Math

Every example on this page runs after these two lines, and ends by sending a color to the Output node:

from pyzed import shading

g = shading.Graph("demo")

Math

Every math node works on numbers and vectors: with a vec3 it works on each component (red, green and blue at once). Their inputs and outputs have the generic type T.

Math

math · Math · g.math(...)

An arithmetic operation on two values (of any type: vectors work per component).

Two values in, one out. In Python you rarely add it by hand: a + b, a * 2 or a ** 2 on ports add Math nodes for you. Each operation is its own entry in the sidebar (Add, Multiply, Step…).

Input	Type	Default
a	T	0
b	T	1

Output	Type
result	T

Setting	Values	Default
op	add, subtract, multiply, divide, modulo, power, min, max, step, atan2, snap	add

Sidebar entries

Entry	What it does	In Python
Add	a + b	g.add(...)
Subtract	a − b	g.subtract(...)
Multiply	a × b	g.multiply(...)
Divide	a ÷ b	g.divide(...)
Modulo	The remainder of a ÷ b (always the sign of b).	g.modulo(...)
Power	a to the power of b.	g.power(...)
Min	The smaller of a and b.	g.min(...)
Max	The larger of a and b.	g.max(...)
Step	0 where b is below the edge a, 1 from there on.	g.step(...)
Atan2	The angle of the point (b, a) in radians: a is y, b is x.	g.atan2(...)
Snap	a rounded to the nearest multiple of b.	g.snap(...)

Example

uv = g.uv()
stripes = g.step(0.5, g.fract(uv["x"] * 8.0))
g.output(g.rgba(stripes * 0.8 + 0.1, 1.0))

Function

func · Math · g.func(...)

A function of one value (vectors work per component).

One value in, one out: rounding, roots, powers, trigonometry and more. Each function is its own entry in the sidebar (Sin, Fract, Abs…) and a method in Python (g.sin(x), g.fract(x)).

Input	Type	Default
x	T	0

Output	Type
result	T

Setting	Values	Default
op	abs, negate, sign, floor, ceil, round, fract, trunc, sqrt, inverse_sqrt, square, exp, exp2, log, log2, sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, one_minus, reciprocal, saturate, degrees, radians	sin

Sidebar entries

Entry	What it does	In Python
Abs	x without its sign.	g.abs(...)
Negate	−x	g.negate(...)
Sign	−1, 0 or 1: the sign of x.	g.sign(...)
Floor	x rounded down.	g.floor(...)
Ceil	x rounded up.	g.ceil(...)
Round	x rounded to the nearest whole number.	g.round(...)
Fract	What is after the point: x − floor(x). Repeats every 1.	g.fract(...)
Trunc	x without what is after the point.	g.trunc(...)
Sqrt	The square root of x.	g.sqrt(...)
Inverse sqrt	1 / √x	g.inverse_sqrt(...)
Square	x × x	g.square(...)
Exp	e to the power of x.	g.exp(...)
Exp2	2 to the power of x.	g.exp2(...)
Log	The natural logarithm of x.	g.log(...)
Log2	The base 2 logarithm of x.	g.log2(...)
Sin	The sine of x (radians).	g.sin(...)
Cos	The cosine of x (radians).	g.cos(...)
Tan	The tangent of x (radians).	g.tan(...)
Asin	The arc sine of x, in radians.	g.asin(...)
Acos	The arc cosine of x, in radians.	g.acos(...)
Atan	The arc tangent of x, in radians.	g.atan(...)
Sinh	The hyperbolic sine of x.	g.sinh(...)
Cosh	The hyperbolic cosine of x.	g.cosh(...)
Tanh	The hyperbolic tangent of x: an S curve from −1 to 1.	g.tanh(...)
One minus	1 − x: turns 0..1 around.	g.one_minus(...)
Reciprocal	1 / x	g.reciprocal(...)
Saturate	x kept between 0 and 1.	g.saturate(...)
Degrees	Radians to degrees.	g.degrees(...)
Radians	Degrees to radians.	g.radians(...)

Example

t = g.time()["time"]
wave = g.abs(g.sin(g.uv()["x"] * 10.0 + t))
g.output(g.rgba(wave, 1.0))

Mix

mix · Math · g.mix(...)

Blends from a (t = 0) to b (t = 1): a lerp.

Blends two values: t = 0 gives a, 1 gives b, 0.5 half of each. The node you will use most to combine colors.

Input	Type	Default
a	T	0
b	T	1
t	T	0.5

Output	Type
result	T

Example

uv = g.uv()
sky = g.mix([0.1, 0.2, 0.5], [0.9, 0.6, 0.3], uv["y"])
g.output(g.rgba(sky, 1.0))

Clamp

clamp · Math · g.clamp(...)

x kept between min and max.

Keeps a value inside a range, so a bright spot never goes over 1 or a dark one under 0.

Input	Type	Default
x	T	0
min	T	0
max	T	1

Output	Type
result	T

Example

v = g.uv()["x"] * 2.0 - 0.5
g.output(g.rgba(g.clamp(v, 0.0, 1.0), 1.0))

Smoothstep

smoothstep · Math · g.smoothstep(...)

0 below edge0, 1 above edge1 and a smooth curve between them.

A soft threshold: 0 below edge0, 1 above edge1, and a smooth curve between. Use it to turn a distance or a noise into a soft-edged mask.

Input	Type	Default
edge0	T	0
edge1	T	1
x	T	0.5

Output	Type
result	T

Example

n = g.noise(scale=6.0)
mask = g.smoothstep(0.45, 0.55, n)
g.output(g.rgba(mask, 1.0))

Remap

remap · Math · g.remap(...)

x moved from the range in_min..in_max to out_min..out_max.

Moves a value from one range to another: −1..1 (a sine) to 0..1 (a color), or 0..1 to 0.2..0.8.

Input	Type	Default
x	T	0.5
in_min · in min	T	0
in_max · in max	T	1
out_min · out min	T	-1
out_max · out max	T	1

Output	Type
result	T

Example

s = g.time()["sin"]
v = g.remap(s, -1.0, 1.0, 0.2, 0.8)
g.output(g.rgba(v, 1.0))

Multiply add

multiply_add · Math · g.multiply_add(...)

a × b + c

a × b + c in one node: scale and shift a value, such as sin × 0.5 + 0.5 to bring −1..1 into 0..1.

Input	Type	Default
a	T	1
b	T	1
c	T	0

Output	Type
result	T

Example

s = g.time()["sin"]
g.output(g.rgba(g.multiply_add(s, 0.5, 0.5), 1.0))

Always up to date

This page is generated from the node catalog of pyzed.shading, so the ports, types and defaults are always those of this version. Each example is compiled when the docs are built.

See also: Getting started · The Shader view · Recipes · Shader graphs in Python