diff options
Diffstat (limited to 'src/2geom/affine.cpp')
| -rw-r--r-- | src/2geom/affine.cpp | 86 |
1 files changed, 57 insertions, 29 deletions
diff --git a/src/2geom/affine.cpp b/src/2geom/affine.cpp index 925f43820..1be5d9fe8 100644 --- a/src/2geom/affine.cpp +++ b/src/2geom/affine.cpp @@ -1,9 +1,3 @@ -#define __Geom_MATRIX_C__ - -/** \file - * Various matrix routines. Currently includes some Geom::Rotate etc. routines too. - */ - /* * Authors: * Lauris Kaplinski <lauris@kaplinski.com> @@ -150,6 +144,7 @@ bool Affine::isNonzeroTranslation(Coord eps) const { 0 & b & 0 \\ 0 & 0 & 1 \end{array}\right]\f$. */ bool Affine::isScale(Coord eps) const { + if (isSingular(eps)) return false; return are_near(_c[1], 0.0, eps) && are_near(_c[2], 0.0, eps) && are_near(_c[4], 0.0, eps) && are_near(_c[5], 0.0, eps); } @@ -162,6 +157,7 @@ bool Affine::isScale(Coord eps) const { 0 & b & 0 \\ 0 & 0 & 1 \end{array}\right]\f$ 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); @@ -171,11 +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); } @@ -184,11 +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); } @@ -272,15 +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); } @@ -296,30 +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); } @@ -387,10 +403,10 @@ Coord Affine::descrim2() const { } /** @brief Calculate the descriminant. - * If the matrix doesn't contain a non-uniform scaling or shearing component, this value says - * how will the length any line segment change after applying this transformation - * to arbitrary objects on a plane (the new length will be - * @code line_seg.length() * m.descrim()) @endcode. + * If the matrix doesn't contain a shearing or non-uniform scaling component, this value says + * how will the length of any line segment change after applying this transformation + * to arbitrary objects on a plane. The new length will be + * @code line_seg.length() * m.descrim()) @endcode * @return \f$\sqrt{|\det A|}\f$. */ Coord Affine::descrim() const { return sqrt(descrim2()); @@ -416,6 +432,9 @@ Affine &Affine::operator*=(Affine const &o) { } //TODO: What's this!?! +/** Given a matrix m such that unit_circle = m*x, this returns the + * quadratic form x*A*x = 1. + * @relates Affine */ Affine elliptic_quadratic_form(Affine const &m) { double od = m[0] * m[1] + m[2] * m[3]; Affine ret (m[0]*m[0] + m[1]*m[1], od, @@ -475,6 +494,15 @@ Eigen::Eigen(double m[2][2]) { vectors[i] = Point(0,0); } +/** @brief Nearness predicate for affine transforms + * @returns True if all entries of matrices are within eps of each other */ +bool are_near(Affine const &a, Affine const &b, Coord eps) +{ + return are_near(a[0], b[0], eps) && are_near(a[1], b[1], eps) && + are_near(a[2], b[2], eps) && are_near(a[3], b[3], eps) && + are_near(a[4], b[4], eps) && are_near(a[5], b[5], eps); +} + } //namespace Geom /* |