Please excuse my poorly drawn doodle here, I'm almost inept at drawing.
I'm attempting to compute i2, j2, x2, y2.
Knowns: x1, y1, xk, yk, i1, j1, the arc is circular
- resulting arc is circular
- cartesian co-ordinate system
- intermediate calculations can be in any co-ord system that makes sense
problem may be arbitrarily rotated, and so can't assume y2=j2 or i2=xk, etc.
x2 and y2 are not known, but the arc length from x1,y1 to x2,y2 is an arbitrary but fixed, known distance, say 100 units.
I suppose where I'm getting most confused is that there's an arc involved. If this were triangles even I could solve this problem. I just don't know my properties of arcs well enough to make valid assumptions.
Is it a valid approach to manipulate the arc length formula to supply x2,y2 and then use similar triangles to solve back for i2,j2?
Can we assume that the line formed by x2,y2-i2,j2 is always parallel to x1,y1 to i1,j1 regardless of rotation because of the constraints (ie since the initial and resulting arcs are circular, do these lines not form a right angle wtih the line (i1,j1), (xk,yk) ) ?
Cannot make this assumption, counterexample let the angle = 180 degrees.
This is not a homework problem, it's something I need to understand for a project I'm involved with.
Any help is greatly appreciated.