vector Reference Manual
0.9
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Contents
1 vector Module Index
1.1
vector Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 vector Compound Index
2.1
vector Compound List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 vector Page Index
3.1
vector Related Pages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 vector Module Documentation
1
1
3
3
5
5
7
4.1
Geometric transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
4.2
Vector functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
5 vector Class Documentation
9
5.1
matrix3 Class Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
5.2
matrix4 Class Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
5.3
quaternion Class Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
5.4
vector3 Class Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
6 vector Page Documentation
21
6.1
Todo List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
6.2
Bug List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
Chapter 1
vector Module Index
1.1
vector Modules
Here is a list of all modules:
Geometric
•
transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Vector•functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
8
2
vector Module Index
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Chapter 2
vector Compound Index
2.1
vector Compound List
Here are the classes, structs, unions and interfaces with brief descriptions:
matrix3 (Square matrix class with nine components (3 by 3))
matrix4 (Square matrix class with 16 components (4 by 4)) .
quaternion (Quaternion class) . . . . . . . . . . . . . . . . . .
vector3 (Vector class with three components (x, y, z)) . . . . .
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4
vector Compound Index
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Chapter 3
vector Page Index
3.1
vector Related Pages
Here is a list of all related documentation pages:
Todo List
•
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bug List
• . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
22
6
vector Page Index
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Chapter 4
vector Module Documentation
4.1
Geometric transforms
Functions
• double deg2rad (double deg)
Convert degrees to radians.
• double rad2deg (double rad)
Convert radians to degrees.
• matrix4 createRotMat (double angle, const vector3 &axis)
Create a 4 by 4 rotation matrix.
• quaternion createRotQuat (double angle, const vector3 &axis)
Create a rotation quaternion.
8
vector Module Documentation
4.2
Vector functions
Functions
• const vector3 operator ∗ (double lhs, const vector3 &rhs)
scalar-vector multiplication.
• const vector3 operator ∗ (const vector3 &lhs, double rhs)
• const vector3 operator/ (const vector3 &lhs, double rhs)
scalar-vector division.
• const vector3 operator+ (const vector3 &lhs, const vector3 &rhs)
binary vector addition.
• const vector3 operator- (const vector3 &lhs, const vector3 &rhs)
binary vector subtraction.
• const vector3 operator ∗ (const vector3 &lhs, const vector3 &rhs)
binary vector multiplication (element-wise).
• const vector3 operator/ (const vector3 &lhs, const vector3 &rhs)
binary vector division (element-wise).
• double dot (const vector3 &lhs, const vector3 &rhs)
Vector dot product.
• vector3 cross (const vector3 &lhs, const vector3 &rhs)
Vector cross product.
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Chapter 5
vector Class Documentation
5.1
matrix3 Class Reference
Square matrix class with nine components (3 by 3).
#include <matrix3.h>
Public Methods
• double & operator() (unsigned int i, unsigned int j)
Indexing operator.
• const double & operator() (unsigned int i, unsigned int j) const
Indexing operator, const version.
• const matrix3 operator ∗= (double rhs)
Unary matrix-scalar multiplication.
• void zeros (void)
Sets all entries to zero.
• void identity (void)
Set matrix to the identity matrix.
• void transponse (void)
Transponse the matrix.
• double trace (void) const
Compute the trace (diagonal sum).
• matrix3 adjoint (void) const
Compute the adjoint.
• double determinant (void) const
Compute the determinant of the matrix.
10
vector Class Documentation
• bool invert (void)
Invert matrix.
• void print (void) const
Simple printout for debugging purposes.
5.1.1
Detailed Description
Square matrix class with nine components (3 by 3).
5.1.2
Member Function Documentation
5.1.2.1
matrix3 matrix3::adjoint (void) const
Compute the adjoint.
Computes and returns the adjoint of the matrix. The adjoint is defined as the transposed matrix
of cofactors.
5.1.2.2
double matrix3::determinant (void) const
Compute the determinant of the matrix.
Compute determinant using row-reduction.
Warning:
This operation is sensitive to the condition of the matrix. please refer to a numrical linear
algebra for more info on this.
5.1.2.3
bool matrix3::invert (void)
Invert matrix.
Compute the determinant and use Cramer’s rule to compute the inverse of this matrix. (in-place)
5.1.2.4
const matrix3 matrix3::operator ∗= (double rhs) [inline]
Unary matrix-scalar multiplication.
In-place matrix-scalar multiplication.
5.1.2.5
void matrix3::print (void) const
Simple printout for debugging purposes.
This function writes the matrix in textual form to cerr (STDERR).
The documentation for this class was generated from the following files:
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5.1 matrix3 Class Reference
• matrix3.h
• matrix3.cpp
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vector Class Documentation
5.2
matrix4 Class Reference
Square matrix class with 16 components (4 by 4).
#include <matrix4.h>
Public Methods
• double & operator() (unsigned int i, unsigned int j)
Indexing operator.
• const double & operator() (unsigned int i, unsigned int j) const
Indexing operator, const version.
• const double ∗ getOpenGLMatrix (void) const
• void zeros (void)
Sets all entries to zero.
• void identity (void)
Set matrix to the identity matrix.
• void transponse (void)
transponse the matrix.
• double trace (void) const
compute the trace (diagonal sum).
• double determinant (void) const
Compute the determinant of the matrix.
• bool invert (void)
Invert matrix.
• void print (void) const
Simple printout for debugging purposes.
• matrix3 getSubmatrix3 (void) const
Get 3x3 submatrix.
5.2.1
Detailed Description
Square matrix class with 16 components (4 by 4).
5.2.2
Member Function Documentation
5.2.2.1
double matrix4::determinant (void) const
Compute the determinant of the matrix.
Compute determinant using row-reduction.
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5.2 matrix4 Class Reference
Warning:
This operation is sensitive to the condition of the matrix. please refer to a numrical linear
algebra for more info on this.
5.2.2.2
matrix3 matrix4::getSubmatrix3 (void) const
Get 3x3 submatrix.
Returns the first 3 rows and columns of the matrix.
5.2.2.3
bool matrix4::invert (void)
Invert matrix.
Compute the determinant and use Cramer’s rule to compute the inverse of this matrix. (in-place)
5.2.2.4
void matrix4::print (void) const
Simple printout for debugging purposes.
This function writes the matrix in textual form to cerr (STDERR).
The documentation for this class was generated from the following files:
• matrix4.h
• matrix4.cpp
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13
14
vector Class Documentation
5.3
quaternion Class Reference
quaternion class.
#include <quaternion.h>
Public Methods
• quaternion (void)
Non-initializing constructor.
• quaternion (double w, double x, double y, double z)
Initialize with scalar part w and vector part [x, y, z].
• quaternion (double w, const vector3 &v)
Initialize with scalar part w and vector v.
• quaternion (const vector3 &v)
Initialize pure quaternion with w = 0.
• double getScalar (void) const
Get the scalar part of the quaternion.
• vector3 getVector (void) const
Get the vector part of the quaternion.
• void setScalar (double w)
Set the scalar part of the quaternion.
• void setVector (vector3 v)
Set the vector part of the quaternion.
•
•
•
•
•
•
•
const quaternion operator+= (const quaternion &rhs)
const quaternion operator-= (const quaternion &rhs)
const quaternion operator ∗= (const quaternion &rhs)
const quaternion operator ∗= (double rhs)
const quaternion operator/= (const quaternion &rhs)
const quaternion operator/= (double rhs)
double getNorm (void) const
Quaternion norm.
• double getMagnitude (void) const
Get magnitude.
• void normalize (void)
Normalize the quaternion.
• void conjugate (void)
Conjugate the quaternion.
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5.3 quaternion Class Reference
• void inverse (void)
Set the quaternion to its multiplicative inverse.
• matrix4 toMatrix (void) const
Create a 4 by 4 matrix from this quaternion.
• void print (void) const
Simple printout for debugging.
5.3.1
Detailed Description
quaternion class.
Models the quaternion mathematical entity. A quaternion is a extension of complex numbers on
the form q = w + xi + yj + bk
5.3.2
Constructor & Destructor Documentation
5.3.2.1
quaternion::quaternion (const vector3 & v) [inline, explicit]
Initialize pure quaternion with w = 0.
This constructor is explicit and cannot be used to implicitly convert a vector3 (p. 17) to a quaternion.
5.3.3
Member Function Documentation
5.3.3.1
void quaternion::conjugate (void) [inline]
Conjugate the quaternion.
Equivelant to q.setVector(-q.getVector())
5.3.3.2
double quaternion::getMagnitude (void) const [inline]
Get magnitude.
Defined to be sqrt(norm)
5.3.3.3
double quaternion::getNorm (void) const [inline]
Quaternion norm.
Defined to be x2 + y 2 + z 2 + w2 .
5.3.3.4
void quaternion::print (void) const
Simple printout for debugging.
This function writes the quaternion in textual form to cerr (STDERR).
The documentation for this class was generated from the following files:
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15
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vector Class Documentation
• quaternion.h
• quaternion.cpp
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5.4 vector3 Class Reference
5.4
vector3 Class Reference
Vector class with three components (x, y, z).
#include <vector3.h>
Public Methods
• vector3 (void)
Default empty constructor.
• vector3 (double x, double y, double z)
Construct vector with components x, y and z.
• const double & operator[ ] (int i) const
Indexing operator, const version.
• double & operator[ ] (int i)
indexing operator.
• bool operator== (const vector3 &rhs)
Equality operator.
• bool operator!= (const vector3 &rhs)
inequality operator.
• const vector3 operator+= (const vector3 &rhs)
Unary vector summation.
• const vector3 operator-= (const vector3 &rhs)
Unary negative vector summation.
• const vector3 operator ∗= (const vector3 &rhs)
Unary vector component-wise multiplication.
• const vector3 operator ∗= (double rhs)
Unary vector-scalar multiplication.
• const vector3 operator/= (const vector3 &rhs)
Unary vector component-wise division.
• const vector3 operator/= (double rhs)
Unary vector-scalar multiplication.
• const vector3 operator- (void) const
unary vector negation.
• double getMagnitude (void) const
Get vector norm.
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vector Class Documentation
• void setSpherical (double r, double theta, double phi)
Set from polar coords.
• void normalize (void)
Normalize vector.
• matrix3 star (void) const
• void print (void) const
Simple printout for debugging.
• void rotate (double angle, const vector3 &axis)
Rotate vector angle degrees around axis.
5.4.1
Detailed Description
Vector class with three components (x, y, z).
5.4.2
Constructor & Destructor Documentation
5.4.2.1
vector3::vector3 (void) [inline]
Default empty constructor.
Constructs new vector3 object with uninitialized values.
5.4.2.2
vector3::vector3 (double x, double y, double z) [inline]
Construct vector with components x, y and z.
Constructs new vector3 with components (x, y, z)
5.4.3
Member Function Documentation
5.4.3.1
double vector3::getMagnitude (void) const
Get vector norm.
Returns the vector norm |v| =
5.4.3.2
p
x2 + y 2 + z 2 .
void vector3::normalize (void)
Normalize vector.
Equal to v /= v.getMagnitude().
Warning:
This function does not test for the (almost) null vector before division. Therefor it is the
users responsibility to ensure that the vector is not near-null.
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5.4 vector3 Class Reference
5.4.3.3
const vector3 vector3::operator ∗= (double rhs) [inline]
Unary vector-scalar multiplication.
In-place vector-scalar multiplication.
5.4.3.4
const vector3 vector3::operator ∗= (const vector3 & rhs) [inline]
Unary vector component-wise multiplication.
In-place vector component-wise multiplication.
5.4.3.5
bool vector3::operator!= (const vector3 & rhs) [inline]
inequality operator.
Tests for inequality between to vector3 objects. To vectors are diffrent if they are component-wise
diffrent. Note that since the components and hence, the vector, are floating point values, testing
for inequality is not always a good idea.
5.4.3.6
const vector3 vector3::operator+= (const vector3 & rhs) [inline]
Unary vector summation.
In-place summation of vectors.
5.4.3.7
const vector3 vector3::operator- (void) const [inline]
unary vector negation.
Negates the vector.
5.4.3.8
const vector3 vector3::operator-= (const vector3 & rhs) [inline]
Unary negative vector summation.
In-place negative summation of vectors
5.4.3.9
const vector3 vector3::operator/= (double rhs) [inline]
Unary vector-scalar multiplication.
In-place vector-scalar multiplication. Equal to @fv ∗= 1/s@f.
5.4.3.10
const vector3 vector3::operator/= (const vector3 & rhs) [inline]
Unary vector component-wise division.
In-place vector component-wise division.
5.4.3.11
bool vector3::operator== (const vector3 & rhs) [inline]
Equality operator.
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vector Class Documentation
Tests for equality between to vector3 objects. To vectors are equal if they are component-wise
equal. Note that since the components and hence, the vector, are floating point values, testing for
equality is not always a good idea.
5.4.3.12
double& vector3::operator[ ] (int i) [inline]
indexing operator.
Access the individual components of a vector3 objects.
5.4.3.13
const double& vector3::operator[ ] (int i) const [inline]
Indexing operator, const version.
Access the individual components of a vector3 objects.
5.4.3.14
void vector3::print (void) const
Simple printout for debugging.
This function writes the vector in textual form to cerr (STDERR). Useful for debugging.
5.4.3.15
void vector3::setSpherical (double rho, double theta, double phi)
Set from polar coords.
Todo:
Test me!
5.4.3.16
matrix3 vector3::star (void) const
The following method computes the matrix w∗ so that w × r = w∗ R where w and r are 3-vectors
and R is a 3x3 rotation matrix.
The documentation for this class was generated from the following files:
• vector3.h
• vector3.cpp
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Chapter 6
vector Page Documentation
6.1
Todo List
Member matrix3::adjoint(void) const Test me
Member matrix3::determinant(void) const Test me
Member matrix3::invert(void) Make it work.
Member matrix4::determinant(void) const Bother to write this out
Member matrix4::invert(void) Not yet implemented
Member vector3::setSpherical(double r, double theta, double phi) Test me!
22
vector Page Documentation
6.2
Bug List
Member matrix3::invert(void) Doesn’t work yet.
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Index
adjoint
matrix3, 10
conjugate
quaternion, 15
createRotMat
transform, 7
createRotQuat
transform, 7
cross
vectorfunc, 8
deg2rad
transform, 7
determinant
matrix3, 10
matrix4, 12
dot
vectorfunc, 8
Geometric transforms, 7
getMagnitude
quaternion, 15
vector3, 18
getNorm
quaternion, 15
getOpenGLMatrix
matrix4, 12
getScalar
quaternion, 14
getSubmatrix3
matrix4, 13
getVector
quaternion, 14
identity
matrix3, 9
matrix4, 12
inverse
quaternion, 15
invert
matrix3, 10
matrix4, 13
matrix3, 9
adjoint, 10
determinant, 10
identity, 9
invert, 10
operator ∗=, 10
operator(), 9
print, 10
trace, 9
transponse, 9
zeros, 9
matrix4, 12
determinant, 12
getOpenGLMatrix, 12
getSubmatrix3, 13
identity, 12
invert, 13
operator(), 12
print, 13
trace, 12
transponse, 12
zeros, 12
normalize
quaternion, 14
vector3, 18
operator ∗
vectorfunc, 8
operator ∗=
matrix3, 10
quaternion, 14
vector3, 18, 19
operator!=
vector3, 19
operator()
matrix3, 9
matrix4, 12
operator+
vectorfunc, 8
operator+=
quaternion, 14
vector3, 19
operatorvector3, 19
vectorfunc, 8
operator-=
24
INDEX
quaternion, 14
vector3, 19
operator/
vectorfunc, 8
operator/=
quaternion, 14
vector3, 19
operator==
vector3, 19
operator[]
vector3, 20
print
matrix3, 10
matrix4, 13
quaternion, 15
vector3, 20
quaternion, 14
conjugate, 15
getMagnitude, 15
getNorm, 15
getScalar, 14
getVector, 14
inverse, 15
normalize, 14
operator ∗=, 14
operator+=, 14
operator-=, 14
operator/=, 14
print, 15
quaternion, 14, 15
setScalar, 14
setVector, 14
toMatrix, 15
rad2deg
transform, 7
rotate
vector3, 18
transform
createRotMat, 7
createRotQuat, 7
deg2rad, 7
rad2deg, 7
transponse
matrix3, 9
matrix4, 12
Vector functions, 8
vector3, 17
getMagnitude, 18
normalize, 18
operator ∗=, 18, 19
operator!=, 19
operator+=, 19
operator-, 19
operator-=, 19
operator/=, 19
operator==, 19
operator[], 20
print, 20
rotate, 18
setSpherical, 20
star, 20
vector3, 18
vectorfunc
cross, 8
dot, 8
operator ∗, 8
operator+, 8
operator-, 8
operator/, 8
zeros
matrix3, 9
matrix4, 12
setScalar
quaternion, 14
setSpherical
vector3, 20
setVector
quaternion, 14
star
vector3, 20
toMatrix
quaternion, 15
trace
matrix3, 9
matrix4, 12
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