C$++$ code for OpenGL

DO NOT USE $""$M$\_$PI$""$

build a parametric torus object based on parameters $r$ and $R,$ and also controlling the resolution $($number

of triangles$)$ of your approximation.

Using Parametric equations:

$x(,)=(R+rcos)cos$

$y(,)=(R+rcos)sin$

$z(,)=rsin$

Requirement $1$ Parameterized torus using triangle primitives:

You will use the torus parametric equation to build a torus based on $3$ parameters: r$,$ R$,$ and

n$,$ where n controls the number of triangles that are generated.

The number of triangles does not need to be parameterized exactly. Parameter n just needs

to control the resolution in a way to properly control a finer or coarser subdivision of the

surface in triangles. You will typically have two nested for loops to vary the $2$ parameters $($r

and R$)$ of the parametric equation, and n will control how large are the increments applied to

the two parameters of the for loops. As triangles are created, $$push$$ them to an array to be

sent to OpenGL. You will likely want to use a dynamically sized structure like a vector.

Note $1$: Remember, for the built$-$in OpenGL $$back$-$face culling$$ to work properly, make sure

the order of the vertices in each triangle is always counter$-$clockwise, when seen from outside

the torus. This is almost always an important thing to get right in Computer Graphics.

Note $2$: It will probably be better to inspect your torus in wireframe since at this point your

object will not be shaded. We will cover shading and illumination in a future assignment. By

default in the support code, pressing $$w$$ will toggle wireframe $($or $$line rendering$)$ mode.

Requirement $2$ Interaction:

In this requirement the previously described parameters are controlled with keys such that

you can test your implementation and generate shapes with different properties. Use the

callback functions to change the values of your parameters in response to key presses, and

then regenerate the torus with the new parameters. Please use the following keys:

$-\text{'}$q$\text{'}$ : increment the number of triangles $($n$)$

$-\text{'}$a$\text{'}$ : decrement the number of triangles $($n$)$

$-\text{'}$w$\text{'}$ : increment the r radius $($by a small value$)$

$-\text{'}$s$\text{'}$ : decrement the r radius $($by a small value$)$

$-\text{'}$e$\text{'}$ : increment the R radius $($by a small value$)$

$-\text{'}$d$\text{'}$ : decrement the R radius $($by a small value$)$