3D Animation Workshop: Lesson 9: Modeling, Modeling | 2

Lesson 9 - Modeling, Modeling - Part 2

The most fundamental concept in modeling is that of EXTRUSION.

Limited as we are to a flat computer screen, we must begin with a two-dimensional object and "draw it out."

Let's start with a rectangle drawn on the surface of the screen.

Let's then place this 2-D object, a flat polygon, in 3-D space.

Here's the trick. We extrude it a little, pulling it out in the third dimension.

We pull it out even more.

Any of you who have ever read that little masterpiece called "Flatland" might be smiling now to recall the experience of the two-dimensional hero as he suddenly became aware of the spaciousness of an unimagined THIRD dimension.

Extrusion allows us to break the process of modeling three-dimensional objects into two 2-D steps. First a flat object is created on a plane. Then the flat object is extruded out along a path. In the simplest and most common case, the path is a straight line that is normal to the polygon being extruded. Thus the front and back faces of the extruded object have the same normals. In other words, the two faces are parallel to each other.

But the extrusion path need not be normal to the plane, nor need it be a straight line.

Here the extrusion path is pointing at an upward angle from the plane of the rectangle. From a side view, the direction of the path is clear. The path being a straight line, the front and back faces of the extruded object are parallel to each other.

This side view is an "orthographic" or parallel projection, which helps us to see the true shape of the object. But let's look as a perspective view, as the human eye or a camera sees.

Notice how the perspective viewpoint changes the apparent shape so that it is no longer evident that the front and back extrusion faces are parallel. This is as important aspect of 3-D graphics. In the real world, our mind often compensates for the visual effect of perspective distortion. We interpret the "true" shape of an object from the environment and think that we see that shape directly. Often we are surprised at how distorted a photograph comes out, when, in fact, the camera had the same perspective as our eyes when we looked through the viewfinder. This experience is even more common with 3-D graphics. Without a spatial environment to interpret the visual data, a 3-D object often appears distorted by a correct perspective rendering. That is one reason why shadows are so important to creating satisfactory 3-D graphics. Shadows give additional visual clues to the true geometry of objects in a scene.

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Created: May 5, 1997
Revised: May 5, 1997

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