Rename AffineTransformation to AffineTransform

This seems like a more appropriate term for the operation.

diff --git a/source/geometry/affinetransform.h b/source/geometry/affinetransform.h
new file mode 100644 (file)
index 0000000..1cd4011
--- /dev/null
+++ b/source/geometry/affinetransform.h
@@ -0,0 +1,228 @@
+#ifndef MSP_GEOMETRY_AFFINETRANSFORM_H_
+#define MSP_GEOMETRY_AFFINETRANSFORM_H_
+
+#include <msp/linal/matrix.h>
+#include "angle.h"
+#include "boundingbox.h"
+#include "ray.h"
+
+namespace Msp {
+namespace Geometry {
+
+template<typename T, unsigned D>
+class AffineTransform;
+
+
+/**
+Helper class to provide specialized operations for AffineTransform.
+*/
+template<typename T, unsigned D>
+class AffineTransformOps
+{
+protected:
+       AffineTransformOps() { }
+};
+
+template<typename T>
+class AffineTransformOps<T, 2>
+{
+protected:
+       AffineTransformOps() { }
+
+public:
+       static AffineTransform<T, 2> rotation(const Angle<T> &);
+};
+
+template<typename T>
+class AffineTransformOps<T, 3>
+{
+protected:
+       AffineTransformOps() { }
+
+public:
+       static AffineTransform<T, 3> rotation(const Angle<T> &, const LinAl::Vector<T, 3> &);
+};
+
+
+/**
+An affine transformation in D dimensions.  Affine transformations preserve
+straightness of lines and ratios of distances.  Angles and distances themselves
+may change.  Internally this is represented by a square matrix of size D+1.
+*/
+template<typename T, unsigned D>
+class AffineTransform: public AffineTransformOps<T, D>
+{
+       friend class AffineTransformOps<T, D>;
+
+private:
+       LinAl::Matrix<T, D+1, D+1> matrix;
+
+public:
+       AffineTransform();
+
+       static AffineTransform<T, D> translation(const LinAl::Vector<T, D> &);
+       static AffineTransform<T, D> scaling(const LinAl::Vector<T, D> &);
+       static AffineTransform<T, D> shear(const LinAl::Vector<T, D> &, const LinAl::Vector<T, D> &);
+
+       AffineTransform &operator*=(const AffineTransform &);
+       AffineTransform &invert();
+
+       const LinAl::Matrix<T, D+1, D+1> &get_matrix() const { return matrix; }
+       operator const LinAl::Matrix<T, D+1, D+1> &() const { return matrix; }
+
+       LinAl::Vector<T, D> transform(const LinAl::Vector<T, D> &) const;
+       LinAl::Vector<T, D> transform_linear(const LinAl::Vector<T, D> &) const;
+       Ray<T, D> transform(const Ray<T, D> &) const;
+       BoundingBox<T, D> transform(const BoundingBox<T, D> &) const;
+};
+
+template<typename T, unsigned D>
+inline AffineTransform<T, D>::AffineTransform()
+{
+       this->matrix = LinAl::Matrix<T, D+1, D+1>::identity();
+}
+
+
+template<typename T, unsigned D>
+AffineTransform<T, D> AffineTransform<T, D>::translation(const LinAl::Vector<T, D> &v)
+{
+       AffineTransform<T, D> r;
+       for(unsigned i=0; i<D; ++i)
+               r.matrix(i, D) = v[i];
+       return r;
+}
+
+template<typename T, unsigned D>
+AffineTransform<T, D> AffineTransform<T, D>::scaling(const LinAl::Vector<T, D> &factors)
+{
+       AffineTransform<T, D> r;
+       for(unsigned i=0; i<D; ++i)
+               r.matrix(i, i) = factors[i];
+       return r;
+}
+
+template<typename T, unsigned D>
+AffineTransform<T, D> AffineTransform<T, D>::shear(const LinAl::Vector<T, D> &normal, const LinAl::Vector<T, D> &shift)
+{
+       AffineTransform<T, D> r;
+       for(unsigned i=0; i<D; ++i)
+               for(unsigned j=0; j<D; ++j)
+                       r.matrix(i, j) += normal[j]*shift[i];
+       return r;
+}
+
+template<typename T>
+AffineTransform<T, 2> AffineTransformOps<T, 2>::rotation(const Angle<T> &angle)
+{
+       AffineTransform<T, 2> r;
+       T c = cos(angle);
+       T s = sin(angle);
+       r.matrix(0, 0) = c;
+       r.matrix(0, 1) = -s;
+       r.matrix(1, 0) = s;
+       r.matrix(1, 1) = c;
+       return r;
+}
+
+template<typename T>
+AffineTransform<T, 3> AffineTransformOps<T, 3>::rotation(const Angle<T> &angle, const LinAl::Vector<T, 3> &axis)
+{
+       AffineTransform<T, 3> r;
+       LinAl::Vector<T, 3> axn = normalize(axis);
+       T c = cos(angle);
+       T s = sin(angle);
+       // http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle
+       r.matrix(0, 0) = c+axn.x*axn.x*(1-c);
+       r.matrix(0, 1) = axn.x*axn.y*(1-c)-axn.z*s;
+       r.matrix(0, 2) = axn.x*axn.z*(1-c)+axn.y*s;
+       r.matrix(1, 0) = axn.y*axn.x*(1-c)+axn.z*s;
+       r.matrix(1, 1) = c+axn.y*axn.y*(1-c);
+       r.matrix(1, 2) = axn.y*axn.z*(1-c)-axn.x*s;
+       r.matrix(2, 0) = axn.z*axn.x*(1-c)-axn.y*s;
+       r.matrix(2, 1) = axn.z*axn.y*(1-c)+axn.x*s;
+       r.matrix(2, 2) = c+axn.z*axn.z*(1-c);
+       return r;
+}
+
+template<typename T, unsigned D>
+inline AffineTransform<T, D> &AffineTransform<T, D>::operator*=(const AffineTransform<T, D> &other)
+{
+       matrix *= other.get_matrix();
+       return *this;
+}
+
+template<typename T, unsigned D>
+inline AffineTransform<T, D> operator*(const AffineTransform<T, D> &at1, const AffineTransform<T, D> &at2)
+{
+       AffineTransform<T, D> r = at1;
+       return r *= at2;
+}
+
+template<typename T, unsigned D>
+inline AffineTransform<T, D> &AffineTransform<T, D>::invert()
+{
+       matrix.invert();
+       return *this;
+}
+
+template<typename T, unsigned D>
+inline AffineTransform<T, D> invert(const AffineTransform<T, D> &at)
+{
+       AffineTransform<T, D> r = at;
+       return r.invert();
+}
+
+template<typename T, unsigned D>
+inline LinAl::Vector<T, D> AffineTransform<T, D>::transform(const LinAl::Vector<T, D> &v) const
+{
+       return (matrix*compose(v, T(1))).template slice<D>(0);
+}
+
+template<typename T, unsigned D>
+inline LinAl::Vector<T, D> AffineTransform<T, D>::transform_linear(const LinAl::Vector<T, D> &v) const
+{
+       return (matrix*compose(v, T(0))).template slice<D>(0);
+}
+
+template<typename T, unsigned D>
+inline Ray<T, D> AffineTransform<T, D>::transform(const Ray<T, D> &ray) const
+{
+       LinAl::Vector<T, D> dir = transform_linear(ray.get_direction());
+       return Ray<T, D>(transform(ray.get_start()), dir, ray.get_limit()*dir.norm());
+}
+
+template<typename T, unsigned D>
+inline BoundingBox<T, D> AffineTransform<T, D>::transform(const BoundingBox<T, D> &bbox) const
+{
+       LinAl::Vector<T, D> min_pt;
+       LinAl::Vector<T, D> max_pt;
+       for(unsigned i=0; i<(1<<D); ++i)
+       {
+               LinAl::Vector<T, D> point;
+               for(unsigned j=0; j<D; ++j)
+                       point[j] = ((i>>j)&1 ? bbox.get_maximum_coordinate(j) : bbox.get_minimum_coordinate(j));
+
+               point = transform(point);
+
+               if(i==0)
+               {
+                       min_pt = point;
+                       max_pt = point;
+               }
+               else
+               {
+                       for(unsigned j=0; j<D; ++j)
+                       {
+                               min_pt[j] = std::min(min_pt[j], point[j]);
+                               max_pt[j] = std::max(max_pt[j], point[j]);
+                       }
+               }
+       }
+
+       return BoundingBox<T, D>(min_pt, max_pt);
+}
+
+} // namespace Geometry
+} // namespace Msp
+
+#endif

diff --git a/source/geometry/affinetransformation.h b/source/geometry/affinetransformation.h
deleted file mode 100644 (file)
index e311b88..0000000
--- a/source/geometry/affinetransformation.h
+++ /dev/null
@@ -1,228 +0,0 @@
-#ifndef MSP_GEOMETRY_AFFINETRANSFORMATION_H_
-#define MSP_GEOMETRY_AFFINETRANSFORMATION_H_
-
-#include <msp/linal/matrix.h>
-#include "angle.h"
-#include "boundingbox.h"
-#include "ray.h"
-
-namespace Msp {
-namespace Geometry {
-
-template<typename T, unsigned D>
-class AffineTransformation;
-
-
-/**
-Helper class to provide specialized operations for AffineTransformation.
-*/
-template<typename T, unsigned D>
-class AffineTransformationOps
-{
-protected:
-       AffineTransformationOps() { }
-};
-
-template<typename T>
-class AffineTransformationOps<T, 2>
-{
-protected:
-       AffineTransformationOps() { }
-
-public:
-       static AffineTransformation<T, 2> rotation(const Angle<T> &);
-};
-
-template<typename T>
-class AffineTransformationOps<T, 3>
-{
-protected:
-       AffineTransformationOps() { }
-
-public:
-       static AffineTransformation<T, 3> rotation(const Angle<T> &, const LinAl::Vector<T, 3> &);
-};
-
-
-/**
-An affine transformation in D dimensions.  Affine transformations preserve
-straightness of lines and ratios of distances.  Angles and distances themselves
-may change.  Internally this is represented by a square matrix of size D+1.
-*/
-template<typename T, unsigned D>
-class AffineTransformation: public AffineTransformationOps<T, D>
-{
-       friend class AffineTransformationOps<T, D>;
-
-private:
-       LinAl::Matrix<T, D+1, D+1> matrix;
-
-public:
-       AffineTransformation();
-
-       static AffineTransformation<T, D> translation(const LinAl::Vector<T, D> &);
-       static AffineTransformation<T, D> scaling(const LinAl::Vector<T, D> &);
-       static AffineTransformation<T, D> shear(const LinAl::Vector<T, D> &, const LinAl::Vector<T, D> &);
-
-       AffineTransformation &operator*=(const AffineTransformation &);
-       AffineTransformation &invert();
-
-       const LinAl::Matrix<T, D+1, D+1> &get_matrix() const { return matrix; }
-       operator const LinAl::Matrix<T, D+1, D+1> &() const { return matrix; }
-
-       LinAl::Vector<T, D> transform(const LinAl::Vector<T, D> &) const;
-       LinAl::Vector<T, D> transform_linear(const LinAl::Vector<T, D> &) const;
-       Ray<T, D> transform(const Ray<T, D> &) const;
-       BoundingBox<T, D> transform(const BoundingBox<T, D> &) const;
-};
-
-template<typename T, unsigned D>
-inline AffineTransformation<T, D>::AffineTransformation()
-{
-       this->matrix = LinAl::Matrix<T, D+1, D+1>::identity();
-}
-
-
-template<typename T, unsigned D>
-AffineTransformation<T, D> AffineTransformation<T, D>::translation(const LinAl::Vector<T, D> &v)
-{
-       AffineTransformation<T, D> r;
-       for(unsigned i=0; i<D; ++i)
-               r.matrix(i, D) = v[i];
-       return r;
-}
-
-template<typename T, unsigned D>
-AffineTransformation<T, D> AffineTransformation<T, D>::scaling(const LinAl::Vector<T, D> &factors)
-{
-       AffineTransformation<T, D> r;
-       for(unsigned i=0; i<D; ++i)
-               r.matrix(i, i) = factors[i];
-       return r;
-}
-
-template<typename T, unsigned D>
-AffineTransformation<T, D> AffineTransformation<T, D>::shear(const LinAl::Vector<T, D> &normal, const LinAl::Vector<T, D> &shift)
-{
-       AffineTransformation<T, D> r;
-       for(unsigned i=0; i<D; ++i)
-               for(unsigned j=0; j<D; ++j)
-                       r.matrix(i, j) += normal[j]*shift[i];
-       return r;
-}
-
-template<typename T>
-AffineTransformation<T, 2> AffineTransformationOps<T, 2>::rotation(const Angle<T> &angle)
-{
-       AffineTransformation<T, 2> r;
-       T c = cos(angle);
-       T s = sin(angle);
-       r.matrix(0, 0) = c;
-       r.matrix(0, 1) = -s;
-       r.matrix(1, 0) = s;
-       r.matrix(1, 1) = c;
-       return r;
-}
-
-template<typename T>
-AffineTransformation<T, 3> AffineTransformationOps<T, 3>::rotation(const Angle<T> &angle, const LinAl::Vector<T, 3> &axis)
-{
-       AffineTransformation<T, 3> r;
-       LinAl::Vector<T, 3> axn = normalize(axis);
-       T c = cos(angle);
-       T s = sin(angle);
-       // http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle
-       r.matrix(0, 0) = c+axn.x*axn.x*(1-c);
-       r.matrix(0, 1) = axn.x*axn.y*(1-c)-axn.z*s;
-       r.matrix(0, 2) = axn.x*axn.z*(1-c)+axn.y*s;
-       r.matrix(1, 0) = axn.y*axn.x*(1-c)+axn.z*s;
-       r.matrix(1, 1) = c+axn.y*axn.y*(1-c);
-       r.matrix(1, 2) = axn.y*axn.z*(1-c)-axn.x*s;
-       r.matrix(2, 0) = axn.z*axn.x*(1-c)-axn.y*s;
-       r.matrix(2, 1) = axn.z*axn.y*(1-c)+axn.x*s;
-       r.matrix(2, 2) = c+axn.z*axn.z*(1-c);
-       return r;
-}
-
-template<typename T, unsigned D>
-inline AffineTransformation<T, D> &AffineTransformation<T, D>::operator*=(const AffineTransformation<T, D> &other)
-{
-       matrix *= other.get_matrix();
-       return *this;
-}
-
-template<typename T, unsigned D>
-inline AffineTransformation<T, D> operator*(const AffineTransformation<T, D> &at1, const AffineTransformation<T, D> &at2)
-{
-       AffineTransformation<T, D> r = at1;
-       return r *= at2;
-}
-
-template<typename T, unsigned D>
-inline AffineTransformation<T, D> &AffineTransformation<T, D>::invert()
-{
-       matrix.invert();
-       return *this;
-}
-
-template<typename T, unsigned D>
-inline AffineTransformation<T, D> invert(const AffineTransformation<T, D> &at)
-{
-       AffineTransformation<T, D> r = at;
-       return r.invert();
-}
-
-template<typename T, unsigned D>
-inline LinAl::Vector<T, D> AffineTransformation<T, D>::transform(const LinAl::Vector<T, D> &v) const
-{
-       return (matrix*compose(v, T(1))).template slice<D>(0);
-}
-
-template<typename T, unsigned D>
-inline LinAl::Vector<T, D> AffineTransformation<T, D>::transform_linear(const LinAl::Vector<T, D> &v) const
-{
-       return (matrix*compose(v, T(0))).template slice<D>(0);
-}
-
-template<typename T, unsigned D>
-inline Ray<T, D> AffineTransformation<T, D>::transform(const Ray<T, D> &ray) const
-{
-       LinAl::Vector<T, D> dir = transform_linear(ray.get_direction());
-       return Ray<T, D>(transform(ray.get_start()), dir, ray.get_limit()*dir.norm());
-}
-
-template<typename T, unsigned D>
-inline BoundingBox<T, D> AffineTransformation<T, D>::transform(const BoundingBox<T, D> &bbox) const
-{
-       LinAl::Vector<T, D> min_pt;
-       LinAl::Vector<T, D> max_pt;
-       for(unsigned i=0; i<(1<<D); ++i)
-       {
-               LinAl::Vector<T, D> point;
-               for(unsigned j=0; j<D; ++j)
-                       point[j] = ((i>>j)&1 ? bbox.get_maximum_coordinate(j) : bbox.get_minimum_coordinate(j));
-
-               point = transform(point);
-
-               if(i==0)
-               {
-                       min_pt = point;
-                       max_pt = point;
-               }
-               else
-               {
-                       for(unsigned j=0; j<D; ++j)
-                       {
-                               min_pt[j] = std::min(min_pt[j], point[j]);
-                               max_pt[j] = std::max(max_pt[j], point[j]);
-                       }
-               }
-       }
-
-       return BoundingBox<T, D>(min_pt, max_pt);
-}
-
-} // namespace Geometry
-} // namespace Msp
-
-#endif

diff --git a/source/geometry/dummy.cpp b/source/geometry/dummy.cpp
index 26aad3807a5ce28d3a3b7582d96707fafc8b0e53..be685b06ef08dc7e5e5054954c357c0e6ca9363d 100644 (file)
--- a/source/geometry/dummy.cpp
+++ b/source/geometry/dummy.cpp
@@ -1,4 +1,4 @@
-#include "affinetransformation.h"
+#include "affinetransform.h"

 #include "angle.h"
 #include "boundingbox.h"
 #include "boundingsphere.h"
 #include "angle.h"
 #include "boundingbox.h"
 #include "boundingsphere.h"

diff --git a/source/geometry/loader.h b/source/geometry/loader.h
index 2aff83fb43371a3160f0a501cda223b9c54bea76..0a9c4b537c9ffbc90b11bb51cb48a28a70c10c87 100644 (file)
--- a/source/geometry/loader.h
+++ b/source/geometry/loader.h
@@ -140,7 +140,7 @@ template<typename T, unsigned D>
 class TransformationLoader: public Loader<T, D>
 {
 protected:
 class TransformationLoader: public Loader<T, D>
 {
 protected:

-       AffineTransformation<T, D> transformation;
+       AffineTransform<T, D> transformation;

 
 public:
        TransformationLoader();
 
 public:
        TransformationLoader();


@@ -349,7 +349,7 @@ inline void TransformationLoader<T, D>::translate(const std::vector<T> &offset)
        if(offset.size()!=D)
                throw std::invalid_argument("TransformationLoader::translate");
 
        if(offset.size()!=D)
                throw std::invalid_argument("TransformationLoader::translate");
 

-       transformation *= AffineTransformation<T, D>::translation(LinAl::Vector<T, D>(&offset[0]));
+       transformation *= AffineTransform<T, D>::translation(LinAl::Vector<T, D>(&offset[0]));

 }
 
 template<typename T, unsigned D>
 }
 
 template<typename T, unsigned D>


@@ -363,10 +363,10 @@ inline void TransformationLoader<T, D>::scale(const std::vector<T> &s)
                LinAl::Vector<T, D> us;
                for(unsigned i=0; i<D; ++i)
                        us[i] = s.front();
                LinAl::Vector<T, D> us;
                for(unsigned i=0; i<D; ++i)
                        us[i] = s.front();

-               transformation *= AffineTransformation<T, D>::scaling(us);
+               transformation *= AffineTransform<T, D>::scaling(us);

        }
        else
        }
        else

-               transformation *= AffineTransformation<T, D>::scaling(LinAl::Vector<T, D>(&s[0]));
+               transformation *= AffineTransform<T, D>::scaling(LinAl::Vector<T, D>(&s[0]));

 }
 
 template<typename T, unsigned D>
 }
 
 template<typename T, unsigned D>


@@ -375,7 +375,7 @@ inline void TransformationLoader<T, D>::shear(const std::vector<T> &s)
        if(s.size()!=2*D)
                throw std::invalid_argument("TransformationLoader::shear");
 
        if(s.size()!=2*D)
                throw std::invalid_argument("TransformationLoader::shear");
 

-       transformation *= AffineTransformation<T, D>::shear(LinAl::Vector<T, D>(&s[0]), LinAl::Vector<T, D>(&s[D]));
+       transformation *= AffineTransform<T, D>::shear(LinAl::Vector<T, D>(&s[0]), LinAl::Vector<T, D>(&s[D]));

 }
 
 
 }
 
 


@@ -388,7 +388,7 @@ inline ShapeLoader<TransformedShape<T, 2> >::ShapeLoader()
 template<typename T>
 inline void ShapeLoader<TransformedShape<T, 2> >::rotate(T a)
 {
 template<typename T>
 inline void ShapeLoader<TransformedShape<T, 2> >::rotate(T a)
 {

-       TransformationLoader<T, 2>::transformation *= AffineTransformation<T, 2>::rotation(Angle<T>::from_degrees(a));
+       TransformationLoader<T, 2>::transformation *= AffineTransform<T, 2>::rotation(Angle<T>::from_degrees(a));

 }
 
 
 }
 
 


@@ -401,7 +401,7 @@ inline ShapeLoader<TransformedShape<T, 3> >::ShapeLoader()
 template<typename T>
 inline void ShapeLoader<TransformedShape<T, 3> >::rotate(T a, T x, T y, T z)
 {
 template<typename T>
 inline void ShapeLoader<TransformedShape<T, 3> >::rotate(T a, T x, T y, T z)
 {

-       TransformationLoader<T, 3>::transformation *= AffineTransformation<T, 3>::rotation(Angle<T>::from_degrees(a), LinAl::Vector<T, 3>(x, y, z));
+       TransformationLoader<T, 3>::transformation *= AffineTransform<T, 3>::rotation(Angle<T>::from_degrees(a), LinAl::Vector<T, 3>(x, y, z));

 }
 
 
 }
 
 

diff --git a/source/geometry/transformedshape.h b/source/geometry/transformedshape.h
index 9387123508dcf081341c076f8c4e41970a10ead0..168fbd9732e960dfbc79dc254cb281e8553859f1 100644 (file)
--- a/source/geometry/transformedshape.h
+++ b/source/geometry/transformedshape.h
@@ -1,7 +1,7 @@
 #ifndef MSP_GEOMETRY_TRANSFORMEDSHAPE_H_
 #define MSP_GEOMETRY_TRANSFORMEDSHAPE_H_
 
 #ifndef MSP_GEOMETRY_TRANSFORMEDSHAPE_H_
 #define MSP_GEOMETRY_TRANSFORMEDSHAPE_H_
 

-#include "affinetransformation.h"
+#include "affinetransform.h"

 #include "shape.h"
 
 namespace Msp {
 #include "shape.h"
 
 namespace Msp {


@@ -15,11 +15,11 @@ class TransformedShape: public Shape<T, D>
 {
 private:
        Shape<T, D> *shape;
 {
 private:
        Shape<T, D> *shape;

-       AffineTransformation<T, D> transformation;
-       AffineTransformation<T, D> inverse_trans;
+       AffineTransform<T, D> transformation;
+       AffineTransform<T, D> inverse_trans;

 
 public:
 
 public:

-       TransformedShape(const Shape<T, D> &, const AffineTransformation<T, D> &);
+       TransformedShape(const Shape<T, D> &, const AffineTransform<T, D> &);

        TransformedShape(const TransformedShape &);
        TransformedShape &operator=(const TransformedShape &);
        ~TransformedShape();
        TransformedShape(const TransformedShape &);
        TransformedShape &operator=(const TransformedShape &);
        ~TransformedShape();


@@ -27,7 +27,7 @@ public:
        virtual TransformedShape *clone() const;
 
        const Shape<T, D> &get_shape() const { return *shape; }
        virtual TransformedShape *clone() const;
 
        const Shape<T, D> &get_shape() const { return *shape; }

-       const AffineTransformation<T, D> &get_transformation() const { return transformation; }
+       const AffineTransform<T, D> &get_transformation() const { return transformation; }

 
        virtual BoundingBox<T, D> get_axis_aligned_bounding_box(unsigned = 0) const;
        virtual bool contains(const LinAl::Vector<T, D> &) const;
 
        virtual BoundingBox<T, D> get_axis_aligned_bounding_box(unsigned = 0) const;
        virtual bool contains(const LinAl::Vector<T, D> &) const;


@@ -37,7 +37,7 @@ public:
 };
 
 template<typename T, unsigned D>
 };
 
 template<typename T, unsigned D>

-inline TransformedShape<T, D>::TransformedShape(const Shape<T, D> &s, const AffineTransformation<T, D> &t):
+inline TransformedShape<T, D>::TransformedShape(const Shape<T, D> &s, const AffineTransform<T, D> &t):

        shape(s.clone()),
        transformation(t),
        inverse_trans(invert(t))
        shape(s.clone()),
        transformation(t),
        inverse_trans(invert(t))