My ellipse for loop calculates the ellipse to small

[Pat512]

I am calculating the points around the parameter of an ellipse using the C++ for loop below. I am starting with the end points of the Major Axis, Minor Axis, the ellipse center point and the angle of the major axis. When the Major Axis is an angle, and I calculate the ellipse, the resulting ellipse does not reach the end points of the Major Axis. It is too small (see the second picture below). When I calculate the eclipse with the Major axis as a horizontal line meaning a zero angle the ellipse covers the complete Major Axis. Can you show me how to adjust my formula so the ellipse drawn at an angle will cover the Major Axis from end to end. Thank you.

double x1=0, y1=0, x2=0, y2=0, x3=0, y3=0, phi=0;
int ZeroX=0, ZeroY=0;
int NUM_POINTS_PER_CONTOUR = 360;
int p=0;
int Major_Axis_Center_X=0, Full_Major_Axis_X=0;
int Major_Axis_Center_Y=0, Full_Major_Axis_Y=0;
int Full_Minor_Axis_X=0;
double AngleOfMajorAxis=0;
UnicodeString temp;




struct ell {
double a; //e.a is semi-major size
double b; //e.b is semi-minor size
double theta;
double x0; //major axis center X
double y0; //major axis center Y
} e;






//seed Values
x1=50; x2=250;
y1=75; y2=275;


//Vertical Line LEFT edge
Canvas->MoveTo(x1, y1);
Canvas->LineTo(x1, y2);


//Vertical Line RIGHT edge
Canvas->MoveTo(x2, y1);
Canvas->LineTo(x2, y2);


Full_Major_Axis_X = (x2 - x1);
Full_Major_Axis_Y = (y2 - y1);
Major_Axis_Center_X = (x1 + (Full_Major_Axis_X/2));
Major_Axis_Center_Y = (y2 - (Full_Major_Axis_Y/2));
Full_Minor_Axis_X = (Full_Major_Axis_X/2);


//Seed values
e.a = (Full_Major_Axis_X/2); //e.a is semi-major size
e.b = (Full_Minor_Axis_X/2); //e.b is semi-minor size
e.x0 = Major_Axis_Center_X;
e.y0 = Major_Axis_Center_Y;


AngleOfMajorAxis = 140.0;
e.theta = DegToRad(AngleOfMajorAxis);


//Calculate 360 points around edge of ellipse
for (p=0; p<NUM_POINTS_PER_CONTOUR; p++) {
phi = p*2*M_PI/(double)NUM_POINTS_PER_CONTOUR;
x1 = e.a * std::sin(phi);
y1 = e.b * std::cos(phi);
x2 = x1 * std::cos(e.theta) + y1 * std::sin(e.theta);
y2 = y1 * std::cos(e.theta) - x1 * std::sin(e.theta);
x3 = x2 + e.x0;
y3 = y2 + e.y0;
if(p==0){
Canvas->MoveTo(x3, y3);
}
Canvas->LineTo(x3, y3);
}