# ベジェ曲線 Bezier Curve
# 引数 次数 値 ($N, $t \@Price)
# 戻り値 ベジェ曲線 (@BezierCurve)
sub BEZIERCURVE{
	my ($N, $t , $Price) = @_;
	my @BezierCurve = ();
	my @BinomialCoefficient = ();
	my $Combination = $N;
	my @PowerT = ();
	my @Power1_T = ();
	my $count = @$Price - ($N + 1);
	
	# 次数,$t,配列数の確認
	if(($N < 0) || ($t < 0) || (1 < $t) || ($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);
		}
	
		$PowerT[$i] = $t ** $i;
		$Power1_T[$i] = (1 - $t) ** ($N - $i);
	}
	
	# 計算
	for(my $i = $count; $i >= 0; $i--){
		my $sum = 0;
		for(my $j = 0; $j <= $N; $j++){
			$sum += $BinomialCoefficient[$j] * $Power1_T[$j] * $PowerT[$j] * $$Price[$i + $j];
		}
	
		# ベジェ曲線 Bezier Curve
		$BezierCurve[$i] = $sum;
	}
	
	return @BezierCurve;
}