Tracing the sides of an equilateral triangle

Question

Is there any way I can get the points in 2D plane on the sides of an equilateral triangle for certain infinite animation sequence?

For example in case of tracing the circumference of the circle, I have the polar coordinates for $x$ and $y$ as $$x=radius\times cosine(\theta)$$ $$y=radius\times sine(\theta)$$

I'm unable to figure how to take care of the discontinuity at the 3 vertexes

Can you plot 3 separate line segments or do you require a path which follows all three edges of the triangle? And what are the co-ordinates of the bottom left corner? — it's a hire car baby, Jul 16 '16 at 16:40
@RobertFrost I've drawn 3 separate lines each have coordinates - x1, y1, x2, y2, x3, y3 — Siddharth Thevaril, Jul 16 '16 at 16:45

score 4 · Answer 1 · answered Jul 16 '16 at 16:42

I found this answer to be useful: Is there an equation to describe regular polygons?

You can use absolute values or modular arithmetic to take care of the discontinuities. Here's one possible formula, which will trace out an equilateral triangle centered on the origin:

Let $k \equiv \frac{2\pi}{3}$. (In general, we divide $2\pi$ by the number of sides of the polygon we want to draw).

$$\begin{align*} r(\theta) = \frac{\cos{\left(\frac{k}{2}\right)}}{\cos{\left(-\frac{k}{2} + \;\theta \,\text{mod}\; k\right)}} \end{align*}$$

And you can plot this for every value of $\theta$ between 0 and $2\pi$.

If you want a larger triangle, multiply $r(\theta)$ by a suitable number. And if you want to rotate the triangle, replace $\theta$ with $\theta+d$ for some rotation amount $d$.

Finally, if you want to have a formula in rectangular coordinates, you can use the polar-to-rectangular transformation:

$$\begin{align*}x(\theta) &= r(\theta)\times \cos{\theta}\\y(\theta)&=r(\theta)\times \sin{\theta} .\end{align*}$$

I hope that helps!

Tracing the sides of an equilateral triangle

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