diff options
Diffstat (limited to 'src/2geom/point.cpp')
| -rw-r--r-- | src/2geom/point.cpp | 149 |
1 files changed, 89 insertions, 60 deletions
diff --git a/src/2geom/point.cpp b/src/2geom/point.cpp index 45e035d4a..9df88df92 100644 --- a/src/2geom/point.cpp +++ b/src/2geom/point.cpp @@ -1,25 +1,46 @@ -#include <2geom/point.h> #include <assert.h> -#include <2geom/coord.h> -#include <2geom/isnan.h> //temporary fix for isnan() +#include <math.h> +#include <2geom/point.h> #include <2geom/transforms.h> namespace Geom { -/** \brief Scales this vector to make it a unit vector (within rounding error). +/** + * @class Point + * @brief Two-dimensional point that doubles as a vector. + * + * Points in 2Geom are represented in Cartesian coordinates, e.g. as a pair of numbers + * that store the X and Y coordinates. Each point is also a vector in \f$\mathbb{R}^2\f$ + * from the origin (point at 0,0) to the stored coordinates, + * and has methods implementing several vector operations (like length()). * - * The current version tries to handle infinite coordinates gracefully, - * but it's not clear that any callers need that. + * \par Operator note + * \par + * Most operators are provided by Boost operator helpers, so they are not visible in this class. + * If @a p, @a q, @a r denote points, @a s a floating-point scalar, and @a m a transformation matrix, + * then the following operations are available: + * @code + p += q; p -= q; r = p + q; r = p - q; + p *= s; p /= s; q = p * s; q = s * p; q = p / s; + p *= m; p /= m; q = p * m; q = m * p; q = p / m; + @endcode + * It is possible to left-multiply a point by a matrix, even though mathematically speaking + * this is undefined. The result is a point identical to that obtained by right-multiplying. + * Division of points by matrices is defined as multiplication by their inverses. * - * \pre \f$this \neq (0, 0)\f$ - * \pre Neither component is NaN. - * \post \f$-\epsilon<\left|this\right|-1<\epsilon\f$ - */ + * @ingroup Primitives */ + +/** @brief Normalize the vector representing the point. + * After this method returns, the length of the vector will be 1 (unless both coordinates are + * zero - the zero point will be returned then). The function tries to handle infinite + * coordinates gracefully. If any of the coordinates are NaN, the function will do nothing. + * @post \f$-\epsilon < \left|this\right| - 1 < \epsilon\f$ + * @see unit_vector(Geom::Point const &) */ void Point::normalize() { double len = hypot(_pt[0], _pt[1]); if(len == 0) return; if(IS_NAN(len)) return; - static double const inf = 1e400; + static double const inf = HUGE_VAL; if(len != inf) { *this /= len; } else { @@ -58,7 +79,10 @@ void Point::normalize() { } } -/** Compute the L1 norm, or manhattan distance, of \a p. */ +/** @brief Compute the first norm (Manhattan distance) of @a p. + * This is equal to the sum of absolutes values of the coordinates. + * @return \f$|p_X| + |p_Y|\f$ + * @relates Point */ Coord L1(Point const &p) { Coord d = 0; for ( int i = 0 ; i < 2 ; i++ ) { @@ -67,7 +91,9 @@ Coord L1(Point const &p) { return d; } -/** Compute the L infinity, or maximum, norm of \a p. */ +/** @brief Compute the infinity norm (maximum norm) of @a p. + * @return \f$\max(p_X, p_Y)\f$ + * @relates Point */ Coord LInfty(Point const &p) { Coord const a(fabs(p[0])); Coord const b(fabs(p[1])); @@ -76,80 +102,83 @@ Coord LInfty(Point const &p) { : 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) -{ +/** @brief True if the point has both coordinates zero. + * NaNs are treated as not equal to zero. + * @relates Point */ +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. */ +/** @brief True if the point has a length near 1. The are_near() function is used. + * @relates Point */ +bool is_unit_vector(Point const &p) { + return are_near(L2(p), 1.0); } - -Coord atan2(Point const p) { +/** @brief Return the angle between the point and the +X axis. + * @return Angle in \f$(-\pi, \pi]\f$. + * @relates Point */ +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) { +/** @brief Compute the angle between a and b relative to the origin. + * The computation is done by projecting b onto the basis defined by a, rot90(a). + * @return Angle in \f$(-\pi, \pi]\f$. + * @relates Point */ +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. - */ +/** @brief Create a normalized version of a point. + * This is equivalent to copying the point and calling its normalize() method. + * The returned point will be (0,0) if the argument has both coordinates equal to zero. + * If any coordinate is NaN, this function will do nothing. + * @param a Input point + * @return Point on the unit circle in the same direction from origin as a, or the origin + * if a has both coordinates equal to zero + * @relates Point */ Point unit_vector(Point const &a) { Point ret(a); ret.normalize(); return ret; } - +/** @brief Return the "absolute value" of the point's vector. + * This is defined in terms of the default lexicographical ordering. If the point is "larger" + * that the origin (0, 0), its negation is returned. This corresponds to making the Y coordinate + * positive. You can check whether the points' vectors have the same direction (e.g. lie + * on the same line passing through the origin) using + * @code abs(a).normalize() == abs(b).normalize() @endcode. + * To check with some margin of error, use + * @code are_near(abs(a).normalize(), abs(b).normalize()) @endcode. + * Although naively this should take the absolute value of each coordinate, such an operation + * is not very useful. + * @return \f$p' = (p_X, -p_Y)\f$ + * @relates Point */ Point abs(Point const &b) { - Point ret; - for ( int i = 0 ; i < 2 ; i++ ) { - ret[i] = fabs(b[i]); - } + Point ret = b; + ret[Y] = fabs(ret[Y]); return ret; } -Point operator*(Point const &v, Matrix const &m) { - Point ret; +/** @brief Transform the point by the specified matrix. */ +Point &Point::operator*=(Affine const &m) { + double x = _pt[X], y = _pt[Y]; for(int i = 0; i < 2; i++) { - ret[i] = v[X] * m[i] + v[Y] * m[i + 2] + m[i + 4]; + _pt[i] = x * m[i] + 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; } +/** @brief Snap the angle B - A - dir to miltiples of \f$2\pi/n\f$. + * The 'dir' argument must be normalized (have an unit length), otherwise the result + * is undefined. + * @return Point with the same distance from A as B, with a snapped angle. + * @post distance(A, B) == distance(A, result) + * @post angle_between(result - A, dir) == \f$2k\pi/n, k \in \mathbb{N}\f$ + * @relates Point */ 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) |