Module: Parametric Surface ()

Description:

This module can be used to define and animate arbitrary parametric surfaces in two, three dimensions. There are some pre-defined surfaces like the Moebius strip, Klein bottle and Random mapping to illustrate the use of the text fields that define expressions for X, Y, and Z.

The expressions may depend on u and v which are Cartesian coordinates of the plane.

They can also depend on theta and r which are their counterparts in polar coordinates:

A separate spherical coordinate system is accessible by the variables lambda and phi:

The variable t is linked to the time port and can be used to perform for example linear interpolations between two mappings like:

Press the Apply button if you want to do an animation because you will need to re-compute the mesh every time t changes.

Surfaces can be exported by the Draw Style port ( more options Create surface).

Connections:

Data [optional]
If a regular scalar field is supplied, the generated mesh will be scaled and shifted according to its bounding box. Using the transform editor of the data is a convenient way of scaling and shifting the generated mesh.

Colormap [optional]
The colormap is used to calculate the color of the mesh based on the expression in the Colorport (initially r, the radial distance of the u-v mesh point from its mean position).

Time [optional]
An additional variable which can be used in all the expression fields. It can be used to generate animations.

Point Cloud [optional]
If you connect to this module a Point Cloud object (points in space), the module will generate a second Point Cloud object and apply the transformation in the expression fields to its x and y coordinates. This may be useful to visualize the u/v plane as a point cloud.

Ports:

Pre-Defined Surfaces

The pre-defined surfaces are some commonly used to illustrate analytically defined meshes. They are mainly here to illustrate the use of the different variables.
As a last entry you will find a Random generator which will generate random entries for the x, y and z ports, i.e., a random mapping. Currently there is a maximum depth of for the randomly generated expressions.
Notice that once you have started typing your own expressions of X, Y... it prevails on the port content. But if you select a new pre-defined surface, all expressions will be reset to the ones corresponding to the selected surface.

Surface Parameters

Time

This slider is directly linked to the expression t which can be used in all x, y, z and Color ports.

U

This port describes the u resolution of the initial mesh (before the transformation was applied). Its values code the minimum value of u (step size) and the maximum value of u. Lowering the step-size will directly increase the resolution of the mesh.

V

This port works the same way as the port for the v parameter of the initial mesh.

X

Enter an expression to be evaluated in order to describe the x-position of a mesh in 3D space. Use the port to see some useful settings for this port.

Y

Enter an expression to be evaluated in order to describe the y-position of a mesh in 3D space. Use the port to see some useful settings for this port.

Z

Enter an expression to be evaluated in order to describe the z-position of a mesh in 3D space. Use the port to see some useful settings for this port.

Color

Enter an expression to be evaluated in order to describe the vertex color of the mesh. All variables of the other fields can be used in this field. By default, it contains r which is the radial distance from the center position of the mesh. This port is hidden if the colormap is constant.

Display Options

Draw Style

Select a specific draw style for the mesh currently on display. For higher resolution meshes usually shaded works best.
Please refer to the View Base documentation.

Colormap

This colormap will be used to map colors per vertex using by the values in the Color port.