105 lines
2.9 KiB
C++
105 lines
2.9 KiB
C++
|
/*
|
||
|
|
* This file is part of libfmr
|
||
|
|
*
|
||
|
|
* File: ISSegCurve.cpp
|
||
|
|
* Author: Florian Heinz <fh@sysv.de>
|
||
|
|
*
|
||
|
|
* Created on September 14, 2016, 4:17 PM
|
||
|
|
|
||
|
|
//paragraph [1] Title: [{\Large \bf \begin {center}] [\end {center}}]
|
||
|
|
//[TOC] [\tableofcontents]
|
||
|
|
|
||
|
|
[1] Class ISSegCurve
|
||
|
|
|
||
|
|
[TOC]
|
||
|
|
|
||
|
|
1 Overview
|
||
|
|
|
||
|
|
This class calculates the intersection points between a curve and a
|
||
|
|
line segment.
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
|
||
|
|
#include "fmr_ISSegCurve.h"
|
||
|
|
|
||
|
|
using namespace fmr;
|
||
|
|
|
||
|
|
/*
|
||
|
|
2 Constructor from a line segment and a curve
|
||
|
|
|
||
|
|
*/
|
||
|
|
ISSegCurve::ISSegCurve(SegT& _segt, Curve& _curve) : segt(_segt),
|
||
|
|
curve(_curve), RootDetect(_segt, _curve) {
|
||
|
|
Seg& seg = segt.seg;
|
||
|
|
|
||
|
|
if (seg.f.x == seg.i.x) { // Line is parallel to y-axis
|
||
|
|
m = nan("");
|
||
|
|
c = seg.i.x; // x = c
|
||
|
|
} else {
|
||
|
|
// Initialize values m and c, so that the segment is
|
||
|
|
// on the line y = m*x + c
|
||
|
|
m = (seg.f.y - seg.i.y) / (seg.f.x - seg.i.x);
|
||
|
|
c = seg.i.y - m * seg.i.x;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/*
|
||
|
|
3 ~f~
|
||
|
|
|
||
|
|
The roots of this function are the intersection times on the ~curve~
|
||
|
|
|
||
|
|
*/
|
||
|
|
double ISSegCurve::f(double t) {
|
||
|
|
if (std::isnan(m)) // Line is parallel to y-axis
|
||
|
|
return curve.fx(t) - c;
|
||
|
|
else
|
||
|
|
return curve.fy(t) - m * curve.fx(t) - c;
|
||
|
|
}
|
||
|
|
|
||
|
|
/*
|
||
|
|
4 ~findIntersectionTimes~
|
||
|
|
|
||
|
|
Determine the roots of ~f~ (3) via ~findRoots~ (defined in class ~RootDetect~)
|
||
|
|
and calculate all valid pairs of times.
|
||
|
|
|
||
|
|
*/
|
||
|
|
std::vector<std::pair<double, double> > ISSegCurve::findIntersectionTimes() {
|
||
|
|
std::vector<std::pair<double, double> > ret;
|
||
|
|
|
||
|
|
std::vector<double> roots = findRoots(0, 1);
|
||
|
|
|
||
|
|
for (int i = 0; i < roots.size(); i++) {
|
||
|
|
double root = roots[i];
|
||
|
|
Point p = curve.project(root);
|
||
|
|
// Calculate the time of the intersection
|
||
|
|
// with the parametric line segment function
|
||
|
|
// This is outside the range [0;1] if the intersection
|
||
|
|
// point is outside the line segment
|
||
|
|
double segtime = segt.getTime(p);
|
||
|
|
|
||
|
|
// Only accept the intersection, if both curves are defined
|
||
|
|
// at the corresponding intersection times.
|
||
|
|
// This is for example not the case, if segtime is outside
|
||
|
|
// [0;1]
|
||
|
|
if (curve.valid(root) && segt.valid(segtime)) {
|
||
|
|
ret.push_back(std::pair<double, double>(segtime, root));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// Extra test for the endpoints of the curve (at times 0 and 1)
|
||
|
|
for (double root = 0.0; root < 2; root += 1.0) {
|
||
|
|
if (!curve.valid(root))
|
||
|
|
continue; // Curve is not defined here
|
||
|
|
if (std::abs(f(root)) < PRECISION) { // We have found a root of f()
|
||
|
|
Point p = curve.project(root); // Calculate intersection point
|
||
|
|
double segtime = segt.getTime(p); // Calculate segment time of is
|
||
|
|
if (!segt.valid(segtime)) // Did we find a valid segment time?
|
||
|
|
continue;
|
||
|
|
ret.push_back(std::pair<double,double>(segtime, root));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return ret;
|
||
|
|
}
|