Visualization-approximation and polygons
Visualization-approximation and polygons
Visualization-approximation and polygons
Dear fiends, now we're going to take a step back to understand better some basic concepts about polygonal modelling: rendering and visualization.
You could think that these concepts are not relevant with polygonal modeling; instead, we believe them necessary to understand the aim of this 3D technique.
As we said in previous tutorials, the rendering is the process by which it generates a 2D image from a 3D scene.
The conversion of some 3D elements present in a scene and their translation in raster images (images made by pixels) depends on some variables. There are several variables, but the one that most of the others determinates a right and different translation in the same time is the algorithm of visualization, category subdivided in wireframe, flat, phong, scanline, ray-tracing, radiosity, etc. Every single algorithm affords to the user a different visualization based on the needs: it's possible to switch from simple sight in wire frame to the one photo-realistic.
Through the optimization of these algorithms in the last years, continuous research and growth of the computing power of computers, now some of them are fully accessible and usable in real time in the software. Naturally, all of this is connected to the number and to the complexity of the 3D elements of the scene, as well as the power of the available hardware.
Surely, you're asking to yourself that has to do with modeling? We'll explain it speaking about a problem: the inability to render curved surfaces by no one of the algorithms introduced previously.
As the aim of the polygonal modeling is that to recreate objects, approximating them to the reality, it's tried to surpass the previous problem using a method called tessellation/discretization to represent curved surfaces (in the reality there aren't perfect objects, but everyone have, more or less, a rounding).
Through tessellation any 3D object, polygonal or not, is changed by a process of discretization (word using to indicate the translation of mathematical models and continuous equations in discrete counterparts).
Theresultofthisactivityis theconversion ofa 3D modelina setoftriangles,with regular intervals, which are essentialfor theproperinterpretation madeby the display algorithms.
The polygonal modeling, in particular the step of the 3D model creation, is characterized by stepof subdivision: through this method it's possible increase the number of polygons contained in an object, using a tessellation process.
The parameters concerning the distribution allow to approximate, more or less, as needed, visualization and processing of the objects: in this way, it'll possible to modify a geometry with few polygons in a more complex and articulated geometry.
There are various types of subdivision/approximation, for example: Catmull Clark; Doo-Sabin; Butterfly, etc.
THE POLYGON
With this article we completed the preface of our tutorials. From the next lessons, we'll go into the detailsof the polygonal modeling. The matter can't take few lines, there are other concepts that would be worth to study in depth.
In this regard, topology,softedge,control cage, artifacts are some of the topics that we'll discuss in the coming tutorial.
After introducing some basic notion about the 3D graphics, now we're going to deep and widen some concepts, with particular attention to the polygonal modeling.
The main element of the modeling is the polygon made up by vertex, edge, face and normal (we spoke about them in the article "POLYGONAL MODELLING: BASIC ELEMENTS"). They are integral part of the polygon. Now, we're going to explain some additional elements concerning the face.
The face is a planar element closed by 3 edges and for this reason called "triangular face". This concept is connected to the 3D graphics: the 3D model, infact, is teselled and transformed in a group of triangular faces during rendering.
For this reason, we can affirm: it could possible to use triangular faces during modeling because it's no possible distinguish the kind of face used to make the final product. This method is used but it can cause some problems: f.e. creation of artefacts that are mistakes of subdivision butwe'll explain them in the future tutorials.
It's possible to clear the hurdle using faces with 4 edges during modeling. Using polygons with 4 edges gives these opportunities:
- making easier the process using special instruments,
- working with some supportino software,
- giving clear and right geometries to the others sections operating in the production (es. Skinning),
- the best subdivision of the model thanks to the approximation algorithm.
It's no possible ruling out a modeling with faces composed by 3 edges because this method is connected to the polygonal modeling and it's used in the video game field (in this case, infact, it's necessary having polygonal models with a low number of faces).
In summary, we have:
- triangular face / planar element closed by 3 edges,
- quadrangular face / planar and not element closed by 4 edges,
- Ngon/ element made by 5 or more edges.
Finally, we can say that one or more faces can be called "polygon"; speaking about "triangular faces", the word "polygon" can be changed with "face".
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