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边界判定

4. 边界判定

4.1 边界函数(Edge Function)

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4.2 判定三角形内外

对于逆时针排列三角形，如果一个点如果在三角形内，那么这个点一定在所有三条边的“左侧”，反之，只要有这个点出现在任意一条边的“右侧”，那么这个点就是在三角形的外部

4.3 判定三角形的边(Top-Left规则)

如果一个点出恰好现在三角形某个边上，也就是某个EdgeFunction的值恰好为零，需要根据Top-Left规则来判定这个点是否归属改三角形。这是由于图形学中会出现两个三角形共享一条边的情况，而这种情况下边上的点应该只归属其中一个三角形，Top-Left是一个约定的规则：

如果边出现三角形左侧或者恰好是水平方向最上面的边，则这种边属于这个三角形

例如上面的三角形，实线边是属于这个三角形的，虚线边则不属于。 DirectX的光栅化规则也是遵守的这个规则

如果一个点是两个边的公有点，则只有在这两条边都是属于三角形的边的情况下，这个顶点才是属于这个三角形的，以保证在光栅化过程中，所有点都属于唯一的某个三角形，例如下面的一个比较极端的例子，对8个小三角形的光栅化

4.4 三角形内部判断

边界函数4.1.1可以变形为

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结合上面对于是否在三角形内以及三角形边上的判断，最终判断某点是否属于三角形，使用下面的函数判断该点是否在三角形三个边的内部

bool Inside(a,b,c, x, y) 
{
	bool is_top_left = (a!=0)?(a>0):(b<0);
	e=a*x+b*y+c;
	return e>0 || (e==0 && is_top_left);
}

如果这个点出现在三个边的内部，则该点在三角形内部

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