Add missing 2geom files

(bzr r10027)

1 files changed, 489 insertions, 0 deletions

diff --git a/src/2geom/affine.cpp b/src/2geom/affine.cpp
new file mode 100644
index 000000000..925f43820
--- /dev/null
+++ b/src/2geom/affine.cpp
@@ -0,0 +1,489 @@
+#define __Geom_MATRIX_C__
+
+/** \file
+ * Various matrix routines.  Currently includes some Geom::Rotate etc. routines too.
+ */
+
+/*
+ * Authors:
+ *   Lauris Kaplinski <lauris@kaplinski.com>
+ *   Michael G. Sloan <mgsloan@gmail.com>
+ *
+ * This code is in public domain
+ */
+
+#include <2geom/utils.h>
+#include <2geom/affine.h>
+#include <2geom/point.h>
+
+namespace Geom {
+
+/** Creates a Affine given an axis and origin point.
+ *  The axis is represented as two vectors, which represent skew, rotation, and scaling in two dimensions.
+ *  from_basis(Point(1, 0), Point(0, 1), Point(0, 0)) would return the identity matrix.
+
+ \param x_basis the vector for the x-axis.
+ \param y_basis the vector for the y-axis.
+ \param offset the translation applied by the matrix.
+ \return The new Affine.
+ */
+//NOTE: Inkscape's version is broken, so when including this version, you'll have to search for code with this func
+Affine from_basis(Point const x_basis, Point const y_basis, Point const offset) {
+    return Affine(x_basis[X], x_basis[Y],
+                  y_basis[X], y_basis[Y],
+                  offset [X], offset [Y]);
+}
+
+Point Affine::xAxis() const {
+    return Point(_c[0], _c[1]);
+}
+
+Point Affine::yAxis() const {
+    return Point(_c[2], _c[3]);
+}
+
+/** Gets the translation imparted by the Affine.
+ */
+Point Affine::translation() const {
+    return Point(_c[4], _c[5]);
+}
+
+void Affine::setXAxis(Point const &vec) {
+    for(int i = 0; i < 2; i++)
+        _c[i] = vec[i];
+}
+
+void Affine::setYAxis(Point const &vec) {
+    for(int i = 0; i < 2; i++)
+        _c[i + 2] = vec[i];
+}
+
+/** Sets the translation imparted by the Affine.
+ */
+void Affine::setTranslation(Point const &loc) {
+    for(int i = 0; i < 2; i++)
+        _c[i + 4] = loc[i];
+}
+
+/** Calculates the amount of x-scaling imparted by the Affine.  This is the scaling applied to
+ *  the original x-axis region.  It is \emph{not} the overall x-scaling of the transformation.
+ *  Equivalent to L2(m.xAxis())
+ */
+double Affine::expansionX() const {
+    return sqrt(_c[0] * _c[0] + _c[1] * _c[1]);
+}
+
+/** Calculates the amount of y-scaling imparted by the Affine.  This is the scaling applied before
+ *  the other transformations.  It is \emph{not} the overall y-scaling of the transformation. 
+ *  Equivalent to L2(m.yAxis())
+ */
+double Affine::expansionY() const {
+    return sqrt(_c[2] * _c[2] + _c[3] * _c[3]);
+}
+
+void Affine::setExpansionX(double val) {
+    double exp_x = expansionX();
+    if(!are_near(exp_x, 0.0)) {  //TODO: best way to deal with it is to skip op?
+        double coef = val / expansionX();
+        for(unsigned i=0;i<2;i++) _c[i] *= coef;
+    }
+}
+
+void Affine::setExpansionY(double val) {
+    double exp_y = expansionY();
+    if(!are_near(exp_y, 0.0)) {  //TODO: best way to deal with it is to skip op?
+        double coef = val / expansionY();
+        for(unsigned i=2; i<4; i++) _c[i] *= coef;
+    }
+}
+
+/** Sets this matrix to be the Identity Affine. */
+void Affine::setIdentity() {
+    _c[0] = 1.0; _c[1] = 0.0;
+    _c[2] = 0.0; _c[3] = 1.0;
+    _c[4] = 0.0; _c[5] = 0.0;
+}
+
+/** @brief Check whether this matrix is an identity matrix.
+ * @param eps Numerical tolerance
+ * @return True iff the matrix is of the form
+ *         \f$\left[\begin{array}{ccc}
+           1 & 0 & 0 \\
+           0 & 1 & 0 \\
+           0 & 0 & 1 \end{array}\right]\f$ */
+bool Affine::isIdentity(Coord eps) const {
+    return are_near(_c[0], 1.0, eps) && are_near(_c[1], 0.0, eps) &&
+           are_near(_c[2], 0.0, eps) && are_near(_c[3], 1.0, eps) &&
+           are_near(_c[4], 0.0, eps) && are_near(_c[5], 0.0, eps);
+}
+
+/** @brief Check whether this matrix represents a pure translation.
+ * Will return true for the identity matrix, which represents a zero translation.
+ * @param eps Numerical tolerance
+ * @return True iff the matrix is of the form
+ *         \f$\left[\begin{array}{ccc}
+           1 & 0 & 0 \\
+           0 & 1 & 0 \\
+           a & b & 1 \end{array}\right]\f$ */
+bool Affine::isTranslation(Coord eps) const {
+    return are_near(_c[0], 1.0, eps) && are_near(_c[1], 0.0, eps) &&
+           are_near(_c[2], 0.0, eps) && are_near(_c[3], 1.0, eps);
+}
+/** @brief Check whether this matrix represents a pure nonzero translation.
+ * @param eps Numerical tolerance
+ * @return True iff the matrix is of the form
+ *         \f$\left[\begin{array}{ccc}
+           1 & 0 & 0 \\
+           0 & 1 & 0 \\
+           a & b & 1 \end{array}\right]\f$ and \f$a, b \neq 0\f$ */
+bool Affine::isNonzeroTranslation(Coord eps) const {
+    return are_near(_c[0], 1.0, eps) && are_near(_c[1], 0.0, eps) &&
+           are_near(_c[2], 0.0, eps) && are_near(_c[3], 1.0, eps) &&
+           (!are_near(_c[4], 0.0, eps) || !are_near(_c[5], 0.0, eps));
+}
+
+/** @brief Check whether this matrix represents pure scaling.
+ * @param eps Numerical tolerance
+ * @return True iff the matrix is of the form
+ *         \f$\left[\begin{array}{ccc}
+           a & 0 & 0 \\
+           0 & b & 0 \\
+           0 & 0 & 1 \end{array}\right]\f$. */
+bool Affine::isScale(Coord eps) const {
+    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);
+}
+
+/** @brief Check whether this matrix represents pure, nonzero scaling.
+ * @param eps Numerical tolerance
+ * @return True iff the matrix is of the form
+ *         \f$\left[\begin{array}{ccc}
+           a & 0 & 0 \\
+           0 & b & 0 \\
+           0 & 0 & 1 \end{array}\right]\f$ and \f$a, b \neq 1\f$. */
+bool Affine::isNonzeroScale(Coord eps) const {
+    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);
+}
+
+/** @brief Check whether this matrix represents pure uniform scaling.
+ * @param eps Numerical tolerance
+ * @return True iff the matrix is of the form
+ *         \f$\left[\begin{array}{ccc}
+           a & 0 & 0 \\
+           0 & a & 0 \\
+           0 & 0 & 1 \end{array}\right]\f$. */
+bool Affine::isUniformScale(Coord eps) const {
+    return are_near(_c[0], _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);
+}
+
+/** @brief Check whether this matrix represents pure, nonzero uniform scaling.
+ * @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$a \neq 1\f$. */
+bool Affine::isNonzeroUniformScale(Coord eps) const {
+    return !are_near(_c[0], 1.0, eps) && are_near(_c[0], _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);
+}
+
+/** @brief Check whether this matrix represents a pure rotation.
+ * @param eps Numerical tolerance
+ * @return True iff the matrix is of the form
+ *         \f$\left[\begin{array}{ccc}
+           a & b & 0 \\
+           -b & a & 0 \\
+           0 & 0 & 1 \end{array}\right]\f$ and \f$a^2 + b^2 = 1\f$. */
+bool Affine::isRotation(Coord eps) const {
+    return are_near(_c[0], _c[3], eps) && are_near(_c[1], -_c[2], eps) &&
+           are_near(_c[4], 0.0, eps) && are_near(_c[5], 0.0, eps) &&
+           are_near(_c[0]*_c[0] + _c[1]*_c[1], 1.0, eps);
+}
+
+/** @brief Check whether this matrix represents a pure, nonzero rotation.
+ * @param eps Numerical tolerance
+ * @return True iff the matrix is of the form
+ *         \f$\left[\begin{array}{ccc}
+           a & b & 0 \\
+           -b & a & 0 \\
+           0 & 0 & 1 \end{array}\right]\f$, \f$a^2 + b^2 = 1\f$ and \f$a \neq 1\f$. */
+bool Affine::isNonzeroRotation(Coord eps) const {
+    return !are_near(_c[0], 1.0, eps) &&
+           are_near(_c[0], _c[3], eps) && are_near(_c[1], -_c[2], eps) &&
+           are_near(_c[4], 0.0, eps) && are_near(_c[5], 0.0, eps) &&
+           are_near(_c[0]*_c[0] + _c[1]*_c[1], 1.0, eps);
+}
+
+/** @brief Check whether this matrix represents pure horizontal shearing.
+ * @param eps Numerical tolerance
+ * @return True iff the matrix is of the form
+ *         \f$\left[\begin{array}{ccc}
+           1 & 0 & 0 \\
+           k & 1 & 0 \\
+           0 & 0 & 1 \end{array}\right]\f$. */
+bool Affine::isHShear(Coord eps) const {
+    return are_near(_c[0], 1.0, eps) && are_near(_c[1], 0.0, eps) &&
+           are_near(_c[3], 1.0, eps) && are_near(_c[4], 0.0, eps) &&
+           are_near(_c[5], 0.0, eps);
+}
+/** @brief Check whether this matrix represents pure, nonzero horizontal shearing.
+ * @param eps Numerical tolerance
+ * @return True iff the matrix is of the form
+ *         \f$\left[\begin{array}{ccc}
+           1 & 0 & 0 \\
+           k & 1 & 0 \\
+           0 & 0 & 1 \end{array}\right]\f$ and \f$k \neq 0\f$. */
+bool Affine::isNonzeroHShear(Coord eps) const {
+    return are_near(_c[0], 1.0, eps) && are_near(_c[1], 0.0, eps) &&
+          !are_near(_c[2], 0.0, eps) && are_near(_c[3], 1.0, eps) &&
+           are_near(_c[4], 0.0, eps) && are_near(_c[5], 0.0, eps);
+}
+
+/** @brief Check whether this matrix represents pure vertical shearing.
+ * @param eps Numerical tolerance
+ * @return True iff the matrix is of the form
+ *         \f$\left[\begin{array}{ccc}
+           1 & k & 0 \\
+           0 & 1 & 0 \\
+           0 & 0 & 1 \end{array}\right]\f$. */
+bool Affine::isVShear(Coord eps) const {
+    return are_near(_c[0], 1.0, eps) && are_near(_c[2], 0.0, eps) &&
+           are_near(_c[3], 1.0, eps) && are_near(_c[4], 0.0, eps) &&
+           are_near(_c[5], 0.0, eps);
+}
+
+/** @brief Check whether this matrix represents pure, nonzero vertical shearing.
+ * @param eps Numerical tolerance
+ * @return True iff the matrix is of the form
+ *         \f$\left[\begin{array}{ccc}
+           1 & k & 0 \\
+           0 & 1 & 0 \\
+           0 & 0 & 1 \end{array}\right]\f$ and \f$k \neq 0\f$. */
+bool Affine::isNonzeroVShear(Coord eps) const {
+    return are_near(_c[0], 1.0, eps) && !are_near(_c[1], 0.0, eps) &&
+           are_near(_c[2], 0.0, eps) && are_near(_c[3], 1.0, eps) &&
+           are_near(_c[4], 0.0, eps) && are_near(_c[5], 0.0, eps);
+}
+
+/** @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.
+ * @param eps Numerical tolerance
+ * @return True iff the matrix is 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 {
+    return are_near(_c[0], _c[3], eps) && are_near(_c[1], 0, eps) && are_near(_c[2], 0, eps);
+}
+
+/** @brief Check whether the transformation preserves areas of polygons.
+ * This means that the transformation can be any combination of translation, rotation,
+ * shearing and squeezing (non-uniform scaling such that the absolute value of the product
+ * of Y-scale and X-scale is 1).
+ * @param eps Numerical tolerance
+ * @return True iff \f$|\det A| = 1\f$. */
+bool Affine::preservesArea(Coord eps) const
+{
+    return are_near(descrim2(), 1.0, eps);
+}
+
+/** @brief Check whether the transformation preserves angles between lines.
+ * This means that the transformation can be any combination of translation, uniform scaling
+ * and rotation.
+ * @param eps Numerical tolerance
+ * @return True iff the matrix is of the form
+ *         \f$\left[\begin{array}{ccc}
+           a & b & 0 \\
+           -b & a & 0 \\
+           c & d & 1 \end{array}\right]\f$. */
+bool Affine::preservesAngles(Coord eps) const
+{
+    return 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.
+ * @param eps Numerical tolerance
+ * @return True iff the matrix is of the form
+ *         \f$\left[\begin{array}{ccc}
+           a & b & 0 \\
+           -b & a & 0 \\
+           c & d & 1 \end{array}\right]\f$ 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) &&
+           are_near(_c[0] * _c[0] + _c[1] * _c[1], 1.0, eps);
+}
+
+/** @brief Check whether this transformation flips objects.
+ * A transformation flips objects if it has a negative scaling component. */
+bool Affine::flips() const {
+    // TODO shouldn't this be det() < 0?
+    return cross(xAxis(), yAxis()) > 0;
+}
+
+/** @brief Check whether this matrix is singular.
+ * Singular matrices have no inverse, which means that applying them to a set of points
+ * results in a loss of information.
+ * @param eps Numerical tolerance
+ * @return True iff the determinant is near zero. */
+bool Affine::isSingular(Coord eps) const {
+    return are_near(det(), 0.0, eps);
+}
+
+/** @brief Compute the inverse matrix.
+ * Inverse is a matrix (denoted \f$A^{-1}) such that \f$AA^{-1} = A^{-1}A = I\f$.
+ * Singular matrices have no inverse (for example a matrix that has two of its columns equal).
+ * For such matrices, the identity matrix will be returned instead.
+ * @param eps Numerical tolerance
+ * @return Inverse of the matrix, or the identity matrix if the inverse is undefined.
+ * @post (m * m.inverse()).isIdentity() == true */
+Affine Affine::inverse() const {
+    Affine d;
+    
+    double mx = std::max(fabs(_c[0]) + fabs(_c[1]), 
+                         fabs(_c[2]) + fabs(_c[3])); // a random matrix norm (either l1 or linfty
+    if(mx > 0) {
+        Geom::Coord const determ = det();
+        if (!rel_error_bound(determ, mx*mx)) {
+            Geom::Coord const ideterm = 1.0 / (determ);
+            
+            d._c[0] =  _c[3] * ideterm;
+            d._c[1] = -_c[1] * ideterm;
+            d._c[2] = -_c[2] * ideterm;
+            d._c[3] =  _c[0] * ideterm;
+            d._c[4] = (-_c[4] * d._c[0] - _c[5] * d._c[2]);
+            d._c[5] = (-_c[4] * d._c[1] - _c[5] * d._c[3]);
+        } else {
+            d.setIdentity();
+        }
+    } else {
+        d.setIdentity();
+    }
+
+    return d;
+}
+
+/** @brief Calculate the determinant.
+ * @return \f$\det A\f$. */
+Coord Affine::det() const {
+    // TODO this can overflow
+    return _c[0] * _c[3] - _c[1] * _c[2];
+}
+
+/** @brief Calculate the square of the descriminant.
+ * This is simply the absolute value of the determinant.
+ * @return \f$|\det A|\f$. */
+Coord Affine::descrim2() const {
+    return fabs(det());
+}
+
+/** @brief Calculate the descriminant.
+ * If the matrix doesn't contain a non-uniform scaling or shearing component, this value says
+ * how will the length any line segment change after applying this transformation
+ * to arbitrary objects on a plane (the new length will be
+ * @code line_seg.length() * m.descrim()) @endcode.
+ * @return \f$\sqrt{|\det A|}\f$. */
+Coord Affine::descrim() const {
+    return sqrt(descrim2());
+}
+
+/** @brief Combine this transformation with another one.
+ * After this operation, the matrix will correspond to the transformation
+ * obtained by first applying the original version of this matrix, and then
+ * applying @a m. */
+Affine &Affine::operator*=(Affine const &o) {
+    Coord nc[6];
+    for(int a = 0; a < 5; a += 2) {
+        for(int b = 0; b < 2; b++) {
+            nc[a + b] = _c[a] * o._c[b] + _c[a + 1] * o._c[b + 2];
+        }
+    }
+    for(int a = 0; a < 6; ++a) {
+        _c[a] = nc[a];
+    }
+    _c[4] += o._c[4];
+    _c[5] += o._c[5];
+    return *this;
+}
+
+//TODO: What's this!?!
+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,
+                od, m[2]*m[2] + m[3]*m[3],
+                0, 0);
+    return ret; // allow NRVO
+}
+
+Eigen::Eigen(Affine const &m) {
+    double const B = -m[0] - m[3];
+    double const C = m[0]*m[3] - m[1]*m[2];
+    double const center = -B/2.0;
+    double const delta = sqrt(B*B-4*C)/2.0;
+    values[0] = center + delta; values[1] = center - delta;
+    for (int i = 0; i < 2; i++) {
+        vectors[i] = unit_vector(rot90(Point(m[0]-values[i], m[1])));
+    }
+}
+
+static void quadratic_roots(double q0, double q1, double q2, int &n, double&r0, double&r1) {
+    std::vector<double> r;
+    if(q2 == 0) {
+        if(q1 == 0) { // zero or infinite roots
+            n = 0;
+        } else {
+            n = 1;
+            r0 = -q0/q1;
+        }
+    } else {
+        double desc = q1*q1 - 4*q2*q0;
+        if (desc < 0)
+            n = 0;
+        else if (desc == 0) {
+            n = 1;
+            r0 = -q1/(2*q2);
+        } else {
+            n = 2;
+            desc = std::sqrt(desc);
+            double t = -0.5*(q1+sgn(q1)*desc);
+            r0 = t/q2;
+            r1 = q0/t;
+        }
+    }
+}
+
+Eigen::Eigen(double m[2][2]) {
+    double const B = -m[0][0] - m[1][1];
+    double const C = m[0][0]*m[1][1] - m[1][0]*m[0][1];
+    //double const desc = B*B-4*C;
+    //double t = -0.5*(B+sgn(B)*desc);
+    int n;
+    values[0] = values[1] = 0;
+    quadratic_roots(C, B, 1, n, values[0], values[1]);
+    for (int i = 0; i < n; i++)
+        vectors[i] = unit_vector(rot90(Point(m[0][0]-values[i], m[0][1])));
+    for (int i = n; i < 2; i++) 
+        vectors[i] = Point(0,0);
+}
+
+}  //namespace Geom
+
+/*
+  Local Variables:
+  mode:c++
+  c-file-style:"stroustrup"
+  c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
+  indent-tabs-mode:nil
+  fill-column:99
+  End:
+*/
+// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :