[top]# camera_transform

This object maps 3D

points into the image plane of a camera. Therefore,
you can use it to compute 2D representations of 3D data from the point of
view of some camera in 3D space.

[top]# centered_rect

There are various overloads of this function but the basic idea is
that it returns a

rectangle with a given
width and height and centered about a given point.

[top]# clip_line_to_rectangle

This function takes a

rectangle and a line segment and
returns the part of the line segment that is entirely contained within the
rectangle.

[top]# dcenter

Returns the center point of a

rectangle. This
is a version of

center() which returns a double version
of the point rather than one which uses integers to represent the
result. Therefore, it is slightly more accurate.

[top]# distance_to_line

This function takes a line and a

point
and returns the distance from the line to the point.

[top]# distance_to_rect_edge

This function takes a

rectangle and a

point and returns the Manhattan distance between
the rectangle's edge and the point.

[top]# drectangle

This object represents a rectangular region inside a Cartesian
coordinate system. It is very similar to the

rectangle
except that it uses double variables instead of longs to represent the location of the rectangle.
Therefore, it can position rectangles with sub-pixel accuracy.

[top]# find_affine_transform

This is a routine that takes in two sets of points and finds the
best

affine transformation
that maps between them.

[top]# find_projective_transform

This is a routine that takes in two sets of points and finds the
best

projective transformation
that maps between them.

[top]# find_similarity_transform

This is a routine that takes in two sets of points and finds the
best

affine transformation
that maps between them. However, it considers only rotations, translations,
and uniform scale changes in finding the mapping. Therefore, it finds
a similarity transformation rather than a general affine transform.

[top]# get_rect

This is a simple template function that returns a rectangle
representing the size of a 2D container (e.g.

matrix or

array2d).

[top]# grow_rect

This function takes a

rectangle object,
grows its borders by a given amount, and returns the result.

[top]# mat

This is a set of simple functions that take objects like std::vector or

array2d and convert them into

matrix objects. Note that the conversion is
done using template expressions so there is no runtime cost associated
with calling mat().

[top]# matrix

This is a 2D matrix object that enables you to write code that deals with
matrices using a simple syntax similar to what can be written in MATLAB. It is implemented using
the

expression templates technique which allows it to eliminate the
temporary matrix objects that would normally be returned from expressions
such as M = A+B+C+D; Normally each invocation of the + operator would
construct and return a temporary matrix object but using this technique
we can avoid creating all these temporary objects and receive a large speed boost.

This object is also capable of using BLAS and LAPACK libraries such as ATLAS or the Intel
MKL when available. To enable BLAS support all you have to do is #define
DLIB_USE_BLAS and then make sure you link your application with your
BLAS library. Similarly, to enable LAPACK support just #define DLIB_USE_LAPACK and
link to your LAPACK library. Finally, the use of BLAS and LAPACK is transparent to
the user, that is, the dlib matrix object uses BLAS and LAPACK internally to optimize
various operations while still allowing the user to use a simple MATLAB like syntax.

Note that the cmake files that come with dlib will automatically link with ATLAS or the Intel
MKL if they are installed. So using cmake makes this easy, but by no means are you required
to use cmake or the dlib cmake files.

It is also worth noting that all the preconditions of every function
related to the matrix object are checked by DLIB_ASSERT
statements and thus can be enabled by #defining ENABLE_ASSERTS or DEBUG. Doing
this will cause your program to run slower but should catch any usage errors.

C++ Example Programs:

matrix_ex.cpp,

matrix_expressions_ex.cpp# Extensions to matrix

**matrix_la**
This extension contains linear algebra functions to calculate
QR, LU, Cholesky, eigenvalue, and singular value decompositions. It also
contains a few other miscellaneous functions that solve systems of
equations or calculate values derived from the above decompositions.

More Details... [top]# move_rect

This function takes a

rectangle and moves
it so that it's upper left corner occupies the given location.

[top]# nearest_point

This function takes a

rectangle and a

point and returns the point in the given
rectangle that is nearest to the given point.

[top]# nearest_rect

This function takes a std::vector<

rectangle> and a

point and identifies the rectangle that is nearest to the point.

[top]# point

This object represents a point inside a Cartesian coordinate system.
Note that a point is simply a typedef for a

vector
that is 2D and uses longs to represent coordinate values.

[top]# point_rotator

This is an object that rotates a 2D

vector or

point object about the origin.

[top]# point_transform

This is an object that rotates a 2D

vector or

point object about the origin and then adds a
displacement vector.

[top]# point_transform_affine

This is an object that applies a 2D affine transformation to a

vector or

point. Note that you can use

find_affine_transform
to easily create affine transforms from sets of point correspondences.

[top]# point_transform_affine3d

This is an object that applies a 3D affine transformation to a

vector.

[top]# point_transform_projective

This is an object that applies a projective transformation to a

vector or

point. Note that you can use

find_projective_transform
to easily create projective transforms from sets of point correspondences.

[top]# rectangle

This object represents a rectangular region inside a Cartesian
coordinate system. It allows you to easily represent and manipulate
rectangles.

[top]# resize_rect

This function takes a

rectangle and
returns a new rectangle with the given size but with the same upper
left corner as the original rectangle.

[top]# resize_rect_height

This function takes a

rectangle and
returns a new rectangle with the given height but otherwise with the
same edge points as the original rectangle.

[top]# resize_rect_width

This function takes a

rectangle and
returns a new rectangle with the given width but otherwise with the
same edge points as the original rectangle.

[top]# rotate_point

This is a function that rotates a 2D

vector or

point object about a given point.

[top]# rotation_matrix

This is a method for creating 2D rotation matrices.

[top]# set_aspect_ratio

This function reshapes a

rectangle so that
it has a user specified aspect ratio.

[top]# shrink_rect

This function takes a

rectangle object,
shrinks its borders by a given amount, and returns the result.

[top]# sparse_to_dense

This is a set of simple functions that take

sparse vectors
and converts them into equivalent dense vectors.

[top]# translate_rect

This function takes a

rectangle and moves
it by a given number of units along the x and y axis relative to
where it was before the move.

[top]# vector

This object represents a two or three dimensional vector.

If you
want to work with general N-dimensional column vectors then you
should the matrix object. In particular, you
should usually use a matrix with this type:
`dlib::matrix<double,0,1>`.