C++ Finding parallel lines Coordinates inside a boundary - c++

Question

I am given a Line PQ and a boundary. I have to find two parallel lines to the given line but lines should intersect the boundary. Also i know the distance between the parallel lines to the given line. I need to find the P'Q' and P"Q".
Please any one give a simple solution.
float vx = x2 - x1;
float vy = y2 - y1;
float mag = sqrt(vx * vx + vy * vy);
float t = (mag / 2.0) / mag;
float px = (1 - t) * x1 + t * x2;
float py = (1 - t) * y1 + t * y2;
I just found the centre point of PQ by the above code. Further i planned to draw a perpendicular line thru (px, py) with the known distance, then drawing lines perpendicular to that new line(those lines will be parallel to PQ), thru the end points of that new line. But i could not achieve it. can anyone help me or suggest me a way who know maths

Answer 1

Finally i got the solution.
The steps are.
First i am getting the center point of PQ.
POINT find_a_point_in_distance(float x1, float y1, float x2, float y2, float len = 0) {
float vx = x2 - x1;
float vy = y2 - y1;
float mag = sqrt(vx * vx + vy * vy);
float t = len == 0 ? ((mag / 2.0) / mag) : (len / mag);
float px = (1 - t) * x1 + t * x2;
float py = (1 - t) * y1 + t * y2;
POINT res = { px, py };
return res;
}
here (px, py) is center point of PQ.
Then i am finding the perpendicular line through (px, py).
Already i have mentioned in the question that i know distance between PQ and P'Q' also PQ and P"Q". So i am getting two points in that perpendicular line using that distance. Finally i know the angle of the line PQ, so P'Q' and P"Q" should be in that same angle, using these details i can get the lines P'Q' and P"Q" what ever length i want. Here in below code i am getting the line P'Q' and P"Q" with the length of the diagonal of the rectangular box.
POINT res = find_a_point_in_distance(x1, y1, x2, y2);
POINT res2 = find_a_point_in_distance(res.x, res.y, x2, y2, halflen);
float cosA = acos((res2.x - res.x) / halflen) * 180 / PI;
float sinA = asin((res2.y - res.y) / halflen) * 180 / PI;
float cosAngle = cos((cosA + 90.0) * PI / 180.0);
float sinAngle = sin((sinA + 90.0) * PI / 180.0);
float cx1 = res.x + halflen * cosAngle;
float cy1 = res.y + halflen * sinAngle;
float cosAngle2 = cos((cosA - 90.0) * PI / 180.0);
float sinAngle2 = sin((sinA - 90.0) * PI / 180.0);
float cx2 = res.x + halflen * cosAngle2;
float cy2 = res.y + halflen * sinAngle2;
float diagonal = sqrt(width * width + height * height);
float halfdiagonal = diagonal / 2.0;
float cosAngleT = cos(cosA * PI / 180.0);
float sinAngleT = sin(sinA * PI / 180.0);
float cosAngleTD = cos((cosA + 180) * PI / 180.0);
float sinAngleTD = sin((sinA + 180) * PI / 180.0);
float cx10 = cx1 + halfdiagonal * cosAngleT;
float cy10 = cy1 + halfdiagonal * sinAngleT;
float cx11 = cx1 + halfdiagonal * cosAngleTD;
float cy11 = cy1 + halfdiagonal * sinAngleTD;
float cx20 = cx2 + halfdiagonal * cosAngleT;
float cy20 = cy2 + halfdiagonal * sinAngleT;
float cx21 = cx2 + halfdiagonal * cosAngleTD;
float cy21 = cy2 + halfdiagonal * sinAngleTD;
here (cx10, cy10) and (cx11, cy11) is line P'Q' and
(cx20, cy20) and (cx21, cy21) is line P"Q".
then finally im finding the intersect point of P'Q' and P"Q" with all sides of rectangle