Creates a mesh in a shape defined by parametric math expressions.

This node creates a mesh whose vertex positions and texture mapping are defined by a set of math expressions. The expressions can use the variables *u* and *v*. This node calculates each expression for evenly spaced values of *u* and *v* ranging from 0 to 1. Each calculation becomes a vertex in the resulting mesh.

`Time`

— The time at which to calculate the expressions. (This only affects the output if the`time`

variable (with a lower-case “t”) is used in the expressions.)`X Expression`

,`Y Expression`

,`Z Expression`

— The math expressions for the (X,Y,Z) position of each vertex. Typically, the values of`X Expression`

should increase as*u*increases, and the values of`Y Expression`

should increase as*v*increases. (Otherwise, the triangles that make up the mesh may be facing backwards, which means they won’t be drawn.)`U Expression`

,`V Expression`

— The math expressions for the texture coordinate of each vertex. This defines how an image or other texture will be stretched across the mesh when the mesh is combined with a shader to create a 3D scene object. Typically, the values of these expressions should fall between 0 and 1, and should either always increase or always decrease, as*u*and*v*range from 0 to 1.`Rows`

,`Columns`

— Each of the above expressions is calculated for`Rows`

number of values of*u*and`Columns`

number of values of*v*. The total number of vertices in the mesh is`rows X columns`

.`U Closed`

,`V Closed`

— If*true*, then the mesh surface will wrap around from the vertices calculated for*u=1*or*v=1*to the vertices calculated for*u=0*or*v=0*. If*false*, then either the mesh surface won’t wrap around or, if the math expressions do cause it to wrap around, any 3D scene object created from the mesh may have a visible seam.

The math expressions can use numbers, operators such as *+* and *-*, functions such as *sin(u)* and *log(u)*, and the constant *PI*. For a complete list of the operators and functions available, see the `Calculate`

(`vuo.math.calculate`

) node’s description.

For help understanding the math used by this node, see Introduction to parametric equations and Introduction to parametrizing a surface with two parameters.

**Keywords**: *expression*, *grid*, *math*, *plane*, *shape*, *surface*

- Spin Shell: Animates a 3D seashell-shaped object.

Back to vuo.mesh node set documentation.