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#include "DataTypes.h"
#include "Intersections.h"
#include "LineIntersection.h"
#include <algorithm> // used for std::swap
/*
Determine the intersection point of two line segments
Return FALSE if the lines don't intersect
from: http://paulbourke.net/geometry/lineline2d/
*/
int intersect(const _Line& a, const _Line& b, double aRange[2], double bRange[2]) {
double axLen = a[1].x - a[0].x;
double ayLen = a[1].y - a[0].y;
double bxLen = b[1].x - b[0].x;
double byLen = b[1].y - b[0].y;
/* Slopes match when denom goes to zero:
axLen / ayLen == bxLen / byLen
(ayLen * byLen) * axLen / ayLen == (ayLen * byLen) * bxLen / byLen
byLen * axLen == ayLen * bxLen
byLen * axLen - ayLen * bxLen == 0 ( == denom )
*/
double denom = byLen * axLen - ayLen * bxLen;
if (approximately_zero_squared(denom)) {
/* See if the axis intercepts match:
ay - ax * ayLen / axLen == by - bx * ayLen / axLen
axLen * (ay - ax * ayLen / axLen) == axLen * (by - bx * ayLen / axLen)
axLen * ay - ax * ayLen == axLen * by - bx * ayLen
*/
if (approximately_equal_squared(axLen * a[0].y - ayLen * a[0].x,
axLen * b[0].y - ayLen * b[0].x)) {
const double* aPtr;
const double* bPtr;
if (fabs(axLen) > fabs(ayLen) || fabs(bxLen) > fabs(byLen)) {
aPtr = &a[0].x;
bPtr = &b[0].x;
} else {
aPtr = &a[0].y;
bPtr = &b[0].y;
}
double aMin = aPtr[0];
double aMax = aPtr[2];
double bMin = bPtr[0];
double bMax = bPtr[2];
if (aMin > aMax) {
std::swap(aMin, aMax);
}
if (bMin > bMax) {
std::swap(bMin, bMax);
}
if (aMax < bMin || bMax < aMin) {
return 0;
}
if (aRange) {
aRange[0] = bMin <= aMin ? 0 : (bMin - aMin) / (aMax - aMin);
aRange[1] = bMax >= aMax ? 1 : (bMax - aMin) / (aMax - aMin);
}
if (bRange) {
bRange[0] = aMin <= bMin ? 0 : (aMin - bMin) / (bMax - bMin);
bRange[1] = aMax >= bMax ? 1 : (aMax - bMin) / (bMax - bMin);
}
return 1 + ((aRange[0] != aRange[1]) || (bRange[0] != bRange[1]));
}
}
double ab0y = a[0].y - b[0].y;
double ab0x = a[0].x - b[0].x;
double numerA = ab0y * bxLen - byLen * ab0x;
if (numerA < 0 && denom > numerA || numerA > 0 && denom < numerA) {
return 0;
}
double numerB = ab0y * axLen - ayLen * ab0x;
if (numerB < 0 && denom > numerB || numerB > 0 && denom < numerB) {
return 0;
}
/* Is the intersection along the the segments */
if (aRange) {
aRange[0] = numerA / denom;
}
if (bRange) {
bRange[0] = numerB / denom;
}
return 1;
}
int horizontalIntersect(const _Line& line, double y, double tRange[2]) {
double min = line[0].y;
double max = line[1].y;
if (min > max) {
std::swap(min, max);
}
if (min > y || max < y) {
return 0;
}
if (approximately_equal(min, max)) {
tRange[0] = 0;
tRange[1] = 1;
return 2;
}
tRange[0] = (y - line[0].y) / (line[1].y - line[0].y);
return 1;
}
// OPTIMIZATION Given: dy = line[1].y - line[0].y
// and: xIntercept / (y - line[0].y) == (line[1].x - line[0].x) / dy
// then: xIntercept * dy == (line[1].x - line[0].x) * (y - line[0].y)
// Assuming that dy is always > 0, the line segment intercepts if:
// left * dy <= xIntercept * dy <= right * dy
// thus: left * dy <= (line[1].x - line[0].x) * (y - line[0].y) <= right * dy
// (clever as this is, it does not give us the t value, so may be useful only
// as a quick reject -- and maybe not then; it takes 3 muls, 3 adds, 2 cmps)
int horizontalLineIntersect(const _Line& line, double left, double right,
double y, double tRange[2]) {
int result = horizontalIntersect(line, y, tRange);
if (result != 1) {
// FIXME: this is incorrect if result == 2
return result;
}
double xIntercept = line[0].x + tRange[0] * (line[1].x - line[0].x);
if (xIntercept > right || xIntercept < left) {
return 0;
}
return result;
}
int horizontalIntersect(const _Line& line, double left, double right,
double y, bool flipped, Intersections& intersections) {
int result = horizontalIntersect(line, y, intersections.fT[0]);
switch (result) {
case 0:
break;
case 1: {
double xIntercept = line[0].x + intersections.fT[0][0]
* (line[1].x - line[0].x);
if (xIntercept > right || xIntercept < left) {
return 0;
}
intersections.fT[1][0] = (xIntercept - left) / (right - left);
break;
}
case 2:
double lineL = line[0].x;
double lineR = line[1].x;
if (lineL > lineR) {
std::swap(lineL, lineR);
}
double overlapL = std::max(left, lineL);
double overlapR = std::min(right, lineR);
if (overlapL > overlapR) {
return 0;
}
if (overlapL == overlapR) {
result = 1;
}
intersections.fT[0][0] = (overlapL - line[0].x) / (line[1].x - line[0].x);
intersections.fT[1][0] = (overlapL - left) / (right - left);
if (result > 1) {
intersections.fT[0][1] = (overlapR - line[0].x) / (line[1].x - line[0].x);
intersections.fT[1][1] = (overlapR - left) / (right - left);
}
break;
}
if (flipped) {
// OPTIMIZATION: instead of swapping, pass original line, use [1].x - [0].x
for (int index = 0; index < result; ++index) {
intersections.fT[1][index] = 1 - intersections.fT[1][index];
}
}
return result;
}
int verticalIntersect(const _Line& line, double x, double tRange[2]) {
double min = line[0].x;
double max = line[1].x;
if (min > max) {
std::swap(min, max);
}
if (min > x || max < x) {
return 0;
}
if (approximately_equal(min, max)) {
tRange[0] = 0;
tRange[1] = 1;
return 2;
}
tRange[0] = (x - line[0].x) / (line[1].x - line[0].x);
return 1;
}
int verticalIntersect(const _Line& line, double top, double bottom,
double x, bool flipped, Intersections& intersections) {
int result = verticalIntersect(line, x, intersections.fT[0]);
switch (result) {
case 0:
break;
case 1: {
double yIntercept = line[0].y + intersections.fT[0][0]
* (line[1].y - line[0].y);
if (yIntercept > bottom || yIntercept < top) {
return 0;
}
intersections.fT[1][0] = (yIntercept - top) / (bottom - top);
break;
}
case 2:
double lineT = line[0].y;
double lineB = line[1].y;
if (lineT > lineB) {
std::swap(lineT, lineB);
}
double overlapT = std::max(top, lineT);
double overlapB = std::min(bottom, lineB);
if (overlapT > overlapB) {
return 0;
}
if (overlapT == overlapB) {
result = 1;
}
intersections.fT[0][0] = (overlapT - line[0].y) / (line[1].y - line[0].y);
intersections.fT[1][0] = (overlapT - top) / (bottom - top);
if (result > 1) {
intersections.fT[0][1] = (overlapB - line[0].y) / (line[1].y - line[0].y);
intersections.fT[1][1] = (overlapB - top) / (bottom - top);
}
break;
}
if (flipped) {
// OPTIMIZATION: instead of swapping, pass original line, use [1].y - [0].y
for (int index = 0; index < result; ++index) {
intersections.fT[1][index] = 1 - intersections.fT[1][index];
}
}
return result;
}
// from http://www.bryceboe.com/wordpress/wp-content/uploads/2006/10/intersect.py
// 4 subs, 2 muls, 1 cmp
static bool ccw(const _Point& A, const _Point& B, const _Point& C) {
return (C.y - A.y) * (B.x - A.x) > (B.y - A.y) * (C.x - A.x);
}
// 16 subs, 8 muls, 6 cmps
bool testIntersect(const _Line& a, const _Line& b) {
return ccw(a[0], b[0], b[1]) != ccw(a[1], b[0], b[1])
&& ccw(a[0], a[1], b[0]) != ccw(a[0], a[1], b[1]);
}
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