mod_cg_transformation::t_cg_transformation Type Reference

Representation of a transformation. More...

Public Member Functions
procedure	initialize (transformation, dimension)
	Initialize the transformation to the identity.
procedure	compose (transformation, target)
	Compose two transformations.
procedure	add_rotation_x (transformation, angle)
	Add a rotation around the x axis.
procedure	add_rotation_y (transformation, angle)
	Add a rotation around the y axis.
procedure	add_rotation_z (transformation, angle)
	Add a rotation around the z axis.
procedure	add_rotation (transformation, axis, angle)
	Add a rotation around a given axis.
procedure	add_rotation_cos_sin (transformation, axis, c, s)
	Add a rotation around a given axis.
procedure	add_translation (transformation, vector)
	Add a translation.
procedure	add_scale_x (transformation, factor)
	Add a scaling factor in direction x.
procedure	add_scale_y (transformation, factor)
	Add a scaling factor in direction y.
procedure	add_scale_z (transformation, factor)
	Add a scaling factor in direction z.
procedure	add_scale (transformation, vector)
	Add a scaling in every direction.
procedure	transform_point (transformation, point)
	Apply a transformation to a point.
procedure	transform_direction (transformation, direction)
	Apply a transformation to a direction.
procedure	inverse_transform_point (transformation, point)
	Apply an inverse transformation to a point.
procedure	inverse_transform_direction (transformation, direction)
	Apply an inverse transformation to a direction.

Public Attributes
double precision, dimension(4, 4)	matrix = reshape([1d0, 0d0, 0d0, 0d0, 0d0, 1d0, 0d0, 0d0, 0d0, 0d0, 1d0, 0d0, 0d0, 0d0, 0d0, 1d0], [4,4])
	Transformation matrix.
double precision, dimension(4, 4)	inverse_matrix = reshape([1d0, 0d0, 0d0, 0d0, 0d0, 1d0, 0d0, 0d0, 0d0, 0d0, 1d0, 0d0, 0d0, 0d0, 0d0, 1d0], [4,4])
	Inverse of the transformation matrix.
integer	dimension = 0
	Dimension of the transformation matrix.

Detailed Description

Representation of a transformation.

Member Function/Subroutine Documentation

add_rotation()

procedure mod_cg_transformation::t_cg_transformation::add_rotation	(	class(t_cg_transformation), intent(inout)	transformation,
		double precision, dimension(3), intent(in)	axis,
		double precision, intent(in)	angle )

Add a rotation around a given axis.

Compose by a rotation matrix. Refer to the code to see the coefficients. Note that the axis can be a non-unit vector. It is normalized in the routine. A null axis results in a null rotation, that is the identity matrix.

Parameters

[in,out]	transformation	transformation that receive the transformation
[in]	axis	rotation axis which will be normalized
[in]	angle	angle of rotation in radians

add_rotation_cos_sin()

procedure mod_cg_transformation::t_cg_transformation::add_rotation_cos_sin	(	class(t_cg_transformation), intent(inout)	transformation,
		double precision, dimension(3), intent(in)	axis,
		double precision, intent(in)	c,
		double precision, intent(in)	s )

Add a rotation around a given axis.

Compose by a rotation matrix. Refer to the code to see the coefficients. Note that the axis can be a non-unit vector. It is normalized in the routine. A null axis results in a null rotation, that is the identity matrix.

Parameters

[in,out]	transformation	transformation that receive the transformation
[in]	axis	rotation axis which will be normalized
[in]	c,s	cosine and sine of the angle of rotation

add_rotation_x()

procedure mod_cg_transformation::t_cg_transformation::add_rotation_x	(	class(t_cg_transformation), intent(inout)	transformation,
		double precision, intent(in)	angle )

Add a rotation around the x axis.

Compose by the following rotation matrix:

  !! ┌─────┬─────┬─────┬─────┐
  !! │  1  │  0  │  0  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  c  │ -s  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  s  │  c  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  0  │  0  │  1  │
  !! └─────┴─────┴─────┴─────┘
  !! 

Where s and c are the sine and the cosine of the angle.

Warning

Do not apply this transformation in 2D

Parameters

[in,out]	transformation	transformation that receive the transformation
[in]	angle	angle of rotation in radians

add_rotation_y()

procedure mod_cg_transformation::t_cg_transformation::add_rotation_y	(	class(t_cg_transformation), intent(inout)	transformation,
		double precision, intent(in)	angle )

Add a rotation around the y axis.

Compose by the following rotation matrix:

  !! ┌─────┬─────┬─────┬─────┐
  !! │  c  │  0  │  s  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  1  │  0  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │ -s  │  0  │  c  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  0  │  0  │  1  │
  !! └─────┴─────┴─────┴─────┘
  !! 

Where s and c are the sine and the cosine of the angle.

Warning

Do not apply this transformation in 2D

Parameters

[in,out]	transformation	transformation that receive the transformation
[in]	angle	angle of rotation in radians

add_rotation_z()

procedure mod_cg_transformation::t_cg_transformation::add_rotation_z	(	class(t_cg_transformation), intent(inout)	transformation,
		double precision, intent(in)	angle )

Add a rotation around the z axis.

Compose by the following rotation matrix:

  !! ┌─────┬─────┬─────┬─────┐
  !! │  c  │ -s  │  0  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  s  │  c  │  0  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  0  │  1  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  0  │  0  │  1  │
  !! └─────┴─────┴─────┴─────┘
  !! 

Where s and c are the sine and the cosine of the angle.

Parameters

[in,out]	transformation	transformation that receive the transformation
[in]	angle	angle of rotation in radians

add_scale()

procedure mod_cg_transformation::t_cg_transformation::add_scale	(	class(t_cg_transformation), intent(inout)	transformation,
		double precision, dimension(:), intent(in)	vector )

Add a scaling in every direction.

Compose by the following translation matrix:

  !! ┌─────┬─────┬─────┬─────┐
  !! │ sx  │  0  │  0  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │ sy  │  0  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  0  │ sz  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  0  │  0  │  1  │
  !! └─────┴─────┴─────┴─────┘
  !! 

Where sx, sy, and sz are the scaling factor in direction x, y, and z.

Parameters

[in,out]	transformation	transformation that receive the transformation
[in]	vector	array containing the scaling factors per direction.

add_scale_x()

procedure mod_cg_transformation::t_cg_transformation::add_scale_x	(	class(t_cg_transformation), intent(inout)	transformation,
		double precision, intent(in)	factor )

Add a scaling factor in direction x.

Compose by the following translation matrix:

  !! ┌─────┬─────┬─────┬─────┐
  !! │ sx  │  0  │  0  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  1  │  0  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  0  │  1  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  0  │  0  │  1  │
  !! └─────┴─────┴─────┴─────┘
  !! 

Where sx is the scale factor in the direction x.

Parameters

[in,out]	transformation	transformation that receive the transformation
[in]	factor	scaling factor in direction x.

add_scale_y()

procedure mod_cg_transformation::t_cg_transformation::add_scale_y	(	class(t_cg_transformation), intent(inout)	transformation,
		double precision, intent(in)	factor )

Add a scaling factor in direction y.

Compose by the following translation matrix:

  !! ┌─────┬─────┬─────┬─────┐
  !! │  1  │  0  │  0  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │ sy  │  0  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  0  │  1  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  0  │  0  │  1  │
  !! └─────┴─────┴─────┴─────┘
  !! 

Where sy is the scale factor in the direction y.

Parameters

[in,out]	transformation	transformation that receive the transformation
[in]	factor	scaling factor in direction y.

add_scale_z()

procedure mod_cg_transformation::t_cg_transformation::add_scale_z	(	class(t_cg_transformation), intent(inout)	transformation,
		double precision, intent(in)	factor )

Add a scaling factor in direction z.

Compose by the following translation matrix:

  !! ┌─────┬─────┬─────┬─────┐
  !! │  1  │  0  │  0  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  1  │  0  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  0  │ sz  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  0  │  0  │  1  │
  !! └─────┴─────┴─────┴─────┘
  !! 

Where sz is the scale factor in the direction z.

Warning

Do not apply this transformation in 2D

Parameters

[in,out]	transformation	transformation that receive the transformation
[in]	factor	scaling factor in direction z.

add_translation()

procedure mod_cg_transformation::t_cg_transformation::add_translation	(	class(t_cg_transformation), intent(inout)	transformation,
		double precision, dimension(:), intent(in)	vector )

Add a translation.

Compose by the following translation matrix:

  !! ┌─────┬─────┬─────┬─────┐
  !! │  1  │  0  │  0  │ tx  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  1  │  0  │ ty  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  0  │  1  │ tz  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  0  │  0  │  1  │
  !! └─────┴─────┴─────┴─────┘
  !! 

Where tx, ty, tz are the coordinates of the translation vector.

Parameters

[in,out]	transformation	transformation that receive the transformation
[in]	vector	translation vector

compose()

procedure mod_cg_transformation::t_cg_transformation::compose	(	class(t_cg_transformation), intent(in)	transformation,
		type(t_cg_transformation), intent(inout)	target )

Compose two transformations.

Add a transformation to an other. Perform a matrix-matrix product.

Parameters

[in]	transformation	transformation to add
[in,out]	target	transformation that receive the transformation

initialize()

procedure mod_cg_transformation::t_cg_transformation::initialize	(	class(t_cg_transformation), intent(inout)	transformation,
		integer, intent(in)	dimension )

Initialize the transformation to the identity.

The initialization results in the following matrix:

  !! ┌─────┬─────┬─────┬─────┐
  !! │  1  │  0  │  0  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  1  │  0  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  0  │  1  │  0  │
  !! ├─────┼─────┼─────┼─────┤
  !! │  0  │  0  │  0  │  1  │
  !! └─────┴─────┴─────┴─────┘
  !! 

Parameters

[in,out]	transformation	transformation
[in]	dimension	spatial dimension

inverse_transform_direction()

procedure mod_cg_transformation::t_cg_transformation::inverse_transform_direction	(	class(t_cg_transformation), intent(in)	transformation,
		double precision, dimension(:), intent(in)	direction )

Apply an inverse transformation to a direction.

Return the transformed direction.

Parameters

[in]	transformation	transformation
[in]	direction	direction to transform

inverse_transform_point()

procedure mod_cg_transformation::t_cg_transformation::inverse_transform_point	(	class(t_cg_transformation), intent(in)	transformation,
		double precision, dimension(:), intent(in)	point )

Apply an inverse transformation to a point.

Return the transformed point.

Parameters

[in]	transformation	transformation
[in]	point	point to transform

transform_direction()

procedure mod_cg_transformation::t_cg_transformation::transform_direction	(	class(t_cg_transformation), intent(in)	transformation,
		double precision, dimension(:), intent(in)	direction )

Apply a transformation to a direction.

Return the transformed direction.

Parameters

[in]	transformation	transformation
[in]	direction	direction to transform

transform_point()

procedure mod_cg_transformation::t_cg_transformation::transform_point	(	class(t_cg_transformation), intent(in)	transformation,
		double precision, dimension(:), intent(in)	point )

Apply a transformation to a point.

Return the transformed point.

Parameters

[in]	transformation	transformation
[in]	point	point to transform

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The documentation for this type was generated from the following file:

• src/lib/geometry/computational_geometry/transformations.f90