diff options
Diffstat (limited to 'src/2geom/affine.cpp')
| -rw-r--r-- | src/2geom/affine.cpp | 60 |
1 files changed, 41 insertions, 19 deletions
diff --git a/src/2geom/affine.cpp b/src/2geom/affine.cpp index c31b9ba90..1be5d9fe8 100644 --- a/src/2geom/affine.cpp +++ b/src/2geom/affine.cpp @@ -144,6 +144,7 @@ bool Affine::isNonzeroTranslation(Coord eps) const { 0 & b & 0 \\ 0 & 0 & 1 \end{array}\right]\f$. */ bool Affine::isScale(Coord eps) const { + if (isSingular(eps)) return false; return are_near(_c[1], 0.0, eps) && are_near(_c[2], 0.0, eps) && are_near(_c[4], 0.0, eps) && are_near(_c[5], 0.0, eps); } @@ -156,6 +157,7 @@ bool Affine::isScale(Coord eps) const { 0 & b & 0 \\ 0 & 0 & 1 \end{array}\right]\f$ and \f$a, b \neq 1\f$. */ bool Affine::isNonzeroScale(Coord eps) const { + if (isSingular(eps)) return false; return (!are_near(_c[0], 1.0, eps) || !are_near(_c[3], 1.0, eps)) && //NOTE: these are the diags, and the next line opposite diags are_near(_c[1], 0.0, eps) && are_near(_c[2], 0.0, eps) && are_near(_c[4], 0.0, eps) && are_near(_c[5], 0.0, eps); @@ -165,11 +167,12 @@ bool Affine::isNonzeroScale(Coord eps) const { * @param eps Numerical tolerance * @return True iff the matrix is of the form * \f$\left[\begin{array}{ccc} - a & 0 & 0 \\ - 0 & a & 0 \\ - 0 & 0 & 1 \end{array}\right]\f$. */ + a_1 & 0 & 0 \\ + 0 & a_2 & 0 \\ + 0 & 0 & 1 \end{array}\right]\f$ where \f$|a_1| = |a_2|\f$. */ bool Affine::isUniformScale(Coord eps) const { - return are_near(_c[0], _c[3], eps) && + if (isSingular(eps)) return false; + return are_near(fabs(_c[0]), fabs(_c[3]), eps) && are_near(_c[1], 0.0, eps) && are_near(_c[2], 0.0, eps) && are_near(_c[4], 0.0, eps) && are_near(_c[5], 0.0, eps); } @@ -178,11 +181,16 @@ bool Affine::isUniformScale(Coord eps) const { * @param eps Numerical tolerance * @return True iff the matrix is of the form * \f$\left[\begin{array}{ccc} - a & 0 & 0 \\ - 0 & a & 0 \\ - 0 & 0 & 1 \end{array}\right]\f$ and \f$a \neq 1\f$. */ + a_1 & 0 & 0 \\ + 0 & a_2 & 0 \\ + 0 & 0 & 1 \end{array}\right]\f$ where \f$|a_1| = |a_2|\f$ + * and \f$a_1, a_2 \neq 1\f$. */ bool Affine::isNonzeroUniformScale(Coord eps) const { - return !are_near(_c[0], 1.0, eps) && are_near(_c[0], _c[3], eps) && + if (isSingular(eps)) return false; + // we need to test both c0 and c3 to handle the case of flips, + // which should be treated as nonzero uniform scales + return !(are_near(_c[0], 1.0, eps) && are_near(_c[3], 1.0, eps)) && + are_near(fabs(_c[0]), fabs(_c[3]), eps) && are_near(_c[1], 0.0, eps) && are_near(_c[2], 0.0, eps) && are_near(_c[4], 0.0, eps) && are_near(_c[5], 0.0, eps); } @@ -266,15 +274,17 @@ bool Affine::isNonzeroVShear(Coord eps) const { } /** @brief Check whether this matrix represents zooming. - * Zooming is any combination of translation and uniform scaling. It preserves angles, ratios - * of distances between arbitrary points and unit vectors of line segments. + * Zooming is any combination of translation and uniform non-flipping scaling. + * It preserves angles, ratios of distances between arbitrary points + * and unit vectors of line segments. * @param eps Numerical tolerance - * @return True iff the matrix is of the form + * @return True iff the matrix is invertible and of the form * \f$\left[\begin{array}{ccc} a & 0 & 0 \\ 0 & a & 0 \\ b & c & 1 \end{array}\right]\f$. */ bool Affine::isZoom(Coord eps) const { + if (isSingular(eps)) return false; return are_near(_c[0], _c[3], eps) && are_near(_c[1], 0, eps) && are_near(_c[2], 0, eps); } @@ -290,30 +300,42 @@ bool Affine::preservesArea(Coord eps) const } /** @brief Check whether the transformation preserves angles between lines. - * This means that the transformation can be any combination of translation, uniform scaling - * and rotation. + * This means that the transformation can be any combination of translation, uniform scaling, + * rotation and flipping. * @param eps Numerical tolerance * @return True iff the matrix is of the form * \f$\left[\begin{array}{ccc} - a & b & 0 \\ - -b & a & 0 \\ - c & d & 1 \end{array}\right]\f$. */ + a & b & 0 \\ + -b & a & 0 \\ + c & d & 1 \end{array}\right]\f$ or + \f$\left[\begin{array}{ccc} + -a & b & 0 \\ + b & a & 0 \\ + c & d & 1 \end{array}\right]\f$. */ bool Affine::preservesAngles(Coord eps) const { - return are_near(_c[0], _c[3], eps) && are_near(_c[1], -_c[2], eps); + if (isSingular(eps)) return false; + return (are_near(_c[0], _c[3], eps) && are_near(_c[1], -_c[2], eps)) || + (are_near(_c[0], -_c[3], eps) && are_near(_c[1], _c[2], eps)); } /** @brief Check whether the transformation preserves distances between points. - * This means that the transformation can be any combination of translation and rotation. + * This means that the transformation can be any combination of translation, + * rotation and flipping. * @param eps Numerical tolerance * @return True iff the matrix is of the form * \f$\left[\begin{array}{ccc} a & b & 0 \\ -b & a & 0 \\ + c & d & 1 \end{array}\right]\f$ or + \f$\left[\begin{array}{ccc} + -a & b & 0 \\ + b & a & 0 \\ c & d & 1 \end{array}\right]\f$ and \f$a^2 + b^2 = 1\f$. */ bool Affine::preservesDistances(Coord eps) const { - return are_near(_c[0], _c[3], eps) && are_near(_c[1], -_c[2], eps) && + return ((are_near(_c[0], _c[3], eps) && are_near(_c[1], -_c[2], eps)) || + (are_near(_c[0], -_c[3], eps) && are_near(_c[1], _c[2], eps))) && are_near(_c[0] * _c[0] + _c[1] * _c[1], 1.0, eps); } |