Mesh Raytrace Tutorial

This tutorial is for Ultrafractal 5 and the use of the Mesh Raytracing ucl in reb5.ucl. The mesh raytracer has the following features:

Raytracing is a process to provide realistic lighting, perspective and hidden surface removal effects to a scene. A raytracer includes includes a camera (or eye) and one or more light sources. The raytrace process can be envisioned as the shooting of rays from the camera to the objects in the scene. The raytracer uses the distance to the intersection point, the surface normal at the intersection point, and the angle and intensity of the light source(s) to determine the coloring at the intersection point. Precise mathematical formulas exist for calculating these parameters for regular solids such as spheres, planes, cubes, etc. To deal with a general curved surface, the surface is often approximated by a mesh of triangles. Precise equations are available for calculating the intersection points, normals, etc for ray-triangle intersections. The triangle approach has the limitation that it doesn't produce a smooth surface. The image below shows a fractal surface simulated with a triangle mesh using exponential smoothing for calculation of the height values. As you can see, it has a chunky, blocky appearance, and the triangles are clearly visible.

With Phong shading the following is done. Each point or vertex within the mesh is shared by six triangles (except for the edges). An average normal is calculated for each vertex, which is the average of the normals of the six triangles. When a ray intersects one of the triangles in the mesh, the value of the normal at the intersection point would normally be the normal of the triangle. With Phong shading a different value is used. It is the interpolated normal from the average normals at the three vertices of the triangle. Phong shading also has an additional factor called specular lighting, which simulates the shiny spots that are seen on smooth surfaces. The next image shows the same surface displayed with Phong shading.

Both of these images were created with a relatively low mesh density, one mesh vertex for 10 pixels in both the x and y directions. Greater detail can be obtained with higher densities, but with considerably slower rendering. It's important for the artist to select the lowest possible density that provides the artistic effects desired.

To use the mesh raytracer, select one of the pixel formulas from the Formula tab in UF5. DO NOT USE ANY OTHER TYPE OF FORMULA! On the Outside tab in UF5 select reb5.ucl and open the Mesh Raytracing formula. With the default settings the user should see the following:

With the default settings the user will see a Phong shaded height field for a Julia fractal.

You have probably already noted that there is a small error in the image above, as the default value for "Maxiter height = 0" is checked. Uncheck the parameter. In the default Phong shading mode the raytracer selects the color at the mid-point of the gradient and uses that color for all the shading. Bring up the gradient editor and change the gradient using the F5 key to see the effect on your image. If the gradient mid-point happens to be a fairly dark color, the specular highlights will be especially pronounced. Here is a upr and image to illustrate.

DarkColorPhong {
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}

Starting with the default image, explore the different height types. These include iteration, exponential smoothing, general smoothing, Vepstas/Härkönen smoothing, Cabs(z) and orbit traps. Return to the general smoothing height type. Click the arrow next to "Illumination model" to make the parameters visible. You should see something like the following:

The distance coloring mode colors by the distance from the camera to the triangle intersection using raw triangles. The Z value coloring mode uses the unrotated height value and an algorithm similar to Phong shading called Gouraud shading. The color value used at the intersection point in the triangle is the interpolated value from the color values at each of the triangle vertices. The next two uprs and images illustrate these coloring modes.

Distance {
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}

ZValue {
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}

Both Distance and Z Value coloring modes can be used in layers to merge with the Phong layer to create interesting effects. Some of the images in the Height Field Gallery were created this way.

At the bottom of the parameters list are slots for texture and coloring plugins. The next example will illustrate the use of a texture plugin, using Damien Jones' fBm plugin. The plugin makes the image look like a fog or mist has rolled in over the fractal.

fBmTexture {
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}

The Colors plugin includes a wide variety of options, including image import. In the following example the Checkers Coloring plugin is used because it illustrates the functionality 'Z component mix' parameter in a clear manner. When textures and colors are applied they usually have a more aesthetically pleasing appearance when they vary with the height value. The 'Z component mix' parameter provides this functionality, and how it works can be clearly seen with the checker pattern.

The parameter snapshot also illustrates how the coloring for any of the Colors plugins are managed. The coloring is merged with the mesh using merge modes everyone should be familiar with. The merging can be done with the coloring on the top or on the bottom, and with any opacity setting. The mesh itself is the base. A sample upr and image are below. The artist should try varying the value of the Z component mix parameter to see its effect, and also vary the merge modes, merge order and opacity.

CheckerBoard {
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}

The shadows option will slow down rendering because each intersection point with a camera ray must be checked against rays from the light source to determine if the intersection point is in shadow. The extra time is often with the effort as some really interesting results can be obtained. In the image and upr that follow the rendering produces a view that looks a bit like parts of Utah. This is a two layer image with Z value coloring on top. Shadows only need to be on the bottom layer, as this will speed up the rendering. The position of the light source has also been changed to enhance the shadow effect.

BluffswithShadows {
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Transparency effects depend upon the unrotated height value, and works by making small height values transparent or partially transparent. The resulting layer can be used as a mask or as a filter to an underlying layer.

For the next image both transparency and shadows will be used, with the parameters in the snapshot above. Overall three layers are used. The top layer is a Z value coloring layer, the middle layer has shadows and transparency, and the bottom layer provides a textured valley. Notice that the transparency doesn't totally remove shadows with the setting used, so shadows appear on the textured valley.

Transparency {
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}

One of the more interesting height value options is the use of an orbit trap to determine the heightfield. The parameter snapshot below should look familiar to anyone who has used the Orbit Traps ucl for UF5.

All of the plugins in this section must be pre-calculated before anything will appear on the screen. Some sets of plugins may produce a substantial delay.

Before the actual rendering begins the entire mesh is calculated. This means that for every vertex in the mesh the trap shape calculation is carried out for every iteration at the vertex location. If a trap texture is also used, there will be additional calculations at each vertex point. This applies to any other plugins used in this section. One of this author's favorite textures is the Monnier's S.F.B.M. II Texture which also has a convolution option. The convolution option triples the number of times the texture is calculated at a given vertex.

As you have already seen the earlier part of this tutorial textures can also be applied to the overall mesh. So why use the orbit trap texture? In the fBm example above, the texture is actually painted on top of the mesh by perturbing a Phong parameter. The Phong parameter has the same granularity as the viewing screen, e.g., a pixel so a smooth texture results. This texture simulates 3D but is not actually 3D, that is, the surface shape is not not actually perturbed and the lighting effects, including shadows, basically ignore the texture. The orbit traps texture has a granularity that is the same as the mesh, and is a true 3D texture in that it actually peturbs the shape of the surface. The perturbed surface will show all the normal lighting effects including specular lighting, light position, and shadows. The disadvantages are that it is usually much slower to render, and the amount of detail has a granularity the same as the mesh. If a texture has a lot of fine detail, the detail will be lost unless the density parameter is increased. The maximum value for the density is 1.0, a setting that gives the mesh the same granularity as the screen. This will, however, dramatically increase the rendering time. The following upr and image use the Monnier texture in the convolution mode. The pre-calculation phase on the author's computer took 8:15 minutes and the total rendering time was 1:27:12.31 hours.

OrbitTexture {
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}

Many fractal height fields tend to have a very spiky appearance which is often not artistically desirable. This can be reduced using a mesh smoothing filter. Four filters are available. The first three are convolution filters that use a 3x3 matrix of mesh points centered on the point to be smoothed. The new parameters on the outside tab appear as follows:

The following five uprs and images show the effects of the various smoothing options. The median filter produces the cleanest appearance.

NoSmoothing {
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}

AverageBlur {
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}

Gaussian {
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}

ReducedGaussian {
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}

Median {
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}

No Smoothing


Average Blur	Gaussian


Reduced Gaussian	Median

Mesh raytracing is not without its problems. The default settings will generally give good results, but like any complex program, not all the bugs and problems show up until it is used for a while. There are a number of parameter settings that can lead to problems. The following list is not meant to be exhaustive.