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diff --git a/src/livarot/Path.h b/src/livarot/Path.h new file mode 100644 index 0000000..f61451d --- /dev/null +++ b/src/livarot/Path.h @@ -0,0 +1,1001 @@ +// SPDX-License-Identifier: GPL-2.0-or-later +/** @file + * TODO: insert short description here + *//* + * Authors: see git history + * + * Copyright (C) 2014 Authors + * Released under GNU GPL v2+, read the file 'COPYING' for more information. + */ +/* + * Path.h + * nlivarot + * + * Created by fred on Tue Jun 17 2003. + * + */ + +#ifndef my_path +#define my_path + +#include <vector> +#include "LivarotDefs.h" +#include <2geom/point.h> + +struct PathDescr; +struct PathDescrLineTo; +struct PathDescrArcTo; +struct PathDescrCubicTo; +struct PathDescrBezierTo; +struct PathDescrIntermBezierTo; + +class SPStyle; + +/* + * the Path class: a structure to hold path description and their polyline approximation (not kept in sync) + * the path description is built with regular commands like MoveTo() LineTo(), etc + * the polyline approximation is built by a call to Convert() or its variants + * another possibility would be to call directly the AddPoint() functions, but that is not encouraged + * the conversion to polyline can salvage data as to where on the path each polyline's point lies; use + * ConvertWithBackData() for this. after this call, it's easy to rewind the polyline: sequences of points + * of the same path command can be reassembled in a command + */ + +// polyline description commands +enum +{ + polyline_lineto = 0, // a lineto + polyline_moveto = 1, // a moveto + polyline_forced = 2 // a forced point, ie a point that was an angle or an intersection in a previous life + // or more realistically a control point in the path description that created the polyline + // forced points are used as "breakable" points for the polyline -> cubic bezier patch operations + // each time the bezier fitter encounters such a point in the polyline, it decreases its treshhold, + // so that it is more likely to cut the polyline at that position and produce a bezier patch +}; + +class Shape; + +// path creation: 2 phases: first the path is given as a succession of commands (MoveTo, LineTo, CurveTo...); then it +// is converted in a polyline +// a polylone can be stroked or filled to make a polygon + +/** + * Path and its polyline approximation. + * + * A Path is exactly analogous to an SVG path element. Like the SVG path element, this class + * stores path commands. A Path can be approximated by line segments and this approximation + * is known as a "polyline approximation". Internally, the polyline approximation is stored + * as a set of points. + * + * Each path command (except the MoveTo), creates a new segment. A path segment can be defined + * as a function of time over the interval [0, 1]. Each point in the polyline approximation can + * store the index of the path command that created the path segment that it came from and the time + * value at which it existed. The midpoint of a line segment would be at \f[ t = 0.5 \f] for + * example. This information is known as "back data" since it preserves the information about the + * original segments that existed in the path and can help us recreate them or their portions back. + * Note that the first point of a subpath stores the index of the moveTo command. + * + * To use this class create a new instance. Call the command functions such as Path::MoveTo, + * Path::LineTo, Path::CubicTo, etc to append path commands. Then call one of Path::Convert, + * Path::ConvertEvenLines or Path::ConvertWithBackData to generate the polyline approximation. + * Then you can do simplification by calling Path::Simplify or fill a Shape by calling Path::Fill + * on the shape to use features such as Offsetting, Boolean Operations and Tweaking. + * + * Path *path = new Path; + * path->MoveTo(Geom::Point(10, 10)); + * path->LineTo(Geom::Point(100, 10)); + * path->LineTo(Geom::Point(100, 100)); + * path->Close(); + * path->ConvertEvenLines(0.001); // You can use the other variants too + * // insteresting stuff here + * + */ +class Path +{ + friend class Shape; + +public: + + // flags for the path construction + enum + { + descr_ready = 0, + descr_adding_bezier = 1, // we're making a bezier spline, so you can expect pending_bezier_* to have a value + descr_doing_subpath = 2, // we're doing a path, so there is a moveto somewhere + descr_delayed_bezier = 4,// the bezier spline we're doing was initiated by a TempBezierTo(), so we'll need an endpoint + descr_dirty = 16 // the path description was modified + }; + + // some data for the construction: what's pending, and some flags + int descr_flags; + int pending_bezier_cmd; + int pending_bezier_data; + int pending_moveto_cmd; + int pending_moveto_data; + + std::vector<PathDescr*> descr_cmd; /*!< A vector of owned pointers to path commands. */ + + /** + * Points of the polyline approximation. + * + * Since the polyline approximation approximates a Path which can have multiple subpaths, the + * approximation can also have a set of continuous polylines. + */ + struct path_lineto + { + path_lineto(bool m, Geom::Point pp) : isMoveTo(m), p(pp), piece(-1), t(0), closed(false) {} + path_lineto(bool m, Geom::Point pp, int pie, double tt) : isMoveTo(m), p(pp), piece(pie), t(tt), closed(false) {} + + int isMoveTo; /*!< A flag that stores one of polyline_lineto, polyline_moveto, polyline_forced */ + Geom::Point p; /*!< The point itself. */ + int piece; /*!< Index of the path command that created the path segment that this point comes from.*/ + double t; /*!< The time at which this point exists in the path segment. A value between 0 and 1. */ + bool closed; /*!< True indicates that subpath is closed (this point is the last point of a closed subpath) */ + }; + + std::vector<path_lineto> pts; /*!< A vector storing the polyline approximation points. */ + + bool back; /*!< If true, indicates that the polyline approximation is going to have backdata. + No need to set this manually though. When Path::Convert or any of its variants is called, it's set automatically. */ + + Path(); + virtual ~Path(); + + // creation of the path description + + /** + * Clears all stored path commands and resets flags that are used by command functions while adding path + * commands. + */ + void Reset(); + + /** + * Clear all stored path commands, resets flags and imports path commands from the passed Path + * object. + * + * @param who Path object whose path commands to copy. + */ + void Copy (Path * who); + + /** + * Appends a forced point path command. + * + * Forced points are places in the path which are preferred to be kept in the simplification + * algorithm. The simplification algorithm will try to retain those points. This can be beneficial + * in situations such as self-intersections where we would want the intersection point to remain + * unchanged after any simplification is done. + * + * TODO: Confirm this with some testing. + * + * A forced point command can't be appended if there is no active subpath that we are drawing on. + * If you imagine calling these command functions as giving instructions to a pen, a forced point + * command requires that the pen is already touching the canvas. The pen is not on the canvas + * when you instantiate the Path object and it also leaves it when you call Path::Close. The term + * "active subpath" simply means that the pen is already touching the canvas. + * + * @return Index of the path command in the path commands array if it got appended, -1 otherwise. + */ + int ForcePoint(); + + /** + * Appends a close path command. + * + * Close path command can't be appended if there is no acive subpath. + * + * @return Index of the path command in the path commands array if it got appended, -1 otherwise. + */ + int Close(); + + /** Appends a MoveTo path command. + * + * @param ip The point to move to. + * + * @return The index of the path description added. + */ + int MoveTo ( Geom::Point const &ip); + + /** Appends a LineTo path command. + * + * @param ip The point to draw a line to. + * + * @return The index of the path description added. + */ + int LineTo ( Geom::Point const &ip); + + /** + * Appends a CubicBezier path command. + * + * In order to understand the parameters let p0, p1, p2, p3 denote the four points of a + * cubic Bezier curve. p0 is the start point. p3 is the end point. p1 and p2 are the + * two control points. + * + * @param ip The final point of the bezier curve or p3. + * @param iStD 3 * (p1 - p0). Weird way to store it but that's how it is. + * @param iEnD 3 * (p3 - p2). Weird way to store it but that's how it is. + * + * @return The index of the path description added. + */ + int CubicTo ( Geom::Point const &ip, Geom::Point const &iStD, Geom::Point const &iEnD); + + /** + * Appends an ArcTo path command. + * + * The parameters are identical to the SVG elliptical arc command. + * + * @param ip The final point of the arc. + * @param iRx The radius in the x direction. + * @param iRy The radius in the y direction. + * @param angle The angle w.r.t x axis in degrees. TODO: Confirm this + * @param iLargeArc If true, it's the larger arc, if false, it's the smaller one. + * @param iClockwise If true, it's the clockwise arc, if false, it's the anti-clockwise one. + * + * @return The index of the path description added. + */ + int ArcTo ( Geom::Point const &ip, double iRx, double iRy, double angle, bool iLargeArc, bool iClockwise); + + /** + * Adds a control point for the last quadratic bezier spline command. + * + * Adds a control point to the quadratic bezier spline that was last inserted with a call to + * Path::BezierTo. + * + * @param ip The control point. + * + * @return The index of the path description added. + */ + int IntermBezierTo ( Geom::Point const &ip); // add a quadratic bezier spline control point + + /** + * Appends a quadratic bezier spline path command. + * + * A quadratic bezier spline is basically a set of quadratic bezier curves. To simply illustrate + * how this spline is made up, let's define some terms first. Let midpoint(a, b) represent the + * midpoint of the points a and b. Let quad(a, b, c) represent a quadratic Bezier curve with a + * as the start point, b as the control point and c as the end point. + * + * Given a set of points: st, p1, p2, p3, p4, en where st and en are the endpoints and the rest + * are control points, we will have the following quadratic Bezier curves connected end to end. + * + * quad(st, p1, midpoint(p1, p2)) + * quad(midpoint(p1, p2), p2, midpoint(p2, p3)) + * quad(midpoint(p2, p3), p3, midpoint(p3, p4)) + * quad(midpoint(p3, p4), p4, en) + * + * No need to specify the number of control points. That'll be done automatically as you call + * Path::IntermBezierTo to add the control points. The sequence of instructions are like: + * 1. Call Path::BezierTo with the final point. + * 2. Call Path::IntermBezierTo with control points. One call for each control point. + * 3. Call Path::EndBezierTo to mark the end of the quadratic bezier spline command. + * + * Basically, the interface has been designed in such a way that you specify the final point and + * then add control points one by one as many as you like. Once you're done, you call + * Path::EndBezierTo to inform that you're done adding points for the spline. + * + * @param ip The final point of the quadratic bezier spline. + * + * @return The index of the path description added. + */ + int BezierTo ( Geom::Point const &ip); // quadratic bezier spline to this point (control points can be added after this) + + /** + * Finish any ongoing BezierTo instruction. + * + * Once Path::BezierTo has been called, the object expects you to specify control points by + * calling Path::IntermBezierTo for each control point. Once you're done specifying the control + * points you call Path::EndBezierTo to finish the quadratic bezier spline. + * + * @return -1 all the time. + */ + int EndBezierTo(); + + /** + * Appends a quadratic bezier spline path command (without specifying a final point). + * + * If you use Path::BezierTo, you have to specify the final point of the spline first and then + * follow it with all the control points. However, this is kinda counter-intuitive. Visually, we + * would look at the control points first and then the final end point. This function allows a + * similar mechanism. You can start a quadratic bezier spline without mentioning any final point, + * specify as many control points as you like and then while finishing it, you can specify the + * final point of the spline. + * + * The sequence of instructions would be: + * 1. Path::TempBezierTo to start. + * 2. Path::IntermBezierTo to specify control points. One call for each control point. + * 3. Path::EndBezierTo(Geom::Point const&) passing the final point of the quadratic bezier spline and finish the + * quadratic bezier spline command. + * + * @return Index of the description added. + */ + int TempBezierTo(); // start a quadratic bezier spline (control points can be added after this) + + /** + * Finish any ongoing TempBezierTo instruction. + * + * Used to specify the final point of a quadratic bezier spline which was started by calling + * Path::TempBezierTo. + * + * @param ip The final point. + * + * @return -1 all the time. + */ + int EndBezierTo ( Geom::Point const &ip); // ends a quadratic bezier spline (for curves started with TempBezierTo) + + // transforms a description in a polyline (for stroking and filling) + // treshhold is the max length^2 (sort of) + + /** + * Creates a polyline approximation of the path. Doesn't keep any back data. Line segments are + * not split into smaller line segments. + * + * Threshold has no strict definition. It means different things for each path segment. + * + * @param threshhold The error threshold used to approximate curves by line segments. The smaller + * this is, the more line segments there will be. + */ + void Convert (double treshhold); + + /** + * Creates a polyline approximation of the path. Line segments are split into further smaller line segments + * such that each of those line segments is no bigger than threshold. + * + * Breaking up into further smaller line segments is useful for path simplification as you can + * then fit cubic Bezier patches on those small line segments. + * + * Threshold has no strict definition. It means different things for each path segment. + * + * @param threshhold The error threshold used to approximate the path. The smaller this is, the + * more line segments there will be and the better the polyline approximation would be. + */ + void ConvertEvenLines (double treshhold); // decomposes line segments too, for later recomposition + + /** + * Creates a polyline approximation of the path. Line segments are + * not split into smaller line segments. Stores back data for later recomposition. + * + * Threshold has no strict definition. It means different things for each path segment. + * + * @param threshhold The error threshold used to approximate the path. The smaller this is, the + * more line segments there will be and the better the polyline approximation would be. + */ + void ConvertWithBackData (double treshhold); + + // creation of the polyline (you can tinker with these function if you want) + + /** + * Sets the back variable to the value passed in and clears the polyline approximation. + * + * @param nVal True if we are going to have backdata and false otherwise. + */ + void SetBackData (bool nVal); // has back data? + + /** + * Clears the polyline approximation. + */ + void ResetPoints(); // resets to the empty polyline + + /** + * Adds a point to the polyline approximation's list of points. + * + * This is used internally by Path::Convert and its variants, so you'd not need to use it by + * yourself. + * + * If back variable of the instance is set to true, dummy back data will be used with the point. + * Piece being -1 and time being 0. Since this function doesn't take any back data you'll have to + * fill in something. + * + * The point doesn't get added if it's a lineto and the point before it has the same coordinates. + * + * @param iPt The point itself. + * @param mvto If true, it's a moveTo otherwise it's a lineto. + * + * @return Index of the point added if it was added, -1 otherwise. + */ + int AddPoint ( Geom::Point const &iPt, bool mvto = false); // add point + + /** + * Adds a point to the polyline approximation's list of points. Let's you specify back data. + * + * This is used internally by Path::Convert and its variants, so you'd not need to use it by + * yourself. + * + * @param iPt The point itself. + * @param ip The index of the path command that created the segment that this point belongs to. + * @param it The time in that path segment at which this point exists. 0 is beginning and 1 + * is end. + * @param mvto If true, it's a moveTo otherwise it's a lineto. + * + * The point doesn't get added if it's a lineto and the point before it has the same coordinates. + * + * @return Index of the point added if it was added, -1 otherwise. + */ + int AddPoint ( Geom::Point const &iPt, int ip, double it, bool mvto = false); + + /** + * Adds a forced point to the polyline approximation's list of points without specifying any back data. + * + * The argument of this function is useless. The point that gets added as a forced point has the + * same coordinates as the last point that was added. If no points exist or the last one isn't a + * lineto, nothing gets added. + * + * Dummy back data will be used if the back variable of the instance is true. + * + * @param iPt Unused argument. + * + * @return Index of the point added if it was added, -1 otherwise. + */ + int AddForcedPoint ( Geom::Point const &iPt); // add point + + /** + * Add a forced point to the polyline approximation's list of points while specifying backdata. + * + * The argument of this function is useless. The point that gets added as a forced point has the + * same coordinates as the last point that was added. If no points exist or the last one isn't a + * lineto, nothing gets added. The back data is also picked up from the last point that was + * added. + * + * @param iPt Unused argument. + * @param ip Unused argument. + * @param it Unused argument. + * + * @return Index of the point added if it was added, -1 otherwise. + */ + int AddForcedPoint ( Geom::Point const &iPt, int ip, double it); + + /** + * Replace the last point in the polyline approximation's list of points with the passed one. + * + * Nothing gets added if no points exist already. + * + * @param iPt The point to replace the last one with. + * + * @return Index of the last point added if it was added, -1 otherwise. + */ + int ReplacePoint(Geom::Point const &iPt); // replace point + + // transform in a polygon (in a graph, in fact; a subsequent call to ConvertToShape is needed) + // - fills the polyline; justAdd=true doesn't reset the Shape dest, but simply adds the polyline into it + // closeIfNeeded=false prevent the function from closing the path (resulting in a non-eulerian graph + // pathID is a identification number for the path, and is used for recomposing curves from polylines + // give each different Path a different ID, and feed the appropriate orig[] to the ConvertToForme() function + + /** + * Fills the shape with the polyline approximation stored in this object. + * + * For each line segment in the polyline approximation, an edge is created in the shape. + * + * One important point to highlight is the closeIfNeeded argument. For each subpath (where a + * sub path is a moveTo followed by one or more lineTo points) you can either have the start and end + * points being identical or very close (a closed contour) or have them apart (an open contour). + * If you set closeIfNeeded to true, it'll automatically add a closing segment if needed and + * close an open contour by itself. If your contour is already closed, it makes sure that the + * first and last point are the same ones in the graph (instead of being two indentical points). + * If closeIfNeeded is false, it just doesn't care at all. Even if your contour is closed, the + * first and last point will be separate (even though they would be duplicates). + * + * @param dest The shape to fill. + * @param pathID A unique number for this path. The shape will associate this number with each + * edge that comes from this path. Later on, when you use Shape::ConvertToForme you'll pass an array + * of Path objects (named orig) and the shape will use that pathID to do orig[pathID] and get the + * original path information. + * @param justAdd If set to true, this will function will just fill stuff in without resetting + * any existing stuff in Shape. If set to false, it'll make sure to reset the shape and already + * make room for the maximum number of possible points and edges. + * @param closeIfNeeded If set to true, the graph will be closed always. Otherwise, it won't be + * closed. + * @param invert If set to true, the graph is drawn exactly in the manner opposite to the actual + * polyline approximation that this object stores, if false, it's stored indentical to how it's + * in the polyline approximation. + * + * @todo "the graph is drawn exactly in the manner opposite"? Does this mean the edges of the + * directed graph are reversed? + */ + void Fill(Shape *dest, int pathID = -1, bool justAdd = false, + bool closeIfNeeded = true, bool invert = false); + + // - stroke the path; usual parameters: type of cap=butt, type of join=join and miter (see LivarotDefs.h) + // doClose treat the path as closed (ie a loop) + void Stroke(Shape *dest, bool doClose, double width, JoinType join, + ButtType butt, double miter, bool justAdd = false); + + // build a Path that is the outline of the Path instance's description (the result is stored in dest) + // it doesn't compute the exact offset (it's way too complicated, but an approximation made of cubic bezier patches + // and segments. the algorithm was found in a plugin for Impress (by Chris Cox), but i can't find it back... + void Outline(Path *dest, double width, JoinType join, ButtType butt, + double miter); + + // half outline with edges having the same direction as the original + void OutsideOutline(Path *dest, double width, JoinType join, ButtType butt, + double miter); + + // half outline with edges having the opposite direction as the original + void InsideOutline (Path * dest, double width, JoinType join, ButtType butt, + double miter); + + // polyline to cubic bezier patches + + /** + * Simplify the path. + * + * Fit the least possible number of cubic Bezier patches on the polyline approximation while + * respecting the threshold (keeping the error small). The function clears existing path commands + * and the resulting cubic Bezier patches will be pushed as path commands in the instance. + * + * The algorithm to fit cubic Bezier curves on the polyline approximation's points. + * + * http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/INT-APP/CURVE-APP-global.html + * + * @param threshold The threshold for simplification. A measure of how much error is okay. The + * smaller this number is, the more conservative the fitting algorithm will be. + */ + void Simplify (double treshhold); + + /** + * Simplify the path with a different approach. + * + * This function is also supposed to do simplification but by merging (coalescing) existing + * path descriptions instead of doing any fitting. But I seriously doubt whether this is useful + * at all or works at all. More experimentation needed. TODO + * + * @param threshold The threshold for simplification. + */ + void Coalesce (double tresh); + + // utilities + // piece is a command no in the command list + // "at" is an abcissis on the path portion associated with this command + // 0=beginning of portion, 1=end of portion. + void PointAt (int piece, double at, Geom::Point & pos); + void PointAndTangentAt (int piece, double at, Geom::Point & pos, Geom::Point & tgt); + + // last control point before the command i (i included) + // used when dealing with quadratic bezier spline, cause these can contain arbitrarily many commands + const Geom::Point PrevPoint (const int i) const; + + // dash the polyline + // the result is stored in the polyline, so you lose the original. make a copy before if needed + void DashPolyline(float head,float tail,float body,int nbD, const float dashs[],bool stPlain,float stOffset); + + void DashPolylineFromStyle(SPStyle *style, float scale, float min_len); + + //utilitaire pour inkscape + + /** + * Load a lib2geom Geom::Path in this path object. + * + * The Geom::Path object is read and path commands making it up are appended in the Path object. + * + * @param path The Geom::Path object to load. + * @param tr A transformation matrix. + * @param doTransformation If set to true, the transformation matrix tr is applied on the path + * before it's loaded in this path object. + * @param append If set to true, any existing path commands in this object are retained. If + * set to false, any existing path commands will be cleared. + */ + void LoadPath(Geom::Path const &path, Geom::Affine const &tr, bool doTransformation, bool append = false); + + /** + * Load a lib2geom Geom::PathVector in this path object. (supports transformation) + * + * Any existing path commands in this object are not cleared. + * + * @param pv The Geom::PathVector object to load. + * @param tr A transformation to apply on each path. + * @param doTransformation If set to true, the transformation in tr is applied. + */ + void LoadPathVector(Geom::PathVector const &pv, Geom::Affine const &tr, bool doTransformation); + + /** + * Load a lib2geom Geom::PathVector in this path object. + * + * Any existing path commands in this object are not cleared. + * + * @param pv A reference to the Geom::PathVector object to load. + */ + void LoadPathVector(Geom::PathVector const &pv); + + /** + * Create a lib2geom Geom::PathVector from this Path object. + * + * Looks like the time this was written Geom::PathBuilder didn't exist or maybe + * the author wasn't aware of it. + * + * @return The Geom::PathVector created. + */ + Geom::PathVector MakePathVector(); + + /** + * Apply a transformation on all path commands. + * + * Done by calling the transform method on each path command. + * + * @param trans The transformation to apply. + */ + void Transform(const Geom::Affine &trans); + + // decompose le chemin en ses sous-chemin + // killNoSurf=true -> oublie les chemins de surface nulle + Path** SubPaths(int &outNb,bool killNoSurf); + // pour recuperer les trous + // nbNest= nombre de contours + // conts= debut de chaque contour + // nesting= parent de chaque contour + Path** SubPathsWithNesting(int &outNb,bool killNoSurf,int nbNest,int* nesting,int* conts); + // surface du chemin (considere comme ferme) + double Surface(); + void PolylineBoundingBox(double &l,double &t,double &r,double &b); + void FastBBox(double &l,double &t,double &r,double &b); + // longueur (totale des sous-chemins) + double Length(); + + void ConvertForcedToMoveTo(); + void ConvertForcedToVoid(); + struct cut_position { + int piece; + double t; + }; + cut_position* CurvilignToPosition(int nbCv,double* cvAbs,int &nbCut); + cut_position PointToCurvilignPosition(Geom::Point const &pos, unsigned seg = 0) const; + //Should this take a cut_position as a param? + double PositionToLength(int piece, double t); + + // caution: not tested on quadratic b-splines, most certainly buggy + void ConvertPositionsToMoveTo(int nbPos,cut_position* poss); + void ConvertPositionsToForced(int nbPos,cut_position* poss); + + void Affiche(); + char *svg_dump_path() const; + + bool IsLineSegment(int piece); + + private: + // utilitary functions for the path construction + void CancelBezier (); + void CloseSubpath(); + void InsertMoveTo (Geom::Point const &iPt,int at); + void InsertForcePoint (int at); + void InsertLineTo (Geom::Point const &iPt,int at); + void InsertArcTo (Geom::Point const &ip, double iRx, double iRy, double angle, bool iLargeArc, bool iClockwise,int at); + void InsertCubicTo (Geom::Point const &ip, Geom::Point const &iStD, Geom::Point const &iEnD,int at); + void InsertBezierTo (Geom::Point const &iPt,int iNb,int at); + void InsertIntermBezierTo (Geom::Point const &iPt,int at); + + // creation of dashes: take the polyline given by spP (length spL) and dash it according to head, body, etc. put the result in + // the polyline of this instance + void DashSubPath(int spL, int spP, std::vector<path_lineto> const &orig_pts, float head,float tail,float body,int nbD, const float dashs[],bool stPlain,float stOffset); + + // Functions used by the conversion. + // they append points to the polyline + /** + * The function is quite similar to RecCubicTo. Some of the maths, specially that in + * ArcAnglesAndCenter is too cryptic and I have not spent enough time deriving it yet either. The + * important thing is how the Arc is split into line segments and that I can explain. Given the + * threshold and the two radii, a maximum angle is calculated. This angle is a measure of how big + * a sub-arc you can substitute with a line segment without breaking the threshold. Then you + * divide the whole arc into sectors such that each one's angle is under or equal to maximum + * angle. + * + * @image html livarot-images/arc-threshold.svg + * + * In this image, the red dashed arc is the actual arc that was to be approximated. The blue arcs + * are sectors, each one having an angle equal to or smaller than maximum angle (which is 20 + * degrees) in this example. The final polyline approximation is shown by the pink dotted line + * segments. + * + * TODO: Understand the maths in ArcAnglesAndCenter and how the maximum angle is calculated. + * + */ + void DoArc ( Geom::Point const &iS, Geom::Point const &iE, double rx, double ry, + double angle, bool large, bool wise, double tresh); + /** + * Approximate the passed cubic bezier with line segments. + * + * Basically the function checks if the passed cubic Bezier is "small enough" and if + * it is, it does nothing, if it however isn't "small enough", it splits the cubic Bezier + * curve into two cubic Bezier curves (split at mid point), recursively calls itself on the + * left cubic, add the midpoint to the polyline approximation, call itself on the right + * cubic and done. lev is the maximum recursion depth possible, once it's reached, the function + * returns doing nothing immediately. See the code to understand more about maxL. + * + * The way the algorithm checks if the curve is "small enough" is maths so I'll try to + * explain it here so you can see the equations printed and probably refer it when reading code. + * + * Let \f$\vec{p_{0}}\f$, \f$\vec{p_{1}}\f$, \f$\vec{p_{2}}\f$ and \f$\vec{p_{3}}\f$ be the four + * points that define a cubic Bezier. The first is the start point, last is the end point, + * the two in between are the control points. Given this let me relate these points to the + * arguments that were passed in. + * + * \f[ \vec{iS} = \vec{p_{0}}\f] + * \f[ \vec{iE} = \vec{p_{3}}\f] + * \f[ \vec{iSd} = 3 (\vec{p_{1}} - \vec{p_{0}})\f] + * \f[ \vec{iEd} = 3 (\vec{p_{3}} - \vec{p_{2}})\f] + * + * This is just how livarot represents a Cubic Bezier, nothing I can do about that. The code + * starts by calculating a vector from start point to end point. + * + * \f[ \vec{se} = \vec{iE} - \vec{iS} ]\f + * + * If the length of \f$\vec{se}\f$ is smaller than 0.01, then the cubic bezier's endpoints are + * kinda close, but if the control points are too far away, it can still be a long tall curve, + * so let's see the control points and see how far away they are from the \f$\vec{se}\f$ vector. + * To do that, we measure the lengths of \f$\vec{iSd}\f$ and \f$\vec{iEd}\f$. If both are below + * threshold, we return immediately since it indicates the cubic bezier is "small enough". + * + * if the length is greater than 0.01, we still check the y projections of the control handles + * on the line between start and end points, if these projections are limited by the threshold + * and we didn't mess up the maxL restriction, we are good. + * + * If we ran out of recursion levels, we return anyways. In case this cubic bezier isn't small + * enough, we split it in two parts. There are math equations in the code that do this and I + * spent hours deriving it and they are totally correct. Basically take the usual maths to split + * a cubic Bezier into two parts and just account for the factor of 3 in the control handles + * that livarot adds and you'll end up with correct equations. + * + * TODO: Add derivation here maybe? + * + */ + void RecCubicTo ( Geom::Point const &iS, Geom::Point const &iSd, Geom::Point const &iE, Geom::Point const &iEd, double tresh, int lev, + double maxL = -1.0); + void RecBezierTo ( Geom::Point const &iPt, Geom::Point const &iS, Geom::Point const &iE, double treshhold, int lev, double maxL = -1.0); + + void DoArc ( Geom::Point const &iS, Geom::Point const &iE, double rx, double ry, + double angle, bool large, bool wise, double tresh, int piece); + void RecCubicTo ( Geom::Point const &iS, Geom::Point const &iSd, Geom::Point const &iE, Geom::Point const &iEd, double tresh, int lev, + double st, double et, int piece); + void RecBezierTo ( Geom::Point const &iPt, Geom::Point const &iS, const Geom::Point &iE, double treshhold, int lev, double st, double et, + int piece); + + // don't pay attention + struct offset_orig + { + Path *orig; + int piece; + double tSt, tEn; + double off_dec; + }; + void DoArc ( Geom::Point const &iS, Geom::Point const &iE, double rx, double ry, + double angle, bool large, bool wise, double tresh, int piece, + offset_orig & orig); + void RecCubicTo ( Geom::Point const &iS, Geom::Point const &iSd, Geom::Point const &iE, Geom::Point const &iEd, double tresh, int lev, + double st, double et, int piece, offset_orig & orig); + void RecBezierTo ( Geom::Point const &iPt, Geom::Point const &iS, Geom::Point const &iE, double treshhold, int lev, double st, double et, + int piece, offset_orig & orig); + + static void ArcAngles ( Geom::Point const &iS, Geom::Point const &iE, double rx, + double ry, double angle, bool large, bool wise, + double &sang, double &eang); + static void QuadraticPoint (double t, Geom::Point &oPt, Geom::Point const &iS, Geom::Point const &iM, Geom::Point const &iE); + static void CubicTangent (double t, Geom::Point &oPt, Geom::Point const &iS, + Geom::Point const &iSd, Geom::Point const &iE, + Geom::Point const &iEd); + + struct outline_callback_data + { + Path *orig; + int piece; + double tSt, tEn; + Path *dest; + double x1, y1, x2, y2; + union + { + struct + { + double dx1, dy1, dx2, dy2; + } + c; + struct + { + double mx, my; + } + b; + struct + { + double rx, ry, angle; + bool clock, large; + double stA, enA; + } + a; + } + d; + }; + + typedef void (outlineCallback) (outline_callback_data * data, double tol, double width); + struct outline_callbacks + { + outlineCallback *cubicto; + outlineCallback *bezierto; + outlineCallback *arcto; + }; + + void SubContractOutline (int off, int num_pd, + Path * dest, outline_callbacks & calls, + double tolerance, double width, JoinType join, + ButtType butt, double miter, bool closeIfNeeded, + bool skipMoveto, Geom::Point & lastP, Geom::Point & lastT); + void DoStroke(int off, int N, Shape *dest, bool doClose, double width, JoinType join, + ButtType butt, double miter, bool justAdd = false); + + static void TangentOnSegAt(double at, Geom::Point const &iS, PathDescrLineTo const &fin, + Geom::Point &pos, Geom::Point &tgt, double &len); + static void TangentOnArcAt(double at, Geom::Point const &iS, PathDescrArcTo const &fin, + Geom::Point &pos, Geom::Point &tgt, double &len, double &rad); + static void TangentOnCubAt (double at, Geom::Point const &iS, PathDescrCubicTo const &fin, bool before, + Geom::Point &pos, Geom::Point &tgt, double &len, double &rad); + static void TangentOnBezAt (double at, Geom::Point const &iS, + PathDescrIntermBezierTo & mid, + PathDescrBezierTo & fin, bool before, + Geom::Point & pos, Geom::Point & tgt, double &len, double &rad); + static void OutlineJoin (Path * dest, Geom::Point pos, Geom::Point stNor, Geom::Point enNor, + double width, JoinType join, double miter, int nType); + + static bool IsNulCurve (std::vector<PathDescr*> const &cmd, int curD, Geom::Point const &curX); + + static void RecStdCubicTo (outline_callback_data * data, double tol, + double width, int lev); + static void StdCubicTo (outline_callback_data * data, double tol, + double width); + static void StdBezierTo (outline_callback_data * data, double tol, + double width); + static void RecStdArcTo (outline_callback_data * data, double tol, + double width, int lev); + static void StdArcTo (outline_callback_data * data, double tol, double width); + + + // fonctions annexes pour le stroke + static void DoButt (Shape * dest, double width, ButtType butt, Geom::Point pos, + Geom::Point dir, int &leftNo, int &rightNo); + static void DoJoin (Shape * dest, double width, JoinType join, Geom::Point pos, + Geom::Point prev, Geom::Point next, double miter, double prevL, + double nextL, int *stNo, int *enNo); + static void DoLeftJoin (Shape * dest, double width, JoinType join, Geom::Point pos, + Geom::Point prev, Geom::Point next, double miter, double prevL, + double nextL, int &leftStNo, int &leftEnNo,int pathID=-1,int pieceID=0,double tID=0.0); + static void DoRightJoin (Shape * dest, double width, JoinType join, Geom::Point pos, + Geom::Point prev, Geom::Point next, double miter, double prevL, + double nextL, int &rightStNo, int &rightEnNo,int pathID=-1,int pieceID=0,double tID=0.0); + static void RecRound (Shape * dest, int sNo, int eNo, + Geom::Point const &iS, Geom::Point const &iE, + Geom::Point const &nS, Geom::Point const &nE, + Geom::Point &origine,float width); + + + /** + * Simpilfy a sequence of points. + * + * Fit cubic Bezier patches on the sequence of points defined by the passed parameters. This + * sequence is just a subset of the polyline approximation points stored in the Path object. + * + * @param off The offset to the first point to process. + * @param N The total number of points in the sequence. + * @param threshhold The threshold to respect during simplification. The higher this number is, + * the more relaxed you're making the simplifier. The smaller the number, the more strict you're + * making the simplifier. + */ + void DoSimplify(int off, int N, double treshhold); + + /** + * Fit a cubic Bezier patch on the sequence of points. + * + * @param off The index of the first point of the sequence to fit on. + * @param N The total number of points you want to fit on. + * @param res Reference to the Cubic Bezier description where the resulting control points will + * be stored. + * @param worstP Reference to a point index. This will be changed to whichever point measures the + * highest deviation from the fitted curve. + * + * @return True if the fit respected threshold, false otherwise. + */ + bool AttemptSimplify(int off, int N, double treshhold, PathDescrCubicTo &res, int &worstP); + /* + * The actual fitting code that takes a sequence and fits stuff on it. + * + * Totally based on the algorithm from: + * http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/INT-APP/CURVE-APP-global.html + * + * @param start The start point of the cubic bezier which is already known. + * @param res The cubic Bezier path command that function will populate after doing the maths. + * @param Xk The array of X coordinates of the point to fit. + * @param Yk The array of Y coordinates of the point to fit. + * @param Qk An array to store some intermediate values. + * @param tk The time values for the points. + * @param nbPt The total points to fit on. + * + * @return True if the fit was done correctly, false if something bad happened. (Non-invertible + * matrix). + */ + static bool FitCubic(Geom::Point const &start, + PathDescrCubicTo &res, + double *Xk, double *Yk, double *Qk, double *tk, int nbPt); + /** + * Structure to keep some data for fitting. + * + * Note that the pointers in the structure are going to store arrays. The comments explain what + * each element of a particular array stores. Also note that the length mentioned in the comment + * for tk and lk is not the straight line distance but the length as measured by walking on the + * line segments connecting the points. + */ + struct fitting_tables { + int nbPt; /*!< The points to fit on in a particular iteration */ + int maxPt; /*!< Maximum number of points these arrays here can store */ + int inPt; /*!< Total points whose X, Y, lk are all populated here */ + double *Xk; /*!< X coordinate of the point */ + double *Yk; /*!< Y coordinate of the point */ + double *Qk; /*!< A special value needed by the fitting algorithm */ + double *tk; /*!< A number between 0 and 1 that is the fraction (length b/w first point to this point along the line segments)/(total length) */ + double *lk; /*!< Length of the line segment from the previous point to this point */ + char *fk; /*!< A flag if 0x01 indicates forced point and if 0x00 indicates a normal point */ + double totLen; /*!< Total length of the polyline or you can say the sum of lengths of all line segments. */ + }; + + /** + * Fit Cubic Bezier patch using the fitting table data. + * + * @param data The fitting_tables data needed for fitting. ExtendFit sets that up for this + * function. + * @param threshhold The threshold to respect. + * @param res The cubic Bezier command which this function will populate. + * @param worstP The point with the worst error. + */ + bool AttemptSimplify (fitting_tables &data,double treshhold, PathDescrCubicTo & res,int &worstP); + + /** + * Fit Cubic Bezier patch on the points. + * + * This uses data already calculated by probably the same function if it exists. + * The data that's reused is apparently the X, Y and lk values. However, I think there is a + * problem with this caching mechanism. See the inline comments of ExtendFit. + * + * This function prepares data in fitting tables and calls the AttemptSimplify version that takes + * fitting_tables data. + * + * @param off The offset to the first point. + * @param N The total number of points in that sequence. + * @param data The data structure which keeps data saved for later use by the same function. + * @param threshhold The threshold to respect. + * @param res cubic Bezier path command where this function will store the control point handles. + * @param worstP Function will set this to the point with the worst error. + * + * @return True if the threshold was respected, otherwise false. + */ + bool ExtendFit(int off, int N, fitting_tables &data,double treshhold, PathDescrCubicTo & res,int &worstP); + /** + * Peform an iteration of Newton-Raphson to improve t values. + * + * TODO: Place derivation here with embedded latex maybe. + */ + double RaffineTk (Geom::Point pt, Geom::Point p0, Geom::Point p1, Geom::Point p2, Geom::Point p3, double it); + void FlushPendingAddition(Path* dest,PathDescr *lastAddition,PathDescrCubicTo &lastCubic,int lastAD); + +private: + /** + * Add a Geom::Curve's equivalent path description. + * + * Any straight curve (line or otherwise that's straight) is added as line. CubicBezier + * and EllipticalArcs are handled manually, while any other Geom::Curve type is handled by + * converting to cubic beziers using Geom::cubicbezierpath_from_sbasis and recursively calling + * the same function. + * + * There is one special reason for using is_straight_curve to figure out if a CubicBezier is + * actually a line and making sure that it is added as a line not as a straight line CubicBezier + * (a CubicBezier with control points being the same as end points). Sometimes when you're drawing + * straight line segments with the Bezier (pen) tool, Inkscape would place a straight CubicBezier + * instead of a line segment. The call to Path::Convert or Path::ConvertWithBackData would break + * up this line segment into smaller line segments which is not what we want (we want it to break + * only real curves) not curves that are actually just straight lines. + * + * @param c The Geom::Curve whose path description to create/add. + */ + void AddCurve(Geom::Curve const &c); + +}; +#endif + +/* + 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 : |