# Maya math node summary

# Maya math nodes

A small list of useful Maya nodes, I only list some of the most useful math nodes here. You can find a list of Maya nodes in the technical documentation as well as other utility nodes here. Some nodes are not documented, you will have to go to the node editor press 'tab' and search for yourself... Some of those undocumented nodes are listed here.

## Expressions

If you don't find the native Maya node you are looking for, Maya animation expressions might do the job. Expression nodes are notoriously slow but allows for quick prototyping, also keep in mind that it is named based and any object renaming will potentially break your expressions.

A list of available functions inside an expression:

- math functions: trunc(), ceil(), floor() clamp(min, max, value), sin(), cos(), tan(), min(), max(), sqrt(), exp(), log(), sign() (and other trig functions ...)

- Random functions: gauss(), noise(), dnoise(), rand(), sphrand(), seed()

- Vector functions: angle(), cross(), dot(), mag(), rot(), unit()

- Conversion functions: deg_to_rad(), rad_to_deg(), hsv_to_rgb(), rgb_to_hsb()

- Array functions: clear(), size(), sort()

- Curve functions: linstep(), smoothstep(), hermite()(vector), hermite()(scalar)

## Bifrost

Bifrost is a powerful node system usually known for its ability to simulate fluids, smokes and such,
but that can be used to work on geometry as well, and provides all the basic and more advanced math nodes and help you with rigging.
(See also Autodesk Japan bifrost tutorials on skin collision)

## Native nodes

**plusMinusAverage** math node specification. Originally designed with shaders in mind those operations work on vectors, i.e. addition, division etc is usually applied on a per component basis (out.x = in1.x + in2.x), (out.y = in1.y + in2.y) etc. only supports **floats**

Related see: "addDoubleLinear", "substract" or "average" nodes for **double** attributes (works only on scalars though).

Note: when disconnecting make sure to reset the value of the attribute, otherwise it will keep adding, subtracting etc. whatever was the value at disconnection. |

**multiplyDivide** math node specification.
(for **float** attributes)

**doubles**see "divide" node or multDoubleLinear) (only scalars though)

NO OPERATION: |

**condition** math node specification. Compare 'firstTerm' and 'secondTerm' with some boolean operator (<,>,== etc.)
OutColor is assigned ColorIfTrue or ColorIfFalse according to the result of the operation.

if( firstTerm operation secondTerm ){ OutColor.r = ColorIfTrue.r OutColor.g = ColorIfTrue.g OutColor.b = ColorIfTrue.b } else { OutColor.r = ColorIfFalse.r OutColor.g = ColorIfFalse.g OutColor.b = ColorIfFalse.b } |

**BlendColors** math node specification. Linear interpolation between Color1 and Color2 given the parameter \( blender \in [0.0, 1.0]\).

Output = Color1.rgb * (1.0 - blender) + Color2.rgb * blender |

**Reverse** math node specification. Reverse a parametric parameter: `Output = 1.0 - Input`

.

Output.x = 1.0 - Input.x Output.y = 1.0 - Input.y Output.z = 1.0 - Input.z |

Note: 'animCurve' node is similar but always prefer 'remapValue' which is really fast to evaluate contrary to the 'animCurve' node.

OutputValue = Curve( InputValue ) Where the function "float Curve(float)" is the curve displayed in the attribute editor and which control points are stored in the "Value[]" attribute; OutputColor.RGB = Gradient( InputValue ) Where the function "Vec3 Gradient(float)" is the gradient strip displayed in the attribute editor and which interpolated colors are stored in the "Color[]" attribute |

Not covered here:

- pointMatrixMult (matrix multiplication against vector or point) (**double**)

- See also (starting Maya 2024) (also **double**):

multiplyPointByMatrix, multiplyVectorByMatrix

- vectorProduct (dot product, cross product, vector or point matrix product) (**floats**)

- For **doubles** (starting Maya 2024):

crossProduct, dotProduct, vectorMatrix, pointMatrix

- clamp (clamp(vec3, minVec3, maxVec3))

- "min", "max" (out = minimum or maximum of a list of **doubles**) (undocumented)

- multDoubleLinear (scalar multiplication: out = realValue1 * realValue2) (**double**)

- addDoubleLinear (scalar addition: out = realValue1 + realValue2) (**double**)

- pointConstraint
can be used to compute the barycenter of several points (outPoint3 = ∑ point_i / n)

## Trigonometry

Although not natively present you can emulate trigonometry functions (sin, cos etc)

## Matrices

Official list of built in matrix nodes

Multiplication order, from right to left as we increase the index:

Indices: n ... 1 0 Matrix : mat_n * ... * mat_1 * mat_0

Other nodes not covered here (see matrix utility doc): addMatrix, aimMatrix, blendMatrix, composeMatrix, fourByFourMatrix, holdMatrix, passMatrix, pickMatrix, uvPin, proximityPin

\( MatrixSum = \prod_{i=n}^{0} MatrixIn[i] \)
MatrixSum = MatrixIn[n] * ... * MatrixIn[1] * MatrixIn[0] |

\( MatrixSum = \sum_{i=n}^{0} WtMatrix[i].MatrixIn * WtMatrix[i].WeightIn \)
MatrixSum = WtMatrix[n].MatrixIn * WtMatrix[n].WeightIn * ... * WtMatrix[0].MatrixIn * WtMatrix[0].WeightIn * WtMatrix[0].MatrixIn * WtMatrix[0].WeightIn |

**float**matrices and outputs its rotation, translation, scale, shear components.

(From Maya 2024) For

**doubles**see also: axisFromMatrix, translationFromMatrix, rotationFromMatrix, columnFromMatrix, rowFromMatrix.

Extra nodes in 'matrixNodes.mll' plugin:

- inverseMatrix node

- transposeMatrix node

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