FitCubicToCircleSlide.cpp File Reference

#include "include/core/SkCanvas.h"
#include "include/core/SkFont.h"
#include "include/core/SkPaint.h"
#include "include/core/SkPath.h"
#include "include/private/base/SkTArray.h"
#include "tools/fonts/FontToolUtils.h"
#include "tools/viewer/ClickHandlerSlide.h"
#include <tuple>

Go to the source code of this file.

Classes
class	SampleFitCubicToCircle
class	SampleFitCubicToCircle::Click

Macros
#define	M_PI   3.14159265358979323846264338327950288
#define	M_SQRT2   1.41421356237309504880168872420969808

Functions
static float	fit_cubic_to_unit_circle (double x0, double y0, double x1, double y1, std::array< double, 4 > *X, std::array< double, 4 > *Y)
static double	lerp (double x, double y, double T)
static std::tuple< double, double, double >	eval_cubic (double x[], double T)
double	find_max_error_T (double cubicX[4], double cubicY[4])

Variables
static constexpr int	kCenterX = 300
static constexpr int	kCenterY = 325
static constexpr int	kRadius = 250

Macro Definition Documentation

M_PI

#define M_PI   3.14159265358979323846264338327950288

Definition at line 22 of file FitCubicToCircleSlide.cpp.

M_SQRT2

#define M_SQRT2   1.41421356237309504880168872420969808

Definition at line 26 of file FitCubicToCircleSlide.cpp.

Function Documentation

eval_cubic()

static std::tuple< double, double, double > eval_cubic ( double  x[], double  T  )

static

Definition at line 92 of file FitCubicToCircleSlide.cpp.

                                                                         {
    // Use De Casteljau's algorithm for better accuracy and stability.
    double ab = lerp(x[0], x[1], T);
    double bc = lerp(x[1], x[2], T);
    double cd = lerp(x[2], x[3], T);
    double abc = lerp(ab, bc, T);
    double bcd = lerp(bc, cd, T);
    double abcd = lerp(abc, bcd, T);
    return {abcd, 3 * (bcd - abc) /*1st derivative.*/, 6 * (cd - 2*bc + ab) /*2nd derivative.*/};
}

find_max_error_T()

double find_max_error_T	(	double	cubicX[4],
		double	cubicY[4]
	)

Definition at line 110 of file FitCubicToCircleSlide.cpp.

                                                            {
    constexpr static double kInitialT = .25;
    double T = kInitialT;
    for (int i = 0; i < 64; ++i) {
        auto [x, dx, ddx] = eval_cubic(cubicX, T);
        auto [y, dy, ddy] = eval_cubic(cubicY, T);
        double dError = 2*(x*dx + y*dy);
        double ddError = 2*(x*ddx + y*ddy + dx*dx + dy*dy);
        T -= dError / ddError;
    }
    return T;
}

fit_cubic_to_unit_circle()

static float fit_cubic_to_unit_circle ( double  x0, double  y0, double  x1, double  y1, std::array< double, 4 > *  X, std::array< double, 4 > *  Y  )

static

Definition at line 76 of file FitCubicToCircleSlide.cpp.

                                                                                      {
    constexpr static double kM = -4.0/3;
    constexpr static double kA = 4*M_SQRT2/3;
    double d = x0*x1 + y0*y1;
    double c = (std::sqrt(1 + d) * kM + kA) / std::sqrt(1 - d);
    *X = {x0, x0 - y0*c, x1 + y1*c, x1};
    *Y = {y0, y0 + x0*c, y1 - x1*c, y1};
    return c;
}

lerp()

static double lerp ( double  x, double  y, double  T  )

static

Definition at line 87 of file FitCubicToCircleSlide.cpp.

                                                 {
    return x + T*(y - x);
}

Variable Documentation

kCenterX

constexpr int kCenterX = 300

staticconstexpr

Definition at line 29 of file FitCubicToCircleSlide.cpp.

kCenterY

constexpr int kCenterY = 325

staticconstexpr

Definition at line 30 of file FitCubicToCircleSlide.cpp.

kRadius

constexpr int kRadius = 250

staticconstexpr

Definition at line 31 of file FitCubicToCircleSlide.cpp.