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#include "CurveIntersection.h"
#include "Extrema.h"
#include "IntersectionUtilities.h"
#include "LineParameters.h"
static double interp_quad_coords(double a, double b, double c, double t)
{
double ab = interp(a, b, t);
double bc = interp(b, c, t);
return interp(ab, bc, t);
}
static int coincident_line(const Quadratic& quad, Quadratic& reduction) {
reduction[0] = reduction[1] = quad[0];
return 1;
}
static int vertical_line(const Quadratic& quad, Quadratic& reduction) {
double tValue;
reduction[0] = quad[0];
reduction[1] = quad[2];
int smaller = reduction[1].y > reduction[0].y;
int larger = smaller ^ 1;
if (findExtrema(quad[0].y, quad[1].y, quad[2].y, &tValue)) {
double yExtrema = interp_quad_coords(quad[0].y, quad[1].y, quad[2].y, tValue);
if (reduction[smaller].y > yExtrema) {
reduction[smaller].y = yExtrema;
} else if (reduction[larger].y < yExtrema) {
reduction[larger].y = yExtrema;
}
}
return 2;
}
static int horizontal_line(const Quadratic& quad, Quadratic& reduction) {
double tValue;
reduction[0] = quad[0];
reduction[1] = quad[2];
int smaller = reduction[1].x > reduction[0].x;
int larger = smaller ^ 1;
if (findExtrema(quad[0].x, quad[1].x, quad[2].x, &tValue)) {
double xExtrema = interp_quad_coords(quad[0].x, quad[1].x, quad[2].x, tValue);
if (reduction[smaller].x > xExtrema) {
reduction[smaller].x = xExtrema;
} else if (reduction[larger].x < xExtrema) {
reduction[larger].x = xExtrema;
}
}
return 2;
}
static int check_linear(const Quadratic& quad, Quadratic& reduction,
int minX, int maxX, int minY, int maxY) {
int startIndex = 0;
int endIndex = 2;
while (quad[startIndex].approximatelyEqual(quad[endIndex])) {
--endIndex;
if (endIndex == 0) {
printf("%s shouldn't get here if all four points are about equal", __FUNCTION__);
assert(0);
}
}
if (!isLinear(quad, startIndex, endIndex)) {
return 0;
}
// four are colinear: return line formed by outside
reduction[0] = quad[0];
reduction[1] = quad[2];
int sameSide;
bool useX = quad[maxX].x - quad[minX].x >= quad[maxY].y - quad[minY].y;
if (useX) {
sameSide = sign(quad[0].x - quad[1].x) + sign(quad[2].x - quad[1].x);
} else {
sameSide = sign(quad[0].y - quad[1].y) + sign(quad[2].y - quad[1].y);
}
if ((sameSide & 3) != 2) {
return 2;
}
double tValue;
int root;
if (useX) {
root = findExtrema(quad[0].x, quad[1].x, quad[2].x, &tValue);
} else {
root = findExtrema(quad[0].y, quad[1].y, quad[2].y, &tValue);
}
if (root) {
_Point extrema;
extrema.x = interp_quad_coords(quad[0].x, quad[1].x, quad[2].x, tValue);
extrema.y = interp_quad_coords(quad[0].x, quad[1].x, quad[2].x, tValue);
// sameSide > 0 means mid is smaller than either [0] or [2], so replace smaller
int replace;
if (useX) {
if (extrema.x < quad[0].x ^ extrema.x < quad[2].x) {
return 2;
}
replace = (extrema.x < quad[0].x | extrema.x < quad[2].x)
^ quad[0].x < quad[2].x;
} else {
if (extrema.y < quad[0].y ^ extrema.y < quad[2].y) {
return 2;
}
replace = (extrema.y < quad[0].y | extrema.y < quad[2].y)
^ quad[0].y < quad[2].y;
}
reduction[replace] = extrema;
}
return 2;
}
bool isLinear(const Quadratic& quad, int startIndex, int endIndex) {
LineParameters lineParameters;
lineParameters.quadEndPoints(quad, startIndex, endIndex);
double normalSquared = lineParameters.normalSquared();
double distance = lineParameters.controlPtDistance(quad); // not normalized
double limit = normalSquared * SquaredEpsilon;
double distSq = distance * distance;
return distSq <= limit;
}
// reduce to a quadratic or smaller
// look for identical points
// look for all four points in a line
// note that three points in a line doesn't simplify a cubic
// look for approximation with single quadratic
// save approximation with multiple quadratics for later
int reduceOrder(const Quadratic& quad, Quadratic& reduction) {
int index, minX, maxX, minY, maxY;
int minXSet, minYSet;
minX = maxX = minY = maxY = 0;
minXSet = minYSet = 0;
for (index = 1; index < 3; ++index) {
if (quad[minX].x > quad[index].x) {
minX = index;
}
if (quad[minY].y > quad[index].y) {
minY = index;
}
if (quad[maxX].x < quad[index].x) {
maxX = index;
}
if (quad[maxY].y < quad[index].y) {
maxY = index;
}
}
for (index = 0; index < 3; ++index) {
if (approximately_equal(quad[index].x, quad[minX].x)) {
minXSet |= 1 << index;
}
if (approximately_equal(quad[index].y, quad[minY].y)) {
minYSet |= 1 << index;
}
}
if (minXSet == 0x7) { // test for vertical line
if (minYSet == 0x7) { // return 1 if all four are coincident
return coincident_line(quad, reduction);
}
return vertical_line(quad, reduction);
}
if (minYSet == 0xF) { // test for horizontal line
return horizontal_line(quad, reduction);
}
int result = check_linear(quad, reduction, minX, maxX, minY, maxY);
if (result) {
return result;
}
memcpy(reduction, quad, sizeof(Quadratic));
return 3;
}
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