Generalize transforms (translation, rotation, scaling)

[Caellian]

There's room left for generalization with respect to dimensionality when it comes to transforms in nalgebra.

Most:

• Translation
• Rotation (see General n-Dimensional Rotations)
• Scaling
• Transform
• Perspective projection
• Orthographic projection

Some of these are relatively easy to generalize. Some are not that useful (like projections), but it would be cool to have code that just works no matter the dimension. Rotation might be useful for topology and scientific applications (beyond just rendering) - implementing this and generalizing Transform was the main motivator for opening this issues.

However, I don't personally need this right now. I just wanted to propose this as I don't see any good alternatives.

[Caellian]

Orthographic projection formula from Wikipedia:

$$ P = ST = \begin{bmatrix} \frac{2}{\text{max}_x-\text{min}_x} & 0 & 0 & 0 \\ 0 & \frac{2}{\text{max}_y-\text{min}_y} & 0 & 0 \\ 0 & 0 & \frac{2}{\text{max}_z-\text{min}_z} & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 0 & -\frac{\text{min}_x+\text{min}_x}{2} \\ 0 & 1 & 0 & -\frac{\text{min}_y+\text{max}_y}{2} \\ 0 & 0 & -1 & -\frac{\text{min}_z+\text{max}_z}{2} \\ 0 & 0 & 0 & 1 \end{bmatrix} $$

This is easily generalized for arbitrary slicing planes. z-axis (self.matrix[(2, 2)]) is flipped because camera looks towards -Z in graphics APIs, though correctness of that depends on use case I guess.

[Caellian]

Related to PR #1366.

[muzammil35]

Can I give this issue a try?