SkCubics.cpp File Reference

#include "src/base/SkCubics.h"
#include "include/private/base/SkAssert.h"
#include "include/private/base/SkFloatingPoint.h"
#include "include/private/base/SkTPin.h"
#include "src/base/SkQuads.h"
#include <algorithm>
#include <cmath>

Go to the source code of this file.

Functions
static bool	nearly_equal (double x, double y)
static bool	close_to_a_quadratic (double A, double B)
static bool	approximately_zero (double x)
static int	find_extrema_valid_t (double A, double B, double C, double t[2])
static double	binary_search (double A, double B, double C, double D, double start, double stop)

Variables
static constexpr double	PI = 3.141592653589793

Function Documentation

approximately_zero()

static bool approximately_zero ( double  x )

static

Definition at line 153 of file SkCubics.cpp.

                                         {
    // This cutoff for our binary search hopefully strikes a good balance between
    // performance and accuracy.
    return std::abs(x) < 0.00000001;
}

binary_search()

static double binary_search ( double  A, double  B, double  C, double  D, double  start, double  stop  )

static

Definition at line 176 of file SkCubics.cpp.

                                                                                               {
    SkASSERT(start <= stop);
    double left = SkCubics::EvalAt(A, B, C, D, start);
    if (approximately_zero(left)) {
        return start;
    }
    double right = SkCubics::EvalAt(A, B, C, D, stop);
    if (!SkIsFinite(left, right)) {
        return -1; // Not going to deal with one or more endpoints being non-finite.
    }
    if ((left > 0 && right > 0) || (left < 0 && right < 0)) {
        return -1; // We can only have a root if one is above 0 and the other is below 0.
    }
 
    constexpr int maxIterations = 1000; // prevent infinite loop
    for (int i = 0; i < maxIterations; i++) {
        double step = (start + stop) / 2;
        double curr = SkCubics::EvalAt(A, B, C, D, step);
        if (approximately_zero(curr)) {
            return step;
        }
        if ((curr < 0 && left < 0) || (curr > 0 && left > 0)) {
            // go right
            start = step;
        } else {
            // go left
            stop = step;
        }
    }
    return -1;
}

close_to_a_quadratic()

static bool close_to_a_quadratic ( double  A, double  B  )

static

Definition at line 31 of file SkCubics.cpp.

                                                     {
    if (sk_double_nearly_zero(B)) {
        return sk_double_nearly_zero(A);
    }
    return std::abs(A / B) < 1.0e-7;
}

find_extrema_valid_t()

static int find_extrema_valid_t ( double  A, double  B, double  C, double  t[2]  )

static

Definition at line 159 of file SkCubics.cpp.

                                             {
    // To find the local min and max of a cubic, we take the derivative and
    // solve when that is equal to 0.
    // d/dt (A*t^3 + B*t^2 + C*t + D) = 3A*t^2 + 2B*t + C
    double roots[2] = {0, 0};
    int numRoots = SkQuads::RootsReal(3*A, 2*B, C, roots);
    int validRoots = 0;
    for (int i = 0; i < numRoots; i++) {
        double tValue = roots[i];
        if (tValue >= 0 && tValue <= 1.0) {
            t[validRoots++] = tValue;
        }
    }
    return validRoots;
}

nearly_equal()

static bool nearly_equal ( double  x, double  y  )

static

Definition at line 20 of file SkCubics.cpp.

                                             {
    if (sk_double_nearly_zero(x)) {
        return sk_double_nearly_zero(y);
    }
    return sk_doubles_nearly_equal_ulps(x, y);
}

Variable Documentation

PI

constexpr double PI = 3.141592653589793

staticconstexpr

Definition at line 18 of file SkCubics.cpp.