C - Structures for point, polygonal line and polygon

Question

Good night

The exercise asks me to implement three structs: Point (coordinates X and Y), polygonal lines (sequence of 2 to 100 points that are the vertices along the line) and polygon (sequence of 3 to 100 points which are the vertices along the polygon and the last coincides with the first).

I implemented the struct for the dots as follows:

typedef struct //Estrutura definida para os pontos.
{
    double x;
    double y;
} Ponto;

For the polygonal lines I defined as follows, but I do not know if it is correct and if it is the best way.

 typedef struct //Estrutura definida para as linhas poligonais.
 {
     Ponto Vertice;
 } Linha;

As for polygons, I had no idea how to do it. But I know that the difference between a polygonal line and a polygon is that, for the polygon, the last and first coordinates are the same (can I specify this already inside the struct?). I would like to have an idea of how to proceed.

Answer 1

Although you do not need this to answer your question, a line is defined by two points : start and end point. Therefore, it should be :

typedef struct {
    Ponto p0, p1;
} Linha;

A polygonal line (polyline or polilinha) consists of several points, each two consecutive forming a segment. As in your problem you have at most 100 elements, we can define a polygonal line as:

typedef struct {
    int n_pontos; /* quantidade de pontos usados nessa polyline */
    Ponto p[100]; /* vetor com os pontos usados */
} Polilinha;

A polygon is a special case of polyline, in which the last vertex binds to the first vertex. For example, to represent a triangle, I need to define three points; let’s say we have the triangle (0,0) , (3,0) , (0,4), is sufficient to deduce the existence of the following segments:

 (0,0) -> (3,0)
 (3,0) -> (0,4)
 (0,4) -> (0,0)

If these same three dots had been passed to a polyline (in the same order), the segments would be:

 (0,0) -> (3,0)
 (3,0) -> (0,4)

Therefore, internally, you can represent with the same structure, but you must manipulate differently; hence:

typedef Polilinha Poligono;