A Fractal Landscape Generator DX Program

Because of the complexity of this program we will divide up the "source code" into visual sections. The secionts will be delimited by transmitters and receivers so that no wires run into or out of the section being discussed.

In the sections below, the numbered lists refer to numbers inserted onto the images of the program. The link in each major bullet is the image of the program for that section.

Sections:

• Generating the land surface height data.
  1. The ScalarList module sets nine height values (3x3 grid) for the desired surface. The list sets the overall features, (e.g. high in the center, low in the front) but the details are generated by the code below. The Construct builds A 3x3 field which will be refined to a denser grid. The dialog box for the Construct shows that the initial, coarse field is defined on a unit square. The Refine module triples the number of height data points and interpolates the height at the new points.
  2. The Compute module moves all of the heights in the new, denser array by a random number multiplied by a roughness factor. The random number generator is an undocumented feature of DX and should be used with caution. It generates a uniformly distributed number between 0 and 1 which is unique for a given seed. In this program the seed is the sum of an interactor and the position of the point (produced by the Mark module).
  3. The field of heights is refined again, then the heights are again modified in a Compute module, by a random offset. The average offset is smaller than in the previous step, reflecting the idea that smaller freatures should have smaller height amplitudes.
  4. The field of heights is refined a last time, then the heights are again modified in a Compute module, by a smaller random offset.
  5. The mean height of the data field is computed by the Statistics module and subtracted from the field to normalize the average height to zero.

• Generating the cloud density data and making the steamlines of cloud density gradient.
  1. The Construct builds a 3x3x3 field in the unit cube and fills it with zeros. The Mark moves the "positions" component to "data" so the Compute module can use it. The Compute module sets the initial density of the center of the field to a value set by a Scalar interactor.
  2. The field is interpolated by the Refine module then the densities are varied by the following compute. The data is then refined and modified randomly one more time to produce the final density data. The density will be used in another section to build a cloud, but is also used here to demonstrate how to build streamlines in a vectorfield.
  3. A vectorfield is produced by taking the gradient of the field and negating it with the Compute module.
  4. The Vector interactor determines the base location used to start the streamlines. The Construct provides a grid of 3x3x3 points used to start 27 actual streamlines.
  5. The Streamline module makes lines which are tangent to the vectorfield, the Color module colors them red, and the Scale module applies a [1.0, 1.0, 0.3] scale to the lines to match the scaling which is performed on the cloud.

• Building the ocean.
  1. The Compute sets the height of the water, based on the value of the water_level interactor. The expression in the Compute module is [0,0,a] . The Construct then builds a field consisting of a single cube of dimension 1x1x0.33.
  2. The cube is then colored blue and converted to a surface by the ShowBoundary module. The Remove module eliminates a "normals" component which is automatically added to the field by the ShowBoundary module. Removing the normals makes flat shaded, featureless water.

• Converting height data to a surface. and adding contour lines.
  1. The RubberSheet module takes a 2D scalar field and converts it to a 3D surface with height prooprtional to the scalar value. The scale parameter input is set to unity.
  2. The Isosurface module extracts coutour lines from the height data. The third input tab sets the number of contours to 15. The color is set to black.
  3. The ColorMap assigns a color range based on the data value so that the mountains are white and lower elevations are green. The Normals module adds a "normals" component to the field so that the Image module can properly compute lighting intensities.

• Converting density data to a cloud.
  1. The first Compute sets a vector to either [1,1,1] or [0,0,0] depending on the density of the 3D scalar field relative to a threshold. This vector will be used to color the cloud. The next Compute produces a scalar value from the vector to use as an opacity.
  2. The Rename module converts the "data" component to "colors", effectively making the vector value the color. The Replace module combines the new scalar opacity with the color data.
  3. The Isosurface module produces a polygonal fit to the points in the 3D scalar field corresponding to the value of the cloud_thresh input.
  4. The Switch module selects either the volume-rendered or isosurface-rendered version of the cloud, which it then scaled by the factor [1,1,0.3].

• Generating rivers from gradient of the surface.
  1. A list of starting points for the rivers is derived either from the VectorList interactor or from the Construct which produces a 9x9 grid of starting points.
  2. The Gradient and Compute modules produce the negative gradient of the height data.
  3. The streamline advects a line through the 2D vector field.
  4. The Map module interpolates the original 2D height data onto the vertices of the lines produced by the Streamline module so that the RubberSheet module can loft the streamlines to the altitude of the surface created earlier. The Tube module extrudes cylinders of .005 diameter around the lines and the Remove module removes the normals automatically added by the Tube module so that the rivers look flat.
  5. The Color and Tube modules make another copy of the streamlines for display, overlayed on the vector field.
  6. The Reduce and Autoglyph modules creat arrows corresponding to the vector field strength.
  7. The Route module selects whether the vector glyphs should be rendered and the ManageImageWindow module causes the Image window to appear if needed.

• Making trees on the surface.
  1. A Reduce module controls the density of the trees to be drawn. The reduce factor was set to 2. The first Compute module adds a small random dither to the altitude to further randomise which trees will be placed on the surface (after the selection by altitude below).
  2. The Include module causes all height data outside a certain range specified by the interactors to be deleted from the field. the next Compute with expression [0,0,random(a)] randomizes the tree height and turns the data into vectors so that the Glyph modules will draw arrows, which look a little like pine trees.
  3. The three Glyph modules generate three sets of arrows to simulate a wide base, a middle, and a pointed top to a tree. A closeup rendering of a few trees shows how they are built.
  4. The trees are then colored green and have normals computed.

• Collecting and rendering the scene.

  This piece of the program just collects everything together and submits it to the Image module for rendering.