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Calculate the point of intersection between two lines if the vectors of both lines are known
I have two vectors (in canvas coordinates), whose coordinates are used to draw lines. I know that at some point, one of the lines (let’s call it line A) intersects the other line (line B). I would like to know the position of that point.
I know that the line is perpendicular, but I don’t know the equation of the line. I can only find the equation of the line after it has been drawn and I do not have the coordinates of the beginning of the line.
What I have found is that given two vectors a and b, where a is the first vector and b is the second vector. You can calculate the vector e by:
e = b – a
Then I can subtract b from a and get the perpendicular vector (just in 2D):
g = e.Normalized()
Then I can calculate the dot product:
h = a.dot(g)
And the line will be A = a + d * h, where d is the length of g.
After this step I have found the line, but I am now stuck to find the position of the point where A and B intersect. I will never know a and b in any other way than when the line is drawn.
If I am right on this, the solution is:
Let X and Y be coordinates for point A
Y = d * h
X = (a.x + d * h.x) / a.y
A:
It is clear that
$$
\mathbf v_B – \mathbf v_A =
0644bf28c6
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