experimental/Intersection/DataTypes.h

/*
 * Copyright 2012 Google Inc.
 *
 * Use of this source code is governed by a BSD-style license that can be
 * found in the LICENSE file.
 */
#ifndef __DataTypes_h__
#define __DataTypes_h__

#include <float.h> // for FLT_EPSILON
#include <math.h> // for fabs, sqrt

#include "SkPoint.h"

#define ONE_OFF_DEBUG 0

// FIXME: move these into SkTypes.h
template <typename T> inline T SkTMax(T a, T b) {
    if (a < b)
        a = b;
    return a;
}

template <typename T> inline T SkTMin(T a, T b) {
    if (a > b)
        a = b;
    return a;
}

extern bool AlmostEqualUlps(float A, float B);
inline bool AlmostEqualUlps(double A, double B) { return AlmostEqualUlps((float) A, (float) B); }

// FIXME: delete
int UlpsDiff(float A, float B);

// FLT_EPSILON == 1.19209290E-07 == 1 / (2 ^ 23)
// DBL_EPSILON == 2.22045e-16
const double FLT_EPSILON_CUBED = FLT_EPSILON * FLT_EPSILON * FLT_EPSILON;
const double FLT_EPSILON_HALF = FLT_EPSILON / 2;
const double FLT_EPSILON_SQUARED = FLT_EPSILON * FLT_EPSILON;
const double FLT_EPSILON_SQRT = sqrt(FLT_EPSILON);
const double FLT_EPSILON_INVERSE = 1 / FLT_EPSILON;
const double DBL_EPSILON_ERR = DBL_EPSILON * 4; // tune -- allow a few bits of error

#ifdef SK_DEBUG
const double ROUGH_EPSILON = FLT_EPSILON * 16;
#endif

inline bool approximately_zero(double x) {
    return fabs(x) < FLT_EPSILON;
}

inline bool precisely_zero(double x) {
    return fabs(x) < DBL_EPSILON_ERR;
}

inline bool approximately_zero(float x) {
    return fabs(x) < FLT_EPSILON;
}

inline bool approximately_zero_cubed(double x) {
    return fabs(x) < FLT_EPSILON_CUBED;
}

inline bool approximately_zero_half(double x) {
    return fabs(x) < FLT_EPSILON_HALF;
}

inline bool approximately_zero_squared(double x) {
    return fabs(x) < FLT_EPSILON_SQUARED;
}

inline bool approximately_zero_sqrt(double x) {
    return fabs(x) < FLT_EPSILON_SQRT;
}

inline bool approximately_zero_inverse(double x) {
    return fabs(x) > FLT_EPSILON_INVERSE;
}

// FIXME: if called multiple times with the same denom, we want to pass 1/y instead
inline bool approximately_zero_when_compared_to(double x, double y) {
    return x == 0 || fabs(x / y) < FLT_EPSILON;
}

// Use this for comparing Ts in the range of 0 to 1. For general numbers (larger and smaller) use
// AlmostEqualUlps instead.
inline bool approximately_equal(double x, double y) {
#if 1
    return approximately_zero(x - y);
#else
// see http://visualstudiomagazine.com/blogs/tool-tracker/2011/11/compare-floating-point-numbers.aspx
// this allows very small (e.g. degenerate) values to compare unequally, but in this case,
// AlmostEqualUlps should be used instead.
    if (x == y) {
        return true;
    }
    double absY = fabs(y);
    if (x == 0) {
        return absY < FLT_EPSILON;
    }
    double absX = fabs(x);
    if (y == 0) {
        return absX < FLT_EPSILON;
    }
    return fabs(x - y) < (absX > absY ? absX : absY) * FLT_EPSILON;
#endif
}

inline bool precisely_equal(double x, double y) {
    return precisely_zero(x - y);
}

inline bool approximately_equal_half(double x, double y) {
    return approximately_zero_half(x - y);
}

inline bool approximately_equal_squared(double x, double y) {
    return approximately_equal(x, y);
}

inline bool approximately_greater(double x, double y) {
    return x - FLT_EPSILON >= y;
}

inline bool approximately_greater_or_equal(double x, double y) {
    return x + FLT_EPSILON > y;
}

inline bool approximately_lesser(double x, double y) {
    return x + FLT_EPSILON <= y;
}

inline bool approximately_lesser_or_equal(double x, double y) {
    return x - FLT_EPSILON < y;
}

inline double approximately_pin(double x) {
    return approximately_zero(x) ? 0 : x;
}

inline float approximately_pin(float x) {
    return approximately_zero(x) ? 0 : x;
}

inline bool approximately_greater_than_one(double x) {
    return x > 1 - FLT_EPSILON;
}

inline bool precisely_greater_than_one(double x) {
    return x > 1 - DBL_EPSILON_ERR;
}

inline bool approximately_less_than_zero(double x) {
    return x < FLT_EPSILON;
}

inline bool precisely_less_than_zero(double x) {
    return x < DBL_EPSILON_ERR;
}

inline bool approximately_negative(double x) {
    return x < FLT_EPSILON;
}

inline bool precisely_negative(double x) {
    return x < DBL_EPSILON_ERR;
}

inline bool approximately_one_or_less(double x) {
    return x < 1 + FLT_EPSILON;
}

inline bool approximately_positive(double x) {
    return x > -FLT_EPSILON;
}

inline bool approximately_positive_squared(double x) {
    return x > -(FLT_EPSILON_SQUARED);
}

inline bool approximately_zero_or_more(double x) {
    return x > -FLT_EPSILON;
}

inline bool approximately_between(double a, double b, double c) {
    return a <= c ? approximately_negative(a - b) && approximately_negative(b - c)
            : approximately_negative(b - a) && approximately_negative(c - b);
}

// returns true if (a <= b <= c) || (a >= b >= c)
inline bool between(double a, double b, double c) {
    SkASSERT(((a <= b && b <= c) || (a >= b && b >= c)) == ((a - b) * (c - b) <= 0));
    return (a - b) * (c - b) <= 0;
}

#ifdef SK_DEBUG
inline bool roughly_equal(double x, double y) {
    return fabs(x - y) < ROUGH_EPSILON;
}
#endif

struct _Point {
    double x;
    double y;

    friend _Point operator-(const _Point& a, const _Point& b) {
        _Point v = {a.x - b.x, a.y - b.y};
        return v;
    }

    void operator+=(const _Point& v) {
        x += v.x;
        y += v.y;
    }

    void operator-=(const _Point& v) {
        x -= v.x;
        y -= v.y;
    }

    void operator/=(const double s) {
        x /= s;
        y /= s;
    }

    void operator*=(const double s) {
        x *= s;
        y *= s;
    }

    friend bool operator==(const _Point& a, const _Point& b) {
        return a.x == b.x && a.y == b.y;
    }

    friend bool operator!=(const _Point& a, const _Point& b) {
        return a.x != b.x || a.y != b.y;
    }

    // note: this can not be implemented with
    // return approximately_equal(a.y, y) && approximately_equal(a.x, x);
    // because that will not take the magnitude of the values
    bool approximatelyEqual(const _Point& a) const {
        double denom = SkTMax(fabs(x), SkTMax(fabs(y), SkTMax(fabs(a.x), fabs(a.y))));
        if (denom == 0) {
            return true;
        }
        double inv = 1 / denom;
        return approximately_equal(x * inv, a.x * inv) && approximately_equal(y * inv, a.y * inv);
    }

    bool approximatelyEqual(const SkPoint& a) const {
        double denom = SkTMax(fabs(x), SkTMax(fabs(y), SkTMax(fabs(a.fX), fabs(a.fY))));
        if (denom == 0) {
            return true;
        }
        double inv = 1 / denom;
        return approximately_equal(x * inv, a.fX * inv) && approximately_equal(y * inv, a.fY * inv);
    }

    bool approximatelyEqualHalf(const _Point& a) const {
        double denom = SkTMax(fabs(x), SkTMax(fabs(y), SkTMax(fabs(a.x), fabs(a.y))));
        if (denom == 0) {
            return true;
        }
        double inv = 1 / denom;
        return approximately_equal_half(x * inv, a.x * inv)
                && approximately_equal_half(y * inv, a.y * inv);
    }

    bool approximatelyZero() const {
        return approximately_zero(x) && approximately_zero(y);
    }

    SkPoint asSkPoint() const {
        SkPoint pt = {SkDoubleToScalar(x), SkDoubleToScalar(y)};
        return pt;
    }

    double cross(const _Point& a) const {
        return x * a.y - y * a.x;
    }

    double distance(const _Point& a) const {
        _Point temp = *this - a;
        return temp.length();
    }

    double distanceSquared(const _Point& a) const {
        _Point temp = *this - a;
        return temp.lengthSquared();
    }

    double dot(const _Point& a) const {
        return x * a.x + y * a.y;
    }

    double length() const {
        return sqrt(lengthSquared());
    }

    double lengthSquared() const {
        return x * x + y * y;
    }

    double roughlyEqual(const _Point& a) const {
        return roughly_equal(a.y, y) && roughly_equal(a.x, x);
    }
};

typedef _Point _Line[2];
typedef _Point Quadratic[3];
typedef _Point Triangle[3];
typedef _Point Cubic[4];

struct _Rect {
    double left;
    double top;
    double right;
    double bottom;

    void add(const _Point& pt) {
        if (left > pt.x) {
            left = pt.x;
        }
        if (top > pt.y) {
            top = pt.y;
        }
        if (right < pt.x) {
            right = pt.x;
        }
        if (bottom < pt.y) {
            bottom = pt.y;
        }
    }

    // FIXME: used by debugging only ?
    bool contains(const _Point& pt) const {
        return approximately_between(left, pt.x, right)
                && approximately_between(top, pt.y, bottom);
    }

    bool intersects(_Rect& r) const {
        SkASSERT(left <= right);
        SkASSERT(top <= bottom);
        SkASSERT(r.left <= r.right);
        SkASSERT(r.top <= r.bottom);
        return r.left <= right && left <= r.right && r.top <= bottom && top <= r.bottom;
    }

    void set(const _Point& pt) {
        left = right = pt.x;
        top = bottom = pt.y;
    }

    void setBounds(const _Line& line) {
        set(line[0]);
        add(line[1]);
    }

    void setBounds(const Cubic& );
    void setBounds(const Quadratic& );
    void setRawBounds(const Cubic& );
    void setRawBounds(const Quadratic& );
};

struct CubicPair {
    const Cubic& first() const { return (const Cubic&) pts[0]; }
    const Cubic& second() const { return (const Cubic&) pts[3]; }
    _Point pts[7];
};

struct QuadraticPair {
    const Quadratic& first() const { return (const Quadratic&) pts[0]; }
    const Quadratic& second() const { return (const Quadratic&) pts[2]; }
    _Point pts[5];
};

// FIXME: move these into SkFloatingPoint.h
#include "SkFloatingPoint.h"

#define sk_double_isnan(a) sk_float_isnan(a)

// FIXME: move these to debugging file
#if SK_DEBUG
void mathematica_ize(char* str, size_t bufferSize);
bool valid_wind(int winding);
void winding_printf(int winding);
#endif

#endif // __DataTypes_h__