# Vector Math (ベクトル演算)ノード

Vector Math (ベクトル演算)ノードは、指定の数式演算を入力ベクトルに行います。

## 入力

ノードの入力は動的です。一部の入力は、特定の操作で使用します。たとえば、 Scale 入力は Scale オペレーターでのみ使用できます。

Vector(ベクトル)

Input vector $$A = \begin{pmatrix} A_x \\ A_y \\ A_z \end{pmatrix}$$.

Vector(ベクトル)

Input vector $$B = \begin{pmatrix} B_x \\ B_y \\ B_z \end{pmatrix}$$.

Scale(スケール)

Input Scale $$s$$.

## Properties(プロパティ)

Operation(処理)

The sum of A and B. $$\begin{pmatrix} A_x + B_x \\ A_y + B_y \\ A_z + B_z \end{pmatrix}$$

Subtract(減算):

The difference between A and B. $$\begin{pmatrix} A_x - B_x \\ A_y - B_y \\ A_z - B_z \end{pmatrix}$$

Multiply(乗算):

The entrywise product of A and B. $$\begin{pmatrix} A_x \cdot B_x \\ A_y \cdot B_y \\ A_z \cdot B_z \end{pmatrix}$$

Divide(除算):

The entrywise division of A by B. Division by zero results in zero. $$\begin{pmatrix} A_x / B_x \\ A_y / B_y \\ A_z / B_z \end{pmatrix}$$

The entrywise combination of the multiply and addition operations. $$A * B + C$$

Cross Product (外積):

The cross product of A and B. $$\begin{pmatrix} A_y \cdot B_z - A_z \cdot B_y \\ A_z \cdot B_x - A_x \cdot B_z \\ A_x \cdot B_y - A_y \cdot B_x \end{pmatrix}$$

Project (プロジェクト):

AのBへのプロジェクション。

Reflect (反射):

Refract:

For a given incident vector A, surface normal B and ratio of indices of refraction (IOR), refract outputs the refraction vector R.

Faceforward:

Orients a vector A to point away from a surface B as defined by its normal C. Computes $$(dot(B, C) < 0) ? A : -A$$.

Dot Product (内積):

The dot product of A and B. $$A_x \cdot B_x + A_y \cdot B_y + A_z \cdot B_z$$

Distance(距離):

AとBの間の距離。

Length(長さ):

The length of A. $$\sqrt{A_x^2 + A_y^2 + A_z^2}$$

Scale(スケール):

The result of multiplying A by the scalar input Scale. $$\begin{pmatrix} s \cdot A_x \\ s \cdot A_y \\ s \cdot A_z \end{pmatrix}$$

Normalize(正規化):

The result of normalizing A. The result vector points to the same direction as A and has a length of 1. If A is (0, 0, 0), the result is (0, 0, 0) as well.

Wrap(ラップ):

The entrywise output of a value between Min and Max based on the absolute difference between the input value and the nearest integer multiple of Max less than the value.

Snap(スナップ):

Aを、A以下のBの最大整数倍数に丸めた結果。

Floor(床):

Rounds the input value entrywise down to the nearest integer.

Ceil(天井):

Rounds the input value entrywise up to the nearest integer.

Modulo(剰余):

AのBによる剰余。

Fraction(小数部):

Returns the fractional part of the value entrywise.

Absolute(絶対):

Aの成分ごとの絶対値。

Minimum(最小):

The entrywise minimum value from A and B.

Maximum(最大):

The entrywise maximum value from A and B.

Sine(サイン):

The entrywise Sine of A.

Cosine(コサイン):

The entrywise Cosine of A.

Tangent(タンジェント):

The entrywise Tangent of A.