Triangulation algorithm - c

Question

I've decided to create a simple demo, dividing a polygon into triangle set. Here what i've got so far:
A sequential vertex list is given (P1) forming polygon edges (polygon is not convex in most cases); a triangle set is needed
Loop through all the vertices within the polygon P1 and find the one (v), which will satisfy next clauses:
remove v from polygon and save the new one to P2 previous vertex to v
connected to its next one form a
line which do not cross any of P2
edges
v is not inside P2
If these are satisfied, we can replace P1 with (P2 + triangle( prev(v), v, next(v)) ) and repeat this action until P1 contains more than 3 vertices.
So, the questions are: is this algorithm correct and how it could be implemented using C / C++ using the most obvious and simple way?

Answer 1

I think you're describing the ear clipping method. There's code for that method at http://cs.smith.edu/~orourke/books/ftp.html ; it's the code described in the book Computational Geometry in C.

Answer 2

Seems that i'm done with this algorithm implementation. Please, verify it someone. Thanks!
typedef struct Point
{
float x, y;
};
class MooPolygon
{
private:
vector<Point> points;
int isVertexEar(int n, const vector<Point> &p)
{
return (isVertexInsideNewPoly(n, p) && !isEdgeIntersect(n, p));
}
int isEdgeIntersect(int n, const vector<Point> &p)
{
Point v = p[n];
vector<Point> a;
for (size_t i = 0; i < p.size(); i++)
if (i != n)
a.push_back(p[i]);
int c = 0, cnt = a.size(), prev = (cnt + (n - 1)) % cnt, next = n % cnt;
Point v1 = a[prev], v2 = a[next];
for (size_t i = 0, j = cnt - 1; i < cnt; j = i++)
{
if (prev == i || prev == j || next == i || next == j)
continue;
Point v4 = a[j], v3 = a[i];
float denominator = ((v4.y - v3.y) * (v2.x - v1.x)) - ((v4.x - v3.x) * (v2.y - v1.y));
if (!denominator)
continue;
float ua = (((v4.x - v3.x) * (v1.y - v3.y)) - ((v4.y - v3.y) * (v1.x - v3.x))) / denominator;
float ub = (((v2.x - v1.x) * (v1.y - v3.y)) - ((v2.y - v1.y) * (v1.x - v3.x))) / denominator;
//float x = v1.x + (ua * (v2.x - v1.x)), y = v1.y + (ua * (v2.y - v1.y));
if (ua >= 0 && ua <= 1 && ub >= 0 && ub <= 1)
{
c = 1;
break;
}
}
return c;
}
int isVertexInsideNewPoly(int n, const vector<Point> &p)
{
Point v = p[n];
vector<Point> a;
for (size_t i = 0; i < p.size(); i++)
if (i != n)
a.push_back(p[i]);
int c = 1;
for (size_t i = 0, j = a.size() - 1; i < a.size(); j = i++)
{
if ((((a[i].y <= v.y) && (v.y < a[j].y)) || ((a[j].y <= v.y) && (v.y < a[i].y))) && (v.x > (a[j].x - a[i].x) * (v.y - a[i].y) / (a[j].y - a[i].y) + a[i].x))
c = !c;
}
return c;
}
float dist(Point a, Point b)
{
return sqrt( ((a.x - b.x) * (a.x - b.x)) + (((a.y - b.y) * (a.y - b.y))) );
}
public:
void push(const Point &p)
{
for (size_t i = 0; i < points.size(); i++)
{
if (dist(points[i], p) < 7.f)
{
points.push_back(points[i]);
return;
}
}
points.push_back(p);
}
void pop()
{
if (points.size() > 0)
points.pop_back();
}
void clear()
{
points.clear();
}
Point v(int index)
{
return points[index];
}
size_t size()
{
return points.size();
}
void triangulate()
{
vector<Point> a;
for (size_t i = 0; i < points.size(); i++)
{
a.push_back(points[i]);
}
points.clear();
for (size_t t = a.size() - 1, i = 0, j = 1; i < a.size(); t = i++, j = (i + 1) % a.size())
{
if (a.size() == 3)
{
points.push_back(a[0]);
points.push_back(a[1]);
points.push_back(a[2]);
break;
}
if (isVertexEar(i, a))
{
points.push_back(a[t]);
points.push_back(a[i]);
points.push_back(a[j]);
a.erase(a.begin() + i, a.begin() + i + 1);
t = a.size() - 1;
i = 0;
j = 1;
}
}
}
};

Answer 3

The code has an error on the line below. The line is in the for loop in the push() function of your class:
points.push_back(points[i]);
You are not passing the pushed Point, but an empty element of the vector itself. I changed the line to
points.push_back(p);
and it worked.