0
$\begingroup$

And a happy new year to you all!

How would you calculate the coordinates of a point on the edge of a triangle?

My question is very similar to this one but I need to work out a number of points along the edge of the triangle - not the projection of the height, as per the link previously.

Apologies, my maths skills are not strong at all.

Thanks in advance.

Cheers, Rudy

$\endgroup$
  • 2
    $\begingroup$ If you have coordinates of the corners of the triangle? If so, $\lambda A + (1-\lambda)B$ for $\lambda \in [0,1]$ will give you all points between the point $A$ and $B$. $\endgroup$ – YukiJ Jan 5 '17 at 23:26
  • $\begingroup$ Thank you Yuki. TBH I have no idea what that means, but I will work that out. $\endgroup$ – Rudy N Jan 5 '17 at 23:33
  • $\begingroup$ If I may ask, how would this example look please, if you could show me the steps to the solution? A = (0,0), and B = (2,4) $\endgroup$ – Rudy N Jan 6 '17 at 2:21
  • $\begingroup$ See the answer by Siong below. $\endgroup$ – YukiJ Jan 6 '17 at 7:01
0
$\begingroup$

The points along the edge $AB$ can be characterized by $$\lambda A + (1-\lambda)B$$ where $\lambda \in [0,1]$.

Credit: YukiJ answered this in the comment.

For example, If $A=(0,0)$ and $B=(2,4)$

The points can be characterized by

$$\lambda(0,0)+(1-\lambda) (2,4)=(2(1-\lambda),4(1-\lambda))$$

If we substitute $\lambda=0$, we obtain $(2,4)=B$.

If we substitute $\lambda =1$, we obtain $(0,0)=A$.

If we substitute $\lambda = \frac12$, we obtain $(1,2)$ which is the mid point.

As $\lambda$ increases, we move from point $B$ to point $A$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.