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

array([[[ 0.33333333, 0.33333333, -0.33333333],

[ 0.19753086, -0.0617284 , 0.02469136], [-0.32098765, -0.02469136, 0.20987654]]])

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