Augusto - 10 months ago 25

Java Question

I'm developing a Processing (Java) sketch that, given a certain angle, draws a dot at the edge of a rhombus.

I know the width of the rhombus, and its position, but I'm not sure how to calculate the x-y coordinates of a dot resting at its edge.

Are there any elegant solutions for this problem? Any help in pseudocode would be welcomed.

Answer

Let's square side length is `A`

, half-length is `H = A/2`

. Angle `Theta`

. Intersection point P.

All coordinates are relative to the square center.

Rotate square by `-Pi/4`

, angle `Alpha = Theta - Pi/4`

```
if Alpha lies in range -Pi/4..Pi/4, then intersection point P' = (H, H*Tan(Alpha))
if Alpha lies in range Pi/4..3*Pi/4, then P' = (H*Cotangent(Alpha), H)
if Alpha lies in range 3*Pi/4..5*Pi/4, then P' = (-H, -H*Tan(Alpha))
if Alpha lies in range 5*Pi/4..7*Pi/4, then P' = (-H*Cotangent(Alpha), -H)
```

Then rotate point `P'`

back by `Pi/4`

:

```
S = Sqrt(2)/2
P.X = S * (P'.X - P'.Y)
P.Y = S * (P'.X + P'.Y)
```

Example (data like your sketch):

```
A = 200, Theta = 5*Pi/12
H = 200/2 = 100, Alpha =Theta-Pi/4 = Pi/6
P'.X = H = 100
P'.Y = H * Tan(Alpha) = 100 * Tan(Pi/6) ~= 57.7
S = 0.707
P.X = 0.707 * (100 - 57.7) = 30
P.Y = 0.707 * (100 + 57.7) = 111
```