Shaders: Math / Vector, Array, Color, Transformation Modules

Introduction

This document describes the built-in Flow Graph modules of the following categories for shaders:

• Shaders: Math / Vector - Modules that compute vector geometry and convert between packed and split vector component layouts.
• Shaders: Math / Array - Modules that read scalar, vector, and color values from shader arrays by index.
• Shaders: Math / Color - Modules that blend, convert, split, merge, and transform shader color values between common representations.
• Shaders: Math / Transformation - Modules that split, merge, concatenate, scale, transpose, and apply transformation matrices to shader vectors.

Shaders: Math / Vector

This section describes the built-in Flow Graph modules that compute vector geometry and convert between packed and split vector component layouts.

Abs Max Component

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Finds the component with the largest absolute magnitude.
• Input pins:
  • ⏺  In (vector) - The source value
• Output pins:
  • ⏺  Maximum (scalar) - Original component value with the largest absolute magnitude.
  • ⏺  Index (integer) - Component index of Maximum (0 for X, 1 for Y, 2 for Z, 3 for W).

Convex

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Normalizes vector components by their total sum.
• Input pins:
  • ⏺  In (vector) - The source value
• Output pins:
  • ⏺  Out (vector) - Input divided by the sum of all components, or zero when the sum is zero.

Cross

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Computes the 3D cross product of two vectors.
• Input pins:
  • ⏺  A (vector) - First vector input.
  • ⏺  B (vector) - Second vector input.
• Output pins:
  • ⏺  Out (vector) - Cross product of A and B using XYZ components.

Direction

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Builds a normalized direction vector from one point to another.
• Input pins:
  • ⏺  A (vector) - Start point.
  • ⏺  B (vector) - End point.
• Output pins:
  • ⏺  Out (vector) - Normalized direction from A to B.

Distance

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Computes the distance between two vectors.
• Input pins:
  • ⏺  A (vector) - First vector position.
  • ⏺  B (vector) - Second vector position.
• Output pins:
  • ⏺  Out (scalar) - Distance between A and B.

Dot

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Computes the dot product of two vectors.
• Input pins:
  • ⏺  A (vector) - First vector input.
  • ⏺  B (vector) - Second vector input.
• Output pins:
  • ⏺  Out (scalar) - Dot product of A and B.

Face Center

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Computes the center point of a triangle face.
• Input pins:
  • ⏺  Point 1 (vector) - First triangle point.
  • ⏺  Point 2 (vector) - Second triangle point.
  • ⏺  Point 3 (vector) - Third triangle point.
• Output pins:
  • ⏺  Out (vector) - Average position of the three points.

Face Normal

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Computes the normal vector of a triangle face.
• Input pins:
  • ⏺  Point 1 (vector) - First triangle point.
  • ⏺  Point 2 (vector) - Second triangle point.
  • ⏺  Point 3 (vector) - Third triangle point.
• Output pins:
  • ⏺  Out (vector) - Normalized face normal from the three points.

Length

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Computes the length of a vector.
• Input pins:
  • ⏺  In (vector) - The source value
• Output pins:
  • ⏺  Out (scalar) - Vector length.

Merge

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Builds a vector from X, Y, Z, and W components.
• Input pins:
  • ⏺  X (scalar) - X component input.
  • ⏺  Y (scalar) - Y component input.
  • ⏺  Z (scalar) - Z component input.
  • ⏺  W (scalar) - W component input.
• Output pins:
  • ⏺  Out (vector) - Vector assembled from X, Y, Z, and W.

Merge XY-Z-W

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Builds a vector from XY, Z, and W inputs.
• Input pins:
  • ⏺  XY (vector) - Source vector for X and Y components.
  • ⏺  Z (scalar) - Z component input.
  • ⏺  W (scalar) - W component input.
• Output pins:
  • ⏺  Out (vector) - Vector assembled from XY, Z, and W.

Merge XY-ZW

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Builds a vector from XY and ZW pairs.
• Input pins:
  • ⏺  XY (vector) - Source vector for X and Y components.
  • ⏺  ZW (vector) - Source vector for Z and W components.
• Output pins:
  • ⏺  Out (vector) - Vector assembled from XY and ZW.

Merge XYZ-W

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Builds a vector from XYZ and W inputs.
• Input pins:
  • ⏺  XYZ (vector) - Source vector for X, Y, and Z components.
  • ⏺  W (scalar) - W component input.
• Output pins:
  • ⏺  Out (vector) - Vector assembled from XYZ and W.

Normalize

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Normalizes a vector to unit length.
• Input pins:
  • ⏺  In (vector) - The source value
• Output pins:
  • ⏺  Out (vector) - Normalized direction of In.

Plane Distance

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Computes signed distance from a point to a plane.
• Input pins:
  • ⏺  Plane (vector) - Plane coefficients.
  • ⏺  Point (vector) - Point to measure.
• Output pins:
  • ⏺  Out (scalar) - Signed distance of Point from Plane.

Reflect

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Reflects an incident direction around a surface normal.
• Input pins:
  • ⏺  Incident (vector) - Incoming direction vector.
  • ⏺  Normal (vector) - Surface normal vector.
• Output pins:
  • ⏺  Out (vector) - Reflected direction from Incident and Normal.

Refract

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Refracts an incident direction through a surface.
• Input pins:
  • ⏺  Incident (vector) - Incoming direction vector.
  • ⏺  Normal (vector) - Surface normal vector.
  • ⏺  Refr Index (scalar) - Refraction index ratio.
• Output pins:
  • ⏺  Out (vector) - Refracted direction from Incident, Normal, and RefrIndex.

Section 2D Intersection

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Tests whether two 2D line segments intersect.
• Input pins:
  • ⏺  A (vector) - Start point of the first segment.
  • ⏺  B (vector) - End point of the first segment.
  • ⏺  C (vector) - Start point of the second segment.
  • ⏺  D (vector) - End point of the second segment.
• Output pins:
  • ⏺  Found (logical) - On when the two segments intersect.
  • ⏺  Factor (scalar) - Intersection position along AB, where 0 is A and 1 is B.

Split

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Splits a vector into X, Y, Z, and W components.
• Input pins:
  • ⏺  In (vector) - The source value
• Output pins:
  • ⏺  X (scalar) - X component of In.
  • ⏺  Y (scalar) - Y component of In.
  • ⏺  Z (scalar) - Z component of In.
  • ⏺  W (scalar) - W component of In.

Split XY-Z-W

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Splits a vector into XY, Z, and W outputs.
• Input pins:
  • ⏺  In (vector) - The source value
• Output pins:
  • ⏺  XY (vector) - X and Y components packed into a vector.
  • ⏺  Z (scalar) - Z component of In.
  • ⏺  W (scalar) - W component of In.

Split XY-ZW

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Splits a vector into XY and ZW pairs.
• Input pins:
  • ⏺  In (vector) - The source value
• Output pins:
  • ⏺  XY (vector) - X and Y components packed into a vector.
  • ⏺  ZW (vector) - Z and W components packed into a vector.

Split XYZ-W

• Category: Shaders: Math / Vector
• Access: All editions.
• Function: Splits a vector into XYZ and W outputs.
• Input pins:
  • ⏺  In (vector) - The source value
• Output pins:
  • ⏺  XYZ (vector) - X, Y, and Z components packed into a vector.
  • ⏺  W (scalar) - W component of In.

Shaders: Math / Array

This section describes the built-in Flow Graph modules that read scalar, vector, and color values from shader arrays by index.

Array Color

• Category: Shaders: Math / Array
• Access: All editions.
• Function: Reads three consecutive scalars from a shader array and builds an RGB color.
• Input pins:
  • ⏺  In (array) - The source value
  • ⏺  Start Index (integer) - Zero-based index of the first element; the next two indices supply the remaining color channels.
• Output pins:
  • ⏺  Out (color) - RGB color from three consecutive array elements.

Array Scalar

• Category: Shaders: Math / Array
• Access: All editions.
• Function: Reads one scalar from a shader array at the given index.
• Input pins:
  • ⏺  In (array) - The source value
  • ⏺  Index (integer) - Zero-based index of the element to output.
• Output pins:
  • ⏺  Out (scalar) - Scalar value stored at Index.

Array Vector

• Category: Shaders: Math / Array
• Access: All editions.
• Function: Reads four consecutive scalars from a shader array and packs them into one vector.
• Input pins:
  • ⏺  In (array) - The source value
  • ⏺  Start Index (integer) - Zero-based index of the first element; the next three indices are read as well.
• Output pins:
  • ⏺  Out (vector) - Vector built from four consecutive array elements (X, Y, Z, W).

Array Vector XY

• Category: Shaders: Math / Array
• Access: All editions.
• Function: Reads two consecutive scalars from a shader array and outputs them as X and Y with Z and W set to zero.
• Input pins:
  • ⏺  In (array) - The source value
  • ⏺  Start Index (integer) - Zero-based index of the first element; the next index is read as the second component.
• Output pins:
  • ⏺  Out (vector) - Vector with X and Y from the array and Z and W set to zero.

Array Vector XYZ

• Category: Shaders: Math / Array
• Access: All editions.
• Function: Reads three consecutive scalars from a shader array and outputs them as X, Y, and Z with W set to zero.
• Input pins:
  • ⏺  In (array) - The source value
  • ⏺  Start Index (integer) - Zero-based index of the first element; the next two indices are read as the remaining components.
• Output pins:
  • ⏺  Out (vector) - Vector with X, Y, and Z from the array and W set to zero.

Shaders: Math / Color

This section describes the built-in Flow Graph modules that blend, convert, split, merge, and transform shader color values between common representations.

Alpha Merge

• Category: Shaders: Math / Color
• Access: All editions.
• Function: Combines RGB color and opacity into one vector output.
• Input pins:
  • ⏺  Color (color) - RGB color for the output.
  • ⏺  Opacity (scalar) - Opacity stored in the output W channel.
• Output pins:
  • ⏺  Out (vector) - Vector with RGB in X–Y–Z and Opacity in W.

Alpha Split

• Category: Shaders: Math / Color
• Access: All editions.
• Function: Splits a vector color into RGB and a separate opacity.
• Input pins:
  • ⏺  In (vector) - The source value
• Output pins:
  • ⏺  Color (color) - RGB taken from the input (channels X, Y, Z).
  • ⏺  Opacity (scalar) - Opacity taken from the W channel of the input.

Blend

• Category: Shaders: Math / Color
• Access: All editions.
• Function: Blends foreground RGB over background RGB using a selectable blend mode, then mixes toward that result by foreground opacity.
• Input pins:
  • ⏺  Blending Mode (integer, Blending Mode) - Selects how foreground and background RGB are combined before opacity mixing.
  • ⏺  Background (color) - Background RGB color.
  • ⏺  Foreground (color) - Foreground RGB color blended against the background.
  • ⏺  Fg Opacity (scalar) - How much of the blended result is applied (0 leaves the background, 1 applies the full blend).
• Output pins:
  • ⏺  Out (color) - Resulting RGB after blending and foreground opacity.

Blend Mix

• Category: Shaders: Math / Color
• Access: All editions.
• Function: Blends foreground and background RGB with a selectable mode, then resolves combined color and opacity for layered compositing.
• Input pins:
  • ⏺  Blending Mode (integer, Blending Mode) - Selects how foreground and background RGB are combined.
  • ⏺  Background (color) - Background RGB color.
  • ⏺  Bg Opacity (scalar) - Opacity applied to the background contribution.
  • ⏺  Foreground (color) - Foreground RGB color.
  • ⏺  Fg Opacity (scalar) - Opacity applied to the foreground contribution.
• Output pins:
  • ⏺  Color (color) - RGB after the blend and opacity mix.
  • ⏺  Opacity (scalar) - Opacity accompanying the Color output.

Color Compose

• Category: Shaders: Math / Color
• Access: All editions.
• Function: Builds an RGB color from hue, saturation, and brightness using either HSV or HSL.
• Input pins:
  • ⏺  Hue (scalar) - Hue for the output color.
  • ⏺  Saturation (scalar) - Saturation for the output color.
  • ⏺  Brightness (scalar) - Value (HSV) or lightness (HSL), depending on Space.
  • ⏺  Space (integer, HSB Space) - Selects whether Brightness is interpreted as HSV value or HSL lightness.
• Output pins:
  • ⏺  Out (color) - RGB color reconstructed from the three components.

Color Decompose

• Category: Shaders: Math / Color
• Access: All editions.
• Function: Splits RGB into hue, saturation, and brightness using either HSV or HSL.
• Input pins:
  • ⏺  In (color) - The source value
  • ⏺  Space (integer, HSB Space) - Selects HSV (value) or HSL (lightness) for the third component.
• Output pins:
  • ⏺  Hue (scalar) - Hue from the selected space.
  • ⏺  Saturation (scalar) - Saturation from the selected space.
  • ⏺  Brightness (scalar) - Value (HSV) or lightness (HSL), depending on Space.

Color Dim

• Category: Shaders: Math / Color
• Access: All editions.
• Function: Scales an RGB color by a single intensity factor.
• Input pins:
  • ⏺  Color (color) - Input RGB color.
  • ⏺  Intensity (scalar) - Multiplier applied to each RGB channel.
• Output pins:
  • ⏺  Out (color) - RGB color scaled by Intensity.

Color From Linear

• Category: Shaders: Math / Color
• Access: All editions.
• Function: Encodes linear RGB through the selected transfer curve (gamma / log) for display-style RGB.
• Input pins:
  • ⏺  In (color) - The source value
  • ⏺  Gamma Function (integer, RGB Gamma) - Transfer curve applied to encode linear RGB.
• Output pins:
  • ⏺  Out (color) - Encoded RGB after the selected curve.

Color Gray Level

• Category: Shaders: Math / Color
• Access: All editions.
• Function: Computes a single brightness value from an RGB color.
• Input pins:
  • ⏺  In (color) - The source value
• Output pins:
  • ⏺  Brightness (scalar) - Brightness derived from the RGB channels.

Color Merge

• Category: Shaders: Math / Color
• Access: All editions.
• Function: Builds one RGB color from separate red, green, and blue inputs.
• Input pins:
  • ⏺  Red (scalar) - Red channel value.
  • ⏺  Green (scalar) - Green channel value.
  • ⏺  Blue (scalar) - Blue channel value.
• Output pins:
  • ⏺  Out (color) - RGB color assembled from the three channels.

Color Multiply

• Category: Shaders: Math / Color
• Access: All editions.
• Function: Multiplies two RGB colors component-wise.
• Input pins:
  • ⏺  A (color) - First RGB color.
  • ⏺  B (color) - Second RGB color.
• Output pins:
  • ⏺  Out (color) - RGB product of A and B per channel.

Color Split

• Category: Shaders: Math / Color
• Access: All editions.
• Function: Splits an RGB color into separate red, green, and blue channel values.
• Input pins:
  • ⏺  In (color) - The source value
• Output pins:
  • ⏺  Red (scalar) - Red channel of In.
  • ⏺  Green (scalar) - Green channel of In.
  • ⏺  Blue (scalar) - Blue channel of In.

Color To Linear

• Category: Shaders: Math / Color
• Access: All editions.
• Function: Decodes display-style RGB through the selected transfer curve (gamma / log) to linear RGB.
• Input pins:
  • ⏺  In (color) - The source value
  • ⏺  Gamma Function (integer, RGB Gamma) - Transfer curve assumed when decoding to linear RGB.
• Output pins:
  • ⏺  Out (color) - Linear RGB after the inverse of the selected curve.

Color Transform

• Category: Shaders: Math / Color
• Access: All editions.
• Function: Applies a linear color transformation matrix to RGB.
• Input pins:
  • ⏺  In (color) - The source value
  • ⏺  Transformation (transformation) - Row-major 4×3 matrix applied as RGB with an implicit 1 for the homogeneous coordinate.
• Output pins:
  • ⏺  Out (color) - Transformed RGB color.

From SRGB

• Category: Shaders: Math / Color
• Access: All editions.
• Function: Converts sRGB-encoded RGB to linear RGB.
• Input pins:
  • ⏺  In (color) - The source value
• Output pins:
  • ⏺  Out (color) - Linear RGB decoded from sRGB.

To SRGB

• Category: Shaders: Math / Color
• Access: All editions.
• Function: Converts linear or scene RGB to the sRGB display encoding.
• Input pins:
  • ⏺  In (color) - The source value
• Output pins:
  • ⏺  Out (color) - RGB encoded for sRGB.

Shaders: Math / Transformation

This section describes the built-in Flow Graph modules that split, merge, concatenate, scale, transpose, and apply transformation matrices to shader vectors.

Inverse Transpose

• Category: Shaders: Math / Transformation
• Access: All editions.
• Function: Gives the inverse-transpose of the linear part of the input transformation (translation cleared).
• Input pins:
  • ⏺  In (transformation) - The source value
• Output pins:
  • ⏺  Out (transformation) - Derived transform with adjusted linear rows and translation cleared.

Transform

• Category: Shaders: Math / Transformation
• Access: All editions.
• Function: Moves a 3D point according to a transformation.
• Input pins:
  • ⏺  In (vector) - The source value
  • ⏺  Transformation (transformation) - Affine transform applied as a row-vector multiply with homogeneous w = 1.
• Output pins:
  • ⏺  Out (vector) - Transformed XYZ with W set to 0.

Transform Dir

• Category: Shaders: Math / Transformation
• Access: All editions.
• Function: Turns a direction or offset through a transformation without applying its shift.
• Input pins:
  • ⏺  In (vector) - The source value
  • ⏺  Transformation (transformation) - Affine transform; only its 3×3 linear block affects the output.
• Output pins:
  • ⏺  Out (vector) - Linearly transformed XYZ with W set to 0.

Transform Homog

• Category: Shaders: Math / Transformation
• Access: All editions.
• Function: Applies a full homogeneous transformation to a four-component vector.
• Input pins:
  • ⏺  In (vector) - The source value
  • ⏺  Transformation (homogeneous space transformation) - Homogeneous 4×4 matrix applied to In.
• Output pins:
  • ⏺  Out (vector) - Full homogeneous result including W.

Transform XY

• Category: Shaders: Math / Transformation
• Access: All editions.
• Function: Places and rotates values in 2D using scale, angle, and offset.
• Input pins:
  • ⏺  In (vector) - The source value
  • ⏺  Position (vector) - Translation added to the rotated XY components.
  • ⏺  Rotation (scalar) - Rotation angle in degrees in the XY plane before translation.
  • ⏺  Scale (vector) - Per-axis scale factors for In.xy before rotation; Z and W are unused.
• Output pins:
  • ⏺  Out (vector) - Transformed XY with Z and W set to 0.

Transformation Concat

• Category: Shaders: Math / Transformation
• Access: All editions.
• Function: Combines two transformations into a single chained result.
• Input pins:
  • ⏺  A (transformation) - First affine factor applied in the composition.
  • ⏺  B (transformation) - Second affine factor applied after A in the composition.
• Output pins:
  • ⏺  Out (transformation) - Product of A (expanded to 4×4 with bottom row 0, 0, 0, 1) and B as a 4×3 affine map.

Transformation Merge

• Category: Shaders: Math / Transformation
• Access: All editions.
• Function: Builds one transformation from a position and three axis directions.
• Input pins:
  • ⏺  Position (vector) - Translation written to the fourth row (XYZ).
  • ⏺  Forward (vector) - Forward axis written to the third row (XYZ).
  • ⏺  Up (vector) - Up axis written to the second row (XYZ).
  • ⏺  Right (vector) - Right axis written to the first row (XYZ).
• Output pins:
  • ⏺  Transformation (transformation) - Affine transform assembled from Right, Up, Forward, and Position.

Transformation Scaling

• Category: Shaders: Math / Transformation
• Access: All editions.
• Function: Extracts the scaling of the transformation.
• Input pins:
  • ⏺  Transformation (transformation) - The source value
• Output pins:
  • ⏺  Scaling (vector) - Per-axis lengths of the right, up, and forward rows in X, Y, and Z; W is 0.

Transformation Split

• Category: Shaders: Math / Transformation
• Access: All editions.
• Function: Splits a transformation into its position and three axis directions.
• Input pins:
  • ⏺  Transformation (transformation) - The source value
• Output pins:
  • ⏺  Position (vector) - Translation taken from the fourth row (XYZ).
  • ⏺  Forward (vector) - Forward axis direction taken from the third row (XYZ).
  • ⏺  Up (vector) - Up axis direction taken from the second row (XYZ).
  • ⏺  Right (vector) - Right axis direction taken from the first row (XYZ).

Transpose

• Category: Shaders: Math / Transformation
• Access: All editions.
• Function: Gives the transpose of the linear part of the input transformation (translation cleared).
• Input pins:
  • ⏺  In (transformation) - The source value
• Output pins:
  • ⏺  Out (transformation) - Transform with transposed linear part and translation cleared.

Unhomog

• Category: Shaders: Math / Transformation
• Access: All editions.
• Function: Turns a projected homogeneous vector into an ordinary 3D position.
• Input pins:
  • ⏺  In (vector) - The source value
• Output pins:
  • ⏺  Out (vector) - XYZ after division by W, with output W set to 0.