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+/* This file is part of the KDE project
+ Copyright (C) 2001, 2002, 2003 The Karbon Developers
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Library General Public
+ License as published by the Free Software Foundation; either
+ version 2 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Library General Public License for more details.
+
+ You should have received a copy of the GNU Library General Public License
+ along with this library; see the file COPYING.LIB. If not, write to
+ the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+ * Boston, MA 02110-1301, USA.
+*/
+
+#include <karbon_part.h>
+#include <karbon_view.h>
+#include <core/vcolor.h>
+#include <core/vcomposite.h>
+#include <core/vfill.h>
+#include <core/vstroke.h>
+#include <core/vglobal.h>
+#include <render/vpainter.h>
+#include <render/vpainterfactory.h>
+#include <commands/vshapecmd.h>
+
+/*
+ An Algorithm for Automatically Fitting Digitized Curves
+ by Philip J. Schneider
+ from "Graphics Gems", Academic Press, 1990
+
+ http://www.acm.org/pubs/tog/GraphicsGems/gems/FitCurves.c
+ http://www.acm.org/pubs/tog/GraphicsGems/gems/README
+*/
+
+
+#include "vcurvefit.h"
+
+#define MAXPOINTS 1000 /* The most points you can have */
+
+
+class FitVector {
+ public:
+ FitVector(KoPoint &p){
+ m_X=p.x();
+ m_Y=p.y();
+ }
+
+ FitVector(){
+ m_X=0;
+ m_Y=0;
+ }
+
+ FitVector(KoPoint &a,KoPoint &b){
+ m_X=a.x()-b.x();
+ m_Y=a.y()-b.y();
+ }
+
+ void normalize(){
+ double len=length();
+ if(len==0.0f)
+ return;
+ m_X/=len; m_Y/=len;
+ }
+
+ void negate(){
+ m_X = -m_X;
+ m_Y = -m_Y;
+ }
+
+ void scale(double s){
+ double len = length();
+ if(len==0.0f)
+ return;
+ m_X *= s/len;
+ m_Y *= s/len;
+ }
+
+ double dot(FitVector &v){
+ return ((m_X*v.m_X)+(m_Y*v.m_Y));
+ }
+
+ double length(){
+ return (double) sqrt(m_X*m_X+m_Y*m_Y);
+ }
+
+ KoPoint operator+(KoPoint &p){
+ KoPoint b(p.x()+m_X,p.y()+m_Y);
+ return b;
+ }
+
+ public:
+ double m_X,m_Y;
+};
+
+double distance(KoPoint *p1,KoPoint *p2){
+ double dx = (p1->x()-p2->x());
+ double dy = (p1->y()-p2->y());
+ return sqrt( dx*dx + dy*dy );
+}
+
+
+FitVector ComputeLeftTangent(TQPtrList<KoPoint> &points,int end){
+ FitVector tHat1(*points.at(end+1),*points.at(end));
+
+ tHat1.normalize();
+
+ return tHat1;
+}
+
+FitVector ComputeRightTangent(TQPtrList<KoPoint> &points,int end){
+ FitVector tHat1(*points.at(end-1),*points.at(end));
+
+ tHat1.normalize();
+
+ return tHat1;
+}
+
+/*
+ * ChordLengthParameterize :
+ * Assign parameter values to digitized points
+ * using relative distances between points.
+ */
+static double *ChordLengthParameterize(TQPtrList<KoPoint> points,int first,int last)
+{
+ int i;
+ double *u; /* Parameterization */
+
+ u = new double[(last-first+1)];
+
+ u[0] = 0.0;
+ for (i = first+1; i <= last; i++) {
+ u[i-first] = u[i-first-1] +
+ distance(points.at(i), points.at(i-1));
+ }
+
+ for (i = first + 1; i <= last; i++) {
+ u[i-first] = u[i-first] / u[last-first];
+ }
+
+ return(u);
+}
+
+static FitVector VectorAdd(FitVector a,FitVector b)
+{
+ FitVector c;
+ c.m_X = a.m_X + b.m_X; c.m_Y = a.m_Y + b.m_Y;
+ return (c);
+}
+static FitVector VectorScale(FitVector v,double s)
+{
+ FitVector result;
+ result.m_X = v.m_X * s; result.m_Y = v.m_Y * s;
+ return (result);
+}
+
+static FitVector VectorSub(FitVector a,FitVector b)
+{
+ FitVector c;
+ c.m_X = a.m_X - b.m_X; c.m_Y = a.m_Y - b.m_Y;
+ return (c);
+}
+
+static FitVector ComputeCenterTangent(TQPtrList<KoPoint> points,int center)
+{
+ FitVector V1, V2, tHatCenter;
+
+ FitVector cpointb = *points.at(center-1);
+ FitVector cpoint = *points.at(center);
+ FitVector cpointa = *points.at(center+1);
+
+ V1 = VectorSub(cpointb,cpoint);
+ V2 = VectorSub(cpoint,cpointa);
+ tHatCenter.m_X= ((V1.m_X + V2.m_X)/2.0);
+ tHatCenter.m_Y= ((V1.m_Y + V2.m_Y)/2.0);
+ tHatCenter.normalize();
+ return tHatCenter;
+}
+
+/*
+ * B0, B1, B2, B3 :
+ * Bezier multipliers
+ */
+static double B0(double u)
+{
+ double tmp = 1.0 - u;
+ return (tmp * tmp * tmp);
+}
+
+
+static double B1(double u)
+{
+ double tmp = 1.0 - u;
+ return (3 * u * (tmp * tmp));
+}
+
+static double B2(double u)
+{
+ double tmp = 1.0 - u;
+ return (3 * u * u * tmp);
+}
+
+static double B3(double u)
+{
+ return (u * u * u);
+}
+
+/*
+ * GenerateBezier :
+ * Use least-squares method to find Bezier control points for region.
+ *
+ */
+KoPoint* GenerateBezier(TQPtrList<KoPoint> &points, int first, int last, double *uPrime,FitVector tHat1,FitVector tHat2)
+{
+ int i;
+ FitVector A[MAXPOINTS][2]; /* Precomputed rhs for eqn */
+ int nPts; /* Number of pts in sub-curve */
+ double C[2][2]; /* Matrix C */
+ double X[2]; /* Matrix X */
+ double det_C0_C1, /* Determinants of matrices */
+ det_C0_X,
+ det_X_C1;
+ double alpha_l, /* Alpha values, left and right */
+ alpha_r;
+ FitVector tmp; /* Utility variable */
+ KoPoint *curve;
+
+ curve = new KoPoint[4];
+ nPts = last - first + 1;
+
+
+ /* Compute the A's */
+ for (i = 0; i < nPts; i++) {
+ FitVector v1, v2;
+ v1 = tHat1;
+ v2 = tHat2;
+ v1.scale(B1(uPrime[i]));
+ v2.scale(B2(uPrime[i]));
+ A[i][0] = v1;
+ A[i][1] = v2;
+ }
+
+ /* Create the C and X matrices */
+ C[0][0] = 0.0;
+ C[0][1] = 0.0;
+ C[1][0] = 0.0;
+ C[1][1] = 0.0;
+ X[0] = 0.0;
+ X[1] = 0.0;
+
+ for (i = 0; i < nPts; i++) {
+ C[0][0] += (A[i][0]).dot(A[i][0]);
+ C[0][1] += A[i][0].dot(A[i][1]);
+ /* C[1][0] += V2Dot(&A[i][0], &A[i][1]);*/
+ C[1][0] = C[0][1];
+ C[1][1] += A[i][1].dot(A[i][1]);
+
+ FitVector vfirstp1(*points.at(first+i));
+ FitVector vfirst(*points.at(first));
+ FitVector vlast(*points.at(last));
+
+ tmp = VectorSub(vfirstp1,
+ VectorAdd(
+ VectorScale(vfirst, B0(uPrime[i])),
+ VectorAdd(
+ VectorScale(vfirst, B1(uPrime[i])),
+ VectorAdd(
+ VectorScale(vlast, B2(uPrime[i])),
+ VectorScale(vlast, B3(uPrime[i])) ))));
+
+
+ X[0] += A[i][0].dot(tmp);
+ X[1] += A[i][1].dot(tmp);
+ }
+
+ /* Compute the determinants of C and X */
+ det_C0_C1 = C[0][0] * C[1][1] - C[1][0] * C[0][1];
+ det_C0_X = C[0][0] * X[1] - C[0][1] * X[0];
+ det_X_C1 = X[0] * C[1][1] - X[1] * C[0][1];
+
+ /* Finally, derive alpha values */
+ if (det_C0_C1 == 0.0) {
+ det_C0_C1 = (C[0][0] * C[1][1]) * 10e-12;
+ }
+ alpha_l = det_X_C1 / det_C0_C1;
+ alpha_r = det_C0_X / det_C0_C1;
+
+
+ /* If alpha negative, use the Wu/Barsky heuristic (see text) */
+ /* (if alpha is 0, you get coincident control points that lead to
+ * divide by zero in any subsequent NewtonRaphsonRootFind() call. */
+ if (alpha_l < 1.0e-6 || alpha_r < 1.0e-6) {
+ double dist = distance(points.at(last),points.at(first)) /
+ 3.0;
+
+ curve[0] = *points.at(first);
+ curve[3] = *points.at(last);
+
+ tHat1.scale(dist);
+ tHat2.scale(dist);
+
+ curve[1] = tHat1 + curve[0];
+ curve[2] = tHat2 + curve[3];
+ return curve;
+ }
+
+ /* First and last control points of the Bezier curve are */
+ /* positioned exactly at the first and last data points */
+ /* Control points 1 and 2 are positioned an alpha distance out */
+ /* on the tangent vectors, left and right, respectively */
+ curve[0] = *points.at(first);
+ curve[3] = *points.at(last);
+
+ tHat1.scale(alpha_l);
+ tHat2.scale(alpha_r);
+
+ curve[1] = tHat1 + curve[0];
+ curve[2] = tHat2 + curve[3];
+
+ return (curve);
+}
+
+/*
+ * Bezier :
+ * Evaluate a Bezier curve at a particular parameter value
+ *
+ */
+static KoPoint BezierII(int degree,KoPoint *V, double t)
+{
+ int i, j;
+ KoPoint Q; /* Point on curve at parameter t */
+ KoPoint *Vtemp; /* Local copy of control points */
+
+ Vtemp = new KoPoint[degree+1];
+
+ for (i = 0; i <= degree; i++) {
+ Vtemp[i] = V[i];
+ }
+
+ /* Triangle computation */
+ for (i = 1; i <= degree; i++) {
+ for (j = 0; j <= degree-i; j++) {
+ Vtemp[j].setX((1.0 - t) * Vtemp[j].x() + t * Vtemp[j+1].x());
+ Vtemp[j].setY((1.0 - t) * Vtemp[j].y() + t * Vtemp[j+1].y());
+ }
+ }
+
+ Q = Vtemp[0];
+ delete[] Vtemp;
+ return Q;
+}
+
+/*
+ * ComputeMaxError :
+ * Find the maximum squared distance of digitized points
+ * to fitted curve.
+*/
+static double ComputeMaxError(TQPtrList<KoPoint> points,int first,int last,KoPoint *curve,double *u,int *splitPoint)
+{
+ int i;
+ double maxDist; /* Maximum error */
+ double dist; /* Current error */
+ KoPoint P; /* Point on curve */
+ FitVector v; /* Vector from point to curve */
+
+ *splitPoint = (last - first + 1)/2;
+ maxDist = 0.0;
+ for (i = first + 1; i < last; i++) {
+ P = BezierII(3, curve, u[i-first]);
+ v = VectorSub(P, *points.at(i));
+ dist = v.length();
+ if (dist >= maxDist) {
+ maxDist = dist;
+ *splitPoint = i;
+ }
+ }
+ return (maxDist);
+}
+
+
+/*
+ * NewtonRaphsonRootFind :
+ * Use Newton-Raphson iteration to find better root.
+ */
+static double NewtonRaphsonRootFind(KoPoint *Q,KoPoint P,double u)
+{
+ double numerator, denominator;
+ KoPoint Q1[3], Q2[2]; /* Q' and Q'' */
+ KoPoint TQ_u, Q1_u, Q2_u; /*u evaluated at Q, Q', & Q'' */
+ double uPrime; /* Improved u */
+ int i;
+
+ /* Compute Q(u) */
+ TQ_u = BezierII(3,Q, u);
+
+ /* Generate control vertices for Q' */
+ for (i = 0; i <= 2; i++) {
+ Q1[i].setX((Q[i+1].x() - Q[i].x()) * 3.0);
+ Q1[i].setY((Q[i+1].y() - Q[i].y()) * 3.0);
+ }
+
+ /* Generate control vertices for Q'' */
+ for (i = 0; i <= 1; i++) {
+ Q2[i].setX((Q1[i+1].x() - Q1[i].x()) * 2.0);
+ Q2[i].setY((Q1[i+1].y() - Q1[i].y()) * 2.0);
+ }
+
+ /* Compute Q'(u) and Q''(u) */
+ Q1_u = BezierII(2, Q1, u);
+ Q2_u = BezierII(1, Q2, u);
+
+ /* Compute f(u)/f'(u) */
+ numerator = (TQ_u.x() - P.x()) * (Q1_u.x()) + (TQ_u.y() - P.y()) * (Q1_u.y());
+ denominator = (Q1_u.x()) * (Q1_u.x()) + (Q1_u.y()) * (Q1_u.y()) +
+ (TQ_u.x() - P.x()) * (Q2_u.x()) + (TQ_u.y() - P.y()) * (Q2_u.y());
+
+ /* u = u - f(u)/f'(u) */
+ uPrime = u - (numerator/denominator);
+ return (uPrime);
+}
+
+/*
+ * Reparameterize:
+ * Given set of points and their parameterization, try to find
+ * a better parameterization.
+ *
+ */
+static double *Reparameterize(TQPtrList<KoPoint> points,int first,int last,double *u,KoPoint *curve)
+{
+ int nPts = last-first+1;
+ int i;
+ double *uPrime; /* New parameter values */
+
+ uPrime = new double[nPts];
+ for (i = first; i <= last; i++) {
+ uPrime[i-first] = NewtonRaphsonRootFind(curve, *points.at(i), u[i-
+ first]);
+ }
+ return (uPrime);
+}
+
+KoPoint *FitCubic(TQPtrList<KoPoint> &points,int first,int last,FitVector tHat1,FitVector tHat2,float error,int &width){
+ double *u;
+ double *uPrime;
+ double maxError;
+ int splitPoint;
+ int nPts;
+ double iterationError;
+ int maxIterations=4;
+ FitVector tHatCenter;
+ KoPoint *curve;
+ int i;
+
+ width=0;
+
+
+ iterationError=error*error;
+ nPts = last-first+1;
+
+ if(nPts == 2){
+ double dist = distance(points.at(last), points.at(first)) / 3.0;
+
+ curve = new KoPoint[4];
+
+ curve[0] = *points.at(first);
+ curve[3] = *points.at(last);
+
+ tHat1.scale(dist);
+ tHat2.scale(dist);
+
+ curve[1] = tHat1 + curve[0];
+ curve[2] = tHat2 + curve[3];
+
+ width=4;
+ return curve;
+ }
+
+ /* Parameterize points, and attempt to fit curve */
+ u = ChordLengthParameterize(points, first, last);
+ curve = GenerateBezier(points, first, last, u, tHat1, tHat2);
+
+
+ /* Find max deviation of points to fitted curve */
+ maxError = ComputeMaxError(points, first, last, curve, u, &splitPoint);
+ if (maxError < error) {
+ delete[] u;
+ width=4;
+ return curve;
+ }
+
+
+ /* If error not too large, try some reparameterization */
+ /* and iteration */
+ if (maxError < iterationError) {
+ for (i = 0; i < maxIterations; i++) {
+ uPrime = Reparameterize(points, first, last, u, curve);
+ curve = GenerateBezier(points, first, last, uPrime, tHat1, tHat2);
+ maxError = ComputeMaxError(points, first, last,
+ curve, uPrime, &splitPoint);
+ if (maxError < error) {
+ delete[] u;
+ width=4;
+ return curve;
+ }
+ delete[] u;
+ u = uPrime;
+ }
+ }
+
+ /* Fitting failed -- split at max error point and fit recursively */
+ delete[] u;
+ delete[] curve;
+ tHatCenter = ComputeCenterTangent(points, splitPoint);
+
+ int w1,w2;
+ KoPoint *cu1=NULL, *cu2=NULL;
+ cu1 = FitCubic(points, first, splitPoint, tHat1, tHatCenter, error,w1);
+
+ tHatCenter.negate();
+ cu2 = FitCubic(points, splitPoint, last, tHatCenter, tHat2, error,w2);
+
+ KoPoint *newcurve = new KoPoint[w1+w2];
+ for(int i=0;i<w1;i++){
+ newcurve[i]=cu1[i];
+ }
+ for(int i=0;i<w2;i++){
+ newcurve[i+w1]=cu2[i];
+ }
+
+ delete[] cu1;
+ delete[] cu2;
+ width=w1+w2;
+ return newcurve;
+}
+
+
+VPath *bezierFit(TQPtrList<KoPoint> &points,float error){
+ FitVector tHat1, tHat2;
+
+ tHat1 = ComputeLeftTangent(points,0);
+ tHat2 = ComputeRightTangent(points,points.count()-1);
+
+ int width=0;
+ KoPoint *curve;
+ curve = FitCubic(points,0,points.count()-1,tHat1,tHat2,error,width);
+
+ VPath *path = new VPath(NULL);
+
+ if(width>3){
+ path->moveTo(curve[0]);
+ path->curveTo(curve[1],curve[2],curve[3]);
+ for(int i=4;i<width;i+=4){
+ path->curveTo(curve[i+1],curve[i+2],curve[i+3]);
+ }
+ }
+
+
+ delete[] curve;
+ return path;
+}
+
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