Module igeVmath

Vector Math Module.

Functions

def abs(...)

compute the absolute value of a vector per element

Forms

vecN = igeVmath.abs(vecN)
    (N = 2 or 3 or 4)

def add(...)

add two vectors or two matrices

Forms

vecN = igeVmath.add(vecN, vecM)
matNN = igeVmath.add(matNN, matMM)
    N,M = 2 or 3 or 4
    type of return value is depend on first parameter type

def almostEqual(...)

Compare two values and if the difference is smaller than EPSILON, it will be considered identical

Forms

vecN = igeVmath.almostEqual(vecN, vecN)
    (N = 2 or 3 or 4)

def appendScale(...)

append (post-multiply) a scale transformation to a matrix faster than creating and multiplying a scale transformation matrix

Forms

matrix = igeVmath.appendScale(matrix, vector)

def conj(...)

compute the conjugate of a quaternion

Forms

quat = igeVmath.conj(quat)

def cross(...)

compute cross product of two vectors

Forms

float = igeVmath.cross(vec2, vec2)
vec3 = igeVmath.cross(vec3, vec3)

def determinant(...)

determinant of a matrix

Forms

scalar = igeVmath.determinant(matrix)

def div(...)

division vector by a scalar

Forms

vecN = igeVmath.div(vecN, float)
vecN = igeVmath.div(vecN, vecN) division vector per element
    (N = 2 or 3 or 4)

def dot(...)

compute the dot product of two vectors

Forms

float = igeVmath.dot(vecN, vecN)
    (N = 2 or 3 or 4)

def frustum(...)

construct a perspective projection matrix based on frustum

Forms

matrix4 = igeVmath.frustum(left, right, bottom, top, zNear, zFar)  (all scalar value)

def inverse(...)

compute the inverse of a matrix or quaternion

Forms

matrix = igeVmath.inverse(matrix)
quat = igeVmath.inverse(quat)

def length(...)

compute the length of a vector

Forms

float = igeVmath.length(vecN)
    (N = 2 or 3 or 4)

def lengthSqr(...)

compute the square of the length of a vector

Forms

float = igeVmath.lengthSqr(vecN)
    (N = 2 or 3 or 4)

def lerp(...)

linear interpolation between two vectors

Forms

vecN = igeVmath.lerp(t, vecN, vecN)  (0<= t <= 1)
    (N = 2 or 3 or 4)

def lookAt(...)

construct viewing matrix based on eye position, position looked at, and up direction

Forms

matrix4 = igeVmath.lookAt(eyeVector, lookatVector, upVector)

def mat_identity(...)

construct an identity matrix

Forms

matrix = igeVmath.mat_identity(dimension)
            dimension : int
                    dimention of output matrix (2,3,4)

def mat_rotation(...)

construct a matrix to rotate around a unit-length 3D vector

Forms

matrix = igeVmath.mat_rotation(radian, dimension, vector)
    dimension is 2 or 3 or 4 to output matrix
    if you omit vector, Zaxis(0,0,1) will be entered as default

def mat_rotationX(...)

construct a matrix to rotate around the Xaxis

Forms

matrix = igeVmath.mat_rotationX(radian, dimension)
            radian : float
            dimension : int
                    dimension of output matrix (2,3,4)

def mat_rotationY(...)

construct a matrix to rotate around the Yaxis

Forms

matrix = igeVmath.mat_rotationY(radian, dimension)
            radian : float
            dimension : int
                    dimension of output matrix (2,3,4)

def mat_rotationZ(...)

construct a matrix to rotate around the Zaxis

Forms

    matrix = igeVmath.mat_rotationZ(radian, dimension)
            radian : float
            dimension : int
                    dimension of output matrix (2,3,4)

def mat_rotationZYX(...)

construct a matrix to rotate around the x, y, and z axes

Forms

    matrix = igeVmath.mat_rotationZYX(dimension, (xradian, yradian, zradian) )              dimension : int
                    dimention of output matrix (2,3,4)
            xradian:float
            yradian:float
            zradian:float

def mat_scale(...)

construct a matrix to perform scaling

Forms

matrix = igeVmath.mat_scale(dimension, vector)
    dimension is 2 or 3 or 4 to output matrix

def mat_transform(...)

construct a 4x4 matrix from vector of position, rotation, scale and matrix of shear

Forms

    matrix = igeVmath.mat_transform(position, rotation, scale, shear)
            position : igeVmath.vec3  (or (...), [...])
            rotation : igeVmath.euler or igeVmath.quat (or (...), [...])
                    Rotateion can be specified in either Euler angles or quaternions.
                    In the case of tuples and lists, if the number of elements is 
                    three it is interpreted as Euler angles, and if it is four it is 
                    interpreted as a quaternion.
            scale : igeVmath.vec3  (or (...), [...])
            shear : igeVmath.mat44 (optional)

def mat_translation(...)

construct a 4x4 matrix to perform translation

Forms

matrix = igeVmath.mat_translation(vector)

def max(...)

maximum element of a vector

Forms

float = igeVmath.max(vecN)
    (N = 2 or 3 or 4)

def maxElem(...)

maximum of two vectors per element

Forms

vecN = igeVmath.maxElem(vecN,vecN)
    (N = 2 or 3 or 4)

def min(...)

minimum element of a vector

Forms

float = igeVmath.min(vecN)
    (N = 2 or 3 or 4)

def minElem(...)

minimum of two vectors per element

Forms

vecN = igeVmath.minElem(vecN,vecN)
    (N = 2 or 3 or 4)

def mul(...)

multiply 2 elements

Forms

vecN = igeVmath.mul(vecN, float)
matNN = igeVmath.mul(matNN, float)
vecN = igeVmath.mul(matNN, vecN)
matNN = igeVmath.mul(matNN, matNN)
quat = igeVmath.mul(quat, quat)
vecN = igeVmath.mul(vecN, vecN) (multiply per element)
    (N = 2 or 3 or 4)

def normalize(...)

normalize a vector

Forms

vecN = igeVmath.normalize(vecN)
    (N = 2 or 3 or 4)

def orthoInverse(...)

compute the inverse of a 4x4 matrix, which is expected to be an affine matrix with an orthogonal upper-left 3x3 submatrix this can be used to achieve better performance than a general inverse when the specified 4x4 matrix meets the given restrictions

Forms

matrix = igeVmath.orthoInverse(matrix)

def orthographic(...)

construct an orthographic projection matrix

Forms

matrix4 = igeVmath.orthographic(left, right, bottom, top, zNear, zFar)  (all scalar value)

def perspective(...)

construct a perspective projection matrix

Forms

matrix4 = igeVmath.perspective(fovyRadians, aspect, zNear, zFar)

def prependScale(...)

prepend (pre-multiply) a scale transformation to a 4x4 matrix faster than creating and multiplying a scale transformation matrix

Forms

matrix = igeVmath.prependScale(matrix, vector)

def quat_look_rotation(...)

Creates a rotation with the specified forward and upwards directions. - Z axis will be aligned with forward - X axis aligned with cross product between forwardand upwards - Y axis aligned with cross product between Z and X

vmath.quat_look_rotation(forward: vmath.vec3, up: vmath.vec3)

Parameters

forward: forward vector
up: up vector

def quat_rotation(...)

construct a quaternion

Forms

quat = igeVmath.quat_rotation(vec3, vec3)
    construct a quaternion to rotate between two unit - length 3D vectors
    the result is unpredictable if 2 vectors point in opposite directions
quat = igeVmath.quat_rotation(float, vec3)
    construct a quaternion to rotate around a unit-length 3D vector
quat = igeVmath.quat_rotation(float)
    construct a quaternion to rotate around a Z(0,0,1) axis

def quat_rotationX(...)

construct a quaternion to rotate around the x axis

Forms

quat = igeVmath.quat_rotationX(radian)

def quat_rotationY(...)

construct a quaternion to rotate around the y axis

Forms

quat = igeVmath.quat_rotationY(radian)

def quat_rotationZ(...)

construct a quaternion to rotate around the z axis

Forms

quat = igeVmath.quat_rotationZ(radian)

def quat_rotationZYX(...)

construct a quaternion to rotate around the x, y, and z axes

Forms

quat = igeVmath.quat_rotationZYX( (xradian, yradian, zradian) )

def recip(...)

compute the reciprocal of a vector per element

Forms

vecN = igeVmath.recip(vecN)
    (N = 2 or 3 or 4)

def rotate(...)

use a unit - length quaternion to rotate a 3D vector

Forms

vec = igeVmath.rotate(vec, quat)

def rsqrt(...)

compute the reciprocal square root of a vector per element

Forms

vecN = igeVmath.rsqrt(vecN)
    (N = 2 or 3 or 4)

def slerp(...)

spherical linear interpolation between two vectors

Forms

vecN = igeVmath.slerp(t, vecN, vecN)  (0<= t <= 1)
    (N = 2 or 3 or 4)

def sqrt(...)

compute the square root of a vector per element

Forms

vecN = igeVmath.sqrt(vecN)
    (N = 2 or 3 or 4)

def squad(...)

spherical quadrangle interpolation

Forms

quat = igeVmath.squad(t,quat, quat, quat, quat)

def sub(...)

sub two vectors or two matrices

Forms

vecN = igeVmath.sub(vecN, vecM)
matNN = igeVmath.sub(matNN, matMM)
    N,M = 2 or 3 or 4
    type of return value is depend on first parameter type

def sum(...)

compute the sum of all elements of a vector

Forms

float = igeVmath.sum(vecN)
    (N = 2 or 3 or 4)

def transpose(...)

transpose of a matrix

Forms

matrix = igeVmath.transpose(matrix)

Classes

class aabb (...)

Axis aligned bounding box.

Instance variables

var area

Return an attribute of instance, which is of type owner.

var center

Return an attribute of instance, which is of type owner.

var extent

Return an attribute of instance, which is of type owner.

var lengthSqr

Return an attribute of instance, which is of type owner.

var maxEdge

Return an attribute of instance, which is of type owner.

var minEdge

Return an attribute of instance, which is of type owner.

var volume

Return an attribute of instance, which is of type owner.

Methods

def insert(...)

def isInside(...)

def repair(...)

def reset(...)

class euler (...)

a structure of auler angles

Constructors

    igeVmath.euler()
            all values are set 0
    igeVmath.euler(tilt, pan, roll)
    igeVmath.euler(euler)
    igeVmath.euler(quat))
            convert from quaternion
    igeVmath.euler(mat3)
            convert from 3x3 rotation matrix

Parameters

    tilt : float
    pan : float
    roll : float
    euler : igeVmath.euler
    quat : igeVmath.quat
    mat3 : igeVmath.mat3

Instance variables

var pan

Return an attribute of instance, which is of type owner.

var roll

Return an attribute of instance, which is of type owner.

var tilt

Return an attribute of instance, which is of type owner.

var x

Return an attribute of instance, which is of type owner.

var y

Return an attribute of instance, which is of type owner.

var z

Return an attribute of instance, which is of type owner.

Methods

def getElem(...)

Get a value using an index

Forms

    value = obj.getElem(index)
            obj : vec2 vec3 vec4 euler
            index : int
            value : float

def setElem(...)

Set a value using an index

Forms

    obj.setElem(index, value)
            obj : vec2 vec3 vec4 euler
            index : int
            value : float

def toQuat(...)

Compute the quaternion corresponding to Euler angles.

Forms

    obj.toQuat()

class mat22 (...)

a 2x2 matrix in array-of-structures format

Constructors

igeVmath.mat22(flaot, ...)
igeVmath.mat22((), ())
igeVmath.mat22([], [])
igeVmath.mat22(vec2, vec2)
        Missing elements will be zero
        Extra elements are ignored
        Any other combination is possible

Instance variables

var m00

Return an attribute of instance, which is of type owner.

var m01

Return an attribute of instance, which is of type owner.

var m10

Return an attribute of instance, which is of type owner.

var m11

Return an attribute of instance, which is of type owner.

Methods

def getCol(...)

Returns the vector of column corresponding to the specified row.

Forms

    vec = obj.getCol(row)
            vec : vec2,vec3,vec4
            obj : mat2,mat3,mat4
            row : int

def getElem(...)

Get a value using an index

Forms

    value = obj.getElem(colmn, row)
            obj : mat2 mat3 mat4
            colmn : int
            row : int
            value : float

def getRow(...)

Returns the vector of row corresponding to the specified column.

Forms

    vec = obj.getRow(row)
            vec : vec2,vec3,vec4
            obj : mat2,mat3,mat4
            column : int

def setCol(...)

Set the column corresponding to the specified row.

Forms

    obj.setCol(row, value)
            obj : mat2,mat3,mat4
            row : int
            value : vec2,vec3,vec4

def setElem(...)

Set a value using an index

Forms

    obj.setElem(colmn, row, value)
            obj : mat2 mat3 mat4
            colmn : int
            row : int
            value : float

def setRow(...)

Set the row corresponding to the specified column.

Forms

    obj.setCol(column, value)
            obj : mat2,mat3,mat4
            column : int
            value : vec2,vec3,vec4

class mat33 (...)

a 3x3 matrix in array-of-structures format

Constructors

igeVmath.mat33(flaot, ...)
igeVmath.mat33((), ...)
igeVmath.mat33([], ...)
igeVmath.mat33(vec3, ...)
        Missing elements will be zero
        Extra elements are ignored
        Any other combination is possible

Instance variables

var m00

Return an attribute of instance, which is of type owner.

var m01

Return an attribute of instance, which is of type owner.

var m02

Return an attribute of instance, which is of type owner.

var m10

Return an attribute of instance, which is of type owner.

var m11

Return an attribute of instance, which is of type owner.

var m12

Return an attribute of instance, which is of type owner.

var m20

Return an attribute of instance, which is of type owner.

var m21

Return an attribute of instance, which is of type owner.

var m22

Return an attribute of instance, which is of type owner.

Methods

def getCol(...)

Returns the vector of column corresponding to the specified row.

Forms

    vec = obj.getCol(row)
            vec : vec2,vec3,vec4
            obj : mat2,mat3,mat4
            row : int

def getElem(...)

Get a value using an index

Forms

    value = obj.getElem(colmn, row)
            obj : mat2 mat3 mat4
            colmn : int
            row : int
            value : float

def getRow(...)

Returns the vector of row corresponding to the specified column.

Forms

    vec = obj.getRow(row)
            vec : vec2,vec3,vec4
            obj : mat2,mat3,mat4
            column : int

def setCol(...)

Set the column corresponding to the specified row.

Forms

    obj.setCol(row, value)
            obj : mat2,mat3,mat4
            row : int
            value : vec2,vec3,vec4

def setElem(...)

Set a value using an index

Forms

    obj.setElem(colmn, row, value)
            obj : mat2 mat3 mat4
            colmn : int
            row : int
            value : float

def setRow(...)

Set the row corresponding to the specified column.

Forms

    obj.setCol(column, value)
            obj : mat2,mat3,mat4
            column : int
            value : vec2,vec3,vec4

class mat44 (...)

a 4x4 matrix in array-of-structures format

Constructors

igeVmath.mat44(flaot, ...)
igeVmath.mat44((), ...)
igeVmath.mat44([], ...)
igeVmath.mat44(vec3, ...)
igeVmath.mat44(vec4, ...)
        Missing elements will be zero but m[3][3] is 1.0
        Extra elements are ignored
        Any other combination is possible

Instance variables

var m00

Return an attribute of instance, which is of type owner.

var m01

Return an attribute of instance, which is of type owner.

var m02

Return an attribute of instance, which is of type owner.

var m03

Return an attribute of instance, which is of type owner.

var m10

Return an attribute of instance, which is of type owner.

var m11

Return an attribute of instance, which is of type owner.

var m12

Return an attribute of instance, which is of type owner.

var m13

Return an attribute of instance, which is of type owner.

var m20

Return an attribute of instance, which is of type owner.

var m21

Return an attribute of instance, which is of type owner.

var m22

Return an attribute of instance, which is of type owner.

var m23

Return an attribute of instance, which is of type owner.

var m30

Return an attribute of instance, which is of type owner.

var m31

Return an attribute of instance, which is of type owner.

var m32

Return an attribute of instance, which is of type owner.

var m33

Return an attribute of instance, which is of type owner.

Methods

def getCol(...)

Returns the vector of column corresponding to the specified row.

Forms

    vec = obj.getCol(row)
            vec : vec2,vec3,vec4
            obj : mat2,mat3,mat4
            row : int

def getElem(...)

Get a value using an index

Forms

    value = obj.getElem(colmn, row)
            obj : mat2 mat3 mat4
            colmn : int
            row : int
            value : float

def getRow(...)

Returns the vector of row corresponding to the specified column.

Forms

    vec = obj.getRow(row)
            vec : vec2,vec3,vec4
            obj : mat2,mat3,mat4
            column : int

def getTransform(...)

construct a 4x4 matrix from vector of position, rotation, scale and matrix of shear

Forms

    position, rotation, scale, shear = mat4.getTransform(rotationInEuler)
            rotationInEuler : bool
                    Retriave the rotation in Euler angles. False, quaternion.
            position : igeVmath.vec3
            rotation : igeVmath.vec3
            scale : igeVmath.vec3
            shear : igeVmath.mat44

def setCol(...)

Set the column corresponding to the specified row.

Forms

    obj.setCol(row, value)
            obj : mat2,mat3,mat4
            row : int
            value : vec2,vec3,vec4

def setElem(...)

Set a value using an index

Forms

    obj.setElem(colmn, row, value)
            obj : mat2 mat3 mat4
            colmn : int
            row : int
            value : float

def setRow(...)

Set the row corresponding to the specified column.

Forms

    obj.setCol(column, value)
            obj : mat2,mat3,mat4
            column : int
            value : vec2,vec3,vec4

class quat (...)

a quaternion in array-of-structures format

Constructors

igeVmath.quat(float, ...)
igeVmath.quat(float,...))
igeVmath.quat([float,...])
igeVmath.quat(vec2)
igeVmath.quat(vec3)
igeVmath.quat(vec4)
igeVmath.quat(quat)
        Missing elements will be zero
        Extra elements are ignored
        Any other combination is possible

Instance variables

var w

Return an attribute of instance, which is of type owner.

var x

Return an attribute of instance, which is of type owner.

var y

Return an attribute of instance, which is of type owner.

var z

Return an attribute of instance, which is of type owner.

Methods

def getElem(...)

Get a value using an index

Forms

    value = obj.getElem(index)
            obj : vec2 vec3 vec4 euler
            index : int
            value : float

def normalize(...)

normalize a vector

Forms

vecN = igeVmath.normalize(vecN)
    (N = 2 or 3 or 4)

def setElem(...)

Set a value using an index

Forms

    obj.setElem(index, value)
            obj : vec2 vec3 vec4 euler
            index : int
            value : float

class vec2 (...)

a 2-D vector in array-of-structures format

Constructors

igeVmath.vec2(float
igeVmath.vec2(float,float)
igeVmath.vec2((float,float))
igeVmath.vec2([float,float])
igeVmath.vec2(vec2)
igeVmath.vec2(vec3)
igeVmath.vec2(vec4)
    Missing elements will be zero
    Extra elements are ignored

Instance variables

var x

Return an attribute of instance, which is of type owner.

var y

Return an attribute of instance, which is of type owner.

Methods

def getElem(...)

Get a value using an index

Forms

    value = obj.getElem(index)
            obj : vec2 vec3 vec4 euler
            index : int
            value : float

def normalize(...)

normalize a vector

Forms

vecN = igeVmath.normalize(vecN)
    (N = 2 or 3 or 4)

def setElem(...)

Set a value using an index

Forms

    obj.setElem(index, value)
            obj : vec2 vec3 vec4 euler
            index : int
            value : float

class vec3 (...)

a 3-D vector in array-of-structures formatn

Constructors

igeVmath.vec3(float, ...)
igeVmath.vec3(float,...))
igeVmath.vec3([float,...])
igeVmath.vec3(vec2)
igeVmath.vec3(vec3)
igeVmath.vec3(vec4)
        Missing elements will be zero
        Extra elements are ignored
        Any other combination is possible

Instance variables

var x

Return an attribute of instance, which is of type owner.

var y

Return an attribute of instance, which is of type owner.

var z

Return an attribute of instance, which is of type owner.

Methods

def getElem(...)

Get a value using an index

Forms

    value = obj.getElem(index)
            obj : vec2 vec3 vec4 euler
            index : int
            value : float

def normalize(...)

normalize a vector

Forms

vecN = igeVmath.normalize(vecN)
    (N = 2 or 3 or 4)

def setElem(...)

Set a value using an index

Forms

    obj.setElem(index, value)
            obj : vec2 vec3 vec4 euler
            index : int
            value : float

class vec4 (...)

a 4-D vector in array-of-structures format

Constructors

igeVmath.vec4(float, ...)
igeVmath.vec4(float,...))
igeVmath.vec4([float,...])
igeVmath.vec4(vec2)
igeVmath.vec4(vec3)
igeVmath.vec4(vec4)
igeVmath.vec4(quat)
        Missing elements will be zero
        Extra elements are ignored
        Any other combination is possible

Instance variables

var w

Return an attribute of instance, which is of type owner.

var x

Return an attribute of instance, which is of type owner.

var y

Return an attribute of instance, which is of type owner.

var z

Return an attribute of instance, which is of type owner.

Methods

def getElem(...)

Get a value using an index

Forms

    value = obj.getElem(index)
            obj : vec2 vec3 vec4 euler
            index : int
            value : float

def normalize(...)

normalize a vector

Forms

vecN = igeVmath.normalize(vecN)
    (N = 2 or 3 or 4)

def setElem(...)

Set a value using an index

Forms

    obj.setElem(index, value)
            obj : vec2 vec3 vec4 euler
            index : int
            value : float