I know $a$, $b$, $c$, $x_1$, $y_1$, $\alpha_1$. I want to move the point with distance ($d$) and then calculate $x_2$, $y_2$, $\alpha_2$.

enter image description here

  • $\begingroup$ I don't think you have enough information to do that. I think you need to know $c$ as well... $\endgroup$ – skyking Nov 1 '17 at 14:04
  • $\begingroup$ Is the $d$ measured along the arc, as you diagram implies? $\endgroup$ – amd Nov 1 '17 at 19:17
  • $\begingroup$ @amd Yes, "d" is measured along the arc $\endgroup$ – Vasil Nikolov Nov 2 '17 at 9:08

I don't think you have enough information for that, you would need $c$ too (or something to calculate $c$).

The point is that the angle that you rotates the triangle is the difference between $\alpha_2$ and $\alpha_1$. You find that by the fact that $\sin{\alpha_2-\alpha_1\over 2} = {d\over 2c}$. Then you use simple trigonometrics to find $x_2$ and $y_2$.

  • $\begingroup$ I know a,b,c. I've edited my question $\endgroup$ – Vasil Nikolov Nov 1 '17 at 14:10
  • $\begingroup$ Nope, it didn't help me. a2 = a1 + c*d ? This can't be an angle. And if i found a2, how to find x2=x1+? and y2=y1+? $\endgroup$ – Vasil Nikolov Nov 1 '17 at 14:35
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    $\begingroup$ @VasilNikolov You're missing the $\sin$. $\endgroup$ – skyking Nov 1 '17 at 14:49
  • $\begingroup$ It looks to me like $d$ is measured along the arc. $\endgroup$ – amd Nov 1 '17 at 19:19
  • $\begingroup$ @amd Unfortunately the picture didn't use a large enough $d$ to clearly show the difference. In that case the arc angle would be $d/c$. $\endgroup$ – skyking Nov 1 '17 at 19:47

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