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#include <2geom/point.h>
#include <assert.h>
#include <2geom/coord.h>
#include <2geom/isnan.h> //temporary fix for isnan()
#include <2geom/transforms.h>
namespace Geom {
/** \brief Scales this vector to make it a unit vector (within rounding error).
*
* The current version tries to handle infinite coordinates gracefully,
* but it's not clear that any callers need that.
*
* \pre \f$this \neq (0, 0)\f$
* \pre Neither component is NaN.
* \post \f$-\epsilon<\left|this\right|-1<\epsilon\f$
*/
void Point::normalize() {
double len = hypot(_pt[0], _pt[1]);
if(len == 0) return;
if(IS_NAN(len)) return;
static double const inf = 1e400;
if(len != inf) {
*this /= len;
} else {
unsigned n_inf_coords = 0;
/* Delay updating pt in case neither coord is infinite. */
Point tmp;
for ( unsigned i = 0 ; i < 2 ; ++i ) {
if ( _pt[i] == inf ) {
++n_inf_coords;
tmp[i] = 1.0;
} else if ( _pt[i] == -inf ) {
++n_inf_coords;
tmp[i] = -1.0;
} else {
tmp[i] = 0.0;
}
}
switch (n_inf_coords) {
case 0: {
/* Can happen if both coords are near +/-DBL_MAX. */
*this /= 4.0;
len = hypot(_pt[0], _pt[1]);
assert(len != inf);
*this /= len;
break;
}
case 1: {
*this = tmp;
break;
}
case 2: {
*this = tmp * sqrt(0.5);
break;
}
}
}
}
/** Compute the L1 norm, or manhattan distance, of \a p. */
Coord L1(Point const &p) {
Coord d = 0;
for ( int i = 0 ; i < 2 ; i++ ) {
d += fabs(p[i]);
}
return d;
}
/** Compute the L infinity, or maximum, norm of \a p. */
Coord LInfty(Point const &p) {
Coord const a(fabs(p[0]));
Coord const b(fabs(p[1]));
return ( a < b || IS_NAN(b)
? b
: a );
}
/** Returns true iff p is a zero vector, i.e.\ Point(0, 0).
*
* (NaN is considered non-zero.)
*/
bool
is_zero(Point const &p)
{
return ( p[0] == 0 &&
p[1] == 0 );
}
bool
is_unit_vector(Point const &p)
{
return fabs(1.0 - L2(p)) <= 1e-4;
/* The tolerance of 1e-4 is somewhat arbitrary. Point::normalize is believed to return
points well within this tolerance. I'm not aware of any callers that want a small
tolerance; most callers would be ok with a tolerance of 0.25. */
}
Coord atan2(Point const p) {
return std::atan2(p[Y], p[X]);
}
/** compute the angle turning from a to b. This should give \f$\pi/2\f$ for angle_between(a, rot90(a));
* This works by projecting b onto the basis defined by a, rot90(a)
*/
Coord angle_between(Point const a, Point const b) {
return std::atan2(cross(b,a), dot(b,a));
}
/** Returns a version of \a a scaled to be a unit vector (within rounding error).
*
* The current version tries to handle infinite coordinates gracefully,
* but it's not clear that any callers need that.
*
* \pre a != Point(0, 0).
* \pre Neither coordinate is NaN.
* \post L2(ret) very near 1.0.
*/
Point unit_vector(Point const &a)
{
Point ret(a);
ret.normalize();
return ret;
}
Point abs(Point const &b)
{
Point ret;
for ( int i = 0 ; i < 2 ; i++ ) {
ret[i] = fabs(b[i]);
}
return ret;
}
Point operator*(Point const &v, Matrix const &m) {
Point ret;
for(int i = 0; i < 2; i++) {
ret[i] = v[X] * m[i] + v[Y] * m[i + 2] + m[i + 4];
}
return ret;
}
Point operator/(Point const &p, Matrix const &m) { return p * m.inverse(); }
Point &Point::operator*=(Matrix const &m)
{
*this = *this * m;
return *this;
}
Point constrain_angle(Point const &A, Point const &B, unsigned int n, Point const &dir)
{
// for special cases we could perhaps use explicit testing (which might be faster)
if (n == 0.0) {
return B;
}
Point diff(B - A);
double angle = -angle_between(diff, dir);
double k = round(angle * (double)n / (2.0*M_PI));
return A + dir * Rotate(k * 2.0 * M_PI / (double)n) * L2(diff);
}
} //namespace Geom
/*
Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
indent-tabs-mode:nil
fill-column:99
End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :
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