openGL ES 项目中需要绘制不规则的多边形，但openGL ES只支持三角形，三角带，三角扇。但后台给的数据只有顶点坐标没有顶点索引，只能根据顶点坐标把多边形切割成三角形：
耳切法切割多边形的几个主要方法：
1.根据顶点坐标计算多边形带方向面积，主要是为了判断顶点时针方向，正时针面积<0，逆时针>0
+ (float)Area:(NSArray<NSValue *> *)contour {
int n = (int)contour.count;
float A = 0.0f;
for(int p = n - 1, q = 0 ; q < n; p = q++) {
CGPoint pPoint = [contour[p] CGPointValue];
CGPoint qPoint = [contour[q] CGPointValue];
A += (pPoint.x * qPoint.y - qPoint.x * pPoint.y);
}
return A * 0.5f;
}
2.判断一个点是否在一个三角形（三个点）之中
+ (BOOL)InsideTriangle:(float)Ax :(float)Ay :(float)Bx :(float)By :(float)Cx :(float)Cy :(float)Px :(float)Py {
float ax, ay, bx, by, cx, cy, apx, apy, bpx, bpy, cpx, cpy;
float cCROSSap, bCROSScp, aCROSSbp;
ax = Cx - Bx; ay = Cy - By;
bx = Ax - Cx; by = Ay - Cy;
cx = Bx - Ax; cy = By - Ay;
apx= Px - Ax; apy= Py - Ay;
bpx= Px - Bx; bpy= Py - By;
cpx= Px - Cx; cpy= Py - Cy;
aCROSSbp = ax*bpy - ay*bpx;
cCROSSap = cx*apy - cy*apx;
bCROSScp = bx*cpy - by*cpx;
BOOL result = (aCROSSbp >= 0.0f) && (bCROSScp >= 0.0f) && (cCROSSap >= 0.0f);
return result;
}
- 是否符合切割条件
static const float EPSILON = 0.0000000001f;
+ (BOOL)Snip:(NSArray<NSValue *> *)contour :(NSMutableArray *)V :(int)u :(int)v :(int)w :(int)n
{
float Ax, Ay, Bx, By, Cx, Cy, Px, Py;
int a = [V[u] intValue];
CGPoint aPoint = [contour[a] CGPointValue];
Ax = aPoint.x;
Ay = aPoint.y;
int b = [V[v] intValue];
CGPoint bPoint = [contour[b] CGPointValue];
Bx = bPoint.x;
By = bPoint.y;
int c = [V[w] intValue];
CGPoint cPoint = [contour[c] CGPointValue];
Cx = cPoint.x;
Cy = cPoint.y;
float temp = ((Bx - Ax) * (Cy - Ay)) - ((By - Ay) * (Cx - Ax));
if ( EPSILON > temp )
return false;
for (int p = 0; p < n ; p++) {
if( (p == u) || (p == v) || (p == w) ) continue;
int z = [V[p] intValue];
CGPoint pPoint = [contour[z] CGPointValue];
Px = pPoint.x;
Py = pPoint.y;
if ([self InsideTriangle:Ax :Ay :Bx :By :Cx :Cy :Px :Py])
return false;
}
return true;
}
- 流程
+ (NSMutableArray *)Process:(NSArray<NSValue *> *)contour
{
NSMutableArray *result = [NSMutableArray array];
NSInteger n = contour.count;
if ( n < 3 ) return result;
NSMutableArray *V = [NSMutableArray arrayWithCapacity:n];
if ( 0.0f < [self Area:contour] ) {
for (int v = 0; v < n; v++) {
NSNumber *num = [NSNumber numberWithInt:v];
[V insertObject:num atIndex:v];
}
} else {
for(int v = 0; v < n; v++) {
NSNumber *num = [NSNumber numberWithInt:(int)(n-1)-v];
[V insertObject:num atIndex:v];
}
}
int nv = (int)n;
int count = 2*nv;
for(int v = nv-1; nv > 2; ) {
if (0 >= (count--)) {
return result;
}
int u = v; if (nv <= u) u = 0; // i - 1
v = u+1; if (nv <= v) v = 0; // i
int w = v+1; if (nv <= w) w = 0; // i + 1
if ( [self Snip:contour :V :u :v :w :nv]) {
int a,b,c;
a = [V[u] intValue];
b = [V[v] intValue];
c = [V[w] intValue];
// 把切下的三角形放入数组
[result addObject:contour[a]];
[result addObject:contour[b]];
[result addObject:contour[c]];
[V removeObjectAtIndex:v];
nv--;
count = 2*nv;
}
}
return result;
}
- 测试
- (void)test
{
CGPoint a = CGPointMake(2, 2);
NSValue *value1 = [NSValue valueWithCGPoint:a];
CGPoint b = CGPointMake(2, -1);
NSValue *value2 = [NSValue valueWithCGPoint:b];
CGPoint c = CGPointMake(-1, -1);
NSValue *value3 = [NSValue valueWithCGPoint:c];
CGPoint d = CGPointMake(-1, 2);
NSValue *value4 = [NSValue valueWithCGPoint:d];
CGPoint e = CGPointMake(0, 2);
NSValue *value5 = [NSValue valueWithCGPoint:e];
CGPoint f = CGPointMake(0, 1);
NSValue *value6 = [NSValue valueWithCGPoint:f];
CGPoint g = CGPointMake(1, 1);
NSValue *value7 = [NSValue valueWithCGPoint:g];
CGPoint h = CGPointMake(1, 2);
NSValue *value8 = [NSValue valueWithCGPoint:h];
NSArray *vs = @[value1, value2, value3, value4, value5, value6, value7, value8];
NSMutableArray *result = [NSMutableArray array];
result = [Triangulate Process:vs];
for (int i = 0; i < result.count/3; i++) {
CGPoint p1 = [result[i*3+0] CGPointValue];
CGPoint p2 = [result[i*3+1] CGPointValue];
CGPoint p3 = [result[i*3+2] CGPointValue];
NSLog(@"Triangle %d => (%0.0f, %0.0f) (%0.0f, %0.0f) (%0.0f, %0.0f)\n", i+1, p1.x, p1.y, p2.x, p2.y, p3.x, p3.y);
}
}
6.结果
测试结果.png
参考：
http://www.flipcode.com/archives/Efficient_Polygon_Triangulation.shtml
