public Polygon2D deleteVertexBefore(int k) {
		int n = vertex.length;
		if (n < 4)
			return this;
		float[] x = new float[n - 1];
		float[] y = new float[n - 1];
		if (k > 0 && k < n) {
			for (int i = 0; i < k; i++) {
				x[i] = vertex[i].x;
				y[i] = vertex[i].y;
			}
			for (int i = k + 1; i < n; i++) {
				x[i - 1] = vertex[i].x;
				y[i - 1] = vertex[i].y;
			}
		} else if (k == 0) {
			for (int i = 1; i < n; i++) {
				x[i - 1] = vertex[i - 1].x;
				y[i - 1] = vertex[i - 1].y;
			}
		} else {
			return this;
		}
		return new Polygon2D(x, y);
	}