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Math

Arithmetic, trigonometry, vector operations and comparisons evaluated per sample across the field.

Studio and Graph › Voxel › Math

Abs

Strips the sign, and it does two quite different jobs depending on what you feed it.

When to use it

Strips the sign, and it does two quite different jobs depending on what you feed it.

On a coordinate you get free mirror symmetry. Abs of X makes everything symmetric about the YZ plane.

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Add

On a density field, adding a constant moves the whole surface in or out. That is how a noise field becomes solid ground: add enough and the surface swallows everything below it.

When to use it

A plus B.

On a density field, adding a constant moves the whole surface in or out. That is how a noise field becomes solid ground: add enough and the surface swallows everything below it.

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Atan2

The angle of a 2D vector in radians, over the whole circle rather than half of it.

When to use it

The angle of a 2D vector in radians, over the whole circle rather than half of it.

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Branch

Compares A and B with the operator you pick and forwards True or False accordingly. The comparison and the choice in one node.

When to use it

Compares A and B with the operator you pick and forwards True or False accordingly. The comparison and the choice in one node.

Equal and NotEqual read the Tolerance pin, which defaults to 0.00001. That default is doing real work. Two values that came out of any arithmetic almost never land on the same float, so an Equal branch with Tolerance set to 0 takes the false arm over and over and reads as a broken wire.

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Ceil

Rounds up to the nearest whole number. Floor's counterpart.

When to use it

Rounds up to the nearest whole number. Floor's counterpart.

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Compare

Compares A against B and hands back 1 or 0. A mask you multiply with, not a branch.

When to use it

Compares A against B and hands back 1 or 0. A mask you multiply with, not a branch.

When the answer is going to be multiplied anyway, this beats Branch and If. The graph stays flat and you avoid the hard edge a branch puts into the field.

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Studio and Graph › Voxel › Math

Cos

Cosine of the input, in radians.

When to use it

Cosine of the input, in radians.

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Curve

Looks the input up on a Curve asset. The escape hatch for a response that would take five maths nodes to approximate and still not look right.

When to use it

Looks the input up on a Curve asset. The escape hatch for a response that would take five maths nodes to approximate and still not look right.

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Studio and Graph › Voxel › Math

Distance To Line

Perpendicular distance to an infinite line.

When to use it

Perpendicular distance to an infinite line.

Subtract a radius and you have an infinite cylinder along any axis, which is the cheapest way to get a tilted cylinder without rotating the domain.

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Studio and Graph › Voxel › Math

Distance To Plane

Signed distance to an infinite plane. Positive on the side the normal points, negative on the other.

When to use it

Signed distance to an infinite plane. Positive on the side the normal points, negative on the other.

The sign is the whole point. It makes an above-or-below test and a half-space cutter the same node.

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Distance To Point

Straight-line distance from the sample point to a target point.

When to use it

Straight-line distance from the sample point to a target point.

Subtract a radius and you have a sphere. Leave it raw and you have a radial falloff to drive something with.

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Divide

A over B. Dividing by zero, or near enough to zero, gives you 0 rather than an infinity, because an infinity reaching the mesher takes the whole chunk with it.

When to use it

A over B. Dividing by zero, or near enough to zero, gives you 0 rather than an infinity, because an infinity reaching the mesher takes the whole chunk with it.

That guard has a side effect worth knowing. A suspiciously flat patch of zero in your result might be a division that tripped the guard rather than a shape. Drop a Visualize node on the wire and read the number.

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Studio and Graph › Voxel › Math

Exp

e raised to the input, with the exponent clamped to plus or minus 80 so it cannot run away to infinity.

When to use it

e raised to the input, with the exponent clamped to plus or minus 80 so it cannot run away to infinity.

It still grows absurdly fast. exp(20) is half a billion. This is a falloff tool, not a scaling tool: exp of a negative squared distance is the Gaussian bump you usually wanted.

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Studio and Graph › Voxel › Math

Float To Int

Converts a float to an integer by flooring it, which means it truncates toward negative infinity rather than toward zero. 1.7 becomes 1. -0.3 becomes -1, not 0.

When to use it

Converts a float to an integer by flooring it, which means it truncates toward negative infinity rather than toward zero. 1.7 becomes 1. -0.3 becomes -1, not 0.

That asymmetry only bites when the value can go negative, and then it bites hard: everything below zero shifts a whole step. Add 0.5 first if you wanted nearest.

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Floor

Rounds down to the nearest whole number.

When to use it

Rounds down to the nearest whole number.

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Frac

The fractional part, meaning the input minus its floor. Always lands between 0 and 1.

When to use it

The fractional part, meaning the input minus its floor. Always lands between 0 and 1.

Compact way to build repeating ramps and tiling patterns out of a coordinate.

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If

Picks one of two inputs from a Condition, treating anything at or above 0.5 as true.

When to use it

Picks one of two inputs from a Condition, treating anything at or above 0.5 as true.

It fits when the condition is already a mask, from a Compare or a thresholded noise. Branch does the comparison and the choice in one node. Select does the same thing with a soft blend.

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Studio and Graph › Voxel › Math

Int To Float

Converts an integer to a float.

When to use it

Converts an integer to a float.

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Inverse Lerp

0 at Range Min, 1 at Range Max, linear between, and clamped to 0 to 1 at both ends.

When to use it

0 at Range Min, 1 at Range Max, linear between, and clamped to 0 to 1 at both ends.

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Lerp

Blends A and B by Alpha. 0 gives A, 1 gives B, and Alpha is clamped so you cannot extrapolate past either end.

When to use it

Blends A and B by Alpha. 0 gives A, 1 gives B, and Alpha is clamped so you cannot extrapolate past either end.

Fine for mixing two parameters or two masks. Select is the one you want when a threshold on a third value drives the blend.

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Studio and Graph › Voxel › Math

Log

Natural logarithm. Zero or negative input returns 0 rather than an infinity.

When to use it

Natural logarithm. Zero or negative input returns 0 rather than an infinity.

Good for squashing a range that spans orders of magnitude down to something you can look at.

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Studio and Graph › Voxel › Math

Max

The larger of A and B, which is the same operation Intersection performs, since positive means outside.

When to use it

The larger of A and B, which is the same operation Intersection performs, since positive means outside.

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Studio and Graph › Voxel › Math

Min

The smaller of A and B.

When to use it

The smaller of A and B.

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Modulo

The remainder of A divided by B. Stripes, rings and repeating bands built out of a coordinate. A divisor at or near zero returns 0 rather than an error.

When to use it

The remainder of A divided by B. Stripes, rings and repeating bands built out of a coordinate. A divisor at or near zero returns 0 rather than an error.

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Studio and Graph › Voxel › Math

Multiply

A times B. The workhorse.

When to use it

A times B. The workhorse.

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Negate

Flips the sign. On a density field that swaps solid and empty, so the inside becomes the outside. Quickest way to turn a shape into the hole it would leave.

When to use it

Flips the sign. On a density field that swaps solid and empty, so the inside becomes the outside. Quickest way to turn a shape into the hole it would leave.

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Studio and Graph › Voxel › Math

One Minus

1 minus the input. The standard way to flip a 0 to 1 mask, and easier to read on the canvas than a Subtract wired to a constant.

When to use it

1 minus the input. The standard way to flip a 0 to 1 mask, and easier to read on the canvas than a Subtract wired to a constant.

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Studio and Graph › Voxel › Math

Power

A raised to the power B, using the absolute value of A so a negative base cannot produce something undefined.

When to use it

A raised to the power B, using the absolute value of A so a negative base cannot produce something undefined.

That guard matters more than it sounds, because a density field is negative half the time. Raise a signed field to a power and the sign quietly disappears, taking the inside of your shape with it. Shape masks with this. Leave signed fields alone.

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Remap

Rescales a value from one range to another, linearly.

When to use it

Rescales a value from one range to another, linearly.

Most noise comes out around -1 to 1 and most things that consume it expect 0 to 1. Forgetting that is the single most common reason a pattern looks half missing: the negative half is being read as zero.

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Round

Rounds to the nearest whole number.

When to use it

Rounds to the nearest whole number.

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Studio and Graph › Voxel › Math

Sign

+1 for positive, -1 for negative, 0 for exactly zero.

When to use it

+1 for positive, -1 for negative, 0 for exactly zero.

On a density field that turns a smooth distance into a hard inside-or-outside flag. Occasionally that is what a mask wants. It is always bad input for the mesher, which needs a slope to find the crossing point in. Give it a sign and the surface snaps to voxel corners.

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Sin

Sine of the input, in radians. One full cycle is 2 pi, so a value in degrees oscillates about 57 times faster than you expected and reads as noise.

When to use it

Sine of the input, in radians. One full cycle is 2 * pi, so a value in degrees oscillates about 57 times faster than you expected and reads as noise.

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Studio and Graph › Voxel › Math

Smooth Step

An S-curve ramp. 0 below Edge0, 1 above Edge1, smooth in between.

When to use it

An S-curve ramp. 0 below Edge0, 1 above Edge1, smooth in between.

The standard way to turn any value into a soft mask, and better than Compare for anything that ends up visible, because the slope is continuous at both ends instead of jumping.

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Sqrt

Square root, taking the absolute value first so a negative input cannot produce nonsense.

When to use it

Square root, taking the absolute value first so a negative input cannot produce nonsense.

Which also means feeding it a signed density silently throws the sign away. Square-root a squared length, not a field.

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Subtract

A minus B. Arithmetic, not a boolean cut.

When to use it

A minus B. Arithmetic, not a boolean cut.

To carve one shape out of another, use the Subtraction node. It computes max(A, -B) and leaves you something that is still a distance field. Plain subtraction does not.

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Terrace

Quantises a smooth value into flat plateaus. Rice-paddy terracing on a height field. Step Size is the height of one plateau, in whatever units the input is in.

When to use it

Quantises a smooth value into flat plateaus. Rice-paddy terracing on a height field. Step Size is the height of one plateau, in whatever units the input is in.

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Studio and Graph › Voxel › Math

Vec2 Add

Component-wise A plus B on two 2D vectors.

When to use it

Component-wise A plus B on two 2D vectors.

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Vec2 Cross

The 2D perp-dot product, A.X B.Y - A.Y B.X. It comes out as a single number, not a vector.

When to use it

The 2D perp-dot product, A.X * B.Y - A.Y * B.X. It comes out as a single number, not a vector.

Positive if B is counter-clockwise from A, negative if clockwise. That makes it the 2D handedness test and the sign of the angle between two directions.

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Vec2 Dot

Dot product of two 2D vectors. Positive when they point the same way, zero when perpendicular, negative when opposed.

When to use it

Dot product of two 2D vectors. Positive when they point the same way, zero when perpendicular, negative when opposed.

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Vec2 Length

Magnitude of a 2D vector.

When to use it

Magnitude of a 2D vector.

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Vec2 Normalize

Unit-length version of a 2D vector. A zero-length input safely returns (0, 0) rather than an error.

When to use it

Unit-length version of a 2D vector. A zero-length input safely returns (0, 0) rather than an error.

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Vec2 Scale

Multiplies a 2D vector by a scalar. Uniform scale only.

When to use it

Multiplies a 2D vector by a scalar. Uniform scale only.

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Vec2 Subtract

Component-wise A minus B on two 2D vectors.

When to use it

Component-wise A minus B on two 2D vectors.

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Vec3 Add

Component-wise A plus B on two 3D vectors. The usual way to offset a position before feeding it to a pattern.

When to use it

Component-wise A plus B on two 3D vectors. The usual way to offset a position before feeding it to a pattern.

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Vec3 Cross

Cross product. The vector perpendicular to both inputs.

When to use it

Cross product. The vector perpendicular to both inputs.

Use it to build a frame, like a tangent from a normal and an up vector.

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Vec3 Dot

Dot product of two 3D vectors. +1 parallel, 0 perpendicular, -1 opposite, but only when both inputs are unit length.

When to use it

Dot product of two 3D vectors. +1 parallel, 0 perpendicular, -1 opposite, but only when both inputs are unit length.

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Vec3 Length

Magnitude of a 3D vector.

When to use it

Magnitude of a 3D vector.

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Vec3 Normalize

Unit-length version of a 3D vector. Zero length safely returns (0, 0, 0).

When to use it

Unit-length version of a 3D vector. Zero length safely returns (0, 0, 0).

Do this before any dot product you intend to read as an angle.

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Vec3 Scale

Multiplies a 3D vector by a scalar. Uniform scale.

When to use it

Multiplies a 3D vector by a scalar. Uniform scale.

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Vec3 Subtract

Component-wise A minus B on two 3D vectors, usually to get the offset from a centre to the sample point.

When to use it

Component-wise A minus B on two 3D vectors, usually to get the offset from a centre to the sample point.

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Vec4 Add

Component-wise A plus B on two 4D vectors.

When to use it

Component-wise A plus B on two 4D vectors.

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Vec4 Dot

Dot product of two 4D vectors.

When to use it

Dot product of two 4D vectors.

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Vec4 Length

Magnitude of a 4D vector.

When to use it

Magnitude of a 4D vector.

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Vec4 Normalize

Unit-length version of a 4D vector. Zero length safely returns zero.

When to use it

Unit-length version of a 4D vector. Zero length safely returns zero.

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Vec4 Scale

Multiplies a 4D vector by a scalar.

When to use it

Multiplies a 4D vector by a scalar.

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Vec4 Subtract

Component-wise A minus B on two 4D vectors.

When to use it

Component-wise A minus B on two 4D vectors.

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