two adjacent sides of the triangle are given.
Syntax
>>> triangle_adj(vector_1,vector_2)
vector_1 - First adjacent side
vector_2 - Second adjacent side
Return type
float
Example
>>> pyvect.area.triangle_adj([1,4,2],[6,4,8])
Output
15.748015748023622 |
pyvect.area.triangle_pos()
About
Returns the area of the triangle based on the given three positional vectors.
Syntax
>>> triangle_pos(p1,p2,p3)
p1,p2,p3 - positional vectors of the triangle.
Return type
float
Example
>>> pyvect.area.triangle_pos([2,3,4],[1,5,7],[4,5,1])
Output
6.87386354243376 |
pyvect.area.quad()
About
Returns the area of a quadrilateral based on the diagonal vectors.
Syntax
>>> quad(diagonal_1,diagonal_2)
diagonal_1 - Primary diagonal of the quadrilateral
diagonal_2 - Secondary diagonal of the quadrilateral
Return type
float
Example
>>> pyvect.area.quad([1,3,5],[2,3,6])
Output
2.9154759474226504 |
pyvect.area.parallelogram()
About
Returns the area of parallelogram based on the two adjacent vectors.
Syntax
>>> parallelogram(vector_1,vector_2)
vector_1 - First vector
vector_2 - Second vector
Return type
float
Example
>>> pyvect.area.parallelogram([1,4,5],[3,2,7])
Output
22.090722034374522 |
pyvect.area.tetrahedron()
About
Returns the area of tetrahedron based on the three position vectors.
Syntax
>>> tetrahedron(p1,p2,p3)
p1,p2,p3 - Positional vectors of the tetrahedron
Return type
float
Example
>>> pyvect.area.tetrahedron([1,4,5],[3,2,7],[2,4,1])
Output
9.6628 |
pyvect.cent.triangle()
About
Returns the centroid vector in the triangle based on the the three given positional vectors.
Syntax
>>> triangle(p1,p2,p3)
p1,p2,p3 - Positional vectors of the triangle
Return type
array
Example
>>> pyvect.cent.triangle([1,4,5],[3,2,7],[2,4,1])
Output
array([[1.98, 3.3 , 4.29]]) |
pyvect.cent.tetrahedron()
About
Returns the centroid vector in the tetrahedron based on the the four given positional vectors.
Syntax
>>> tetrahedron(p1,p2,p3,p4)
p1,p2,p3,p4 - Positional vectors of the tetrahedron
Return type
array
Example
>>> pyvect.cent.tetrahedron([1,4,5],[3,2,7],[2,4,1],[3,5,6])
Output
array([[2.25, 3.75, 4.75]]) |
pyvect.dist.pl_line()
About
Returns the distance between two parallel lines.
Syntax
>>> pl_line(a1_vector,a2_vector,u_vector)
a1_vector, a2_vector - position vectors
u_vector - vector part of arbitrary constants s, t
Return type
float
Example
>>> pyvect.dist.pl_line([1,2,3],[4,5,6],[7,8,9])
Output
0.5275893435844943 |
pyvect.dist.sk_line()
About
Returns the distance between two skew lines.
Syntax
>>> sk_line(a1_vector,a2_vector,u_vector,v_vector)
a1_vector, a2_vector - position vectors
u_vector - vector part of arbitrary constant t , v_vector - vector part of arbitrary constant s
Return type
float
Example
>>> pyvect.dist.sk_line([1,2,3],[2,6,7],[5,2,5],[6,8,1])
Output
3.2576045465500365 |
pyvect.dist.pt_plane()
About
Returns the distance between a point and a plane.
Syntax
>>> pt_plane(x_co_ordinate,y_co_ordinate,z_co_ordinate,x_coeff,y_coeff,z_coeff,constant)
x_co_ordinate - x co-ordinate value of the point, y_co_ordinate - y co-ordinate value of the point, z_co_ordinate - z co-ordinate value of the point.
x_coeff - coefficient of x in the plane equation, y_coeff - coefficient of y in the plane equation, z_coeff - coefficient of z in the plane equation.
constant - constant value of plane equation.
Return type
float
Example
>>> pyvect.dist.pt_plane(1,2,3,4,5,6,7)
Output
4.444462481925879 |
pyvect.dist.or_plane()
About
Returns the distance between origin and a plane.
Syntax
>>> or_plane(x_coeff,y_coeff,z_coeff,constant)
x_coeff - coefficient of x in the plane equation, y_coeff - coefficient of y in the plane equation, z_coeff - coefficient of z in the plane equation.
constant - constant value of plane equation.
Return type
array
Example
>>> pyvect.dist.or_plane(1,2,3,4)
Output
array([1.06904497]) |
pyvect.dist.pl_planes()
About
Returns the distance between two parallel planes.
Syntax
>>> pl_planes(x_coeff,y_coeff,z_coeff,constant1,constant2)
x_coeff - coefficient of x in the plane equation, y_coeff - coefficient of y in the plane equation, z_coeff - coefficient of z in the plane equation,
constant1 - constant value of first plane.
constant2 - constant value of second plane.
Return type
float
Example
>>> pyvect.dist.pl_planes(2,3,8,1,6)
Output
0.5698028822981898 |
pyvect.dist.distance()
About
Returns the magnitude of vector.
Syntax
>>> distance(x1,x2,y1,y2,z1,z2)
x1 - x_co_ordinate of first vector, x2 - x_co_ordinate of second vector
y1 - y_co_ordinate of first vector, y2 - x_co_ordinate of second vector
z1 - z_co_ordinate of first vector, z2 - z_co_ordinate of second vector
Return type
float
Example
>>> pyvect.dist.distance(2,6,4,7,8,0)
Output
9.433981132056603 |
pyvect.prod.s3()
About
Returns the scalar triple product of the given three vectors.
Syntax
>>> s3(vector_1,vector_2,vector_3)
vector_1 - First vector
vector_2 - Second vector
vector_3 - Third vector
Return type
int
Example
>>> pyvect.prod.s3([7,9,6],[6,8,5],[3,5,4])
Output
4 |
pyvect.prod.s4()
About
Returns the scalar product of the given four vectors.
Syntax
>>> s4(vector_1,vector_2,vector_3,vector_4)
vector_1 - First vector
vector_2 - Second vector
vector_3 - Third vector
vector_4 - Fourth vector
Return type
int
Example
>>> pyvect.prod.s4([7,9,6],[6,8,5],[3,5,4],[2,3,1])
Output
24 |
pyvect.prod.v3()
About
Returns the vector triple product of the given three vectors.
Syntax
>>> pyvect.prod.v3(vector_1,vector_2,vector_3)
vector_1 - First vector
vector_2 - Second vector
vector_3 - Third vector
Return type
array
Example
>>> pyvect.prod.v3([7,9,6],[6,8,5],[3,5,4])
Output
[-6 18 -18] |
pyvect.prod.v4()
About
Returns the vector product of given four vectors.
Syntax
>>> v4(vector_1,vector_2,vector_3,vector_4)
vector_1 - First vector
vector_2 - Second vector
vector_3 - Third vector
vector_4 - Fourth vector
Return type
array
Example
>>> pyvect.prod.v4([1,2,3],[4,5,6],[7,8,9],[1,5,10])
Output
array([[[-21, -24, -27]]]) |
pyvect.section.internal()
About
Returns a vector using section formula using internal method
Syntax
>>> internal(p_vector1,p_vector2,m,n)
p_vector1, p_vector2 - Positional vectors
m, n - Parameters of the ratio (m:n)
Return type
array
Example
>>> pyvect.section.internal([1,2,3],[4,5,6],3,2)
Output
array([[-5., -4., -3.]]) |
pyvect.section.external()
About
Returns a vector using section formula using external method
Syntax
>>> external(p_vector1,p_vector2,m,n)
p_vector1, p_vector2 - Positional vectors
m, n - Parameters of the ratio (m:n)
Return type
array
Example
>>> pyvect.section.external([1,2,3],[4,5,6],3,2)
Output
array([[ 4.6, 8. , 11.4]]) |
pyvect.volume.parallelopiped()
About
Returns the volume of the parallelopiped formed by three vectors.
Syntax
>>> parallelopiped(vector_1,vector_2,vector_3)
vector_1, vector_2, vector_3 - Respective first, second and third vectors.
Return type
int
Example
>>> pyvect.volume.parallelopiped([9,3,6],[4,5,6],[7,8,9])
Output
27 |