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/* -*- Mode: c++ -*- */
/***************************************************************************
* powermap.cc
*
* Fri Apr 17 23:06:12 CEST 2020
* Copyright 2020 André Nusser
* andre.nusser@googlemail.com
****************************************************************************/
/*
* This file is part of DrumGizmo.
*
* DrumGizmo is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 3 of the License, or
* (at your option) any later version.
*
* DrumGizmo 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with DrumGizmo; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.
*/
#include "powermap.h"
#include <cassert>
#include <cmath>
namespace
{
using Power = Powermap::Power;
using PowerPair = Powermap::PowerPair;
Power h00(Power x) { return (1+2*x)*pow(1-x,2); }
Power h10(Power x) { return x*pow(1-x,2); }
Power h01(Power x) { return x*x*(3-2*x); }
Power h11(Power x) { return x*x*(x-1); }
Power computeValue(
Power const x, PowerPair const& P0, PowerPair const& P1, Power const m0, Power const m1)
{
auto const x0 = P0.in;
auto const x1 = P1.in;
auto const y0 = P0.out;
auto const y1 = P1.out;
auto const dx = x1 - x0;
auto const x_prime = (x - x1)/dx;
return h00(x_prime)*y0 + h10(x_prime)*dx*m0 + h01(x_prime)*y1 + h11(x_prime)*dx*m1;
}
} // end anonymous namespace
Powermap::Powermap()
{
reset();
}
Power Powermap::map(Power in)
{
if (spline_needs_update) {
updateSpline();
}
if (in < fixed[0].in) {
return shelf ? fixed[0].out : computeValue(in, {0.,0.}, fixed[0], m[0], m[1]);
}
else if (in < fixed[1].in) {
return computeValue(in, fixed[0], fixed[1], m[1], m[2]);
}
else if (in < fixed[2].in) {
return computeValue(in, fixed[1], fixed[2], m[2], m[3]);
}
else { // in >= fixed[2].in
return shelf ? fixed[2].out : computeValue(in, fixed[2], {1.,1.}, m[3], m[4]);
}
}
void Powermap::reset()
{
fixed[0] = {0., 0.};
fixed[1] = {.5, .5};
fixed[2] = {1., 1.};
shelf = false;
updateSpline();
}
void Powermap::setFixed0(PowerPair new_value)
{
if (fixed[0] != new_value) {
spline_needs_update = true;
this->fixed[0] = new_value;
}
}
void Powermap::setFixed1(PowerPair new_value)
{
if (fixed[1] != new_value) {
spline_needs_update = true;
this->fixed[1] = new_value;
}
}
void Powermap::setFixed2(PowerPair new_value)
{
if (fixed[2] != new_value) {
spline_needs_update = true;
this->fixed[2] = new_value;
}
}
void Powermap::setShelf(bool enable)
{
if (shelf != enable) {
spline_needs_update = true;
this->shelf = enable;
}
}
// This mostly followes the wikipedia article for monotone cubic splines:
// https://en.wikipedia.org/wiki/Monotone_cubic_interpolation
void Powermap::updateSpline()
{
assert(0. <= fixed[0].in && fixed[0].in < fixed[1].in &&
fixed[1].in < fixed[2].in && fixed[2].in <= 1.);
assert(0. <= fixed[0].out && fixed[0].out <= fixed[1].out &&
fixed[1].out <= fixed[2].out && fixed[2].out <= 1.);
Powers X = shelf ? Powers{fixed[0].in, fixed[1].in, fixed[2].in}
: Powers{0., fixed[0].in, fixed[1].in, fixed[2].in, 1.};
Powers P = shelf ? Powers{fixed[0].out, fixed[1].out, fixed[2].out}
: Powers{0., fixed[0].out, fixed[1].out, fixed[2].out, 1.};
Powers deltas(X.size()-1);
Powers m(X.size());
// 1
for (std::size_t i = 0; i < deltas.size(); ++i) {
deltas[i] = (P[i+1]-P[i])/(X[i+1]-X[i]);
}
// 2
m[0] = deltas[0];
for (std::size_t i = 1; i < deltas.size(); ++i) {
m[i] = (deltas[i-1] + deltas[i])/2.;
}
m.back() = deltas.back();
// 3
std::vector<bool> ignore(deltas.size(), false);
for (std::size_t i = 0; i < deltas.size(); ++i) {
if (deltas[i] == 0) {
m[i] = 0;
m[i+1] = 0;
ignore[i] = true;
}
}
for (std::size_t i = 0; i < deltas.size(); ++i) {
if (ignore[i]) {
continue;
}
// 4
auto alpha = m[i]/deltas[i];
auto beta = m[i+1]/deltas[i];
assert(alpha >= 0.);
assert(beta >= 0.);
// 5
// TODO: expose this parameter for testing both
bool const option1 = true;
if (option1) {
if (alpha > 3 || beta > 3) {
m[i] = 3*deltas[i];
}
}
else {
auto const a2b2 = alpha*alpha + beta*beta;
if (a2b2 > 9) {
auto const tau = 3./sqrt(a2b2);
m[i] = tau*alpha*deltas[i];
m[i+1] = tau*alpha*deltas[i];
}
}
}
if (shelf) {
assert(m.size() == 3);
this->m[1] = m[0];
this->m[2] = m[1];
this->m[3] = m[2];
}
else {
assert(m.size() == 5);
for (std::size_t i = 0; i < m.size(); ++i) {
this->m[i] = m[i];
}
}
spline_needs_update = false;
}
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