Math Functions¶

These reusable DSL functions are provided by the installed nodeforge.math package and are imported from functions.

The functions catalog of the Math library contains reusable functions written in the DSL. Import a function before calling it. See Imports for import syntax and name-resolution rules.

Math Helpers¶

inverse_lerp(a=0.0, b=1.0, x=0.0)¶

Computes the unbounded interpolation factor of x between a and b.

Parameter	Type	Default	Description
a	Float	0.0	Range start.
b	Float	1.0	Range end.
x	Float	0.0	Value to measure inside the range.

Returns: Float.

from functions import inverse_lerp
value_1 = input_float('Value', default=4.0)
t = inverse_lerp(2.0, 6.0, value_1)
output('Factor', t)

remap(x=0.0, in_min=0.0, in_max=1.0, out_min=0.0, out_max=1.0)¶

Maps x from one numeric range to another. The result is not clamped.

Parameter	Type	Default	Description
x	Float	0.0	Input value.
in_min	Float	0.0	Source range lower bound.
in_max	Float	1.0	Source range upper bound.
out_min	Float	0.0	Target range lower bound.
out_max	Float	1.0	Target range upper bound.

Returns: Float.

from functions import remap
count = input_int('Count', default=32)
pts = points(count)
value_1 = index()
z = remap(value_1, in_min=0.0, in_max=count - 1.0, out_min=-1.0, out_max=1.0)
value_2 = index()
vec_3 = vector(value_2 * 0.1, 0, z)
pts = set_position(pts, vec_3)
output('Geometry', pts)

saturate(x=0.0)¶

Clamps x to the 0..1 range.

Parameter	Type	Default	Description
x	Float	0.0	Input value.

Returns: Float.

from functions import saturate
value = input_float('Value', default=1.25)
value_1 = saturate(value)
output('Clamped', value_1)

step(edge=0.0, x=0.0)¶

Returns 1.0 when x >= edge; otherwise returns 0.0.

Parameter	Type	Default	Description
edge	Float	0.0	Threshold.
x	Float	0.0	Value to test.

Returns: Float.

from functions import step
value_1 = position()
value_2 = noise(value_1, scale=3.0)
mask_value = step(0.5, value_2)
output('Mask', mask_value)

smoothstep(edge0=0.0, edge1=1.0, x=0.0)¶

Returns a clamped Hermite interpolation from 0 to 1 between edge0 and edge1.

Parameter	Type	Default	Description
edge0	Float	0.0	Lower transition edge.
edge1	Float	1.0	Upper transition edge.
x	Float	0.0	Input value.

Returns: Float.

from functions import smoothstep
pts = points(64)
value_1 = index()
t = smoothstep(0.0, 63.0, value_1)
value_2 = index()
vec_3 = vector(value_2 * 0.05, 0, t)
pts = set_position(pts, vec_3)
output('Geometry', pts)

smootherstep(edge0=0.0, edge1=1.0, x=0.0)¶

Returns a clamped smoother interpolation from 0 to 1 between edge0 and edge1.

Parameter	Type	Default	Description
edge0	Float	0.0	Lower transition edge.
edge1	Float	1.0	Upper transition edge.
x	Float	0.0	Input value.

Returns: Float.

from functions import smootherstep
x = input_float('X', default=0.35)
value_1 = smootherstep(0.0, 1.0, x)
output('Value', value_1)

pingpong(x=0.0, length=1.0)¶

Wraps x into a repeating triangular wave between 0 and length.

Parameter	Type	Default	Description
x	Float	0.0	Input value.
length	Float	1.0	Peak value of the wave.

Returns: Float.

from functions import pingpong
pts = points(80)
value_1 = index()
z = pingpong(value_1 * 0.1, 1.0)
value_2 = index()
vec_3 = vector(value_2 * 0.05, 0, z)
pts = set_position(pts, vec_3)
output('Geometry', pts)

wrap(x=0.0, min=0.0, max=1.0)¶

Wraps x into the half-open range [min, max) using modulo arithmetic.

Parameter	Type	Default	Description
x	Float	0.0	Input value.
min	Float	0.0	Lower bound.
max	Float	1.0	Upper bound.

Returns: Float.

from functions import wrap
value_1 = input_float('Angle', default=7.0)
angle = wrap(value_1, min=0.0, max=tau)
output('Angle', angle)

sign(x=0.0)¶

Returns -1.0 for negative values, 0.0 for zero, and 1.0 for positive values.

Parameter	Type	Default	Description
x	Float	0.0	Input value.

Returns: Float.

from functions import sign
x = input_float('X', default=-2.0)
value_1 = sign(x)
output('Direction', value_1)

Vector Helpers¶

rotate2d(v=vector(1, 0, 0), angle=0.0)¶

Rotates the XY components of v around the Z axis. The original Z component is preserved.

Parameter	Type	Default	Description
v	Vector	vector(1, 0, 0)	Input vector.
angle	Float	0.0	Rotation angle in radians.

Returns: Vector.

from functions import rotate2d
vec_1 = vector(1, 0, 0)
value_2 = radians(45)
v = rotate2d(vec_1, value_2)
output('Vector', v)

polar(radius=1.0, angle=0.0)¶

Creates an XY vector from polar coordinates. Z is 0.0.

Parameter	Type	Default	Description
radius	Float	1.0	Distance from origin.
angle	Float	0.0	Angle in radians.

Returns: Vector.

from functions import polar
value_1 = radians(30)
pos = polar(radius=2.0, angle=value_1)
output('Vector', pos)

angle_between(a=vector(1, 0, 0), b=vector(0, 1, 0))¶

Computes the angle between two vectors. Inputs are normalized internally and the dot product is clamped to -1..1 before acos(...).

Parameter	Type	Default	Description
a	Vector	vector(1, 0, 0)	First vector.
b	Vector	vector(0, 1, 0)	Second vector.

Returns: Float.

from functions import angle_between
vec_1 = vector(1, 0, 0)
value_2 = position()
vec_3 = normalize(value_2)
angle = angle_between(vec_1, vec_3)
output('Angle', angle)

rotate_around_axis(v=vector(1, 0, 0), axis=vector(0, 0, 1), angle=0.0)¶

Rotates v around axis using Rodrigues' rotation formula. axis is normalized internally.

Parameter	Type	Default	Description
v	Vector	vector(1, 0, 0)	Input vector.
axis	Vector	vector(0, 0, 1)	Rotation axis.
angle	Float	0.0	Rotation angle in radians.

Returns: Vector.

from functions import rotate_around_axis
vec_1 = vector(1, 0, 0)
vec_2 = vector(0, 1, 0)
value_3 = radians(90)
v = rotate_around_axis(vec_1, axis=vec_2, angle=value_3)
output('Vector', v)

Point Creation and Layouts¶

Layout functions operate on point-domain geometry. They use the current point index() field and the explicit count parameter when present; they do not inspect the input geometry's point count.

layout_grid(geometry, count=vector(1, 1, 1), spacing=vector(1, 1, 1), centered=False)¶

Places existing points in a 3D lattice.

Parameter	Type	Default	Description
geometry	Geometry	required	Point geometry to position.
count	Vector	vector(1, 1, 1)	Lattice dimensions interpreted as (count_x, count_y, count_z). Components are clamped to at least 1.0 for index math.
spacing	Vector	vector(1, 1, 1)	Per-axis spacing. Use vector(s, s, s) for uniform spacing.
centered	Bool	False	When true, positions are shifted by half of the layout extent so the lattice is centered around the origin. When false, positions use raw lattice coordinates from the origin.

Returns: Geometry.

from functions import layout_grid
pts = points(12)
vec_1 = vector(4, 3, 1)
vec_2 = vector(0.5, 0.5, 0.0)
pts = layout_grid(pts, count=vec_1, spacing=vec_2, centered=False)
output('Geometry', pts)

grid_points(count=vector(1, 1, 1), spacing=vector(1, 1, 1), centered=False)¶

Creates points and places them with layout_grid(...). The point count is max(count.x, 0) * max(count.y, 0) * max(count.z, 0).

Parameter	Type	Default	Description
count	Vector	vector(1, 1, 1)	Number of generated points per axis. Zero or negative components produce zero generated points for that component.
spacing	Vector	vector(1, 1, 1)	Per-axis spacing.
centered	Bool	False	Passed to layout_grid(...).

Returns: Geometry.

from functions import grid_points
vec_1 = vector(5, 4, 1)
vec_2 = vector(0.5, 0.5, 0.0)
grid = grid_points(count=vec_1, spacing=vec_2, centered=False)
output('Geometry', grid)

layout_circle(geometry, count=16, radius=1.0, start_angle=0.0, end_angle=tau, include_endpoint=False)¶

Places existing points on an XY circle or arc.

Parameter	Type	Default	Description
geometry	Geometry	required	Point geometry to position.
count	Int	16	Explicit count used to compute the normalized index.
radius	Float	1.0	Circle or arc radius.
start_angle	Float	0.0	Start angle in radians.
end_angle	Float	tau	End angle in radians.
include_endpoint	Bool	False	When true, the last point reaches end_angle. For full circles the default avoids duplicating the first point.

Returns: Geometry.

from functions import layout_circle
pts = points(24)
pts = layout_circle(pts, count=24, radius=2.0, start_angle=0.0, end_angle=tau)
output('Geometry', pts)

circle_points(count=16, radius=1.0, start_angle=0.0, end_angle=tau, include_endpoint=False)¶

Creates point geometry and places the points with the same circle/arc formula used by layout_circle(...).

Parameter	Type	Default	Description
count	Int	16	Number of generated points. Negative values are clamped to zero for point generation.
radius	Float	1.0	Circle or arc radius.
start_angle	Float	0.0	Start angle in radians.
end_angle	Float	tau	End angle in radians.
include_endpoint	Bool	False	When true, the last point reaches end_angle.

Returns: Geometry.

from functions import circle_points
arc = circle_points(count=16, radius=2.0, start_angle=0.0, end_angle=pi, include_endpoint=True)
output('Geometry', arc)

layout_spiral(geometry, count=16, radius=1.0, turns=1.0, height=0.0, start_radius=0.0, start_angle=0.0)¶

Places existing points along a radial spiral in the XY plane, with optional Z height.

Parameter	Type	Default	Description
geometry	Geometry	required	Point geometry to position.
count	Int	16	Explicit count used to compute the normalized index.
radius	Float	1.0	Final radius.
turns	Float	1.0	Number of full revolutions.
height	Float	0.0	Final Z height.
start_radius	Float	0.0	Initial radius.
start_angle	Float	0.0	Initial angle in radians.

Returns: Geometry.

from functions import layout_spiral
pts = points(96)
pts = layout_spiral(pts, count=96, radius=3.0, turns=4.0, height=1.5)
output('Geometry', pts)

spiral_points(count=16, radius=1.0, turns=1.0, height=0.0, start_radius=0.0, start_angle=0.0)¶

Creates point geometry and places the points with layout_spiral(...).

Parameter	Type	Default	Description
count	Int	16	Number of generated points. Negative values are clamped to zero for point generation.
radius	Float	1.0	Final radius.
turns	Float	1.0	Number of full revolutions.
height	Float	0.0	Final Z height.
start_radius	Float	0.0	Initial radius.
start_angle	Float	0.0	Initial angle in radians.

Returns: Geometry.

from functions import spiral_points
spiral = spiral_points(count=128, radius=3.0, turns=5.0, height=2.0, start_radius=0.25)
output('Geometry', spiral)

layout_random(geometry, min=vector(-1, -1, -1), max=vector(1, 1, 1), seed=0)¶

Places existing points at random positions between vector bounds. The point index is used as the random ID.

Parameter	Type	Default	Description
geometry	Geometry	required	Point geometry to position.
min	Vector	vector(-1, -1, -1)	Lower random bound.
max	Vector	vector(1, 1, 1)	Upper random bound.
seed	Int	0	Random seed.

Returns: Geometry.

from functions import layout_random
pts = points(50)
vec_1 = vector(-2, -2, 0)
vec_2 = vector(2, 2, 1)
pts = layout_random(pts, min=vec_1, max=vec_2, seed=7)
output('Geometry', pts)

random_points(count=16, min=vector(-1, -1, -1), max=vector(1, 1, 1), seed=0)¶

Creates point geometry and places the points with layout_random(...).

Parameter	Type	Default	Description
count	Int	16	Number of generated points. Negative values are clamped to zero for point generation.
min	Vector	vector(-1, -1, -1)	Lower random bound.
max	Vector	vector(1, 1, 1)	Upper random bound.
seed	Int	0	Random seed.

Returns: Geometry.

from functions import random_points
vec_1 = vector(-3, -3, 0)
vec_2 = vector(3, 3, 2)
pts = random_points(count=100, min=vec_1, max=vec_2, seed=42)
output('Geometry', pts)

Geometry Helper¶

copy_by_offsets(geometry, scale=vector(1/3, 1/3, 1))¶

Duplicates input geometry into the eight cells around the center of a 3x3 grid. This is the offset pattern used for Sierpinski-carpet style subdivision.

Parameter	Type	Default	Description
geometry	Geometry	required	Source geometry.
scale	Vector	vector(1/3, 1/3, 1)	Per-copy scale.

Returns: Geometry.

from functions import copy_by_offsets
geo = cube(size=1.0)
vec_1 = vector(1 / 3, 1 / 3, 1 / 3)
geo = copy_by_offsets(geo, scale=vec_1)
output('Geometry', geo)

Fractal Helper¶

sierpinski_carpet(geometry, steps=2, scale=vector(1/3, 1/3, 1))¶

Repeatedly applies copy_by_offsets to create a Sierpinski-carpet-style arrangement. steps is a runtime Int; non-positive values perform no repeat iterations.

from functions import sierpinski_carpet

source = cube(size=1.0)
geometry = sierpinski_carpet(source, steps=2)
output('Geometry', geometry)

Sequence Helper¶

fibonacci(n=8)¶

Computes the Fibonacci sequence with a runtime Repeat Zone. F(0)=0, F(1)=1, and F(n)=F(n-1)+F(n-2).

Parameter	Type	Default	Description
n	Int	8	Iteration count.

Returns: Int or numeric value compatible with the Repeat Zone state.

from functions import fibonacci
n = input_int('N', default=10)
value = fibonacci(n)
output('Value', value)

For complete scripts included with the package, see Math Examples.