# ベジェ曲線 Bezier Curve
# 引数 次数 値 ($N, \@Price)
# 戻り値 ベジェ曲線 (@BezierCurve)
sub BEZIERCURVE{
	my ($N, $Price) = @_;
	my @BezierCurve = ();
	my @BinomialCoefficient = ();
	my $Combination = $N;
	my $count = @$Price - ($N + 1);
	
	# 次数と配列数の確認
	if(($N < 0) || ($count < 0)){
		return 0;
	}
	
	# 二項係数
	for(my $i = 0; $i <= $N; $i++){
		if(($i == 0) || ($i == $N)){
			$BinomialCoefficient[$i] = 1;
		}else {
			$Combination = $Combination / $i;
			$BinomialCoefficient[$i] = $Combination;
			$Combination = $Combination * ($N - $i);
		}
	}
	
	# 計算
	my $p = int((@$Price - 1) / $N) - 1;
	while ($p >= 0){
		my $Pos = ($p * $N);

		for(my $i = 0; $i <= $N; $i++){
			my $t = $i / $N;
			my $sum = 0;

			for(my $j = 0; $j <= $N; $j++){
				my $PowerT = $t ** $j;
				my $Power1_T = (1 - $t) ** ($N - $j);

				$sum += $BinomialCoefficient[$j] * $PowerT * $Power1_T * $$Price[$Pos + $j];
			}
		
			# ベジェ曲線 Bezier Curve
			$BezierCurve[$Pos + $i] = $sum;
		}

		$p--;
	}
	
	return @BezierCurve;
}