8. Alternative modeling methods¶

8.1. Modelling methods¶

8.1.1. Wireframe modeling¶

We define the boundary edges, typical lines of the modeled shape by using line segments, arcs and curves.
The representation is ambiguous. We can describe fairly different shapes by the same wireframe model.
In this modeling method, we only know the edges, therefore it is not appropriate for collision detection and volume calculation.
Nowadays, we consider it as an elementary, auxiliary phase of the modeling process.

8.1.2. Surface modeling¶

We describe the boundary surfaces of the modeled object by joining surface patches to each others.
This model is unable to handle topological information. It requires further analysis to determine the compoundness, continuity and the open/closed property of the surface.
This representation is closer to the real objects. We can use shading, shadows and textures for more realistic visualization.

8.1.3. Boundary representation¶

It is often abbreviated as B-rep.
It represents the objects as a finite, closed shape, mostly by using polymesh approximation.
It assumes that the physical models has finite and closed surface.
It describes the model from topological aspect also.
It is proper for physical simulations, finite element methods.

8.1.4. Solid geometry¶

It is also called volumetric modeling or CSG modeling.
It describes the model as a finite, closed set of points.
It has a higher abstraction level than in the case of the previous models.

8.2. CSG modellezés¶

Constructive Solid Geometry

Let assume that we know the shapes of the solids as implicit functions. These can tell us that an arbitrary point of the space whether belongs to a solid or not.

The value of these functions are logical values. Therefore, we can apply logical operators on them.
Considering the solids as set of points, we can use the set operations also.

The commonly used operators are the union (\(\cup\)), the intersection (\(\cap\)) and the subtraction (\(\setminus\)).

We can combine multiple set operations to expressions. These expressions can be represented as binary trees. These show the process of the making of the model.

We call this kind of tree as CSG tree.
We (usually) consider binary operations which means that the tree is a binary tree.

For using this kind of model, we have to use a set of predefined primitive shapes. In most cases the followings are available in the CAD systems:

rectangle,
pyramid,
cylinder,
cone,
sphere.

We can also use geometric transformations in the modeling process.

This kind of modeling approach suits well with ray tracing/casting rendering algorithms.
It is a common solution, to convert the resulted shapes to triangle mesh for visualization and/or model format export.
This method is also benefitial when we design the model for manufacturing and assembly.

8.3. Metaball modeling¶

https://en.wikipedia.org/wiki/Metaballs

8.4. Volumetric modeling¶

We can use raster-based approach for planar and spatial object modeling also.

It is called volumetric modeling or voxel graphics when we assign properties to the cells/blocks in the three dimensional space.

8.5. Softwares for 3D modeling¶

8.6. Further exercises¶

Let implement an application, which is able to render CSG scenes by using simple ray tracing methods!
Let try to approximate a surface by using metaball modeling technique!