## Make Parametric Grid Mesh (vuo.mesh.make.parametric) 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

### Example compositions:

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

Back to vuo.mesh node set documentation.