static unsigned
_PolygonToTriangles(const PT *points, unsigned num_points,
GLushort *triangles, typename PT::scalar_type min_distance)
{
// no redundant start/end please
if (num_points >= 1 && points[0] == points[num_points - 1])
num_points--;
if (num_points < 3)
return 0;
assert(num_points < 65536);
// next vertex pointer
auto next = new GLushort[num_points];
// index of the first vertex
GLushort start = 0;
// initialize next pointer counterclockwise
if (PolygonRotatesLeft(points, num_points)) {
for (unsigned i = 0; i < num_points-1; i++)
next[i] = i + 1;
next[num_points - 1] = 0;
} else {
next[0] = num_points - 1;
for (unsigned i = 1; i < num_points; i++)
next[i] = i - 1;
}
// thinning
if (min_distance > 0) {
for (unsigned a = start, b = next[a], c = next[b], heat = 0;
num_points > 3 && heat < num_points;
a = b, b = c, c = next[c], heat++) {
bool point_removeable = TriangleEmpty(points[a], points[b], points[c]);
if (!point_removeable) {
typename PT::scalar_type distance = ManhattanDistance(points[a],
points[b]);
if (distance < min_distance) {
point_removeable = true;
if (distance > 0) {
for (unsigned p = next[c]; p != a; p = next[p]) {
if (InsideTriangle(points[p], points[a], points[b], points[c])) {
point_removeable = false;
break;
}
}
}
}
}
if (point_removeable) {
// remove node b from polygon
if (b == start)
// keep track of the smallest index
start = std::min(a, c);
next[a] = c;
num_points--;
// 'a' should stay the same in the next loop
b = a;
// reset heat
heat = 0;
}
}
//LogDebug(_T("polygon thinning (%u) removed %u of %u vertices"),
// min_distance, orig_num_points-num_points, orig_num_points);
}
// triangulation
auto t = triangles;
for (unsigned a = start, b = next[a], c = next[b], heat = 0;
num_points > 2; a = b, b = c, c = next[c]) {
typename PT::product_type bendiness =
LeftBend(points[a], points[b], points[c]);
// left bend, spike or line with a redundant point in the middle
bool ear_cuttable = (bendiness >= 0);
if (bendiness > 0) {
// left bend
for (unsigned prev_p = c, p = next[c]; p != a;
prev_p = p, p = next[p]) {
typename PT::product_type ab = PointLeftOfLine(points[p], points[a],
points[b]);
typename PT::product_type bc = PointLeftOfLine(points[p], points[b],
points[c]);
typename PT::product_type ca = PointLeftOfLine(points[p], points[c],
points[a]);
if (ab > 0 && bc > 0 && ca > 0) {
// p is inside a,b,c
ear_cuttable = false;
break;
} else if (ab >= 0 && bc >= 0 && ca >= 0) {
// p is on one or two edges of a,b,c
bool outside_ab = (ab == 0) &&
PointLeftOfLine(points[prev_p], points[a], points[b]) <= 0;
bool outside_bc = (bc == 0) &&
PointLeftOfLine(points[prev_p], points[b], points[c]) <= 0;
bool outside_ca = (ca == 0) &&
PointLeftOfLine(points[prev_p], points[c], points[a]) <= 0;
if (!(outside_ab || outside_bc || outside_ca)) {
// line p,prev_p intersects with triangle a,b,c
ear_cuttable = false;
break;
}
outside_ab = (ab == 0) &&
PointLeftOfLine(points[next[p]], points[a], points[b]) <= 0;
outside_bc = (bc == 0) &&
PointLeftOfLine(points[next[p]], points[b], points[c]) <= 0;
outside_ca = (ca == 0) &&
PointLeftOfLine(points[next[p]], points[c], points[a]) <= 0;
if (!(outside_ab || outside_bc || outside_ca)) {
// line p,next[p] intersects with triangle a,b,c
ear_cuttable = false;
break;
}
}
}
if (ear_cuttable) {
// save triangle indices
*t++ = a;
*t++ = b;
*t++ = c;
}
}
if (ear_cuttable) {
// remove node b from polygon
next[a] = c;
num_points--;
// 'a' should stay the same in the next loop
b = a;
// reset heat
heat = 0;
}
if (heat++ > num_points) {
// if polygon edges overlap we may loop endlessly
//LogDebug(_T("polygon_to_triangle: bad polygon"));
delete[] next;
return 0;
}
}
delete[] next;
return t - triangles;
}
static inline bool
TriangleEmpty(const PT &a, const PT &b, const PT &c)
{
return LeftBend(a, b, c) == 0;
}
static unsigned
_PolygonToTriangles(const PT *points, unsigned num_points,
GLushort *triangles, unsigned min_distance)
#endif
{
// no redundant start/end please
if (num_points >= 1 &&
points[0].x == points[num_points - 1].x &&
points[0].y == points[num_points - 1].y)
num_points--;
if (num_points < 3)
return 0;
assert(num_points < 65536);
// next vertex pointer
GLushort *next = new GLushort[num_points];
// index of the first vertex
GLushort start = 0;
// initialize next pointer counterclockwise
if (PolygonRotatesLeft(points, num_points)) {
for (unsigned i = 0; i < num_points-1; i++)
next[i] = i + 1;
next[num_points - 1] = 0;
} else {
next[0] = num_points - 1;
for (unsigned i = 1; i < num_points; i++)
next[i] = i - 1;
}
// thinning
if (min_distance > 0) {
for (unsigned a = start, b = next[a], c = next[b], heat = 0;
num_points > 3 && heat < num_points;
a = b, b = c, c = next[c], heat++) {
bool point_removeable = TriangleEmpty(points[a], points[b], points[c]);
if (!point_removeable) {
unsigned distance = manhattan_distance(points[a], points[b]);
if (distance < min_distance) {
point_removeable = true;
if (distance != 0) {
for (unsigned p = next[c]; p != a; p = next[p]) {
if (InsideTriangle(points[p], points[a], points[b], points[c])) {
point_removeable = false;
break;
}
}
}
}
}
if (point_removeable) {
// remove node b from polygon
if (b == start)
// keep track of the smallest index
start = std::min(a, c);
next[a] = c;
num_points--;
// 'a' should stay the same in the next loop
b = a;
// reset heat
heat = 0;
}
}
//LogDebug(_T("polygon thinning (%u) removed %u of %u vertices"),
// min_distance, orig_num_points-num_points, orig_num_points);
}
// triangulation
GLushort *t = triangles;
for (unsigned a = start, b = next[a], c = next[b], heat = 0;
num_points > 2; a = b, b = c, c = next[c]) {
if (LeftBend(points[a], points[b], points[c])) {
bool ear_cuttable = true;
for (unsigned p = next[c]; p != a; p = next[p]) {
if (InsideTriangle(points[p], points[a], points[b], points[c])) {
ear_cuttable = false;
break;
}
}
if (ear_cuttable) {
// save triangle indices
*t++ = a;
*t++ = b;
*t++ = c;
// remove node b from polygon
next[a] = c;
num_points--;
// 'a' should stay the same in the next loop
b = a;
// reset heat
heat = 0;
}
}
if (heat++ > num_points) {
// if polygon edges overlap we may loop endlessly
//LogDebug(_T("polygon_to_triangle: bad polygon"));
delete[] next;
return 0;
}
}
delete[] next;
return t - triangles;
}