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/****************************************************************************
**
** Copyright (C) 2020 The Qt Company Ltd.
** Contact: https://www.qt.io/licensing/
**
** This file is part of the Qt Design Tooling
**
** Commercial License Usage
** Licensees holding valid commercial Qt licenses may use this file in
** accordance with the commercial license agreement provided with the
** Software or, alternatively, in accordance with the terms contained in
** a written agreement between you and The Qt Company. For licensing terms
** and conditions see https://www.qt.io/terms-conditions. For further
** information use the contact form at https://www.qt.io/contact-us.
**
** GNU General Public License Usage
** Alternatively, this file may be used under the terms of the GNU
** General Public License version 3 as published by the Free Software
** Foundation with exceptions as appearing in the file LICENSE.GPL3-EXCEPT
** included in the packaging of this file. Please review the following
** information to ensure the GNU General Public License requirements will
** be met: https://www.gnu.org/licenses/gpl-3.0.html.
**
****************************************************************************/
#include "axis.h"
#include <algorithm>
#include <assert.h>
#include <cmath>
#include <limits>
namespace DesignTools {
// The following is based on: "An Extension of Wilkinson's Algorithm for Positioning Tick Labels on Axes"
// by Justin Talbot, Sharon Lin and Pat Hanrahan.
// The Implementation uses the conventions and variable names found in the paper where:
// Inputs:
// Q Preference ordered list of nice steps
// dmin/dmax Data range
// pt Target label density
// fst Target font size (currently ignored)
// Formats set of label formats (currently ignored)
// Other:
// q Element of Q
// i Index of q in Q
// j Label skipping amount (taking only jth label into account)
// lmin/lmax Labeling sequence range
// v Indicator if labeling should include 0. (1 means yes / 0 no)
double simplicity(int i, std::vector<double> &Q, int j, int v = 1)
{
assert(Q.size() > 1);
return 1.0 - ((static_cast<double>(i) - 1.0) / (static_cast<double>(Q.size()) - 1.0))
- static_cast<double>(j) + static_cast<double>(v);
}
double coverage(double dmin, double dmax, double lmin, double lmax)
{
return 1.0 - 0.5 *
((std::pow(dmax - lmax, 2.0) + std::pow(dmin - lmin, 2.0)) /
(std::pow(0.1 * (dmax - dmin), 2.0)));
}
double coverageMax(double dmin, double dmax, double labelingRange)
{
double dataRange = dmax - dmin;
if (labelingRange > dataRange) {
double range = (labelingRange - dataRange) / 2.;
return 1 - 0.5 * ((std::pow(range, 2.0) * 2.0) / (std::pow(0.1 * (dmax - dmin), 2.0)));
}
return 1;
}
double density(double p, double pt)
{
return 2.0 - std::max(p / pt, pt / p);
}
double densityMax(double p, double pt)
{
if (p >= pt)
return 2 - p / pt;
else
return 1;
}
namespace Legibility {
class Format
{
public:
double legibility() const { return 1.0; }
};
class FontSize
{
public:
double legibility() const { return 1.0; }
};
class Orientation
{
public:
double legibility() const { return 1.0; }
};
class Overlap
{
public:
double legibility() const { return 1.0; }
};
} // End namespace Legibility.
using namespace Legibility;
double legibility(const Format &fmt, const FontSize &fs, const Orientation &ori, const Overlap &ovl)
{
return (fmt.legibility() + fs.legibility() + ori.legibility() + ovl.legibility()) / 4.0;
}
struct LabelingInfo
{
double l;
Format lformat;
};
LabelingInfo optLegibility(int k, double lmin, double lstep)
{
std::vector<double> stepSequence;
for (int i = 0; i < k; ++i)
stepSequence.push_back(lmin + i * lstep);
Format fmt;
FontSize fs;
Orientation ori;
Overlap ovl;
LabelingInfo info;
info.l = legibility(fmt, fs, ori, ovl);
info.lformat = fmt;
return info;
}
Axis Axis::compute(double dmin, double dmax, double height, double pt)
{
Axis result = {0.0, 0.0, 0.0};
auto score = [](double a, double b, double c, double d) {
return a * 0.2 + b * 0.25 + c * 0.5 + d * 0.05;
};
std::vector<double> Q = {1., 5., 2., 2.5, 3.};
//std::vector<double> Q = {1., 5., 2., 2.5, 3., 4., 1.5, 7., 6., 8., 9.};
double best_score = -2.0;
int j = 1;
while (j < std::numeric_limits<int>::max()) {
for (int i = 0; i < static_cast<int>(Q.size()); ++i) {
double q = Q[i];
auto simMax = simplicity(i, Q, j);
if (score(simMax, 1.0, 1.0, 1.0) < best_score) {
j = std::numeric_limits<int>::max() - 1;
break;
}
int k = 2; // label count
while (k < std::numeric_limits<int>::max()) {
auto p = k / height;
auto denMax = densityMax(p, pt);
if (score(simMax, 1.0, denMax, 1.0) < best_score)
break;
auto delta = (dmax - dmin) / (k + 1) / (j * q);
int z = std::ceil(std::log10(delta));
while (z < std::numeric_limits<int>::max()) {
auto lstep = q * static_cast<double>(j) * std::pow(10, z);
auto covMax = coverageMax(dmin, dmax, lstep * (k - 1));
if (score(simMax, covMax, denMax, 1.0) < best_score)
break;
int start = (std::floor(dmax / lstep) - (k - 1)) * j;
int end = std::ceil(dmin / lstep) * j;
for (; start <= end; ++start) {
double lmin = start * lstep / j;
double lmax = lmin + lstep * (k - 1);
double s = simplicity(i, Q, j);
double d = density(p, pt);
double c = coverage(dmin, dmax, lmin, lmax);
if (score(s, c, d, 1.0) < best_score)
continue;
auto info = optLegibility(k, lmin, lstep);
const double cscore = score(s, c, d, info.l);
if (cscore > best_score) {
best_score = cscore;
result = {lmin, lmax, lstep};
}
}
z++;
}
k++;
}
}
j++;
}
return result;
}
} // End namespace DesignTools.
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