Figure 1: Rock shape
For this, we design a procedural definition of the basic shape feature that we want to paste on a surface at some scale level. This procedure is a function that synthesizes the difference between the feature at two successive scale levels. The input of the function is a point on the surface and a scale level. The output is a displacement to be added as a detail at that level.
det = f(p, l)where p is a point given either in local intrinsic surface coordinates (u,v) or in global extrinsic coordinates (x,y,z); and detail is a displacement relative to the surface at level l.
Models based on global coordinates lead to volumetric shape definitions, i.e. features are taken from the three dimensional space in which the surface is embeded. Models based on local coordinates lead to surface shape definitions, i.e. features are "grown" on the surface. Some of our models are based on intrinsic coordinates and some on extrinsic coordinates.
The magnitude of the displacements is usually related to the scale level. Models in which the displacement is inversely proportional to scale lead to fractal-like features. Models in which the displacement is directly proportional to scale lead to morphogenic-like features. When the magnitude of the displacement is independent of scale, the features are essentially arbitrary. This is appropriate for man-made shapes or even physical phenomena, such as small waves. We experimented with all these kinds of displacement.
Below we present a chart relating this classification
with examples of the shape detail procedural models.
.------------------------------------------------------.
| | Fractal | Morphogenic |
|------------------------------------------------------|
| Global | "rock" | "mushroom cloud" |
|------------------------------------------------------|
| Local | "berry" | "tentacle" |
.------------------------------------------------------.
We have designed and experimented with a few shape detail procedural models. These models exploit the two basic characteristics of the procedural definition, discussed above: the type of coordinates and the magnitude of displacements relative to the level.
Figure 1 shows an image of rock synthesis using this procedure on a sphere-like base subdivision surface.
Figure 1: Rock shape
Figure 2 shows the construction process for the berry shape.
Figure 2: Berry;
(a) Base domes from initial sed points -- level 1 of detail;
(b) first recursion added to domes -- level 2 of detail;
(c) final berry -- 3 levels of detail.
Figure 3: Growth process of the tentacle.
Levels 1 to 4.
The shape feature model has two parameters
Figure 4 shows a tentacle creature produced by applying uniform tentacles to an spherical subdivision surface. The tentacles grow from Figure 4(a) to 4(c).
Figure 4: "Tentacle creature". Tentacles grow and rotate
from (a) to (c).
We remark that the basic structure of the tentacle shape detail model can be used as the basis to create other types of models such as the one shown in Figure 5.
Figure 5. Submarine mine.
Other variations of the growth model are possible. One ideia is to use L-Systems to create branching structures. For this type of model, in addition to the feature grown from the inital seed point, branching features are grown at higher levels of detail
Figure 6 shows an example of mushroom cloud features placed on a spherical shape.
Figure 6. Mushroom clouds on a planet.
(inspired on the planet from "The Little Prince" of Saint-Exupery).
We can also apply the shape detail procedures as a local operation to construct a single feature at a given seed point of the surface. This can be a very powerful modeling tool if applied interactively.
We now describe some results of interactive modeling using local multiscale detail operations. We have experimented with two kinds of operations: feature placement and local shape modification.
Figure 7. Local feature placement at the same level.
Figure 8 shows one example of feature placement at different levels. In Figure 8(a), we applied a "spur" shape detail procedures to several points only at level 1 of a spherical base surface. In Figure 8(b), we applied the same local feature operations only at level 3 of the surface. In Figure 8(c), we applied the local feature operations at both levels. Note that we obtained a combination of features at different scales.
Figure 8. Combination of features at different levels.
To implement this operation is important to have two components: a distance function from a point on the surface that extends over the neighborhood where the modification is applied; and a smooth drop-off function of distance. These components together provide a way to apply the modification without creating discontinuities on the surface.
Figure 9 shows an example of surface detail local signal processing applied to the skull model. In Figure 9(a) we present the original skull model and in Figure 9(b) we present the modified result. We smoothed the nose area and enhanced the jaw and details on top of the head to create a horny carnival mask. The interactive edit session took less than 5 minutes.
Figure 9. Local signal processing for meshes.
Figure 10 shows the result of blending between these two shapes. The blending is specified by a plane oriented in the (1,2,0) direction. In order to avoid aliasing a "soft" transition region is used to blend between the the detail coefficients of the two models. This region changes from level to level according to c*1/2^l.. Note the while the transition is sharp at the finest level, the coarse level features of one shape influences the other beyond the dividing blending plane.
Figure 10. Rusted fuse.
Figure 11 shows the blending of these two shapes to create a corroded skull. In Figure 11(a) we used the same transition regions as in the previous example to produce a sharp blend. In Figure 11(b) we used a transition region that has the same extent at all levels to create a "soft" blend between the two shapes.
Figure 11. Skull.
Figure 12(c) shows a synthetic planet which is the result blending in multiscale an "earth-like" planet, shown in Figure 12(a), with an "alien" planet, shown in Figure 12(b). Note how the different characteristics of the coastlines and topography blend seamlessly. One can see, scanning across individual features which straddle the transition region, that they gradually change their (statistically defined) appearance. For example, a single lake that appears jagged, with high fractal dimension, on one side of the transition, gradually turns into a smoothly contoured lake.
Figure 12. Planet.