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#include "DataTypes.h"
#include <sys/types.h>
#include <stdlib.h>
#ifdef __cplusplus
extern "C" {
#endif
void *memcpy(void *, const void *, size_t);
#ifdef __cplusplus
}
#endif
const double PointEpsilon = 0.000001;
const double SquaredEpsilon = PointEpsilon * PointEpsilon;
bool rotate(const Cubic& cubic, int zero, int index, Cubic& rotPath) {
double dy = cubic[index].y - cubic[zero].y;
double dx = cubic[index].x - cubic[zero].x;
if (approximately_equal(dy, 0)) {
if (approximately_equal(dx, 0)) {
return false;
}
memcpy(rotPath, cubic, sizeof(Cubic));
return true;
}
for (int index = 0; index < 4; ++index) {
rotPath[index].x = cubic[index].x * dx + cubic[index].y * dy;
rotPath[index].y = cubic[index].y * dx - cubic[index].x * dy;
}
return true;
}
double t_at(const _Line& line, const _Point& pt) {
double dx = line[1].x - line[0].x;
double dy = line[1].y - line[0].y;
if (fabs(dx) > fabs(dy)) {
if (approximately_zero(dx)) {
return 0;
}
return (pt.x - line[0].x) / dx;
}
if (approximately_zero(dy)) {
return 0;
}
return (pt.y - line[0].y) / dy;
}
static void setMinMax(double x, double y1, double y2, int flags,
double& minX, double& maxX) {
if (minX > x && (flags & (kFindTopMin | kFindBottomMin))) {
minX = x;
}
if (maxX < x && (flags & (kFindTopMax | kFindBottomMax))) {
maxX = x;
}
}
void x_at(const _Point& p1, const _Point& p2, double top, double bottom,
int flags, double& minX, double& maxX) {
if (approximately_equal(p1.y, p2.y)) {
// It should be OK to bail early in this case. There's another edge
// which shares this end point which can intersect without failing to
// have a slope ... maybe
return;
}
// p2.x is always greater than p1.x -- the part of points (p1, p2) are
// moving from the start of the cubic towards its end.
// if p1.y < p2.y, minX can be affected
// if p1.y > p2.y, maxX can be affected
double slope = (p2.x - p1.x) / (p2.y - p1.y);
int topFlags = flags & (kFindTopMin | kFindTopMax);
if (topFlags && (top <= p1.y && top >= p2.y
|| top >= p1.y && top <= p2.y)) {
double x = p1.x + (top - p1.y) * slope;
setMinMax(x, p1.y, p2.y, topFlags, minX, maxX);
}
int bottomFlags = flags & (kFindBottomMin | kFindBottomMax);
if (bottomFlags && (bottom <= p1.y && bottom >= p2.y
|| bottom >= p1.y && bottom <= p2.y)) {
double x = p1.x + (bottom - p1.y) * slope;
setMinMax(x, p1.y, p2.y, bottomFlags, minX, maxX);
}
}
void xy_at_t(const Cubic& cubic, double t, double& x, double& y) {
double one_t = 1 - t;
double one_t2 = one_t * one_t;
double a = one_t2 * one_t;
double b = 3 * one_t2 * t;
double t2 = t * t;
double c = 3 * one_t * t2;
double d = t2 * t;
if (&x) {
x = a * cubic[0].x + b * cubic[1].x + c * cubic[2].x + d * cubic[3].x;
}
if (&y) {
y = a * cubic[0].y + b * cubic[1].y + c * cubic[2].y + d * cubic[3].y;
}
}
void xy_at_t(const _Line& line, double t, double& x, double& y) {
double one_t = 1 - t;
if (&x) {
x = one_t * line[0].x + t * line[1].x;
}
if (&y) {
y = one_t * line[0].y + t * line[1].y;
}
}
void xy_at_t(const Quadratic& quad, double t, double& x, double& y) {
double one_t = 1 - t;
double a = one_t * one_t;
double b = 2 * one_t * t;
double c = t * t;
if (&x) {
x = a * quad[0].x + b * quad[1].x + c * quad[2].x;
}
if (&y) {
y = a * quad[0].y + b * quad[1].y + c * quad[2].y;
}
}
// from http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
union Float_t
{
Float_t(float num = 0.0f) : f(num) {}
// Portable extraction of components.
bool Negative() const { return (i >> 31) != 0; }
int32_t RawMantissa() const { return i & ((1 << 23) - 1); }
int32_t RawExponent() const { return (i >> 23) & 0xFF; }
int32_t i;
float f;
#ifdef _DEBUG
struct
{ // Bitfields for exploration. Do not use in production code.
uint32_t mantissa : 23;
uint32_t exponent : 8;
uint32_t sign : 1;
} parts;
#endif
};
bool AlmostEqualUlps(float A, float B, int maxUlpsDiff)
{
Float_t uA(A);
Float_t uB(B);
// Different signs means they do not match.
if (uA.Negative() != uB.Negative())
{
// Check for equality to make sure +0==-0
return A == B;
}
// Find the difference in ULPs.
int ulpsDiff = abs(uA.i - uB.i);
return ulpsDiff <= maxUlpsDiff;
}
int UlpsDiff(float A, float B)
{
Float_t uA(A);
Float_t uB(B);
return abs(uA.i - uB.i);
}
int FloatAsInt(float A)
{
Float_t uA(A);
return uA.i;
}
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