Adding upstream version 1.0.2.upstream/1.0.2upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 352 insertions, 0 deletions

diff --git a/src/2geom/bezier-curve.h b/src/2geom/bezier-curve.h
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+/**
+ * \file
+ * \brief Bezier curve
+ *//*
+ * Authors:
+ *   MenTaLguY <mental@rydia.net>
+ *   Marco Cecchetti <mrcekets at gmail.com>
+ *   Krzysztof Kosiński <tweenk.pl@gmail.com>
+ * 
+ * Copyright 2007-2011 Authors
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it either under the terms of the GNU Lesser General Public
+ * License version 2.1 as published by the Free Software Foundation
+ * (the "LGPL") or, at your option, under the terms of the Mozilla
+ * Public License Version 1.1 (the "MPL"). If you do not alter this
+ * notice, a recipient may use your version of this file under either
+ * the MPL or the LGPL.
+ *
+ * You should have received a copy of the LGPL along with this library
+ * in the file COPYING-LGPL-2.1; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * You should have received a copy of the MPL along with this library
+ * in the file COPYING-MPL-1.1
+ *
+ * The contents of this file are subject to the Mozilla Public License
+ * Version 1.1 (the "License"); you may not use this file except in
+ * compliance with the License. You may obtain a copy of the License at
+ * http://www.mozilla.org/MPL/
+ *
+ * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
+ * OF ANY KIND, either express or implied. See the LGPL or the MPL for
+ * the specific language governing rights and limitations.
+ */
+
+#ifndef LIB2GEOM_SEEN_BEZIER_CURVE_H
+#define LIB2GEOM_SEEN_BEZIER_CURVE_H
+
+#include <2geom/curve.h>
+#include <2geom/sbasis-curve.h> // for non-native winding method
+#include <2geom/bezier.h>
+#include <2geom/transforms.h>
+
+namespace Geom 
+{
+
+class BezierCurve : public Curve {
+protected:
+    D2<Bezier> inner;
+    BezierCurve() {}
+    BezierCurve(Bezier const &x, Bezier const &y) : inner(x, y) {}
+    BezierCurve(std::vector<Point> const &pts);
+
+public:
+    explicit BezierCurve(D2<Bezier> const &b) : inner(b) {}
+
+    /// @name Access and modify control points
+    /// @{
+    /** @brief Get the order of the Bezier curve.
+     * A Bezier curve has order() + 1 control points. */
+    unsigned order() const { return inner[X].order(); }
+    /** @brief Get the number of control points. */
+    unsigned size() const { return inner[X].order() + 1; }
+    /** @brief Access control points of the curve.
+     * @param ix The (zero-based) index of the control point. Note that the caller is responsible for checking that this value is <= order().
+     * @return The control point. No-reference return, use setPoint() to modify control points. */
+    Point controlPoint(unsigned ix) const { return Point(inner[X][ix], inner[Y][ix]); }
+    Point operator[](unsigned ix) const { return Point(inner[X][ix], inner[Y][ix]); }
+    /** @brief Get the control points.
+     * @return Vector with order() + 1 control points. */
+    std::vector<Point> controlPoints() const { return bezier_points(inner); }
+    D2<Bezier> const &fragment() const { return inner; }
+
+    /** @brief Modify a control point.
+     * @param ix The zero-based index of the point to modify. Note that the caller is responsible for checking that this value is <= order().
+     * @param v The new value of the point */
+    void setPoint(unsigned ix, Point const &v) {
+        inner[X][ix] = v[X];
+        inner[Y][ix] = v[Y];
+    }
+    /** @brief Set new control points.
+     * @param ps Vector which must contain order() + 1 points.
+     *           Note that the caller is responsible for checking the size of this vector.
+     * @throws LogicalError Thrown when the size of the vector does not match the order. */
+    virtual void setPoints(std::vector<Point> const &ps) {
+        // must be virtual, because HLineSegment will need to redefine it
+        if (ps.size() != order() + 1)
+            THROW_LOGICALERROR("BezierCurve::setPoints: incorrect number of points in vector");
+        for(unsigned i = 0; i <= order(); i++) {
+            setPoint(i, ps[i]);
+        }
+    }
+    /// @}
+
+    /// @name Construct a Bezier curve with runtime-determined order.
+    /// @{
+    /** @brief Construct a curve from a vector of control points.
+     * This will construct the appropriate specialization of BezierCurve (i.e. LineSegment,
+     * QuadraticBezier or Cubic Bezier) if the number of control points in the passed vector
+     * does not exceed 4. */
+    static BezierCurve *create(std::vector<Point> const &pts);
+    /// @}
+
+    // implementation of virtual methods goes here
+    virtual Point initialPoint() const { return inner.at0(); }
+    virtual Point finalPoint() const { return inner.at1(); }
+    virtual bool isDegenerate() const;
+    virtual bool isLineSegment() const { return size() == 2; }
+    virtual void setInitial(Point const &v) { setPoint(0, v); }
+    virtual void setFinal(Point const &v) { setPoint(order(), v); }
+    virtual Rect boundsFast() const { return *bounds_fast(inner); }
+    virtual Rect boundsExact() const { return *bounds_exact(inner); }
+    virtual OptRect boundsLocal(OptInterval const &i, unsigned deg) const {
+        if (!i) return OptRect();
+        if(i->min() == 0 && i->max() == 1) return boundsFast();
+        if(deg == 0) return bounds_local(inner, i);
+        // TODO: UUUUUUGGGLLY
+        if(deg == 1 && order() > 1) return OptRect(bounds_local(Geom::derivative(inner[X]), i),
+                                                   bounds_local(Geom::derivative(inner[Y]), i));
+        return OptRect();
+    }
+    virtual Curve *duplicate() const {
+        return new BezierCurve(*this);
+    }
+    virtual Curve *portion(Coord f, Coord t) const {
+        return new BezierCurve(Geom::portion(inner, f, t));
+    }
+    virtual Curve *reverse() const {
+        return new BezierCurve(Geom::reverse(inner));
+    }
+
+    using Curve::operator*=;
+    virtual void operator*=(Translate const &tr) {
+        for (unsigned i = 0; i < size(); ++i) {
+            inner[X][i] += tr[X];
+            inner[Y][i] += tr[Y];
+        }
+    }
+    virtual void operator*=(Scale const &s) {
+        for (unsigned i = 0; i < size(); ++i) {
+            inner[X][i] *= s[X];
+            inner[Y][i] *= s[Y];
+        }
+    }
+    virtual void operator*=(Affine const &m) {
+        for (unsigned i = 0; i < size(); ++i) {
+            setPoint(i, controlPoint(i) * m);
+        }
+    }
+
+    virtual Curve *derivative() const {
+        return new BezierCurve(Geom::derivative(inner[X]), Geom::derivative(inner[Y]));
+    }
+    virtual int degreesOfFreedom() const {
+        return 2 * (order() + 1);
+    }
+    virtual std::vector<Coord> roots(Coord v, Dim2 d) const {
+        return (inner[d] - v).roots();
+    }
+    virtual Coord nearestTime(Point const &p, Coord from = 0, Coord to = 1) const;
+    virtual Coord length(Coord tolerance) const;
+    virtual std::vector<CurveIntersection> intersect(Curve const &other, Coord eps = EPSILON) const;
+    virtual Point pointAt(Coord t) const { return inner.pointAt(t); }
+    virtual std::vector<Point> pointAndDerivatives(Coord t, unsigned n) const {
+        return inner.valueAndDerivatives(t, n);
+    }
+    virtual Coord valueAt(Coord t, Dim2 d) const { return inner[d].valueAt(t); }
+    virtual D2<SBasis> toSBasis() const {return inner.toSBasis(); }
+    virtual bool isNear(Curve const &c, Coord precision) const;
+    virtual bool operator==(Curve const &c) const;
+    virtual void feed(PathSink &sink, bool) const;
+};
+
+template <unsigned degree>
+class BezierCurveN
+    : public BezierCurve
+{
+    template <unsigned required_degree>
+    static void assert_degree(BezierCurveN<required_degree> const *) {}
+
+public:
+    /// @name Construct Bezier curves
+    /// @{
+    /** @brief Construct a Bezier curve of the specified order with all points zero. */
+    BezierCurveN() {
+        inner = D2<Bezier>(Bezier(Bezier::Order(degree)), Bezier(Bezier::Order(degree)));
+    }
+
+    /** @brief Construct from 2D Bezier polynomial. */
+    explicit BezierCurveN(D2<Bezier > const &x) {
+        inner = x;
+    }
+
+    /** @brief Construct from two 1D Bezier polynomials of the same order. */
+    BezierCurveN(Bezier x, Bezier y) {
+        inner = D2<Bezier > (x,y);
+    }
+
+    /** @brief Construct a Bezier curve from a vector of its control points. */
+    BezierCurveN(std::vector<Point> const &points) {
+        unsigned ord = points.size() - 1;
+        if (ord != degree) THROW_LOGICALERROR("BezierCurve<degree> does not match number of points");
+        for (unsigned d = 0; d < 2; ++d) {
+            inner[d] = Bezier(Bezier::Order(ord));
+            for(unsigned i = 0; i <= ord; i++)
+                inner[d][i] = points[i][d];
+        }
+    }
+
+    /** @brief Construct a linear segment from its endpoints. */
+    BezierCurveN(Point c0, Point c1) {
+      assert_degree<1>(this);
+      for(unsigned d = 0; d < 2; d++)
+          inner[d] = Bezier(c0[d], c1[d]);
+    }
+
+    /** @brief Construct a quadratic Bezier curve from its control points. */
+    BezierCurveN(Point c0, Point c1, Point c2) {
+      assert_degree<2>(this);
+      for(unsigned d = 0; d < 2; d++)
+          inner[d] = Bezier(c0[d], c1[d], c2[d]);
+    }
+
+    /** @brief Construct a cubic Bezier curve from its control points. */
+    BezierCurveN(Point c0, Point c1, Point c2, Point c3) {
+      assert_degree<3>(this);
+      for(unsigned d = 0; d < 2; d++)
+          inner[d] = Bezier(c0[d], c1[d], c2[d], c3[d]);
+    }
+
+    // default copy
+    // default assign
+
+    /// @}
+
+    /** @brief Divide a Bezier curve into two curves
+     * @param t Time value
+     * @return Pair of Bezier curves \f$(\mathbf{D}, \mathbf{E})\f$ such that
+     *         \f$\mathbf{D}[ [0,1] ] = \mathbf{C}[ [0,t] ]\f$ and
+     *         \f$\mathbf{E}[ [0,1] ] = \mathbf{C}[ [t,1] ]\f$ */
+    std::pair<BezierCurveN, BezierCurveN> subdivide(Coord t) const {
+        std::pair<Bezier, Bezier> sx = inner[X].subdivide(t), sy = inner[Y].subdivide(t);
+        return std::make_pair(
+                   BezierCurveN(sx.first, sy.first),
+                   BezierCurveN(sx.second, sy.second));
+    }
+
+    virtual bool isDegenerate() const {
+        return BezierCurve::isDegenerate();
+    }
+
+    virtual bool isLineSegment() const {
+        return size() == 2;
+    }
+
+    virtual Curve *duplicate() const {
+        return new BezierCurveN(*this);
+    }
+    virtual Curve *portion(Coord f, Coord t) const {
+        if (degree == 1) {
+            return new BezierCurveN<1>(pointAt(f), pointAt(t));
+        } else {
+            return new BezierCurveN(Geom::portion(inner, f, t));
+        }
+    }
+    virtual Curve *reverse() const {
+        if (degree == 1) {
+            return new BezierCurveN<1>(finalPoint(), initialPoint()); 
+        } else {
+            return new BezierCurveN(Geom::reverse(inner));
+        }
+    }
+    virtual Curve *derivative() const;
+
+    virtual Coord nearestTime(Point const &p, Coord from = 0, Coord to = 1) const {
+        return BezierCurve::nearestTime(p, from, to);
+    }
+    virtual std::vector<CurveIntersection> intersect(Curve const &other, Coord eps = EPSILON) const {
+        // call super. this is implemented only to allow specializations
+        return BezierCurve::intersect(other, eps);
+    }
+    virtual int winding(Point const &p) const {
+        return Curve::winding(p);
+    }
+    virtual void feed(PathSink &sink, bool moveto_initial) const {
+        // call super. this is implemented only to allow specializations
+        BezierCurve::feed(sink, moveto_initial);
+    }
+};
+
+// BezierCurveN<0> is meaningless; specialize it out
+template<> class BezierCurveN<0> : public BezierCurveN<1> { private: BezierCurveN();};
+
+/** @brief Line segment.
+ * Line segments are Bezier curves of order 1. They have only two control points,
+ * the starting point and the ending point.
+ * @ingroup Curves */
+typedef BezierCurveN<1> LineSegment;
+
+/** @brief Quadratic (order 2) Bezier curve.
+ * @ingroup Curves */
+typedef BezierCurveN<2> QuadraticBezier;
+
+/** @brief Cubic (order 3) Bezier curve.
+ * @ingroup Curves */
+typedef BezierCurveN<3> CubicBezier;
+
+template <unsigned degree>
+inline
+Curve *BezierCurveN<degree>::derivative() const {
+    return new BezierCurveN<degree-1>(Geom::derivative(inner[X]), Geom::derivative(inner[Y]));
+}
+
+// optimized specializations
+template <> inline bool BezierCurveN<1>::isDegenerate() const {
+    return inner[X][0] == inner[X][1] && inner[Y][0] == inner[Y][1];
+}
+template <> inline bool BezierCurveN<1>::isLineSegment() const { return true; }
+template <> Curve *BezierCurveN<1>::derivative() const;
+template <> Coord BezierCurveN<1>::nearestTime(Point const &, Coord, Coord) const;
+template <> std::vector<CurveIntersection> BezierCurveN<1>::intersect(Curve const &, Coord) const;
+template <> int BezierCurveN<1>::winding(Point const &) const;
+template <> void BezierCurveN<1>::feed(PathSink &sink, bool moveto_initial) const;
+template <> void BezierCurveN<2>::feed(PathSink &sink, bool moveto_initial) const;
+template <> void BezierCurveN<3>::feed(PathSink &sink, bool moveto_initial) const;
+
+inline Point middle_point(LineSegment const& _segment) {
+    return ( _segment.initialPoint() + _segment.finalPoint() ) / 2;
+}
+
+inline Coord length(LineSegment const& seg) {
+    return distance(seg.initialPoint(), seg.finalPoint());
+}
+
+Coord bezier_length(std::vector<Point> const &points, Coord tolerance = 0.01);
+Coord bezier_length(Point p0, Point p1, Point p2, Coord tolerance = 0.01);
+Coord bezier_length(Point p0, Point p1, Point p2, Point p3, Coord tolerance = 0.01);
+
+} // end namespace Geom
+
+#endif // LIB2GEOM_SEEN_BEZIER_CURVE_H
+
+/*
+  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 :