quspline.cpp

/**********************************************************************
 * File:        quspline.cpp  (Formerly qspline.c)
 * Description: Code for the QSPLINE class.
 * Author:      Ray Smith
 *
 * (C) Copyright 1991, Hewlett-Packard Ltd.
 ** Licensed under the Apache License, Version 2.0 (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.apache.org/licenses/LICENSE-2.0
 ** Unless required by applicable law or agreed to in writing, software
 ** distributed under the License is distributed on an "AS IS" BASIS,
 ** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 ** See the License for the specific language governing permissions and
 ** limitations under the License.
 *
 **********************************************************************/

#include "quspline.h"
#include "allheaders.h"  // for pixRenderPolyline, pixGetDepth, pixGetHeight
#include "pix.h"         // for L_CLEAR_PIXELS, L_SET_PIXELS, Pix (ptr only)
#include "points.h"      // for ICOORD
#include "quadlsq.h"     // for QLSQ
#include "quadratc.h"    // for QUAD_COEFFS

// Include automatically generated configuration file if running autoconf.
#ifdef HAVE_CONFIG_H
#include "config_auto.h"
#endif

#define QSPLINE_PRECISION 16     //no of steps to draw

/**********************************************************************
 * QSPLINE::QSPLINE
 *
 * Constructor to build a QSPLINE given the components used in the old code.
 **********************************************************************/

QSPLINE::QSPLINE(                 //constructor
                 int32_t count,     //no of segments
                 int32_t *xstarts,  //start coords
                 double *coeffs   //coefficients
                ) {
  int32_t index;                   //segment index

                                 //get memory
  xcoords = new int32_t[count + 1];
  quadratics = new QUAD_COEFFS[count];
  segments = count;
  for (index = 0; index < segments; index++) {
                                 //copy them
    xcoords[index] = xstarts[index];
    quadratics[index] = QUAD_COEFFS (coeffs[index * 3],
      coeffs[index * 3 + 1],
      coeffs[index * 3 + 2]);
  }
                                 //right edge
  xcoords[index] = xstarts[index];
}


/**********************************************************************
 * QSPLINE::QSPLINE
 *
 * Constructor to build a QSPLINE by appproximation of points.
 **********************************************************************/

QSPLINE::QSPLINE (               //constructor
int xstarts[],                   //spline boundaries
int segcount,                    //no of segments
int xpts[],                      //points to fit
int ypts[], int pointcount,      //no of pts
int degree                       //fit required
) {
  int pointindex;                /*no along text line */
  int segment;                   /*segment no */
  int32_t *ptcounts;               //no in each segment
  QLSQ qlsq;                     /*accumulator */

  segments = segcount;
  xcoords = new int32_t[segcount + 1];
  ptcounts = new int32_t[segcount + 1];
  quadratics = new QUAD_COEFFS[segcount];
  memmove (xcoords, xstarts, (segcount + 1) * sizeof (int32_t));
  ptcounts[0] = 0;               /*none in any yet */
  for (segment = 0, pointindex = 0; pointindex < pointcount; pointindex++) {
    while (segment < segcount && xpts[pointindex] >= xstarts[segment]) {
      segment++;                 /*try next segment */
                                 /*cumulative counts */
      ptcounts[segment] = ptcounts[segment - 1];
    }
    ptcounts[segment]++;         /*no in previous partition */
  }
  while (segment < segcount) {
    segment++;
                                 /*zero the rest */
    ptcounts[segment] = ptcounts[segment - 1];
  }

  for (segment = 0; segment < segcount; segment++) {
    qlsq.clear ();
                                 /*first blob */
    pointindex = ptcounts[segment];
    if (pointindex > 0
      && xpts[pointindex] != xpts[pointindex - 1]
      && xpts[pointindex] != xstarts[segment])
      qlsq.add (xstarts[segment],
        ypts[pointindex - 1]
        + (ypts[pointindex] - ypts[pointindex - 1])
        * (xstarts[segment] - xpts[pointindex - 1])
        / (xpts[pointindex] - xpts[pointindex - 1]));
    for (; pointindex < ptcounts[segment + 1]; pointindex++) {
      qlsq.add (xpts[pointindex], ypts[pointindex]);
    }
    if (pointindex > 0 && pointindex < pointcount
      && xpts[pointindex] != xstarts[segment + 1])
      qlsq.add (xstarts[segment + 1],
        ypts[pointindex - 1]
        + (ypts[pointindex] - ypts[pointindex - 1])
        * (xstarts[segment + 1] - xpts[pointindex - 1])
        / (xpts[pointindex] - xpts[pointindex - 1]));
    qlsq.fit (degree);
    quadratics[segment].a = qlsq.get_a ();
    quadratics[segment].b = qlsq.get_b ();
    quadratics[segment].c = qlsq.get_c ();
  }
  delete[] ptcounts;
}


/**********************************************************************
 * QSPLINE::QSPLINE
 *
 * Constructor to build a QSPLINE from another.
 **********************************************************************/

QSPLINE::QSPLINE(  //constructor
                 const QSPLINE &src) {
  segments = 0;
  xcoords = nullptr;
  quadratics = nullptr;
  *this = src;
}


/**********************************************************************
 * QSPLINE::~QSPLINE
 *
 * Destroy a QSPLINE.
 **********************************************************************/

QSPLINE::~QSPLINE () {
  delete[] xcoords;
  delete[] quadratics;
}


/**********************************************************************
 * QSPLINE::operator=
 *
 * Copy a QSPLINE
 **********************************************************************/

QSPLINE & QSPLINE::operator= (   //assignment
const QSPLINE & source) {
  delete[] xcoords;
  delete[] quadratics;

  segments = source.segments;
  xcoords = new int32_t[segments + 1];
  quadratics = new QUAD_COEFFS[segments];
  memmove (xcoords, source.xcoords, (segments + 1) * sizeof (int32_t));
  memmove (quadratics, source.quadratics, segments * sizeof (QUAD_COEFFS));
  return *this;
}


/**********************************************************************
 * QSPLINE::step
 *
 * Return the total of the step functions between the given coords.
 **********************************************************************/

double QSPLINE::step(            //find step functions
                     double x1,  //between coords
                     double x2) {
  int index1, index2;            //indices of coords
  double total;                  /*total steps */

  index1 = spline_index (x1);
  index2 = spline_index (x2);
  total = 0;
  while (index1 < index2) {
    total +=
      (double) quadratics[index1 + 1].y ((float) xcoords[index1 + 1]);
    total -= (double) quadratics[index1].y ((float) xcoords[index1 + 1]);
    index1++;                    /*next segment */
  }
  return total;                  /*total steps */
}


/**********************************************************************
 * QSPLINE::y
 *
 * Return the y value at the given x value.
 **********************************************************************/

double QSPLINE::y(          //evaluate
                  double x  //coord to evaluate at
                 ) const {
  int32_t index;                   //segment index

  index = spline_index (x);
  return quadratics[index].y (x);//in correct segment
}


/**********************************************************************
 * QSPLINE::spline_index
 *
 * Return the index to the largest xcoord not greater than x.
 **********************************************************************/

int32_t QSPLINE::spline_index(          //evaluate
                            double x  //coord to evaluate at
                           ) const {
  int32_t index;                   //segment index
  int32_t bottom;                  //bottom of range
  int32_t top;                     //top of range

  bottom = 0;
  top = segments;
  while (top - bottom > 1) {
    index = (top + bottom) / 2;  //centre of range
    if (x >= xcoords[index])
      bottom = index;            //new min
    else
      top = index;               //new max
  }
  return bottom;
}


/**********************************************************************
 * QSPLINE::move
 *
 * Reposition spline by vector
 **********************************************************************/

void QSPLINE::move(            // reposition spline
                   ICOORD vec  // by vector
                  ) {
  int32_t segment;                 //index of segment
  int16_t x_shift = vec.x ();

  for (segment = 0; segment < segments; segment++) {
    xcoords[segment] += x_shift;
    quadratics[segment].move (vec);
  }
  xcoords[segment] += x_shift;
}


/**********************************************************************
 * QSPLINE::overlap
 *
 * Return true if spline2 overlaps this by no more than fraction less
 * than the bounds of this.
 **********************************************************************/

bool QSPLINE::overlap(                   //test overlap
        QSPLINE* spline2,  //2 cannot be smaller
        double fraction    //by more than this
) {
  int leftlimit = xcoords[1];             /*common left limit */
  int rightlimit = xcoords[segments - 1]; /*common right limit */
                                 /*or too non-overlap */
  return !(spline2->segments < 3 || spline2->xcoords[1] > leftlimit + fraction * (rightlimit - leftlimit) ||
           spline2->xcoords[spline2->segments - 1] < rightlimit - fraction * (rightlimit - leftlimit));
}


/**********************************************************************
 * extrapolate_spline
 *
 * Extrapolates the spline linearly using the same gradient as the
 * quadratic has at either end.
 **********************************************************************/

void QSPLINE::extrapolate(                  //linear extrapolation
                          double gradient,  //gradient to use
                          int xmin,         //new left edge
                          int xmax          //new right edge
                         ) {
  int segment;                   /*current segment of spline */
  int dest_segment;              //dest index
  int32_t* xstarts;              //new boundaries
  QUAD_COEFFS *quads;            //new ones
  int increment;                 //in size

  increment = xmin < xcoords[0] ? 1 : 0;
  if (xmax > xcoords[segments])
    increment++;
  if (increment == 0)
    return;
  xstarts = new int32_t[segments + 1 + increment];
  quads = new QUAD_COEFFS[segments + increment];
  if (xmin < xcoords[0]) {
    xstarts[0] = xmin;
    quads[0].a = 0;
    quads[0].b = gradient;
    quads[0].c = y (xcoords[0]) - quads[0].b * xcoords[0];
    dest_segment = 1;
  }
  else
    dest_segment = 0;
  for (segment = 0; segment < segments; segment++) {
    xstarts[dest_segment] = xcoords[segment];
    quads[dest_segment] = quadratics[segment];
    dest_segment++;
  }
  xstarts[dest_segment] = xcoords[segment];
  if (xmax > xcoords[segments]) {
    quads[dest_segment].a = 0;
    quads[dest_segment].b = gradient;
    quads[dest_segment].c = y (xcoords[segments])
      - quads[dest_segment].b * xcoords[segments];
    dest_segment++;
    xstarts[dest_segment] = xmax + 1;
  }
  segments = dest_segment;
  delete[] xcoords;
  delete[] quadratics;
  xcoords = xstarts;
  quadratics = quads;
}


/**********************************************************************
 * QSPLINE::plot
 *
 * Draw the QSPLINE in the given colour.
 **********************************************************************/

#ifndef GRAPHICS_DISABLED
void QSPLINE::plot(                //draw it
                   ScrollView* window,  //window to draw in
                   ScrollView::Color colour   //colour to draw in
                  ) const {
  int32_t segment;                 //index of segment
  int16_t step;                    //index of poly piece
  double increment;              //x increment
  double x;                      //x coord

  window->Pen(colour);
  for (segment = 0; segment < segments; segment++) {
    increment =
      (double) (xcoords[segment + 1] -
      xcoords[segment]) / QSPLINE_PRECISION;
    x = xcoords[segment];
    for (step = 0; step <= QSPLINE_PRECISION; step++) {
      if (segment == 0 && step == 0)
        window->SetCursor(x, quadratics[segment].y (x));
      else
        window->DrawTo(x, quadratics[segment].y (x));
      x += increment;
    }
  }
}
#endif

void QSPLINE::plot(Pix *pix) const {
  if (pix == nullptr) {
    return;
  }

  int32_t segment;  // Index of segment
  int16_t step;  // Index of poly piece
  double increment;  // x increment
  double x;  // x coord
  auto height = static_cast<double>(pixGetHeight(pix));
  Pta* points = ptaCreate(QSPLINE_PRECISION * segments);
  const int kLineWidth = 5;

  for (segment = 0; segment < segments; segment++) {
    increment = static_cast<double>((xcoords[segment + 1] -
        xcoords[segment])) / QSPLINE_PRECISION;
    x = xcoords[segment];
    for (step = 0; step <= QSPLINE_PRECISION; step++) {
      double y = height - quadratics[segment].y(x);
      ptaAddPt(points, x, y);
      x += increment;
    }
  }

  switch (pixGetDepth(pix)) {
    case 1:
      pixRenderPolyline(pix, points, kLineWidth, L_SET_PIXELS, 1);
      break;
    case 32:
      pixRenderPolylineArb(pix, points, kLineWidth, 255, 0, 0, 1);
      break;
    default:
      pixRenderPolyline(pix, points, kLineWidth, L_CLEAR_PIXELS, 1);
      break;
  }
  ptaDestroy(&points);
}