// 将本矢量在两个不共线的非零矢量上进行矢量分解, vec = u*uAxis+v*vAxis
bool Vector2d::resolveVector(const Vector2d& uAxis, const Vector2d& vAxis,
Vector2d& uv) const
{
float denom = uAxis.crossProduct(vAxis);
if (mgIsZero(denom)) {
uv.x = 0.f; uv.y = 0.f;
return false;
}
float c = uAxis.crossProduct(*this);
uv.x = crossProduct(vAxis) / denom;
uv.y = c / denom;
return true;
}
// 将本矢量在两个不共线的非零矢量上进行矢量分解, vec = u*uAxis+v*vAxis
bool Vector2d::resolveVector(const Vector2d& uAxis, const Vector2d& vAxis,
float& u, float& v) const
{
float denom = uAxis.crossProduct(vAxis);
if (mgIsZero(denom))
{
u = 0.f; v = 0.f;
return false;
}
u = crossProduct(vAxis) / denom;
v = uAxis.crossProduct(*this) / denom;
return true;
}
// 求本矢量投影到矢量xAxis上的垂直距离
// 在xAxis的逆时针方向时返回正值，顺时针则返回负值
float Vector2d::distanceToVector(const Vector2d& xAxis) const
{
float len = xAxis.length();
if (len < _MGZERO)
return length();
return xAxis.crossProduct(*this) / len;
}
bool mgcurv::arcTan(
const Point2d& start, const Point2d& end, const Vector2d& startTan,
Point2d& center, float& radius,
float* startAngle, float* sweepAngle)
{
float a, b, c;
// 弦的中垂线方程系数
a = end.x - start.x;
b = end.y - start.y;
c = -0.5f * (a*(end.x + start.x) + b*(end.y + start.y));
// 求中垂线和切线的交点center
if (!mglnrel::crossLineAbc(a, b, c, startTan.x, startTan.y,
-startTan.x * start.x - startTan.y * start.y, center, Tol::gTol()))
return false;
radius = mgHypot(center.x - start.x, center.y - start.y);
if (startAngle && sweepAngle)
{
float sa = atan2f(start.y - center.y, start.x - center.x);
float ea = atan2f(end.y - center.y, end.x - center.x);
*startAngle = sa;
if (startTan.crossProduct(start - center) > 0.f)
*sweepAngle = -mgbase::to0_2PI(sa - ea);
else
*sweepAngle = mgbase::to0_2PI(ea - sa);
}
return true;
}
