114 lines
3.7 KiB
C++
114 lines
3.7 KiB
C++
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#include "tcubicbezier.h"
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//-----------------------------------------------------------------------------
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DVAPI double invCubicBezierX(double x, const TPointD &a, const TPointD &aSpeed,
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const TPointD &bSpeed, const TPointD &b) {
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double aSpeedX = aSpeed.x;
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double bSpeedX = bSpeed.x;
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if (aSpeedX == 0) aSpeedX = epsilon;
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if (bSpeedX == 0) bSpeedX = -epsilon;
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// a*u^3+b*u^2+c*u+d
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double x0 = a.x;
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double x1 = x0 + aSpeedX;
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double x3 = b.x;
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double x2 = x3 + bSpeedX;
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double aX = x3 + 3 * (x1 - x2) - x0;
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double bX = 3 * (x2 - 2 * x1 + x0);
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double cX = 3 * (x1 - x0);
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double dX = x0 - x;
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return cubicRoot(aX, bX, cX, dX);
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}
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//-----------------------------------------------------------------------------
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DVAPI double getCubicBezierY(double x, const TPointD &a, const TPointD &aSpeed,
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const TPointD &bSpeed, const TPointD &b) {
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double y0 = a.y;
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double y1 = y0 + aSpeed.y;
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double y3 = b.y;
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double y2 = y3 + bSpeed.y;
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double aY = y3 + 3 * (y1 - y2) - y0;
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double bY = 3 * (y2 - 2 * y1 + y0);
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double cY = 3 * (y1 - y0);
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double dY = y0;
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double u = invCubicBezierX(x, a, aSpeed, bSpeed, b);
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u = tcrop(u, 0.0, 1.0);
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return aY * u * u * u + bY * u * u + cY * u + dY;
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}
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//-----------------------------------------------------------------------------
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DVAPI std::pair<TPointD, TPointD> getMinMaxCubicBezierY(const TPointD &a,
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const TPointD &aSpeed,
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const TPointD &bSpeed,
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const TPointD &b) {
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double y0 = a.y;
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double y1 = y0 + aSpeed.y;
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double y3 = b.y;
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double y2 = y3 + bSpeed.y;
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double aY = y3 + 3 * (y1 - y2) - y0;
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double bY = 3 * (y2 - 2 * y1 + y0);
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double cY = 3 * (y1 - y0);
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double dY = y0;
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double x0 = a.x;
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double x1 = x0 + aSpeed.x;
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double x3 = b.x;
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double x2 = x3 + bSpeed.x;
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double aX = x3 + 3 * (x1 - x2) - x0;
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double bX = 3 * (x2 - 2 * x1 + x0);
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double cX = 3 * (x1 - x0);
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double dX = x0;
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double aaY = 3 * (y1 - y2) - y0 + y3;
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double bbY = 2 * (y0 + y2 - 2 * y1);
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double ccY = y1 - y0;
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if (aaY == 0) {
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if (a.y < b.y)
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return std::pair<TPointD, TPointD>(TPointD(a.x, a.y), TPointD(b.x, b.y));
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else
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return std::pair<TPointD, TPointD>(TPointD(b.x, b.y), TPointD(a.x, a.y));
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} else {
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double discr = bbY * bbY - 4 * aaY * ccY;
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if (discr < 0) {
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if (a.y < b.y)
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return std::pair<TPointD, TPointD>(TPointD(a.x, a.y),
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TPointD(b.x, b.y));
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else
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return std::pair<TPointD, TPointD>(TPointD(b.x, b.y),
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TPointD(a.x, a.y));
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} else {
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double sqrt_discr = sqrt(discr);
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double inv_2aY = 1.0 / (2.0 * aaY);
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double u0 = (-bbY + sqrt_discr) * inv_2aY;
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double u1 = (-bbY - sqrt_discr) * inv_2aY;
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if (u0 > 1.0) u0 = 1.0;
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if (u0 < 0.0) u0 = 0.0;
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if (u1 > 1.0) u1 = 1.0;
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if (u1 < 0.0) u1 = 0.0;
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double y_0 = aY * u0 * u0 * u0 + bY * u0 * u0 + cY * u0 + dY;
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double y_1 = aY * u1 * u1 * u1 + bY * u1 * u1 + cY * u1 + dY;
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double x_0 = aX * u0 * u0 * u0 + bX * u0 * u0 + cX * u0 + dX;
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double x_1 = aX * u1 * u1 * u1 + bX * u1 * u1 + cX * u1 + dX;
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if (y_0 < y_1)
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return std::pair<TPointD, TPointD>(TPointD(x_0, y_0),
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TPointD(x_1, y_1));
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else
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return std::pair<TPointD, TPointD>(TPointD(x_1, y_1),
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TPointD(x_0, y_0));
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}
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}
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}
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//-----------------------------------------------------------------------------
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