#include <transf.hxx>
Inherited by HH_Trans.
Public Member Functions | |
| SPAmatrix | affine () const |
| Returns the affine portion of the transformation. | |
| logical | compose (const transf_decompose_data &data, logical rotate_xyz_axes) |
Interprets the transf_decompose_data structure as a series of transformations. | |
| void | debug (char const *strlead, FILE *fp=debug_file_ptr) const |
| Outputs the details of a transform to the specified file. | |
| logical | decompose (transf_decompose_data &data) const |
| Decomposes a non-degenerate transformation into data that represent a unique sequence of scaling, shearing, rotating, and translating. | |
| logical | identity () const |
| Queries whether or not the transformation is the identity. | |
| SPAtransf | inverse () const |
| Returns the inverse transformation. | |
| logical | operator!= (SPAtransf const &rhs) const |
| Compares two transformations. | |
| SPAtransf const & | operator*= (SPAtransf const &t) |
| Composes this transformation with another. | |
| logical | operator== (SPAtransf const &t) const |
| Compares two transformations. | |
| void | print () const |
| Prints the transform data. | |
| logical | reflect () const |
| Queries whether or not the transformation is reflecting. | |
| logical | rotate () const |
| Queries whether or not the transformation has a rotational component. | |
| double | scaling () const |
| Returns the scaling factor of the transformation. | |
| logical | shear () const |
| Queries whether or not the transformation has a shearing component. | |
| SPAtransf (SPAtransf const &t) | |
| C++ copy constructor requests memory for this object and populates it with the data from the object supplied as an argument. | |
| SPAtransf () | |
| C++ allocation constructor requests memory for this object but does not populate it. | |
| SPAvector | translation () const |
| Returns the vector representing the translational portion of the transformation. | |
Friends | |
| SPAtransf | coordinate_transf (SPAposition const &new_origin, SPAunit_vector const &new_x_axis, SPAunit_vector const &new_y_axis) |
| Constructs a coordinate transformation. | |
| SPAposition | operator* (SPAposition const &p, SPAtransf const &t) |
| Transforms a position. | |
| SPAunit_vector | operator* (SPAunit_vector const &uv, SPAtransf const &t) |
| Transforms a unit vector by the rotation matrix in a transformation. | |
| SPAvector | operator* (SPAvector const &v, SPAtransf const &t) |
| Transforms a vector by an affine transformation. | |
| SPAtransf | operator* (SPAtransf const &t1, SPAtransf const *t2) |
| Creates the composition of two transforms. | |
| SPAtransf | operator* (SPAtransf const &t1, SPAtransf const &t2) |
| Creates the composition of two transforms. | |
| SPAtransf | reflect_transf (SPAvector const &axis) |
| Constructs a transformation corresponding to a reflection through a plane, specified by its normal. | |
| SPAtransf | rotate_transf (double angle, SPAvector const &axis) |
| Constructs a transformation corresponding to a simple rotation by an angle about a given axis. | |
| SPAtransf | scale_transf (double xs, double ys, double zs, double xys, double xzs, double yzs) |
| Constructs a transformation that both scales non-uniformly and shears. | |
| SPAtransf | scale_transf (double xs, double ys, double zs) |
| Constructs a transformation that scales non-uniformly in the x, y, and z directions. | |
| SPAtransf | scale_transf (double scale) |
| Constructs a transformation that scales uniformly in all directions. | |
| SPAtransf | shear_transf (double shearxy, double shearxz, double shearyz) |
| Constructs a shear transformation. | |
| SPAtransf | translate_transf (SPAvector const &disp) |
| Constructs a transformation corresponding to a translation by a given vector. | |
Role: This class is used to represent any combination of translations, rotations, reflections, shearing, and scaling. When shearing and/or non-uniform scaling are present, the application of such transforms to an ENTITY makes use of the Space Warping component.
| SPAtransf::SPAtransf | ( | ) |
C++ allocation constructor requests memory for this object but does not populate it.
| SPAtransf::SPAtransf | ( | SPAtransf const & | t | ) |
C++ copy constructor requests memory for this object and populates it with the data from the object supplied as an argument.
| t | transformation. |
| SPAmatrix SPAtransf::affine | ( | ) | const |
Returns the affine portion of the transformation.
Role: Always normalized: det == + or -1.
| logical SPAtransf::compose | ( | const transf_decompose_data & | data, | |
| logical | rotate_xyz_axes | |||
| ) |
Interprets the transf_decompose_data structure as a series of transformations.
Role: If the logical rotate_xyz_axes is TRUE, the sequence is: [scalex] [scaley] [scalez] [shearxy] [shearxz] [shearyz] [rotatex] [rotatey] [rotatez] [translatex] [translatey] [translatez].
Or, if the logical rotate_xyz_axes is FALSE, the sequence is: [scalex] [scaley] [scalez] [shearxy] [shearxz] [shearyz] [rotate_radians / rotate_axis] [translatex] [translatey] [translatez].
| data | input data. | |
| rotate_xyz_axes | flag indicating the format of rotation data. |
| void SPAtransf::debug | ( | char const * | strlead, | |
| FILE * | fp = debug_file_ptr | |||
| ) | const |
Outputs the details of a transform to the specified file.
| strlead | leader string. | |
| fp | file pointer. |
| logical SPAtransf::decompose | ( | transf_decompose_data & | data | ) | const |
Decomposes a non-degenerate transformation into data that represent a unique sequence of scaling, shearing, rotating, and translating.
| data | output data. |
| logical SPAtransf::identity | ( | ) | const [inline] |
Queries whether or not the transformation is the identity.
| SPAtransf SPAtransf::inverse | ( | ) | const |
Returns the inverse transformation.
Role: There must be no shear in the given transformation.
| logical SPAtransf::operator!= | ( | SPAtransf const & | rhs | ) | const [inline] |
Compares two transformations.
Role: This method does not allow any tolerance. It is therefore not a general equality operator, but returns FALSE if one transform is a copy of the other.
| rhs | transformation with which to compare. |
Composes this transformation with another.
| t | transformation with which to form a composition. |
| logical SPAtransf::operator== | ( | SPAtransf const & | t | ) | const |
Compares two transformations.
Role: This method does not allow any tolerance. It is therefore not a general equality operator, but returns TRUE if one transform is a copy of the other.
| t | transformation with which to compare. |
| void SPAtransf::print | ( | ) | const |
Prints the transform data.
| logical SPAtransf::reflect | ( | ) | const [inline] |
Queries whether or not the transformation is reflecting.
| logical SPAtransf::rotate | ( | ) | const [inline] |
Queries whether or not the transformation has a rotational component.
| double SPAtransf::scaling | ( | ) | const [inline] |
Returns the scaling factor of the transformation.
| logical SPAtransf::shear | ( | ) | const [inline] |
Queries whether or not the transformation has a shearing component.
| SPAvector SPAtransf::translation | ( | ) | const |
Returns the vector representing the translational portion of the transformation.
| SPAtransf coordinate_transf | ( | SPAposition const & | new_origin, | |
| SPAunit_vector const & | new_x_axis, | |||
| SPAunit_vector const & | new_y_axis | |||
| ) | [friend] |
Constructs a coordinate transformation.
Role: Creates a transformation that carries the origin to the given position, and the x-axis and y-axis to the given unit vectors. If the second unit vector is not orthogonal to the first, this method uses an orthogonal unit vector in the plane of the two given vectors to direct the y-axis.
Effect: System routine
| new_origin | position to which the origin is to be translated. | |
| new_x_axis | vector with which the x-axis is to be aligned. | |
| new_y_axis | vector with which the y-axis is to be aligned. |
| SPAposition operator* | ( | SPAposition const & | p, | |
| SPAtransf const & | t | |||
| ) | [friend] |
Transforms a position.
| p | position. | |
| t | transformation. |
| SPAunit_vector operator* | ( | SPAunit_vector const & | uv, | |
| SPAtransf const & | t | |||
| ) | [friend] |
Transforms a unit vector by the rotation matrix in a transformation.
Role: This method returns an error if the transformation contains a shear component.
| uv | unit vector. | |
| t | transformation. |
Transforms a vector by an affine transformation.
| v | vector. | |
| t | transformation. |
Creates the composition of two transforms.
| t1 | first transformation. | |
| t2 | second transformation. |
Creates the composition of two transforms.
| t1 | first transformation. | |
| t2 | second transformation. |
Constructs a transformation corresponding to a reflection through a plane, specified by its normal.
Role: The vector defines the normal to a plane passing through the origin. The function generates a transformation matrix describing a reflection across this plane.
Effect: Read-only
| axis | normal to the reflection plane. |
Constructs a transformation corresponding to a simple rotation by an angle about a given axis.
Role: The angle should be specified in radians.
Effect: Read-only
| angle | rotation angle in radians. | |
| axis | axis of rotation. |
| SPAtransf scale_transf | ( | double | xs, | |
| double | ys, | |||
| double | zs, | |||
| double | xys, | |||
| double | xzs, | |||
| double | yzs | |||
| ) | [friend] |
Constructs a transformation that both scales non-uniformly and shears.
Role: When the desired transformation is effectively scalar (i.e., the x, y, and z scale factors are within SPAresabs of one another and the shear factors are all within SPAresabs of zero), this function uses scale_transf(double) to construct the desired transformation. In all other cases, application of the returned transformation to an ENTITY invokes the Space Warping component.
Effect: Read-only
| xs | x scale factor. | |
| ys | y scale factor. | |
| zs | z scale factor. | |
| xys | xy shear factor. | |
| xzs | xz shear factor. | |
| yzs | yz shear factor. |
| SPAtransf scale_transf | ( | double | xs, | |
| double | ys, | |||
| double | zs | |||
| ) | [friend] |
Constructs a transformation that scales non-uniformly in the x, y, and z directions.
Role: When the desired transformation is effectively scalar (i.e., all three scale factors are within SPAresabs of one another), this function uses scale_transf(double) to construct the desired transformation. In all other cases, application of the returned transformation to an ENTITY invokes the Space Warping component.
Effect: Read-only
| xs | x scale factor. | |
| ys | y scale factor. | |
| zs | z scale factor. |
| SPAtransf scale_transf | ( | double | scale | ) | [friend] |
Constructs a transformation that scales uniformly in all directions.
Role: The scale factor must be positive definite. If a transformation producing an inversion is desired, one should use a combination of reflections rather than a negative scaling. For example, the transformation
T = reflect_transf(x_axis) * reflect_transf(y_axis) * reflect_transf(z_axis)may be used to point-reflect an object about the origin.
| scale | scale factor. |
| SPAtransf shear_transf | ( | double | shearxy, | |
| double | shearxz, | |||
| double | shearyz | |||
| ) | [friend] |
Constructs a shear transformation.
Role: Non-zero values supplied as input to this function result in a transformation that involves changing the angles between axes. This shearing is more than just non-uniform scaling. Shearxy is a ratio of the displacement of the x coordinate as the y coordinate changes. When shearxy = 1, the x axis appears at a 45-degree angle to how it normally appears; a value of 2 results in a 63.435-degree angle. Note that application of such a transformation to an ENTITY makes use of the Space Warping component.
Effect: Read-only
| shearxy | Shears the x coord as the y coord changes. | |
| shearxz | Shears the x coord as the z coord changes. | |
| shearyz | Shears the y coord as the z coord changes. |
Constructs a transformation corresponding to a translation by a given vector.
Effect: Read-only
| disp | displacement vector defining the translation. |