# 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.