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diff --git a/include/2geom/sbasis-curve.h b/include/2geom/sbasis-curve.h new file mode 100644 index 0000000..93d6772 --- /dev/null +++ b/include/2geom/sbasis-curve.h @@ -0,0 +1,160 @@ +/** + * \file + * \brief Symmetric power basis curve + *//* + * Authors: + * MenTaLguY <mental@rydia.net> + * Marco Cecchetti <mrcekets at gmail.com> + * Krzysztof Kosiński <tweenk.pl@gmail.com> + * + * Copyright 2007-2009 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_SBASIS_CURVE_H +#define LIB2GEOM_SEEN_SBASIS_CURVE_H + +#include <2geom/curve.h> +#include <2geom/exception.h> +#include <2geom/nearest-time.h> +#include <2geom/sbasis-geometric.h> +#include <2geom/transforms.h> + +namespace Geom +{ + +/** @brief Symmetric power basis curve. + * + * Symmetric power basis (S-basis for short) polynomials are a versatile numeric + * representation of arbitrary continuous curves. They are the main representation of curves + * in 2Geom. + * + * S-basis is defined for odd degrees and composed of the following polynomials: + * \f{align*}{ + P_k^0(t) &= t^k (1-t)^{k+1} \\ + P_k^1(t) &= t^{k+1} (1-t)^k \f} + * This can be understood more easily with the help of the chart below. Each square + * represents a product of a specific number of \f$t\f$ and \f$(1-t)\f$ terms. Red dots + * are the canonical (monomial) basis, the green dots are the Bezier basis, and the blue + * dots are the S-basis, all of them of degree 7. + * + * @image html sbasis.png "Illustration of the monomial, Bezier and symmetric power bases" + * + * The S-Basis has several important properties: + * - S-basis polynomials are closed under multiplication. + * - Evaluation is fast, using a modified Horner scheme. + * - Degree change is as trivial as in the monomial basis. To elevate, just add extra + * zero coefficients. To reduce the degree, truncate the terms in the highest powers. + * Compare this with Bezier curves, where degree change is complicated. + * - Conversion between S-basis and Bezier basis is numerically stable. + * + * More in-depth information can be found in the following paper: + * J Sanchez-Reyes, "The symmetric analogue of the polynomial power basis". + * ACM Transactions on Graphics, Vol. 16, No. 3, July 1997, pages 319--357. + * http://portal.acm.org/citation.cfm?id=256162 + * + * @ingroup Curves + */ +class SBasisCurve : public Curve { +private: + D2<SBasis> inner; + +public: + explicit SBasisCurve(D2<SBasis> const &sb) : inner(sb) {} + explicit SBasisCurve(Curve const &other) : inner(other.toSBasis()) {} + + Curve *duplicate() const override { return new SBasisCurve(*this); } + Point initialPoint() const override { return inner.at0(); } + Point finalPoint() const override { return inner.at1(); } + bool isDegenerate() const override { return inner.isConstant(0); } + bool isLineSegment() const override { return inner[X].size() == 1; } + Point pointAt(Coord t) const override { return inner.valueAt(t); } + std::vector<Point> pointAndDerivatives(Coord t, unsigned n) const override { + return inner.valueAndDerivatives(t, n); + } + Coord valueAt(Coord t, Dim2 d) const override { return inner[d].valueAt(t); } + void setInitial(Point const &v) override { + for (unsigned d = 0; d < 2; d++) { inner[d][0][0] = v[d]; } + } + void setFinal(Point const &v) override { + for (unsigned d = 0; d < 2; d++) { inner[d][0][1] = v[d]; } + } + Rect boundsFast() const override { return *bounds_fast(inner); } + Rect boundsExact() const override { return *bounds_exact(inner); } + void expandToTransformed(Rect &bbox, Affine const &transform) const override { + bbox |= bounds_exact(inner * transform); + } + OptRect boundsLocal(OptInterval const &i, unsigned deg) const override { + return bounds_local(inner, i, deg); + } + std::vector<Coord> roots(Coord v, Dim2 d) const override { return Geom::roots(inner[d] - v); } + Coord nearestTime( Point const& p, Coord from = 0, Coord to = 1 ) const override { + return nearest_time(p, inner, from, to); + } + std::vector<Coord> allNearestTimes( Point const& p, Coord from = 0, + Coord to = 1 ) const override + { + return all_nearest_times(p, inner, from, to); + } + Coord length(Coord tolerance) const override { return ::Geom::length(inner, tolerance); } + Curve *portion(Coord f, Coord t) const override { + return new SBasisCurve(Geom::portion(inner, f, t)); + } + + using Curve::operator*=; + void operator*=(Affine const &m) override { inner = inner * m; } + + Curve *derivative() const override { + return new SBasisCurve(Geom::derivative(inner)); + } + D2<SBasis> toSBasis() const override { return inner; } + bool operator==(Curve const &c) const override { + SBasisCurve const *other = dynamic_cast<SBasisCurve const *>(&c); + if (!other) return false; + return inner == other->inner; + } + bool isNear(Curve const &/*c*/, Coord /*eps*/) const override { + THROW_NOTIMPLEMENTED(); + return false; + } + int degreesOfFreedom() const override { + return inner[0].degreesOfFreedom() + inner[1].degreesOfFreedom(); + } +}; + +} // end namespace Geom + +#endif // LIB2GEOM_SEEN_SBASIS_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 : |