MathUtils.md

Math Utils

Coarse Normal Reconstruction

Description	Node Showcase:
Creates a faceted face normal from any derivable input. (typically the depth buffer.)

Input	Type	Description
Input	Float3	The functional input to compute the face direction for.

Output	Type	Description
Output	Float3	A crude face normal of the Input.

Direction To Signed Cube

Description	Node Showcase:
Calculates the hit position on a -S to +S 3D cube.

Input	Type	Description
Direction	Float3	The direction vector (doesn't need to be normalized.)
Scale	Float3	The scale of the cube.

Output	Type	Description
Direction On Cube	Float3	The reprojected direction, hitting the surface of the cube.
Tangents	Float3	The individual side lengths.
Distance	Float	The distance from the current direction vector to the surface of the cube.

Filtered Cosine

Description	Node Showcase:
Implements the analytical model of the cosine function for band limiting.

Input	Type	Description
Input	Float	The cosine input.

Output	Type	Description
Output	Float	The filtered cosine value.

Get Tangent Delta

Description	Node Showcase:
Calculates the scaling factor for a given projection angle.

Input	Type	Description
Angle (Degrees)	Float	The projection angle in degrees.

Output	Type	Description
FOV Slope	Float	The tangent derivative of the projection angle.

Get UV Analytic Model

Description	Node Showcase:
Calculates the primitive values for a filtered procedural function.

Input	Type	Description
UV	Float2	The texture coordinate.

Output	Type	Description
Domain Size	Float2	The UV space the pixel on your screen takes up.
Sample A	The left hand side sample point.
Sample B	The right hand side sample point.

This follows the integral convention of $$ \int{f(x)dx} = \lim_{w \rightarrow 0}{\frac{F(x+w) - F(x-w)}{w}} $$ Where $x-w$ is Sample A, $x+w$ is Sample B, and $w$ is the Domain Size.

Integral Circle Approximation

Note

Basically, don't worry about this node.

Description	Node Showcase:
Used in Analytical Dot Matrix node, representing a circles filtered procedural function.

Input	Type	Description
UV	Float2	The texture coordinate.
Domain Width	Float2	The UV space the pixel on your screen takes up.

Output	Type	Description
F(x, y)	Float2	The evaluated integral parts.

Is Inside 01 Range

Description	Node Showcase:
Validates the bounds of a UV coordinate are within 0 to 1 range.

Input	Type	Description
Input	Float4	Any dimension of inputs.

Output	Type	Description
Inside [0 | 1]	Float	Returns 1 if all components are inside range, otherwise returns 0.

Smooth Max

Description	Node Showcase:
Implements a smoother maximum function.

Input	Type	Description
A	Float	The first input.
B	Float	The second input.
Smooth Term	Float	the square smoothness value.

Output	Type	Description
Output	Float	smoothmax(A, B)

Smooth Min

Description	Node Showcase:
Implements a smoother minimum function.

Input	Type	Description
A	Float	The first input.
B	Float	The second input.
Smooth Term	Float	the square smoothness value.

Output	Type	Description
Output	Float	smoothmin(A, B)

Smoothstep 10

Description	Node Showcase:
Implements a better form of smoothstep(x, 1, 0)

Input	Type	Description
Input	Float	The input value.

Output	Type	Description
Output	Float	Roughly smoothstep(x, 1, 0)

This function follows as such:

$$ \left( x^2-1 \right)^2 $$

Stairstep (Terracing)

Description	Node Showcase:
Splits the UV coordinate space into steps.

Input	Type	Description
Input	Float2	The texture coordinate.
Steps	Float	The amount of steps to truncate precision by.

Output	Type	Description
Terraced Output	Float2	The stairstepped input.
Continuous Domain	Float2	The scaled UV without stairstepping for mipmap level selection.

Step AA

Description	Node Showcase:
Implements the step function with anti aliasing.

Input	Type	Description
Lesser (A)	Float4	The less-than component input.
Greater (B)	Float4	The greater-than component input.

Output	Type	Description
B >= A?	Float4	The step evaluation with anti-aliasing.

UV ddxy

Description	Node Showcase:
All the ddx ddy values you could possibly want.

Input	Type	Description
UV	Float2	The texture coordinate.

Output	Type	Description
dx dy	Float2	ddx(u), ddy(v)
dx dy (abs)	Float2	abs(ddx(u)), abs(ddy(v))
max( dx dy )	Float	max( abs(ddx(u)), abs(ddy(v)) )
ddxy	Float4	xy: ddx(uv), zw: ddy(uv)
ddxy (abs)	Float4	xy: abs(ddx(uv)), zw: abs(ddy(uv))
max( ddx ddy )	Float2	max( abs(ddx(uv)), abs(ddy(uv)) )